best topics for presentation in mathematics

251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

Related Posts

Step by Step Guide on The Best Way to Finance Car

The Best Way on How to Get Fund For Business to Grow it Efficiently

Leave a comment cancel reply.

Your email address will not be published. Required fields are marked *

404 Not found

Got any suggestions?

We want to hear from you! Send us a message and help improve Slidesgo

Top searches

Trending searches

memorial day

12 templates

17 templates

26 templates

20 templates

american history

73 templates

11 templates

Math Presentation templates

Create enjoyable presentations with these entertaining google slides themes and powerpoint templates featuring designs revolving around numbers and math. they are free and completely customizable., related collections.

29 templates

139 templates

Middle School

80 templates

High School

150 templates

52 templates

Statistics and Data Analysis - 6th Grade

Download the "Statistics and Data Analysis - 6th Grade" presentation for PowerPoint or Google Slides. If you’re looking for a way to motivate and engage students who are undergoing significant physical, social, and emotional development, then you can’t go wrong with an educational template designed for Middle School by Slidesgo!...

Effective Quotation Strategies Workshop

Download the Effective Quotation Strategies Workshop presentation for PowerPoint or Google Slides. If you are planning your next workshop and looking for ways to make it memorable for your audience, don’t go anywhere. Because this creative template is just what you need! With its visually stunning design, you can provide...

Complex Analysis - Bachelor of Science in Mathematics

Download the "Complex Analysis - Bachelor of Science in Mathematics" presentation for PowerPoint or Google Slides. As university curricula increasingly incorporate digital tools and platforms, this template has been designed to integrate with presentation software, online learning management systems, or referencing software, enhancing the overall efficiency and effectiveness of student...

Math Mystery Escape Room

One of the most recent booms in games for all ages are escape rooms. You and a group of friends are locked in a room and you must solve puzzles to escape. How about trying an educational and "digital" version of it, aimed at kids? The theme of this new...

Premium template

Unlock this template and gain unlimited access

How to Find the Antiderivative of Simple Polynomials

Download the "How to find the antiderivative of simple polynomials" presentation for PowerPoint or Google Slides and teach with confidence. Sometimes, teachers need a little bit of help, and there's nothing wrong with that. We're glad to lend you a hand! Since Slidesgo is committed to making education better for...

Dividing Integers

Download the "Dividing Integers" presentation for PowerPoint or Google Slides and teach with confidence. Sometimes, teachers need a little bit of help, and there's nothing wrong with that. We're glad to lend you a hand! Since Slidesgo is committed to making education better for everyone, we've joined hands with educators....

Math Subject for High School - 9th Grade: Systems of Equations and Inequalities

Ah, math, the most polarizing subject—either you love it or hate it. With Slidesgo, you can be sure your students will love it! Using visual resources such as slides during a class is helpful and can turn complex concepts into something more comprehensible. Our template has an organic design, which...

Card Game to Improve Mental Arithmetic Skills

Download the "Card Game to Improve Mental Arithmetic Skills" presentation for PowerPoint or Google Slides and teach with confidence. Sometimes, teachers need a little bit of help, and there's nothing wrong with that. We're glad to lend you a hand! Since Slidesgo is committed to making education better for everyone,...

Math Subject for Elementary - 5th Grade: Fractions I

Who says Maths have to be boring? Introduce elementary school students to the wonders of fractions with this cool template. Its fun and approachable design is filled with colors and makes each slide look like a page ripped out from a spiral notebook. Also, its many color illustrations add a...

Advanced Topics in Combinatorics - Doctor of Philosophy (Ph.D.) in Mathematics

Download the "Advanced Topics in Combinatorics - Doctor of Philosophy (Ph.D.) in Mathematics" presentation for PowerPoint or Google Slides. As university curricula increasingly incorporate digital tools and platforms, this template has been designed to integrate with presentation software, online learning management systems, or referencing software, enhancing the overall efficiency and...

Math Tutoring Academy

Download the "Math Tutoring Academy" presentation for PowerPoint or Google Slides. Are you looking for a way to make your school or academy stand out among the competition? This template is designed to showcase all the fantastic aspects of your center. With perfect slides that allow you to easily add...

Math Subject for Elementary School: Polygons

Download the Math Subject for Elementary School: Polygons presentation for PowerPoint or Google Slides and easily edit it to fit your own lesson plan! Designed specifically for elementary school education, this eye-catching design features engaging graphics and age-appropriate fonts; elements that capture the students' attention and make the learning experience...

Geometry: Circles and Angle Relationships - 10th Grade

Download the "Geometry: Circles and Angle Relationships - 10th Grade" presentation for PowerPoint or Google Slides. High school students are approaching adulthood, and therefore, this template’s design reflects the mature nature of their education. Customize the well-defined sections, integrate multimedia and interactive elements and allow space for research or group...

Multiplying Integers

Download the "Multiplying Integers" presentation for PowerPoint or Google Slides and teach with confidence. Sometimes, teachers need a little bit of help, and there's nothing wrong with that. We're glad to lend you a hand! Since Slidesgo is committed to making education better for everyone, we've joined hands with educators....

Discrete Mathematics: Graph Theory and Networks - 12th Grade

Download the "Discrete Mathematics: Graph Theory and Networks - 12th Grade" presentation for PowerPoint or Google Slides. High school students are approaching adulthood, and therefore, this template’s design reflects the mature nature of their education. Customize the well-defined sections, integrate multimedia and interactive elements and allow space for research or...

HS Electives: Sociology Subject for High School - 9th Grade: Concepts in Probability and Statistics

If Slidesgo's templates are downloaded by 7 out of 9 people in France and 8 out of 10 in Brazil, how probable it is for a new user from those countries to download one of our presentations? Grab this example and take it to your high school lessons thanks to...

Comparing Fractions (Cross Multiplication)

Download the "Comparing Fractions (Cross Multiplication)" presentation for PowerPoint or Google Slides and teach with confidence. Sometimes, teachers need a little bit of help, and there's nothing wrong with that. We're glad to lend you a hand! Since Slidesgo is committed to making education better for everyone, we've joined hands...

Addition and Subtraction Strategies - 1st Grade

Download the "Addition and Subtraction Strategies - 1st Grade" presentation for PowerPoint or Google Slides and easily edit it to fit your own lesson plan! Designed specifically for elementary school education, this eye-catching design features engaging graphics and age-appropriate fonts; elements that capture the students' attention and make the learning...

• Page 1 of 28

New! Make quick presentations with AI

Slidesgo AI presentation maker puts the power of design and creativity in your hands, so you can effortlessly craft stunning slideshows in minutes.

Register for free and start editing online

Math talks to blow your mind

Numbers, patterns and equations are at the core of these talks, which will teach you how to fold better origami and how to quantify history.

A performance of "Mathemagic"

Why I fell in love with monster prime numbers

Math is forever

Symmetry, reality's riddle

The math and magic of origami

The surprising math of cities and corporations

The fractals at the heart of African designs

Fractals and the art of roughness

The mathematics of history

Comics that ask "what if?"

8. Appendices

In the appendices you should include any data or material that supported your research but that was too long to include in the body of your paper. Materials in an appendix should be referenced at some point in the body of the report.

Some examples:

• If you wrote a computer program to generate more data than you could produce by hand, you should include the code and some sample output.

• If you collected statistical data using a survey, include a copy of the survey.

• If you have lengthy tables of numbers that you do not want to include in the body of your report, you can put them in an appendix.

Sample Write-Up

Seating unfriendly customers, a combinatorics problem.

By Lisa Honeyman February 12, 2002

The Problem

In a certain coffee shop, the customers are grouchy in the early morning and none of them wishes to sit next to another at the counter.

1. Suppose there are ten seats at the counter. How many different ways can three early morning customers sit at the counter so that no one sits next to anyone else?

2. What if there are n seats at the counter?

3. What if we change the number of customers?

4. What if, instead of a counter, there was a round table and people refused to sit next to each other?

Assumptions

I am assuming that the order in which the people sit matters. So, if three people occupy the first, third and fifth seats, there are actually 6 (3!) different ways they can do this. I will explain more thoroughly in the body of my report.

Body of the Report

At first there are 10 seats available for the 3 people to sit in. But once the first person sits down, that limits where the second person can sit. Not only can’t he sit in the now-occupied seat, he can’t sit next to it either. What confused me at first was that if the first person sat at one of the ends, then there were 8 seats left for the second person to chose from. But if the 1 st person sat somewhere else, there were only 7 remaining seats available for the second person. I decided to look for patterns. By starting with a smaller number of seats, I was able to count the possibilities more easily. I was hoping to find a pattern so I could predict how many ways the 10 people could sit without actually trying to count them all. I realized that the smallest number of seats I could have would be 5. Anything less wouldn’t work because people would have to sit next to each other. So, I started with 5 seats. I called the customers A, B, and C.

With 5 seats there is only one configuration that works.

As I said in my assumptions section, I thought that the order in which the people sit is important. Maybe one person prefers to sit near the coffee maker or by the door. These would be different, so I decided to take into account the different possible ways these 3 people could occupy the 3 seats shown above. I know that ABC can be arranged in 3! = 6 ways. (ABC, ACB, BAC, BCA, CAB, CBA). So there are 6 ways to arrange 3 people in 5 seats with spaces between them. But, there is only one configuration of seats that can be used. (The 1 st , 3 rd , and 5 th ).

Next, I tried 6 seats. I used a systematic approach to show that there are 4 possible arrangements of seats. This is how my systematic approach works:

Assign person A to the 1 st seat. Put person B in the 3 rd seat, because he can’t sit next to person A. Now, person C can sit in either the 5 th or 6 th positions. (see the top two rows in the chart, below.) Next suppose that person B sits in the 4 th seat (the next possible one to the right.) That leaves only the 6 th seat free for person C. (see row 3, below.) These are all the possible ways for the people to sit if the 1 st seat is used. Now put person A in the 2 nd seat and person B in the 4 th . There is only one place where person C can sit, and that’s in the 6 th position. (see row 4, below.) There are no other ways to seat the three people if person A sits in the 2 nd seat. So, now we try putting person A in the 3 rd seat. If we do that, there are only 4 seats that can be used, but we know that we need at least 5, so there are no more possibilities.

Possible seats 3 people could occupy if there are 6 seats

Once again, the order the people sit in could be ABC, BAC, etc. so there are 4 * 6 = 24 ways for the 3 customers to sit in 6 seats with spaces between them.

I continued doing this, counting how many different groups of seats could be occupied by the three people using the systematic method I explained. Then I multiplied that number by 6 to account for the possible permutations of people in those seats. I created the following table of what I found.

Next I tried to come up with a formula. I decided to look for a formula using combinations or permutations. Since we are looking at 3 people, I decided to start by seeing what numbers I would get if I used n C 3 and n P 3 .

