seminar presentation on maths

201+ Mathematics Seminar Topics: Presentation Ideas For Students

Mathematics Seminar Topics: Mathematics is the magical study of patterns, numbers, variables, quantities, magnitudes, and relations. Mathematics includes various sections such as arithmetic, algebra, integrals, statistics, and geometry. Mathematicians are the people who solve various mysteries of space, change, and quantities.

Mathematics helps you build mental discipline and also prepares you for various careers. Mathematics is used in many fields, like business, finance, and engineering. Join us in this series of seminar topics where you will be exploring topics such as number theory, cryptography, mathematical modeling, and many more. You will get mathematics seminar topics for all branches for bsc, msc college and school students 2024.

Calculus and Analysis

Number theory, combinatorics and graph theory, statistics and probability, mathematical physics, operations research and optimization, mathematical logic and set theory, discrete mathematics, applied mathematics, financial mathematics, computational mathematics, mathematics education, history and philosophy of mathematics.

• Group Theory: Basics and Applications
• Ring Theory: Structures and Examples
• Field Theory and Algebraic Extensions
• Linear Algebra: Matrix Operations and Applications
• Abstract Algebra: Concepts and Theorems
• Polynomial Algebra: Roots and Factorization
• Commutative Algebra: Ideals and Modules
• Algebraic Geometry: Varieties and Schemes
• Lie Algebras and Lie Groups
• Algebraic Structures in Computer Science
• Differential Calculus: Derivatives and Applications
• Integral Calculus: Techniques and Applications
• Multivariable Calculus: Gradients and Divergence
• Complex Analysis: Functions of Complex Variables
• Real Analysis: Limits and Continuity
• Fourier Analysis: Transforms and Applications
• Functional Analysis: Spaces and Operators
• Differential Equations: Ordinary and Partial
• Integral Equations: Types and Solutions
• Numerical Analysis: Approximations and Errors
• Euclidean Geometry: Concepts and Theorems
• Non-Euclidean Geometry: Hyperbolic and Elliptic
• Projective Geometry: Points, Lines, and Planes
• Differential Geometry: Curvature and Surfaces
• Algebraic Geometry: Intersection Theory
• Convex Geometry: Polytopes and Convex Sets
• Computational Geometry: Algorithms and Applications
• Fractal Geometry: Self-Similarity and Dimensions
• Topology: Basic Concepts and Applications
• Discrete Geometry: Combinatorial Structures
• Elementary Number Theory: Primes and Divisibility
• Analytic Number Theory: Zeta Functions and L-Functions
• Algebraic Number Theory: Algebraic Integers
• Modular Forms and Modular Functions
• Diophantine Equations: Solutions and Approximations
• Cryptography and Number Theory
• p-adic Numbers: Concepts and Applications
• Quadratic Forms and Quadratic Reciprocity
• Distribution of Prime Numbers
• Applications of Number Theory in Cryptography
• Enumerative Combinatorics: Counting Techniques
• Graph Theory: Graphs and Subgraphs
• Combinatorial Optimization: Problems and Solutions
• Combinatorial Design Theory
• Matroid Theory: Structures and Applications
• Graph Algorithms: Shortest Paths and Minimum Spanning Trees
• Ramsey Theory: Combinatorial Inference
• Combinatorial Game Theory: Games and Strategies
• Graph Colorings: Techniques and Theorems
• Applications of Combinatorics in Computer Science
• Descriptive Statistics: Measures of Central Tendency
• Inferential Statistics: Hypothesis Testing and Confidence Intervals
• Bayesian Statistics: Concepts and Applications
• Probability Distributions: Discrete and Continuous
• Stochastic Processes: Random Walks and Brownian Motion
• Markov Chains and Markov Processes
• Statistical Inference: Methods and Techniques
• Statistical Machine Learning: Concepts and Applications
• Time Series Analysis: Autoregressive Models
• Monte Carlo Simulations and Random Sampling
• Classical Mechanics: Lagrangian and Hamiltonian Formulations
• Quantum Mechanics: Wave Functions and Operators
• Statistical Mechanics: Concepts and Applications