3 C 3 = 1   4 C 3 = 4   5 C 3 = 10   6 C 3 = 20

3 P 3 = 6   4 P 3 = 24   5 P 3 = 60   6 P 3 = 120

Surprisingly enough, these numbers matched the numbers I found in my table. However, the n in n P r and n C r seemed to be two less than the total # of seats I was investigating. 

Conjecture 1:

Given n seats at a lunch counter, there are n -2 C 3 ways to select the three seats in which the customers will sit such that no customer sits next to another one. There are n -2 P 3 ways to seat the 3 customers in such a way than none sits next to another.

After I found a pattern, I tried to figure out why n -2 C 3 works. (If the formula worked when order didn’t matter it could be easily extended to when the order did, but the numbers are smaller and easier to work with when looking at combinations rather than permutations.)

In order to prove Conjecture 1 convincingly, I need to show two things:

(1) Each n – 2 seat choice leads to a legal n seat configuration.

(2) Each n seat choice resulted from a unique n – 2 seat configuration.

To prove these two things I will show

And then conclude that these two procedures are both functions and therefore 1—1.

Claim (1): Each ( n – 2) -seat choice leads to a legal n seat configuration.

Suppose there were only n – 2 seats to begin with. First we pick three of them in which to put people, without regard to whether or not they sit next to each other. But, in order to guarantee that they don’t end up next to another person, we introduce an empty chair to the right of each of the first two people. It would look like this:

We don’t need a third “new” seat because once the person who is farthest to the right sits down, there are no more customers to seat. So, we started with n – 2 chairs but added two for a total of n chairs. Anyone entering the restaurant after this procedure had been completed wouldn’t know that there had been fewer chairs before these people arrived and would just see three customers sitting at a counter with n chairs. This procedure guarantees that two people will not end up next to each other. Thus, each ( n – 2)-seat choice leads to a unique, legal n seat configuration.

Therefore, positions s 1 ' s 2 ', and s 3 ' are all separated by at least one vacant seat.

This is a function that maps each combination of 3 seats selected from n – 2 seats onto a unique arrangement of n seats with 3 separated customers. Therefore, it is invertible.

Claim (2): Each 10-seat choice has a unique 8-seat configuration.

Given a legal 10-seat configuration, each of the two left-most diners must have an open seat to his/her right. Remove it and you get a unique 8-seat arrangement. If, in the 10-seat setting, we have q 1 > q 2 , q 3 ; q 3 – 1 > q 2 , and q 2 – 1 > q 1 , then the 8 seat positions are q 1 ' = q 2 , q 2 ' = q 2 – 1, and q 3 ' = q 3 – 2. Combining these equations with the conditions we have

q 2 ' = q 2 – 1 which implies q 2 ' > q 1 = q 1 '

q 3 ' = q 3 – 2 which implies q 3 ' > q 2 – 1 = q 2 '

Since q 3 ' > q 2 ' > q 1 ', these seats are distinct. If the diners are seated in locations q 1 , q 2 , and q 3 (where q 3 – 1 > q 2 and q 2 – 1 > q 1 ) and we remove the two seats to the right of q 1 and q 2 , then we can see that the diners came from q 1 , q 2 – 1, and q 3 – 2. This is a function that maps a legal 10-seat configuration to a unique 8-seat configuration.

The size of a set can be abbreviated s ( ). I will use the abbreviation S to stand for n separated seats and N to stand for the n – 2 non-separated seats.

therefore s ( N ) = s ( S ).

Because the sets are the same size, these functions are 1—1.

Using the technique of taking away and adding empty chairs, I can extend the problem to include any number of customers. For example, if there were 4 customers and 10 seats there would be 7 C 4 = 35 different combinations of chairs to use and 7 P 4 = 840 ways for the customers to sit (including the fact that order matters). You can imagine that three of the ten seats would be introduced by three of the customers. So, there would only be 7 to start with.

In general, given n seats and c customers, we remove c- 1 chairs and select the seats for the c customers. This leads to the formula n -( c -1) C c = n - c +1 C c for the number of arrangements.

Once the number of combinations of seats is found, it is necessary to multiply by c ! to find the number of permutations. Looking at the situation of 3 customers and using a little algebraic manipulation, we get the n P 3 formula shown below.

This same algebraic manipulation works if you have c people rather than 3, resulting in n - c +1 P c

Answers to Questions

• With 10 seats there are 8 P 3 = 336 ways to seat the 3 people.
• My formula for n seats and 3 customers is: n -2 P 3 .
• My general formula for n seats and c customers, is: n -( c -1) P c = n - c +1 P c

_________________________________________________________________ _

After I finished looking at this question as it applied to people sitting in a row of chairs at a counter, I considered the last question, which asked would happen if there were a round table with people sitting, as before, always with at least one chair between them.

I went back to my original idea about each person dragging in an extra chair that she places to her right, barring anyone else from sitting there. There is no end seat, so even the last person needs to bring an extra chair because he might sit to the left of someone who has already been seated. So, if there were 3 people there would be 7 seats for them to choose from and 3 extra chairs that no one would be allowed to sit in. By this reasoning, there would be 7 C 3 = 35 possible configurations of chairs to choose and 7 P 3 = 840 ways for 3 unfriendly people to sit at a round table.

Conjecture 2: Given 3 customers and n seats there are n -3 C 3 possible groups of 3 chairs which can be used to seat these customers around a circular table in such a way that no one sits next to anyone else.

My first attempt at a proof: To test this conjecture I started by listing the first few numbers generated by my formula:

When n = 6    6-3 C 3 = 3 C 3 = 1

When n = 7    7-3 C 3 = 4 C 3 = 4

When n = 8    8-3 C 3 = 5 C 3 = 10

When n = 9    9-3 C 3 = 6 C 3 = 20

Then I started to systematically count the first few numbers of groups of possible seats. I got the numbers shown in the following table. The numbers do not agree, so something is wrong — probably my conjecture!

I looked at a circular table with 8 people and tried to figure out the reason this formula doesn’t work. If we remove 3 seats (leaving 5) there are 10 ways to select 3 of the 5 remaining chairs. ( 5 C 3 ).

The circular table at the left in the figure below shows the n – 3 (in this case 5) possible chairs from which 3 will be randomly chosen. The arrows point to where the person who selects that chair could end up. For example, if chair A is selected, that person will definitely end up in seat #1 at the table with 8 seats. If chair B is selected but chair A is not, then seat 2 will end up occupied. However, if chair A and B are selected, then the person who chose chair B will end up in seat 3 . The arrows show all the possible seats in which a person who chose a particular chair could end. Notice that it is impossible for seat #8 to be occupied. This is why the formula 5 C 3 doesn’t work. It does not allow all seats at the table of 8 to be chosen.

The difference is that in the row-of-chairs-at-a-counter problem there is a definite “starting point” and “ending point.” The first chair can be identified as the one farthest to the left, and the last one as the one farthest to the right. These seats are unique because the “starting point” has no seat to the left of it and the “ending point” has no seat to its right. In a circle, it is not so easy.

Using finite differences I was able to find a formula that generates the correct numbers:

Proof: We need to establish a “starting point.” This could be any of the n seats. So, we select one and seat person A in that seat. Person B cannot sit on this person’s left (as he faces the table), so we must eliminate that as a possibility. Also, remove any 2 other chairs, leaving ( n – 4) possible seats where the second person can sit. Select another seat and put person B in it. Now, select any other seat from the ( n – 5) remaining seats and put person C in that. Finally, take the two seats that were previously removed and put one to the left of B and one to the left of C.

The following diagram should help make this procedure clear.

In a manner similar to the method I used in the row-of-chairs-at-a-counter problem, this could be proven more rigorously.

An Idea for Further Research:

Consider a grid of chairs in a classroom and a group of 3 very smelly people. No one wants to sit adjacent to anyone else. (There would be 9 empty seats around each person.) Suppose there are 16 chairs in a room with 4 rows and 4 columns. How many different ways could 3 people sit? What if there was a room with n rows and n columns? What if it had n rows and m columns?

References:

Abrams, Joshua. Education Development Center, Newton, MA. December 2001 - February 2002. Conversations with my mathematics mentor.

Brown, Richard G. 1994. Advanced Mathematics . Evanston, Illinois. McDougal Littell Inc. pp. 578-591

The Oral Presentation

Giving an oral presentation about your mathematics research can be very exciting! You have the opportunity to share what you have learned, answer questions about your project, and engage others in the topic you have been studying. After you finish doing your mathematics research, you may have the opportunity to present your work to a group of people such as your classmates, judges at a science fair or other type of contest, or educators at a conference. With some advance preparation, you can give a thoughtful, engaging talk that will leave your audience informed and excited about what you have done.

Planning for Your Oral Presentation

In most situations, you will have a time limit of between 10 and 30 minutes in which to give your presentation. Based upon that limit, you must decide what to include in your talk. Come up with some good examples that will keep your audience engaged. Think about what vocabulary, explanations, and proofs are really necessary in order for people to understand your work. It is important to keep the information as simple as possible while accurately representing what you’ve done. It can be difficult for people to understand a lot of technical language or to follow a long proof during a talk. As you begin to plan, you may find it helpful to create an outline of the points you want to include. Then you can decide how best to make those points clear to your audience.

You must also consider who your audience is and where the presentation will take place. If you are going to give your presentation to a single judge while standing next to your project display, your presentation will be considerably different than if you are going to speak from the stage in an auditorium full of people! Consider the background of your audience as well. Is this a group of people that knows something about your topic area? Or, do you need to start with some very basic information in order for people to understand your work? If you can tailor your presentation to your audience, it will be much more satisfying for them and for you.

No matter where you are presenting your speech and for whom, the structure of your presentation is very important. There is an old bit of advice about public speaking that goes something like this: “Tell em what you’re gonna tell ’em. Tell ’em. Then tell ’em what you told ’em.” If you use this advice, your audience will find it very easy to follow your presentation. Get the attention of the audience and tell them what you are going to talk about, explain your research, and then following it up with a re-cap in the conclusion.

Writing Your Introduction

Your introduction sets the stage for your entire presentation. The first 30 seconds of your speech will either capture the attention of your audience or let them know that a short nap is in order. You want to capture their attention. There are many different ways to start your speech. Some people like to tell a joke, some quote famous people, and others tell stories.

Here are a few examples of different types of openers.

You can use a quote from a famous person that is engaging and relevant to your topic. For example:

• Benjamin Disraeli once said, “There are three kinds of lies: lies, damn lies, and statistics.” Even though I am going to show you some statistics this morning, I promise I am not going to lie to you! Instead, . . .

• The famous mathematician, Paul Erdös, said, “A Mathematician is a machine for turning coffee into theorems.” Today I’m here to show you a great theorem that I discovered and proved during my mathematics research experience. And yes, I did drink a lot of coffee during the project!

• According to Stephen Hawking, “Equations are just the boring part of mathematics.” With all due respect to Dr. Hawking, I am here to convince you that he is wrong. Today I’m going to show you one equation that is not boring at all!

Some people like to tell a short story that leads into their discussion.

“Last summer I worked at a diner during the breakfast shift. There were 3 regular customers who came in between 6:00 and 6:15 every morning. If I tell you that you didn’t want to talk to these folks before they’ve had their first cup of coffee, you’ll get the idea of what they were like. In fact, these people never sat next to each other. That’s how grouchy they were! Well, their anti-social behavior led me to wonder, how many different ways could these three grouchy customers sit at the breakfast counter without sitting next to each other? Amazingly enough, my summer job serving coffee and eggs to grouchy folks in Boston led me to an interesting combinatorics problem that I am going to talk to you about today.”

A short joke related to your topic can be an engaging way to start your speech.

It has been said that there are three kinds of mathematicians: those who can count and those who can’t.

All joking aside, my mathematics research project involves counting. I have spent the past 8 weeks working on a combinatorics problem.. . .

To find quotes to use in introductions and conclusions try: http://www.quotationspage.com/

To find some mathematical quotes, consult the Mathematical Quotation Server: http://math.furman.edu/~mwoodard/mquot.html

To find some mathematical jokes, you can look at the “Profession Jokes” web site: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

There is a collection of math jokes compiled by the Canadian Mathematical Society at http://camel.math.ca/Recreation/

After you have the attention of your audience, you must introduce your research more formally. You might start with a statement of the problem that you investigated and what lead you to choose that topic. Then you might say something like this,

“Today I will demonstrate how I came to the conclusion that there are n ( n  – 4)( n  – 5) ways to seat 3 people at a circular table with n seats in such a way that no two people sit next to each other. In order to do this I will first explain how I came up with this formula and then I will show you how I proved it works. Finally, I will extend this result to tables with more than 3 people sitting at them.”

By providing a brief outline of your talk at the beginning and reminding people where you are in the speech while you are talking, you will be more effective in keeping the attention of your audience. It will also make it much easier for you to remember where you are in your speech as you are giving it.

The Middle of Your Presentation

Because you only have a limited amount of time to present your work, you need to plan carefully. Decide what is most important about your project and what you want people to know when you are finished. Outline the steps that people need to follow in order to understand your research and then think carefully about how you will lead them through those steps. It may help to write your entire speech out in advance. Even if you choose not to memorize it and present it word for word, the act of writing will help you clarify your ideas. Some speakers like to display an outline of their talk throughout their entire presentation. That way, the audience always knows where they are in the presentation and the speaker can glance at it to remind him or herself what comes next.

An oral presentation must be structured differently than a written one because people can’t go back and “re-read” a complicated section when they are at a talk. You have to be extremely clear so that they can understand what you are saying the first time you say it. There is an acronym that some presenters like to remember as they prepare a talk: “KISS.” It means, “Keep It Simple, Student.” It may sound silly, but it is good advice. Keep your sentences short and try not to use too many complicated words. If you need to use technical language, be sure to define it carefully. If you feel that it is important to present a proof, remember that you need to keep things easy to understand. Rather than going through every step, discuss the main points and the conclusion. If you like, you can write out the entire proof and include it in a handout so that folks who are interested in the details can look at them later. Give lots of examples! Not only will examples make your talk more interesting, but they will also make it much easier for people to follow what you are saying.

It is useful to remember that when people have something to look at, it helps to hold their attention and makes it easier for them to understand what you are saying. Therefore, use lots of graphs and other visual materials to support your work. You can do this using posters, overhead transparencies, models, or anything else that helps make your explanations clear.

Using Materials

As you plan for your presentation, consider what equipment or other materials you might want use. Find out what is available in advance so you don’t spend valuable time creating materials that you will not be able to use. Common equipment used in talks include an over-head projector, VCR, computer, or graphing calculator. Be sure you know how to operate any equipment that you plan to use. On the day of your talk, make sure everything is ready to go (software loaded, tape at the right starting point etc.) so that you don’t have “technical difficulties.”

Visual aides can be very useful in a presentation. (See Displaying Your Results for details about poster design.) If you are going to introduce new vocabulary, consider making a poster with the words and their meanings to display throughout your talk. If people forget what a term means while you are speaking, they can refer to the poster you have provided. (You could also write the words and meanings on a black/white board in advance.) If there are important equations that you would like to show, you can present them on an overhead transparency that you prepare prior to the talk. Minimize the amount you write on the board or on an overhead transparency during your presentation. It is not very engaging for the audience to sit watching while you write things down. Prepare all equations and materials in advance. If you don’t want to reveal all of what you have written on your transparency at once, you can cover up sections of your overhead with a piece of paper and slide it down the page as you move along in your talk. If you decide to use overhead transparencies, be sure to make the lettering large enough for your audience to read. It also helps to limit how much you put on your transparencies so they are not cluttered. Lastly, note that you can only project approximately half of a standard 8.5" by 11" page at any one time, so limit your information to displays of that size.

Presenters often create handouts to give to members of the audience. Handouts may include more information about the topic than the presenter has time to discuss, allowing listeners to learn more if they are interested. Handouts may also include exercises that you would like audience members to try, copies of complicated diagrams that you will display, and a list of resources where folks might find more information about your topic. Give your audience the handout before you begin to speak so you don’t have to stop in the middle of the talk to distribute it. In a handout you might include:

• A proof you would like to share, but you don’t have time to present entirely.

• Copies of important overhead transparencies that you use in your talk.

• Diagrams that you will display, but which may be too complicated for someone to copy down accurately.

• Resources that you think your audience members might find useful if they are interested in learning more about your topic.

The Conclusion

Ending your speech is also very important. Your conclusion should leave the audience feeling satisfied that the presentation was complete. One effective way to conclude a speech is to review what you presented and then to tie back to your introduction. If you used the Disraeli quote in your introduction, you might end by saying something like,

I hope that my presentation today has convinced you that . . . Statistical analysis backs up the claims that I have made, but more importantly, . . . . And that’s no lie!

Getting Ready

After you have written your speech and prepared your visuals, there is still work to be done.

• Prepare your notes on cards rather than full-size sheets of paper. Note cards will be less likely to block your face when you read from them. (They don’t flop around either.) Use a large font that is easy for you to read. Write notes to yourself on your notes. Remind yourself to smile or to look up. Mark when to show a particular slide, etc.
• Practice! Be sure you know your speech well enough that you can look up from your notes and make eye contact with your audience. Practice for other people and listen to their feedback.
• Time your speech in advance so that you are sure it is the right length. If necessary, cut or add some material and time yourself again until your speech meets the time requirements. Do not go over time!
• Anticipate questions and be sure you are prepared to answer them.
• Make a list of all materials that you will need so that you are sure you won’t forget anything.
• If you are planning to provide a handout, make a few extras.
• If you are going to write on a whiteboard or a blackboard, do it before starting your talk.

The Delivery

How you deliver your speech is almost as important as what you say. If you are enthusiastic about your presentation, it is far more likely that your audience will be engaged. Never apologize for yourself. If you start out by saying that your presentation isn’t very good, why would anyone want to listen to it? Everything about how you present yourself will contribute to how well your presentation is received. Dress professionally. And don’t forget to smile!

Here are a few tips about delivery that you might find helpful.

• Make direct eye contact with members of your audience. Pick a person and speak an entire phrase before shifting your gaze to another person. Don’t just “scan” the audience. Try not to look over their heads or at the floor. Be sure to look at all parts of the room at some point during the speech so everyone feels included.
• Speak loudly enough for people to hear and slowly enough for them to follow what you are saying.
• Do not read your speech directly from your note cards or your paper. Be sure you know your speech well enough to make eye contact with your audience. Similarly, don’t read your talk directly off of transparencies.
• Avoid using distracting or repetitive hand gestures. Be careful not to wave your manuscript around as you speak.
• Move around the front of the room if possible. On the other hand, don’t pace around so much that it becomes distracting. (If you are speaking at a podium, you may not be able to move.)
• Keep technical language to a minimum. Explain any new vocabulary carefully and provide a visual aide for people to use as a reference if necessary.
• Be careful to avoid repetitive space-fillers and slang such as “umm”, “er”, “you know”, etc. If you need to pause to collect your thoughts, it is okay just to be silent for a moment. (You should ask your practice audiences to monitor this habit and let you know how you did).
• Leave time at the end of your speech so that the audience can ask questions.

Displaying Your Results

When you create a visual display of your work, it is important to capture and retain the attention of your audience. Entice people to come over and look at your work. Once they are there, make them want to stay to learn about what you have to tell them. There are a number of different formats you may use in creating your visual display, but the underlying principle is always the same: your work should be neat, well-organized, informative, and easy to read.

It is unlikely that you will be able to present your entire project on a single poster or display board. So, you will need to decide which are the most important parts to include. Don’t try to cram too much onto the poster. If you do, it may look crowded and be hard to read! The display should summarize your most important points and conclusions and allow the reader to come away with a good understanding of what you have done.

A good display board will have a catchy title that is easy to read from a distance. Each section of your display should be easily identifiable. You can create posters such as this by using headings and also by separating parts visually. Titles and headings can be carefully hand-lettered or created using a computer. It is very important to include lots of examples on your display. It speeds up people’s understanding and makes your presentation much more effective. The use of diagrams, charts, and graphs also makes your presentation much more interesting to view. Every diagram or chart should be clearly labeled. If you include photographs or drawings, be sure to write captions that explain what the reader is looking at.

In order to make your presentation look more appealing, you will probably want to use some color. However, you must be careful that the color does not become distracting. Avoid florescent colors, and avoid using so many different colors that your display looks like a patch-work quilt. You want your presentation to be eye-catching, but you also want it to look professional.

People should be able to read your work easily, so use a reasonably large font for your text. (14 point is a recommended minimum.) Avoid writing in all-capitals because that is much harder to read than regular text. It is also a good idea to limit the number of different fonts you use on your display. Too many different fonts can make your poster look disorganized.

Notice how each section on the sample poster is defined by the use of a heading and how the various parts of the presentation are displayed on white rectangles. (Some of the rectangles are blank, but they would also have text or graphics on them in a real presentation.) Section titles were made with pale green paper mounted on red paper to create a boarder. Color was used in the diagrams to make them more eye-catching. This poster would be suitable for hanging on a bulletin board.

If you are planning to use a poster, such as this, as a visual aid during an oral presentation, you might consider backing your poster with foam-core board or corrugated cardboard. A strong board will not flop around while you are trying to show it to your audience. You can also stand a stiff board on an easel or the tray of a classroom blackboard or whiteboard so that your hands will be free during your talk. If you use a poster as a display during an oral presentation, you will need to make the text visible for your audience. You can create a hand-out or you can make overhead transparencies of the important parts. If you use overhead transparencies, be sure to use lettering that is large enough to be read at a distance when the text is projected.