• Electromagnetism: Maxwell’s Equations and Applications
• General Relativity: Space-Time and Curvature
• Quantum Field Theory: Particles and Fields
• Mathematical Cosmology: Models and Theories
• Fluid Dynamics: Equations of Motion
• Plasma Physics: Magnetohydrodynamics
• Mathematical Techniques in Quantum Computing
• Linear Programming: Formulations and Solutions
• Integer Programming: Applications and Techniques
• Combinatorial Optimization: Knapsack and Traveling Salesman Problems
• Nonlinear Programming: Methods and Applications
• Game Theory: Nash Equilibrium and Strategies
• Queuing Theory: Models and Applications
• Inventory Management: Optimization Techniques
• Dynamic Programming: Techniques and Examples
• Network Optimization: Flows and Cuts
• Applications of Operations Research in Logistics
• Propositional Logic: Concepts and Operators
• Predicate Logic: Quantifiers and Formulas
• Mathematical Proofs: Techniques and Methods
• Gödel’s Incompleteness Theorems
• Set Theory: Axioms and Applications
• Cardinal Numbers and Ordinal Numbers
• Constructibility and Large Cardinals
• Model Theory: Structures and Interpretations
• Recursion Theory: Recursive Functions and Sets
• Applications of Logic in Computer Science
• Discrete Structures: Sets, Functions, and Relations
• Boolean Algebra: Concepts and Applications
• Automata Theory: Finite Automata and Regular Languages
• Formal Languages and Context-Free Grammars
• Graph Theory in Discrete Mathematics
• Discrete Probability: Concepts and Applications
• Combinatorial Problems in Discrete Mathematics
• Recurrence Relations and Generating Functions
• Applications of Discrete Mathematics in Computer Science
• Applications of Discrete Mathematics in Cryptography
• Mathematical Modeling: Techniques and Applications
• Numerical Methods: Root Finding and Interpolation
• Operations Research: Linear and Nonlinear Programming
• Game Theory: Strategies and Applications
• Control Theory: Linear and Nonlinear Systems
• Systems Theory: State Space and Feedback Control
• Applications of Mathematics in Engineering
• Applications of Mathematics in Economics
• Applications of Mathematics in Biology
• Applications of Mathematics in Finance
• Mathematical Models in Finance
• Portfolio Optimization and Asset Allocation
• Derivatives and Option Pricing
• Risk Management and Value-at-Risk (VaR)
• Fixed-Income Securities and Yield Curves
• Stochastic Calculus in Finance
• Quantitative Risk Management
• Monte Carlo Simulation in Financial Models
• Financial Time Series Analysis
• Financial Engineering and Structured Products
• Numerical Analysis: Approximation Techniques
• Computational Linear Algebra: Algorithms and Applications
• Computational Geometry: Algorithms and Data Structures
• Computational Fluid Dynamics (CFD)
• Computational Topology: Techniques and Applications
• Computational Number Theory: Algorithms and Applications
• Computational Complexity: P vs. NP Problem
• Computational Graph Theory: Graph Algorithms
• Parallel and Distributed Computation
• Applications of Computational Mathematics in Machine Learning
• Mathematics Teaching Methods and Strategies
• Technology in Mathematics Education
• Curriculum Development in Mathematics
• Online Learning and E-Learning in Mathematics
• Assessment and Evaluation in Mathematics
• Inclusive Education in Mathematics
• Mathematical Competitions and Olympiads
• Collaborative Learning in Mathematics
• Innovative Teaching Tools for Mathematics
• Mathematics Education Research and Development
• Historical Development of Mathematical Concepts
• Famous Mathematicians and Their Contributions
• Mathematics in Ancient Civilizations
• Philosophy of Mathematics: Platonism and Formalism
• Mathematical Discoveries in the 20th Century
• The Role of Mathematics in the Renaissance
• Mathematics and Art: Symmetry and Proportion
• Mathematics and Music: Harmonics and Ratios
• The Impact of Mathematics on Modern Science
• The Future of Mathematics: Trends and Challenges

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topics for an undergraduate Math seminar

What are some good topics for an undergraduate Math seminar?