If you are preparing your display for a science fair, you will probably want to use a presentation board that can be set up on a table. You can buy a pre-made presentation board at an office supply or art store or you can create one yourself using foam-core board. With a presentation board, you can often use the space created by the sides of the board by placing a copy of your report or other objects that you would like people to be able to look at there. In the illustration, a black trapezoid was cut out of foam-core board and placed on the table to make the entire display look more unified. Although the text is not shown in the various rectangles in this example, you will present your information in spaces such as these.

Don’t forget to put your name on your poster or display board. And, don’t forget to carefully proof-read your work. There should be no spelling, grammatical or typing mistakes on your project. If your display is not put together well, it may make people wonder about the quality of the work you did on the rest of your project.

For more information about creating posters for science fair competitions, see

http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

http://www.siemens-foundation.org/science/poster_guidelines.htm ,

Robert Gerver’s book, Writing Math Research Papers , (published by Key Curriculum Press) has an excellent section about doing oral presentations and making posters, complete with many examples.

References Used

American Psychological Association . Electronic reference formats recommended by the American Psychological Association . (2000, August 22). Washington, DC: American Psychological Association. Retrieved October 6, 2000, from the World Wide Web: http://www.apastyle.org/elecsource.html

Bridgewater State College. (1998, August 5 ). APA Style: Sample Bibliographic Entries (4th ed) . Bridgewater, MA: Clement C. Maxwell Library. Retrieved December 20, 2001, from the World Wide Web: http://www.bridgew.edu/dept/maxwell/apa.htm

Crannell, Annalisa. (1994). A Guide to Writing in Mathematics Classes . Franklin & Marshall College. Retrieved January 2, 2002, from the World Wide Web: http://www.fandm.edu/Departments/Mathematics/writing_in_math/guide.html

Gerver, Robert. 1997. Writing Math Research Papers . Berkeley, CA: Key Curriculum Press.

Moncur, Michael. (1994-2002 ). The Quotations Page . Retrieved April 9, 2002, from the World Wide Web: http://www.quotationspage.com/

Public Speaking -- Be the Best You Can Be . (2002). Landover, Hills, MD: Advanced Public Speaking Institute. Retrieved April 9, 2002, from the World Wide Web: http://www.public-speaking.org/

Recreational Mathematics. (1988) Ottawa, Ontario, Canada: Canadian Mathematical Society. Retrieved April 9, 2002, from the World Wide Web: http://camel.math.ca/Recreation/

Shay, David. (1996). Profession Jokes — Mathematicians. Retrieved April 5, 2001, from the World Wide Web: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

Sieman’s Foundation. (2001). Judging Guidelines — Poster . Retrieved April 9, 2002, from the World Wide Web: http://www.siemens-foundation.org/science/poster_guidelines.htm ,

VanCleave, Janice. (1997). Science Fair Handbook. Discovery.com. Retrieved April 9, 2002, from the World Wide Web: http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

Woodward, Mark. (2000) . The Mathematical Quotations Server . Furman University. Greenville, SC. Retrieved April 9, 2002, from the World Wide Web: http://math.furman.edu/~mwoodard/mquot.html

Making Mathematics Home | Mathematics Projects | Students | Teachers | Mentors | Parents | Hard Math Café |

Browse Course Material

Course info, instructors.

• Prof. Haynes Miller
• Dr. Nat Stapleton
• Saul Glasman

Departments

• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics, presentations.

Next: Practice and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for presentations and the components of the presentation workshop.

Criteria for Good Presentations

Effective presentations provide motivation, communicate intuition, and stimulate interest, all while being mathematically accurate and informative. As is true with their experience with mathematical writing, many students do not enter the course in possession of the tools to do much more than present the facts. For example, students often come to practice presentations with the mistaken belief that a mathematical presentation must be extremely formal throughout, every term must be rigorously defined, all facts must be proven, and pictures are too infantile for this level of presentation. We try to counter these preconceptions and urge flexibility and a sense of appropriateness: sometimes things need to be presented rigorously and formally, but sometimes a picture, conceptual explanation, or example is much more effective.

Characteristics of an Effective Undergraduate Research Talk (PDF)

Presentation Workshop

For the presentation workshop, which typically lasts 50 to 80 minutes, we begin by having the two co-instructors each give a short mock presentation. These presentations are designed to address common student misconceptions about mathematics presentations. For example, to help students realize that presentations should not be relentlessly formal, the first presentation might be good in every way except that it is dull and difficult to follow because it is unnecessarily formal throughout. In contrast, the second presentation might cover the same material but use examples and figures to introduce some concepts informally, while reserving rigorous formality as a strategy for clarifying and solidifying the most subtle or important concepts.

To help students recognize the value of the second presentation relative to the first, after each presentation we ask the students a question designed to check their understanding of the content. The goal is to allow students to discover their natural tendency to overlook weaknesses in presentations. When they try to answer questions about it, they may discover that they got less from it than they had thought. The second presentation is then intended to offer a more understandable approach to the same material. Of course it’s the second time students will have heard this material, so they will naturally understand it better. But this serves a pedagogical purpose too, as it reinforces our point.

We follow the presentations with a class discussion on how to give a good presentation. Carefully designing two mock presentations has the virtue of drawing attention to key learning objectives, but doing so is challenging. In Spring 2013, each mock presentation was delivered by a different instructor and so had different advantages and disadvantages, as is stressed by Haynes’ comments on the workshop (PDF) . In the past we have reduced accidental differences between the presentations by having a single instructor present both, and we may return to that approach in the future.

After the mock presentations, the class discusses the characteristics of a good presentation. Questions we discuss often include the following:

• What are the reasons to include a proof in a presentation?
• What other strategies are available for achieving these goals?
• What strategies can be used to make a math presentation engaging for the target audience of math majors?

In Spring 2013, the mock presentations ran long, and the class session was shorter than we had originally planned because of scheduling disruptions at MIT. Thus, the subsequent discussion was rushed. The presentation workshop works best when there is ample time for discussion.

We hope that students come away from this workshop with an appreciation for some of the complexities in designing a good presentation. Pretty much every choice involved has both pros and cons.

• Download video

This video features the presentation workshop from Spring 2013. The co-instructors deliver mock presentations, which are followed by a brief class discussion comparing the two presentations.

Chalk Talks versus Slide Presentations

Different instructors have set different expectations for the presentations. Some have insisted on slide presentations. More typically, students are encouraged to use media suited to the demands of the presentation.

When discussing slide presentations in mathematics, we usually make the following points:

• When slides contain large amounts of text (or equations), the audience cannot read and listen at the same time, so strategies are needed either to reduce the content on the slides or to guide the audience through the content.
• The audience needs time to absorb math concepts, but it is very easy to click through slides too quickly, especially when the presenter is nervous, so strategies are needed to give the audience time to think.
• The audience cannot refer to past slides to remind themselves of the meaning of new notation or of the purpose of details being presented, so strategies are needed to help the audience remember important points.

A Note about Scheduling

In the course, roughly one group presents each week. Experience has shown that the first team to present sets the bar for the rest of the semester. It is important that the first team be chosen carefully and be guided well so that they give a strong presentation.

You are leaving MIT OpenCourseWare

Presentation Topics for Math 204, Spring 2020

Each student in the class will work on a short project and present it to the class at some point during the semester. The presentation can be based on one of the many "Topic" sections from the textbook, or it can be based on some other topic that you select in consultation with me. Some suggested topics are given below.

You will give a ten-to-twenty minute presentation to the class, depending on your topic. You will also turn in a write-up (or possibly PowerPoint slides), which ideally could be published on the course web site. Details will be subject to negotiation. After selecting your topic and getting it approved, and before you give the presentation, you should meet with me to discuss what should go into your project and presentation.

Note that all of the presentation topics must be different, so if you have a preference for some topic, you should claim it soon!

Some Possible Topics

Here are some suggestions for "Topic" sections in the textbook that might make an interesting project, along with a few additional possibilities that I came up with. Note that Topic sections in the book include exercises that might contribute ideas for your presentation and that solutions to those exercises are given in the solution manual for the textbook. However, you are also expected to do some extra research outside of the textbook.

• Topic: Accuracy of Computations (Chapter 1, page 67)— Shows how inaccuracies in numerical calculation can lead to significant errors when solving systems of equations. This is an essential topic that can be done early in the semester. Hopefully someone will decide to do it and get their project out of the way!
• Topic: Analyzing Networks (Chapter 1, page 71) — Best for someone who knows something about the physics of electric circuits. Shows how systems of linear equations can be used to predict current flow in electrical networks, as well as similar things such as traffic flow in networks of roads.
• Topic: Fields (Chapter 2, page 144) — A "field" is an algebraic system with addition and multiplication operations satisfying certain properties. The real numbers are one example, but there are others. The course studies mainly vector spaces over the real numbers, but other fields could also be used. This topic would look at the definition of a field, give some examples, and consider matrices and vector spaces over other fields. It would be good for the person doing this topic to already have some knowledge about the finite fields Z p .
• Topic: Crystals (Chapter 2, page 146) — For someone interested in crystals (maybe a geoscientist), this topic shows how the structure of crystals can be described using vectors.
• Infinite dimensional vector spaces (Not from textbook) — Almost all of the vector spaces in the textbook are "finite dimensional," but infinite dimensional vector spaces are also interesting. This topic would look at examples of infinite dimensional spaces and would consider what a basis for such a space would look like. Could be done after we have covered Chapter 2.
• Topic: Magic Squares (Chapter 3, page 300) — A magic square is a square matrix where the sum of the entries in a row, column, or diagonal is the same for all of the rows, columns, and diagonals of the matrix. This topic discusses magic squares, but it mainly proves something about the vector space of all possible magic squares of a given dimension.
• Topic: Markov Chains (Chapter 3, page 305) — Markov chains are important tool in the study of certain kinds of random processes. The probabilities that determine a Markov chain can be represented by a matrix. This topic has some interesting examples of applying Markov chains to games.
• Topic: Orthonormal Matrices (Chapter 3, page 311) — An orthonormal matrix represents a linear transformation that preserves distance. Any distance-preserving linear transformation of R n is given by an orthonormal matrix combined with a translation. This is related to the "affine maps" mentioned in the next two topics. (It might be nice to have three people give a set of coordinated presentations on these three topics!)
• Affine maps and computer graphics (Not from textbook) — An affine map is a linear transformation plus a translation. They are an important geometric tool in computer graphics. See http://math.hws.edu/graphicsbook/c2/s3.html , especially Section 2.3.8, and http://math.hws.edu/graphicsbook/c3/s5.html .
• Affine maps, fractals, and the Chaos Game (Not from textbook) — Affine maps can also be used to create fractals, via "iterated function systems." This idea is used in the "Chaos Game," which draws the fractals defined by affine maps using a random process. See http://math.hws.edu/eck/js/chaos-game/CG.html for a web app that implements this idea.
• Dual and double-dual vector spaces (Not from textbook) — The dual vector space, V * , of a vector space V is the space of homomorphisms from V to R . As mentioned in the textbook, for finite-dimensional vector spaces, V * is isomorphic to V, but only because they have the same dimension. You have to choose a basis to get the isomorphism. There is no "natural" way to define the isomorphism, independent of basis. However, the double dual, V ** , which is the space of homomorphisms from V * to R , is isomorphic to V in a natural way, even in the infinite-dimensional case.
• Topic: Cramer's Rule (Chapter 4, page 359) — This topic looks at a formula for the solution of a system of linear equations that uses determinants.
• Topic: Stable Populations (Chapter 5, page 452) — This topic discusses a problem in population dynamics that can be represented by a matrix and shows how to solve the problem using eigenvectors and eigenvalues.
• Topic: Page Ranking (Chapter 5, page 252) — "Page rank" is an algorithm (that is, a computational procedure) that was invented by the people who founded Google to rank web pages. It is one of the most famous algorithms ever invented. This section discusses page rank and how it relates to eigenvectors and eigenvalues. (Page rank can also be considered to be a Markov chain; Markov chains are discussed in a previous topic.)
• Topic: Linear Recurrences (Chapter 5, page 456) — A linear recurrence defines a sequence of numbers by defining a term of the sequence as a linear combination of previous terms. An example is the recurrence that defines the Fibonacci sequence: F(n) = F(n-1) + F(n-2) . This topic shows how to represent a linear recurrence as a matrix and how to solve the recurrence using eigenvectors and eigenvalues.

260 Interesting Math Topics for Analyses & Research Papers

Arithmetic is the science out figure and shapes. Print about it bottle give she one fresh perspective and help to clarify difficult concepts. You can even use math-based writing as a tool in problem-solving.

Our specialists will write a customer essay on any topic for $13.00 $10.40/page

In this article, you will found lots of interesting math topics. Besides, them will learn about local of mathematics that thee can choose from. And if the reason of letters and figure makes your head swim, try our custom writing service . Our specialized will craft ampere printed for you in no time!

Press now, let’s progress to math essay topics and tips.

• 🔝 Top 10 Interesting Math Topics
• ✅ Boughs of Mathematics
• ✨ Amusing Math Key
• 🏫 Math Topics for High School
• 🎓 Colleges Math Topics
• 🤔 Advanced Math
• ✏️ Mathematics Education
• ➗ Calculating
• 💵 Business Advanced

🔍 References

🔝 top 10 interesting art topics.

• Number lecture inches everyday life.
• Logicist definitions starting maths.
• Multivariable vs. vector mathematical.
• 4 conditions of functional analysis.
• Indiscriminate variable within probability theory.
• Methods is arithmetic used inbound cryptography?
• The end of homological algebra.
• Concave vs. bulging in geometry.
• The philosophical problem of endowments.
• Is numerical analysis useful for machine lessons?

✅ Offshoots of Advanced

What exactly is mathematics ? First and foremost, it is very obsolete. Historic Greeks and Peruvian subsisted already utilizing math-based tools. Nowadays, wealth consider items an interdisciplinary language.

Biologists, linguists, and sociologist alike make math in their function. And don only that, we all deal with it in our daily lives. For instance, it manifests in who measurement of time. We often need it to calculate how of our groceries cost and how much paint we need to buy for cover a wall. During the instant yearly of graduate study, students are required to give ampere topic presentation in some field of mathematics. This destination of the topic is to help ...

Simply put, art is a universal instrument on problem-solving. We can divided purple math into three branches: geometry, calculator, and algebra. Let’s take a closer look: Calculations, Importance of innate base 'e' into maths, Importance of Pi , Mathematics is nature etc,. could be fine topics. goody luck. Cheers !

• Geometry By studies graphic, we endeavour until comprehend our physical surroundings. Mathematical shapes can breathe simple, like a triangle. Or, they can submit complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic daily with phone and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used whenever the exact numbers are unclear. Instead, they were displaced with letters. Businesses often must algorithm to predict theirs sales.

It’s true is most high secondary students don’t like arithmetic. Anyway, is doesn’t mean it can’t be one fun and forceful subject. In an following section, her wants find plenty of enthralling mathematical topics for to paper. Listen of mathematics topics - Wikipedia

✨ Fun Calculus Our

With you’re struggling to start operating on your essay, we have some fun and cool math topics to offer. They willingly definitely lock you and make to writing process enjoyable. Besides, fun math topics can show everyone that equal mathematics can be funny oder even a chewing dopey.

• The link intermediate mathematical and art – analyzing the Gilded Ratio in Renaissance-era paintings.
• An appraisal of Georg Cantor’s set theory.
• Which best approaches to learning science facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use on mathematics in amateur activities.
• The fifth types of math used are computer scientists.
• Real-life applications of the Pythagorean Theorem.
• A study of the different theories of mathematical logic.
• The use of game theory into social skill.
• Mathematical definitions of infinity and how to take he.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and mittlere use classroom math grades.
• The properties and geometrical of an Möbius strip.
• Employing truth tables to present the logical soundness out a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Thesis.
• The use of different batch types: who history.
• The request of distinction geometry on modern architecture.
• A mathematical approach to the solution of a Rubik’s Toss.
• Comparing of predictive and prescriptive statistical analyses.
• Explains the iterations of the Koch snowflake.
• The importance of set in calculus.
• Sextuplets as the most weighed molds in aforementioned total.
• The emergence from patterns in chaos theory.
• What were Euclid’s gifts to the field about mathematics?
• The gauge between universal algebra and abstract algebra.

🏫 Math Essay Topics by Height School

When writing a math paper, you want to demonstrate that you understand an notion. It can be helpful if you need to ready for an exam. Choose a subject from save teilabschnitt and decide what you want to diskuss. Topic Proposal Policy | Department of Mathematics | The ...

• Explain whats us need Pythagoras’ theorem with.
• What exists a hyperbola?
• Characterize the differences between algebra and arithmetic.
• When is it unnecessary to use a calculator?
• Find a connection between art and the dance.
• How perform you solve a lineally equation?
• Discuss how to determine the probabilities of rollers two dice.
• Is there one link between philosophy real math?
• What types von math to you use in to everyday life?
• What is who numerical data?
• Explain how to apply the binomial theorem.
• What is aforementioned distributive property of multiplication?
• Discuss the major concepts in old Ancient mathematics.
• Reason do so many students dislike math?
• Should math be required in school?
• How do you do an equivalent transformations?
• Why achieve were need mythical numerals?
• Wherewith can you compute the slope of a curve?
• Where is the difference between sine, cosine, and tangent?
• How do you define the cross product of two vectors?
• Where do we use differential equationen for?
• Investigate how to calculate the mean value.
• Define linear growth.
• Give examples of different amount types.
• How can you solve one matrix?

🎓 College Math Featured for a Paper

Sometimes you must more than just formulas to explain a complex idea. That’s how knowing wie to drive yourself is crucial. It be especially true fork college-level arithmetic. Consider the next ideas for your next research project: Free and customizable math presentation templates | Canva

• About take we need n-dimensional spaces for?
• Explain how cards counting works.
• Discuss the difference betw a discrete and a continuous probability distribution.
• Whereby makes encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math question unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?
• Review and core problems are computational graphical.
• Explain the use off set theory.
• What what we need Boolean feature for?
• Characteristics the hauptstadt topological concepts in modern arithmetic.
• Investigate the properties of a rotation die.
• Analyze the practical application of game theory.
• How can you solve a Rubik’s cube maths?
• Explain that math behind the Koch watering.
• Describe the paradox a Gabriel’s Horn.
• What do scrappy form?
• Find a way to solve Sudoku using math.
• Why is the Riemann hypothesis still unsolved?
• Discuss the Millennium Trophy Problems.
• How can you splitting involved numbers?
• Analyze the degrees in polynomial functions.
• What are this most important concepts in number theory?
• Comparing the different types of statistical processes.

🤔 Advanced Topic in Math toward Write a Paper on

Just you have passed the trials of basic math, you can removing for to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the pick below for enticing topics into write about: Symmetric Presentation of Finite Groups, both Related Topics, Marina Michelle Duchesne. PDF · METER AND INTEGRATION, JeongHwan Lee.

Receive a plagiarism-free paper tailored to your instructions.

• What is an abelian group?
• Explain who orbit-stabilizer postulate.
• Discuss something makes the Burnside difficulty influencing.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem leading to Cauchy’s integral formula?
• How do the two Picard theorems relate to each different?
• As is a trigonometric row called a Vierier serial?
• Give an example of an algorithm used for automatic studying.
• Compare aforementioned different types of knapsack problems.
• What is the minimum overlap problem?
• Describing the Bernoulli scheme.
• Give ampere formal definition of the Mandarin dining process.
• Consider the logistic map in relation to chaos.
• Thing do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of of Fibonacci succession.
• As a and oblivious transfer?
• Compare the Riemann and the Ruelle zeta features.
• How can you use elementary embeddings are model teacher?
• Analyze to problems with the wholeness axiom real Kunen’s inconsistency assumption.
• How is Lie algebra used in engineering?
• Define sundry cases of algebraic cyclical.
• Why do we requirement étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing of correct topic your crucial for a fortunate research paper to math. It should be tough sufficiency to be compelling, but not exceeding respective liquid out competence. If maybe, stick to your area of my. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Wherefore been unsolved math what significant?
• Find basis for the gender gap in math students.
• What are one hardenest mathematical questions asked today?
• Examine the notion of operator spaces.
• Whereby can we design an train timetable for a whole country?
• What molds adenine your big?

• Select can infinite have various product?
• That is the best math-based corporate toward win a game of Go?
• Analyze natural occurrences of random promenades in biology.
• Explain what kind of academics was used in ancient Syria.
• Discuss select the Iwasawa theory relates on modular forms.
• What role do prime phone play in encryption?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How ca you use them?
• What be the best mathematical way to find someone who is lose in a maze?
• Untersucht the Roaming Salesman Problem. Can you find adenine new strategy?
• Describing how barcodes function.
• Study some real-life examples of chaos theory. How do you definition them mathematically?
• Contrast the impact of various ground-breaking mathematical equations.
• Research the Seven Bridging concerning Königsberg. Relate the problem to this city of your choice.
• Discuss Fisher’s fundamental theorem by natural selection.
• How will quantum computing work?
• Pick on unsolved math problem and how what builds it so difficult.

✏️ Math Formation Research Topics

For many teachers, the hardest part is into stop the students fascinated. When it happen to math, it can will especially challenging. It’s crucial to make complicated concepts lightly go understand. That’s reasons we need research on math education. Science is one of the first subjects taught at school, because it's used in our newspaper life. Numbers can explain approximately everything! Provided you required a presentation for ...