I am looking for topics which are:

• Approachable for at least second or third year students and beyond (The students have taken all of the introductory Math courses, Logic, Real Analysis, Discrete, Algebra, etc)
• outside of standard course material.
• tangentially connected to things the students already know.
• presentable from 45 to 90 minutes

Not all of the above points are required, but as long as it satisfies most of the above it should be relevant. Above all else, if you think it is a good topic idea please share it.

Edit: If you have books or resources for the seminar topic, that is also very helpful.

• undergraduate-education
• presentation

• $\begingroup$ Seminar in the sense of a voluntary meeting that undergraduates can attend (presumably with presentations given by faculty?), to learn some "extracurricular" math? $\endgroup$ –  pjs36 Commented Jan 31, 2017 at 3:23
• 1 $\begingroup$ @pjs36 That is precisely what I am referring to. I am trying to help one of my professors choose a topic for the next one. I tried to distance the question from my particular situation, so that it would be more useful. I'm just looking for a topic that will draw attention and that my professor would like to present on. $\endgroup$ –  Tom Commented Jan 31, 2017 at 15:43
• 2 $\begingroup$ If your professor can't come up with any ideas for a talk to undergraduates, why is the professor involved in this activity? $\endgroup$ –  KCd Commented Feb 1, 2017 at 11:03
• 2 $\begingroup$ @KCd He has plenty of ideas I am sure. I think he would like a fresh take on ideas, though he is probably just giving me a chance to be involved in planning events. $\endgroup$ –  Tom Commented Feb 2, 2017 at 5:52
• $\begingroup$ See also: math.stackexchange.com/questions/2095649/… $\endgroup$ –  Anamaki Commented Sep 21, 2017 at 15:21

11 Answers 11

We run a weekly seminar at my university where undergrads give math talks to other undergrads. To encourage people to give talks we collected a list of suggested topics which may be useful to you -- https://uwseminars.com/potential-topics/

EDIT: As suggested by Joel, I'll add a few of my favourite ones from the list (there are 83 topics now, but the number will increase this term).

1) Continued Fractions and Hyperbolic Geometry (Farey tesselation etc): Example Reference: http://homepages.warwick.ac.uk/~masbb/HypGeomandCntdFractions-2.pdf

2) Optimal Stopping Theory and the Secretary Problem: Example reference: https://www.math.upenn.edu/~ted/210F10/References/Secretary.pdf

3) Penrose tilings (and possible connections to the dynamics of tiling): Example reference: https://people.maths.ox.ac.uk/ritter/masterclasses.html , Miles of Tiles by Charles Radin

4) The Rental Harmony Theorem Example reference: http://www3.math.tu-berlin.de/combi/wp_henk/wp-content/uploads/2011/05/rentsu.pdf

5) Representation Theory and Voting Theory Example reference: https://arxiv.org/abs/1508.05891

6) Ultrafilters and Nonstandard analysis: Example reference: https://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Davis.pdf

This one is not exactly on that list but occurs elsewhere on the site

7) Automated Verification of Computatational systems : Example reference: http://www.cmi.ac.in/~madhavan/papers/pdf/resonance-jul2009.pdf

8) Differential Equations on Fractals : Example reference: Differential equations on fractals, R. Strichartz

9) Fuzzy Logic : Example reference: http://www.francky.me/doc/course/fuzzy_logic.pdf

10) General Secure Multi-party computation from any Linear Secret Sharing Scheme : Example reference: https://www.iacr.org/archive/eurocrypt2000/1807/18070321-new.pdf

I'm sorry for the slant towards some topics but there's a "tag" option on the webpage which allows you to see topics by area.

Almost any chapter of this wonderful book could serve as a seminar topic. Each chapter is pretty much self-contained.

Matoušek, Jiří. Thirty-three miniatures: Mathematical and Algorithmic applications of Linear Algebra . Vol. 53. American Mathematical Soc., 2010. ( AMS link .)