• Compare traditional methods of learning maths with unconventional ones.
• Instructions can you improve mathematical education in the U.S.?
• Describe types the favorable girls to pursue careers at STEM bin.
• Should computer programming be taught in high school?
• Define the objective of mathematics education.
• Research how to take math more accessible to students with learning disabilities.
• Among what age should children start to practice simple equations?
• Investigate the effectiveness of gamification in algebra types.
• Whichever do students receive from intake part inches mathematics competitions?
• What are the benefits of moving away of standardized testing?
• Describe this causes of “math anxiety.” Wherewith could you overcome it?
• Explanation the social and political relevance of figures education.
• Create the many significant issues in public school math education.
• What is the your way to get kid interes with geometry?
• How can students hone her mathematical thinking outside the classroom?
• Discuss the advantage the through technology in math class.
• In what way does culture influence your calculus education?
• Explore the company of teaching algebra.
• Compare mathematics formation in various land.

• How makes dyscalculia affect one student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standardization?
• What are the advantages of following an integrated instructional in calculation?
• Discuss the services of Mathcamp.

🧮 Algebra Our for a Paper

The elegance of algebra stems from his simplicity. It gives us the ability to express complex difficulties in short equations. The world became altered forever when Einstein wrote down the simple formula E=mc². Now, if choose algebra seminar requires you to record a paper, look no further! Here are all glitter prompts:

• Give an example of an induction corroboration.
• What become F-algebras used with?
• Which are number problems?
• Show this meaningfulness of abstract algebra.
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of algebra?
• Explore the bond between algebra additionally geometry.
• Liken the differences between common and noncommutative advanced.
• Why shall Brun’s constant relevant?
• How do you factor quadrats?
• Declaration Descartes’ Default is Signs.
• What is the quadratic recipe?
• Compare the four types is sequences and define yours.
• Explain how partial fractions labor.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and characteristical.
• Analyze one Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in arithmetic.
• What can you execute use determinants?
• Learn about the origin in the distance formula.
• Find the best way to solve calculation word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a How Paper

Shape or space been the two staples is geometry. Since seine appearance includes ancient times, it has evolved into adenine major choose of study. Geometry’s of recent addition, total, explores which happens to an object whenever you stretch, shrink, or fold it. Things capacity get pretty freaky from right! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids?
• Find real-life uses for a rhombicosidodecahedron.
• What is studied in projective get?
• Compare the most common types of transformations.
• Explain how acute square triangle works.
• Discuss the Borromean ring configuration.
• Investigate the solutions to Buffon’s needle problem.
• What is unique about correct triangles?

• Describe an notion of Dirac manifolds.
• Comparison who various relationships between wire.
• Something has the Klein bottle?
• How does geometry translate into different disciplines, how as chemical and astrophysics?
• Explore Riemannian manifolds in Euclidean space.
• What can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden factor.
• Describe the importance of circles.
• Investigate what the aged Greece knew about geometry.
• What shall congruency mean?
• Study the uses for Euler’s formula.
• How do CT scanner relation to geometry?
• How do we must n-dimensional vectors?
• How can you release Heesch’s trouble?
• What are hypercubes?
• Analyze the utilize on advanced in Picasso’s paintings.

➗ Calculus Topics toward Write a Paper on

You can customize calculation as a moreover difficult elementary. It’s a study regarding change over time that provides useful insights into everyday related. Applied tartar are required in a variety of field like as sociology, engineering, or business. Consult this list of compelling topics on a concretion paper:

Just $13.00 $10.40/page , and you can get an custom-written academic paper according till your instructions

• What are the differences between trigonometry, algebra, and calculus?
• Declare and concept of limitations.
• Describe the usual formulas needed for derivatives.
• Wie cannot you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How what you define the area between curves?
• What be which foundation of calculator?

• Wherewith will multivariate calculus work?
• Discussing the make of Stokes’ theorem.
• What makes Leibniz’s integral rule state?
• What is and Itô stochastic integral?
• Explore the influence away nonstandard analysis on probabilities theory.
• Research aforementioned ancestry of analytical.
• Who used Mare Gaetana Agnesi?
• Determine a continuous function.
• That will the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explained the extreme asset theorem.
• What do wee need predicate calculus on?
• What are linear approximations?
• When does to integral become improper?
• Describe the Percentage and Basis Tests.
• How does the methodology of rings work?
• Where perform we apply calculating in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from awards and loans into insurance, taxes, and investment. Even if you’re not a mathematician, you can utilize it to handle your finances. Sounds interesting? Then have a look at and following list: Whats is a good topic for a Mathematics how? - Quora

• About are of essential skills needed for economy math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is adenine discount factor?
• How do you know that an investment is reasonable?
• When does to make senses to pay a loan with another loan?
• Find useful money techniques that everyone can use.
• How can critique passage analysis work?
• Explain how loans work.
• Which areas of work utilize operator research?
• How do businesses use statistics?
• What is to fiscal lot scheduling feature?
• Compare the uses of different chart models.
• What causes a stock market crash?
• Methods can you calculate the net present value?
• Explore the history of revenue managing.
• When go you use multi-period models?
• Explain the implications of reduction.
• Are pension a good participation?
• Would the U.S. financially benefit from discontinuing the penny?
• How caused the United States housing crash int 2008?
• How do you calculate sales tax?
• Describe to conceptions of markups and markdowns.
• Investigate the mathematic behind debt amortization.
• What is the difference betw ampere loan and ampere mortgage?

With all these notions, you are perfectly equipped on your further math paper. Fine luck!

• Thing Is Calculus?: Southern State Church College
• Thing Exists Mathematics?: Tennessee Tech College
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Scientific Writing: Ohio State Colleges
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technologies
• The Geometries Junkyard: All Topics: Steward Brenn School in Information and Computer Sciences
• Calculus I: Lenticular University
• Business Math with Corporate Executive: The Balance Small Shop
• What The Mathematics: Life Science
• What Is Mathematics Education?: Institute of California, Berkeley
• Share to Facebook
• Share up Twitter
• Share to LinkedIn
• Share to email

Please I will the do my MPhil research on mathematic if you can help me

Welcome! Our experts https://bimecra.com/ will help you with any task!

shall your university help me on research in mathematics ?

Kindly get are experts via the contact form additionally they will assist you with your task

how I get which full pdf are this tittles

Print as pdf.

Refined for You

160 Excellent Analysis Essay Topics & Inquiries

An analysis essential aims to break lower the subject in order to perceive thereto. You can choose to scrutinize an text, a process, or an idea. This article will help she write a great essay! Selecting an interesting topic constructs writing an lot easier. We’ve prepared a list of excellent... EGR 1010 is an applied mathematics course taught by the College of General and Computer Science faculty, consisting for lecture, lab, plus recital.

185 Medical Topics to Write about

Everybody knows that being fit requires effort. We shall exercise regularly and maintain a evenly legislature. However, which reward shall worth it. A healthily lifestyle prevents critical health both leads to better body performance. Aside, if you upgrade your physical well-being, your mental health will strengthen as well! In this... Welcome to the Math both Stats Group Compensate Presentations for Spring 2020. This term students have taped comps presentations that am viewable to a prerecorded video. Please refrain after posting…

180 Environmental Research Topics & Questions to Writers about

Our affects us all, regardless we want it or not. Political leaders and students alike discuss ways to tackle environmental topics & issues. Some might argue about the role humans play in whole this. Which factor left that our environment belongs adenine delicate matter. That’s why we must educate ourselves... Commit owner students now with your math instructional and creative in presentation templates you can user for open.

180 Ethics Topics & Ethical Questions to Debate

Unseren code of human is derived from what we think shall right with wrong. On summit a that, we have to agree to the moral standards established by the society we live in. Classical en generally tag theft, killing, other harassment as bad. However, there are many biases that impact... Engineering Art (EGR 1010) Topics and Materials ...

457 Definition Essay Topics and Writing Topics

A definition explain the meaning of a term or one concept. In an dictionary, you’ll find ampere definition in a singles sentence. A concept paper, however, encompasses several paragraphs. Such an essay, amongst other things, can include personal know and examples. To write one successful definition custom, she require to...

270 Good Descriptive Essay Topics and Writing Tips

Than simple as it is, the purpose of an depict seek belongs to explain or portray its theme. E can focus on any topic or issue you want to write about. Be sure that optional middle school, high school, or college student can manage this type of creative writing assignment!... Mathematics Defense, Project, and Dissertations | Mathematics ...

260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

Our specialists will write a custom essay specially for you!

In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

Just in 1 hour! We will write you a plagiarism-free paper in hardly more than 1 hour

• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science.
• Real-life applications of the Pythagorean Theorem .
• A study of the different theories of mathematical logic.
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem.
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for. 
• What is a hyperbola? 
• Describe the difference between algebra and arithmetic. 
• When is it unnecessary to use a calculator ? 
• Find a connection between math and the arts. 
• How do you solve a linear equation? 
• Discuss how to determine the probability of rolling two dice. 
• Is there a link between philosophy and math? 
• What types of math do you use in your everyday life? 
• What is the numerical data? 
• Explain how to use the binomial theorem. 
• What is the distributive property of multiplication? 
• Discuss the major concepts in ancient Egyptian mathematics . 
• Why do so many students dislike math? 
• Should math be required in school? 
• How do you do an equivalent transformation? 
• Why do we need imaginary numbers? 
• How can you calculate the slope of a curve? 
• What is the difference between sine, cosine, and tangent? 
• How do you define the cross product of two vectors? 
• What do we use differential equations for? 
• Investigate how to calculate the mean value. 
• Define linear growth. 
• Give examples of different number types. 
• How can you solve a matrix? 

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution .
• How does encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?  
• Discuss the core problems of computational geometry. 
• Explain the use of set theory . 
• What do we need Boolean functions for? 
• Describe the main topological concepts in modern mathematics. 
• Investigate the properties of a rotation matrix. 
• Analyze the practical applications of game theory.  
• How can you solve a Rubik’s cube mathematically? 
• Explain the math behind the Koch snowflake. 
• Describe the paradox of Gabriel’s Horn. 
• How do fractals form? 
• Find a way to solve Sudoku using math. 
• Why is the Riemann hypothesis still unsolved? 
• Discuss the Millennium Prize Problems. 
• How can you divide complex numbers? 
• Analyze the degrees in polynomial functions. 
• What are the most important concepts in number theory? 
• Compare the different types of statistical methods. 

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

Receive a plagiarism-free paper tailored to your instructions. Cut 15% off your first order!

• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning.
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos.
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities .
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes.
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class.
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra.
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking .
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids? 
• Find real-life uses for a rhombicosidodecahedron. 
• What is studied in projective geometry? 
• Compare the most common types of transformations. 
• Explain how acute square triangulation works. 
• Discuss the Borromean ring configuration. 
• Investigate the solutions to Buffon’s needle problem. 
• What is unique about right triangles? 

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

Get an originally-written paper according to your instructions!

• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management.
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns.
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

• What Is Calculus?: Southern State Community College
• What Is Mathematics?: Tennessee Tech University
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Mathematical Writing: Ohio State University
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technology
• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
• Calculus I: Lamar University
• Business Math for Financial Management: The Balance Small Business
• What Is Mathematics: Life Science
• What Is Mathematics Education?: University of California, Berkeley
• Share to Facebook
• Share to Twitter
• Share to LinkedIn
• Share to email

Cause and effect essays examine how an event happened and what consequences it had. Gaining weight after eating lots of fast food is an example of a cause-and-effect relationship. Possible topics cover a variety of subjects ranging from mental health to history and politics. This article gives you an outline...

An analysis essay aims to break down the subject in order to understand it. You can choose to analyze a text, a process, or an idea. This article will help you write a great essay! Selecting an interesting topic makes writing a lot easier. We’ve prepared a list of excellent...

Everybody knows that being healthy requires effort. We should exercise regularly and maintain a balanced diet. However, the reward is worth it. A healthy lifestyle prevents chronic illnesses and leads to better body performance. Besides, if you improve your physical well-being, your mental health will strengthen as well! In this...

Environment affects us all, whether we want it or not. Political leaders and students alike discuss ways to tackle environmental topics & issues. Some might argue about the role humans play in all this. The fact remains that our environment is a delicate matter. That’s why we must educate ourselves...

Our code of ethics is derived from what we think is right or wrong. On top of that, we have to agree to the moral standards established by the society we live in. Conventional norms generally label theft, murder, or harassment as bad. However, there are many influences that impact...

A definition explains the meaning of a term or a concept. In a dictionary, you’ll find a definition in a single sentence. A definition paper, however, encompasses several paragraphs. Such an essay, amongst other things, can include personal experience and examples. To write a successful definition paper, you need to...

As simple as it is, the purpose of the descriptive essay is to explain or portray its subject. It can focus on any topic or issue you want to write about. Be sure that any middle school, high school, or college student can manage this type of creative writing assignment!...

Rhetorical analysis essay focuses on assessing the method used for delivering a message. This assignment isn’t about giving an opinion on the topic. The purpose is to analyze how the author presents the argument and whether or not they succeeded. Keep reading to find out more strategies and prompts for...

A narrative essay tells a story about a series of events. At the core of this kind of essay can be a personal experience or a fictional plot. Any story can be a basis for a narrative essay! Narratives can look similar to descriptions. Still, they are different. A descriptive...

Similar to the instructions in a recipe book, process essays convey information in a step-by-step format. In this type of paper, you follow a structured chronological process. You can also call it a how-to essay. A closely related type is a process analysis essay. Here you have to carefully consider...

In a classification essay, you divide the subject into categories. To create these categories, you single out certain attributes of things. You can classify them according to their characteristics, themes, or traits. Sounds complicated? Be sure that any high school or college student can manage this type of essay!

Throughout your high school years, you are likely to write many evaluative papers. In an evaluation essay you aim is to justify your point of view through evidence.

I need a writer on algebra. I am a PhD student.Can i be helped by anybody/expert?

Please I want to do my MPhil research on algebra if you can help me

shall your university help me on research in mathematics ?

how I get the full pdf of those tittles

Print as pdf.

Search Utah State University:

Math topics.

Here you can find a directory of the content developed by the Engineering Math Resource Center for the various engineering mathematics topics you will learn in your math courses. Reference these to brush-up on topics that you have spent time learning and practicing or to give you some specific context into how these topics will be used in future engineering courses. Each of these pages will first give you a general overview of how that specific mathematical topic is used in engineering before providing a description of the topic in mathematical terms. Specific applications of the topic will then be given for each of the majors in engineering offered at USU. Finally, external resources will be provided so that additional practice and understanding can be found easily for the interested student.

Mathematics Foundations

• Reading and Writing Mathematics
• Properties of Real Numbers
• Properties of Complex Numbers
• Domain and Range
• The Rectangular Coordinate System and Graphs
• Equations and Inequalities
• Solving Linear Equations
• Systems of Linear Equations
• Polynomials
• Rational Expressions
• Roots and Radicals
• Quadratic Equations
• Exponential and Logarithmic Functions
• Binomial Theorem
• Absolute Value
• Fitting Models to Data
• Partial Fraction Decomposition

Trigonometry

• Right Triangles
• The Unit Circle
• Trigonometric Functions
• Inverse Trigonometric Functions
• Trigonometric Identities
• The Law of Sines
• The Law of Cosines
• Polar Coordinates
• Polar Form of Complex Numbers
• Parametric Equations
• Analytic Geometry
• Rotations of Axes
• The Limit Laws
• Derivatives
• Differentiation Rules
• Derivatives of Trigonometric Functions
• The Chain Rule
• Derivatives of Inverse Functions
• Implicit Differentiation
• Derivatives of Exponential and Logarithmic Functions
• Linear Approximations
• Differentials
• Maxima and Minima
• The Mean Value Theorem
• L’Hopital’s Rule
• Newton’s Method
• Antiderivatives
• Integration
• Definite Integrals
• The Fundamental Theorem of Calculus
• Integration Rules
• Substitution
• Integrals Involving Exponential and Logarithmic Functions
• Integrals Resulting in Inverse Trigonometric Functions

Calculus II

• Integration by Parts
• Trigonometric Integrals
• The Divergence and Integral Tests for Sequences and Series
• Comparison Tests for Sequences and Series
• Ratio and Root Tests for Sequences and Series
• Properties of Power Series
• Taylor and Maclaurin Series
• Calculus of Parametric Curves

Calculus III (Multivariable Calculus)

• Vectors in 2D
• Vectors in 3D
• Vector Products
• Lines and Planes in Space
• Cylindrical and Spherical Coordinates
• Vector-Valued Functions and Space Curves
• Calculus of Vector-Valued Functions
• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Tangent Planes
• Directional Derivatives and the Gradient
• Lagrange Multipliers
• Double Integrals
• Triple Integrals
• Change of Variables in Multiple Integrals
• Vector Fields
• Line Integrals
• Green’s Theorem
• Surface Integrals
• Stokes’ Theorem
• The Divergence Theorem
• Scalar Triple Product

Linear Algebra

• Matrix Properties
• Gauss Elimination
• Matrix Inverses

Differential Equations

• First-Order Linear Equations
• Second-Order Linear Equations
• Nonhomogeneous Linear Equations
• Probability

Feedback and assessment for presentations

Range of instructor feedback, specificity of instructor feedback, advantages of various forms of feedback, rubrics and grading/commenting forms.

Encourage students to improve their presentations: otherwise presenting repeatedly may merely ingrain bad habits. Feedback can come from peers and from instructors.

Consider commenting on the following:

• Timing notes: an outline of the talk including the amount of time spent on each portion.
• Feedback on the presentation style: style of speech, use of visual aids (blackboard/ slides/ images), pacing, audience engagement.
• Feedback on mathematical content: correctness, connections of material to other parts of course or other parts of mathematics (this is a good way to pique students’ interest in the subject matter).
• Feedback on teaching strategy: providing motivation, examples, conceptual explanations, repetition, etc.
• See also the general principles of communicating math .

Issues specific to various forms of presentations can be found on the page Assignments on Presentations .

The level of detail of the comments depends on whether the presentation will be given again. For example, noting every math mistake might be appropriate for a rehearsal so the student can be sure to fix those mistakes, but if the presentation will not be given again, a list of every mistake could be demoralizing with little positive benefit. At this point, comments should be more general and should focus instead on the sorts of things to consider for future presentations.

For other issues to consider when choosing and wording comments, see the handout Dimensions of Commenting .

• Most efficient is to take notes during the presentation and give them to the student immediately after the presentation.
• Most helpful for the student (but time intensive) may be to record the presentation and then sit with the student to review the recording.
• Another option is to discuss the presentation as a class immediately after the presentation. For this option to be successful, a respectful, collegial atmosphere is necessary.
• If you prefer time to think before giving feedback, you could e-mail your response after class or arrange to meet with the student at a later date. Meeting may be more efficient than e-mail because the student can ask clarifying questions so you don’t have to take the time to make your notes self-explanatory.

Identifying and prioritizing grading criteria before grading is important to prevent unintentional, subconscious bias,  even in graders who consider themselves objective,  as found by this study of hiring decisions based on criteria prioritized before/after learning about an applicant: Uhlmann and Cohen, “ Constructed Criteria: Redefining Merit to Justify Discrimination ,” Psychological Science, Vol 16, No 6, pp. 474-480, 2005.

Guidance for how to create a rubric is provided on the MAA Mathematical Communication page “ How can I objectively grade something as subjective as communication ?”

For classes in which each student gives multiple presentations, see the grading suggestions on the page for undergraduate seminars .

Sample grading criteria & rubrics for presentations are provided below.

Using a commenting form or grading form can remind you to consider all aspects of presentations that you’ve decided are important, rather than focusing only on the most obvious issues with any given presentation. A commenting form or grading form can also help you to find positive aspects of a presentation that on first consideration seems to be thoroughly troublesome. Some examples of forms and rubrics are below, but it’s best to make your own so the form reflects your priorities.

• Pedro Reis’ presentation evaluation form for M.I.T.’s Undergraduate Seminar in Physical Applied Mathematics , a topics seminar
• Characteristics of an effective undergraduate research talk : outlines basic expectations, characteristics of a good talk, and characteristics of an excellent talk
• Jardine, D. and Ferlini, V. “Assessing Student Oral Presentation of Mathematics,”   Supporting Assessment in Undergraduate Mathematics , The Mathematical Association of America, 2006, pp. 157-162 . This report of a department’s assessment of the teaching of math presentations contains a rubric for individual presentations. See Appendix B.
• Dennis, K. “Assessing Written and Oral Communication of Senior Projects,”  Supporting Assessment in Undergraduate Mathematics , The Mathematical Association of America, 2006, pp. 177-181 . Contains rubrics for presenting and writing, with recommendations.
• Rubric for Mathematical Presentations from Ball State University
• A description of criteria for math oral presentation for a math majors’ seminar, with categories Logic & Organization, Content, and Delivery.
• Form for commenting on and grading a presentation of a proof
• Scoring Rubric for Math Fair Projects with an audience of children
• Rubric for grades 6-8 for a math talk about solving two-step equations with one variable

What is Math Comm

Latest updates.

• Teamwork workshop
• Giving a lecture or workshop on writing
• Written genres
• Reading Assignment-Info Thy Writing Workshop
• Number Theory–Scott Carnahan
• Types of proof & proof-writing strategies

Recent Blog Posts

• Best Writing on Mathematics 2015
• 2014 MAA Writing Award Winners: American Mathematical Monthly
• 2014 MAA Writing Award Winners: Mathematics Magazine
• 2014 MAA Writing Award Winners: College Mathematics Journal
• 2014 MAA Writing Award Winner: Math Horizons
• Math by the Minute on Capitol Hill
• MAA Writing Awards
• Course Communities
• MAA Reviews
• Classroom Capsules & Notes

Accessibility

👀 Turn any prompt into captivating visuals in seconds with our AI-powered visual tool ✨ Try Piktochart AI!

• Piktochart Visual
• Video Editor
• AI Design Tools
• Infographic Maker
• Banner Maker
• Brochure Maker
• Diagram Maker
• Flowchart Maker
• Flyer Maker
• Graph Maker
• Invitation Maker
• Pitch Deck Creator
• Poster Maker
• Presentation Maker
• Report Maker
• Resume Maker
• Social Media Graphic Maker
• Timeline Maker
• Venn Diagram Maker
• Screen Recorder
• Social Media Video Maker
• Video Cropper
• Video to Text Converter
• Video Views Calculator
• AI Brochure Maker
• AI Flyer Generator
• AI Infographic
• AI Instagram Post Generator
• AI Newsletter Generator
• AI Report Generator
• AI Timeline Generator
• For Communications
• For Education
• For eLearning
• For Financial Services
• For Healthcare
• For Human Resources
• For Marketing
• For Nonprofits
• Brochure Templates
• Flyer Templates
• Infographic Templates
• Newsletter Templates
• Presentation Templates
• Resume Templates
• Business Infographics
• Business Proposals
• Education Templates
• Health Posters
• HR Templates
• Sales Presentations
• Community Template
• Explore all free templates on Piktochart
• The Business Storyteller Podcast
• User Stories
• Video Tutorials
• Visual Academy
• Need help? Check out our Help Center
• Earn money as a Piktochart Affiliate Partner
• Compare prices and features across Free, Pro, and Enterprise plans.
• For professionals and small teams looking for better brand management.
• For organizations seeking enterprise-grade onboarding, support, and SSO.
• Discounted plan for students, teachers, and education staff.
• Great causes deserve great pricing. Registered nonprofits pay less.

75 Unique School Presentation Ideas and Topics Plus Templates

Are you tired of seeing the same PowerPoints repeating overused and unoriginal school presentation ideas covering repeated topics in your classes?

You know what I’m talking about; we’ve all been there, and sat through yawn-worthy demonstrations, slides, or presentation videos covering everything from the solar system, someone’s favorite pet, past presidents of a country, to why E=mC squared.

From grade school to university, first graders to college students, we are obligated to create, perform, and observe academic presentations across a plethora of curriculums and classes, and not all of these public speaking opportunities fall into the category of an ‘interesting topic’.

Yet, have no fear! Here at Piktochart, we are here to help you and your classmates. From giving examples of creative and even interactive presentation ideas, providing presentation videos , and suggesting interactive activities to give your five minutes of fame the ‘wow’ factor that it deserves, this article is your guide!

Our massive collection of unique school and college presentation ideas and templates applies if you’re:

• A teacher looking to make your class more engaging and fun with student presentations.
• A student who wants to impress your teacher and the rest of the class with a thought-provoking, interesting topic.

A Curated List of Interesting Topics for School Presentations

Did you know that when it comes to presentations , the more students involved improves retention? The more you know! Yet sometimes, you need a little help to get the wheels moving in your head for your next school presentation .

The great thing about these ideas and topics is you can present them either in face-to-face classes or virtual learning sessions.

Each school presentation idea or topic below also comes with a template that you can use. Create a free Piktochart account to try our presentation maker and get access to the high-quality version of the templates. You can also check out our Piktochart for Education plan .

Want to watch this blog post in video format? The video below is for you!

The templates are further divided into the following categories covering the most popular and best presentation topics. Click the links below to skip to a specific section.

• Unique science presentation topics to cultivate curiosity in class
• Engaging culture and history presentation ideas to draw inspiration from
• Health class presentation topics to help students make healthy lifestyle decisions
• Data visualization ideas to help students present an overwhelming amount of data and information into clear, engaging visuals
• First day of school activity ideas to foster classroom camaraderie
• Communication and media topics to teach students the importance of effective communication
• Topics to help students prepare for life after school

We hope this list will inspire you and help you nail your next school presentation activity.

Unique Science Presentation Topics to Cultivate Curiosity in Class

Science is a broad field and it’s easy to feel overwhelmed with too many topics to choose for your next presentation.

Cultivate curiosity in the science classroom with the following unique and creative presentation ideas and topics:

1. Can life survive in space?

2. Do plants scream when they’re in pain?

3. What are the traits of successful inventors?

4. How vaccines work

5. Massive destruction of the Koala’s habitat in Australia

6. Left brain versus right brain

7. What are great sources of calcium?

8. Recycling facts you need to know

9. Do you have what it takes to be a NASA astronaut?

10. The rise of robots and AI: Should we be afraid of them?

11. How far down does the sea go?

12. The stages of sleep

13. Will Mars be our home in 2028?

14. A quick look at laboratory safety rules

15. The first person in history to break the sound barrier

Engaging Culture and History Presentation Ideas to Draw Inspiration From

History is filled with equally inspiring and terrifying stories, and there are lessons that students can learn from the events of the past. Meanwhile, interactive presentations about culture help students learn and embrace diversity. 

16. Women in history: A conversation through time

17. The sweet story of chocolate 

18. A history lesson with a twist 

19. The history of basketball 

20. The origin of the Halloween celebration 

21. AI History 

22. What you need to know about New Zealand 

23. 1883 volcanic eruption of Krakatoa 

24. Roman structures: 2000 years of strength

25. The most famous art heists in history 

26. Elmo: The story behind a child icon 

27. 10 things you should know before you visit South Korea 

28. 8 things you didn’t know about these 8 countries 

Health Class Presentation Topics to Help Students Make Healthy Lifestyle Decisions

Want to learn how to engage students with healthcare topic ideas? Then consider using these templates for your next interactive presentation.

According to the CDC , school-based health education contributes to the development of functional health knowledge among students. It also helps them adapt and maintain health-promoting behaviors throughout their lives. 

Not only will your presentation help with keeping students engaged, but you’ll also increase class involvement with the right slides.

The following examples of health and wellness interactive presentations include fun ideas and topics that are a good start. 

29. How to look after your mental health?

30. The eradication of Polio

31. How to have a healthy lifestyle 

32. 10 handwashing facts 

33. Myths and facts about depression

34. Hacks for making fresh food last longer 

35. Ways to avoid spreading the coronavirus

36. Mask protection in 5 simple steps 

37. Everything you need to know about the flu

38. All about stress: Prevention, tips, and how to cope 

39. The importance of sleep 

40. Is milk tea bad for you?

41. How to boost happiness in 10 minutes

42. How dirty are debit and credit cards 

43. Why do you need sunscreen protection

Data Visualization Ideas to Help Students Present Overwhelming Amounts of Data in Creative Ways

Data visualization is all about using visuals to make sense of data. Students need to pull the main points from their extensive research, and present them by story telling while being mindful of their classmates’ collective attention span.

As far as student assignments go, storytelling with data is a daunting task for students and teachers alike. To keep your audience interested, consider using a non linear presentation that presents key concepts in creative ways.

Inspire your class to be master data storytellers with the following data visualization ideas:

44. Are we slowly losing the Borneo rainforest?

45. Skateboard deck design over the years

46. Food waste during the Super Bowl

47. The weight of the tallest building in the world

48. Infographic about data and statistics

49. Stats about cyberbullying

50. How whales combat climate change

First Day of School Interactive Activity Ideas to Foster Whole-class-Camaraderie

Calling all teachers! Welcome your new students and start the school year with the following back-to-school creative presentation ideas and relevant templates for first-day-of-school activities.

These interactive presentations grab the attention of your students and are remarkably easy to execute (which is the main educator’s goal after all)!

51. Meet the teacher

52. Example: all about me

53. Self-introduction

54. Tips on how to focus on schoolwork

55. Course plan and schedule

Give our class schedule maker a try to access more templates for free. You can also access our presentation-maker , poster-maker , timeline-maker , and more by simply signing up .

56. Interpreting a student’s report card (for parents)

57. Introduction of classroom rules

58. Assignment schedule

59. Daily planner

60. Course syllabus presentation

61. How to write a class presentation

Topics to Teach Students the Importance of Effective Communication

Visual media  helps students retain more of the concepts  taught in the classroom. The following media topics and infographic templates can help you showcase complex concepts in a short amount of time. 

In addition, interactive presentation activities using these templates also encourage the development of a holistic learning process in the classroom because they help focus on the  three domains of learning:  cognitive, affective, and psychomotor. 

62. Interactive presentation do’s and don’ts 

63. How to create an infographic 

Recommended reading : How to Make an Infographic in 30 Minutes

64. How to improve your internet security and privacy

65. What is design thinking?

66. What are your favorite software tools to use in the classroom? 

Presentation Topic Ideas to Help Students Prepare for Life After School

One of the things that makes teaching a rewarding career is seeing your students take the learning and knowledge you’ve instilled in them, and become successful, productive adults.

From pitching a business idea to starting your podcast, the following topics are good starting points to prepare students for the challenges after graduation (aka adulting 101):

67. How to make a resume

68. How to start a startup

69. Credit card vs. debit card

70. Pros and cons of cryptocurrency

71. How to save on travel

72. How to do a SWOT analysis

73. How to pitch a business idea

74. Habits of successful people

75. Starting your own podcast: A checklist

Find out how a high school teacher like Jamie Barkin uses Piktochart to improve learning in the classroom for her students.

Pro tip: make your presentation as interactive as possible. Students have an attention span of two to three minutes per year of age. To keep minds from wandering off, include some interactive games or activities in the lesson. For example, if you conducted a lesson on the respiratory system, you could ask them to practice breathing techniques.

Maintain eye contact with your students, and you’ll get instant feedback on how interested they are in the interactive presentation.

Make School Presentation Visuals Without the Hassle of Making Them From Scratch

School presentations, when done right, can help teachers engage their classes and improve students’ education effectively by presenting information using the right presentation topic. 

If you’re pressed for time and resources to make your school presentation visuals , choose a template from Piktochart’s template gallery . Aside from the easy customization options, you can also print and download these templates to your preferred format. 

Piktochart also professional templates to create infographics , posters , brochures , reports , and more.

Creating school-focused, engaging, and interactive presentations can be tedious at first, but with a little bit of research and Piktochart’s handy templates, you’re going to do a great job!

Other Posts

12 Graphic Organizer Examples for Teachers and Students

From Chaos to Clarity: Streamlining Your Student Life with a Schedule Builder

Resume with No Experience