(1) I am shocked that no one has mentioned the so-called Monty Hall problem/paradox. :)

(2) The point that "probability" does not directly describe "randomness", e.g., although the sequence of heads-tails HHHHHHHHHH seems "unlikely/not-random", it has the same probability ($2^{-10}$) as "random-seeming" sequences such as HHTHTTTHHT.

(3) "The other quadratic formula" (this one is more shallow, but fun): if $ax^2+bx+c=0$, and $c\not=0$, then also $a+b(1/x)+c(1/x)^2=0$, and the quadratic formula for $1/x$, inverted, gives an unexpected formula for $x$ itself.

(4) Using linear algebra of 2x2 matrices to get the formula for the $n$th Fibonnaci number.

(5) Liouville's theorem (really just a corollary of the mean value theorem!) that an irrational real number that "can be approximated too well" by rationals must be transcendental .

Here are three books I have used in various ways for such a course, focused on mathematics history.

• Journey Through Genius - lower level in some ways but easy to supplement for any background
• Mathematical Expeditions
• Mathematical Masterpieces

Any book by Eli Maor is also definitely game. Again, supplementing for higher levels - but there is a surprising amount that they won't know! So much math, so little time.

How about a talk on the continuum hypothesis (CH) and related topics? It's a fascinating subject and can be tailored for basically any level depending on how detailed you get.

Full disclosure, I'm biased because I gave such a talk aimed at MS students and upper-level undergrads on this topic almost 9 years ago. And I think this meets all four of your criteria listed as of the time I write this, since they're very similar to what I was trying to do. Here's an outline of my presentation as best as I can remember it; feel free to draw from it as you wish:

• Different sets of numbers: $\Bbb N, \Bbb Z, \Bbb Q, \Bbb R$.
• $\Bbb N$ and $\Bbb Z$ have the same size.
• More surprisingly, $\Bbb Q$ has the same size as both $\Bbb N$ and $\Bbb Z$.
• But the size of $\Bbb R$ is strictly larger. (Cantor's diagonalization argument.)
• Is there a set whose size is strictly larger than $\Bbb N$ and strictly smaller than $\Bbb R$?

This question in the last bullet point above is the perfect way to bring up the CH (since the question is basically, "Is the continuum hypothesis false?"). And what's interesting about the CH is the answer is independent of ZFC set theory, meaning we can take the answer to be "yes" or "no" and either way we won't get a contradiction in ZFC set theory. We know this from work done independently by Kurt Gödel and Paul Cohen.

I think there were some slightly related topics and/or generalities I discussed, such as cardinal numbers and transfiniteness, etc. It's been too long to say for sure.

This was my main reference:

• The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir Aczel.

Oh, and bonus points if you take it to the next level like I might have .

EDIT: Another idea for a talk is how linear algebra can be used to determine solvability of a lights out game . A good starting resource is this site on Wolfram MathWorld . I expanded on it in this post on Puzzling.SE . I'm sure the paper referenced in that Wiki article would also be a good resource.

Personally I would discuss Graph theory, in a diverse and conceptual way with a few deeper dives. Students of that level should be familiar of weighted graphs, have an intuition for the size of functions (which could be leveraged in a discussion of travelling salesman, big O notation, how quickly networks can grow, Ramsey Theory R(3,3), chromatic polynomials, etc). There is so much novelty in graph theory, and it draws many areas of maths together in novel ways.

At a minimum, I'd include Erdös Renyi Random Graph models, and the emergance of a large connected cluster. It is an accessible mention of asymptoic analysis, simple graph enumeration, and probability distributions(as the edges per node modelled via Poisson is appreciably different to edges as randomly selected pairs of nodes).

Depends on time and how quickly you move through content, but you could try to mention dynamical systems, such as predator-prey models, and how graph theory can be applied in the spread of diseases and informtion.

I think this topic is well suited, because it is an example of three important chracteristics of matha: Interconnected, Rich in application, and the sheer enormity of open problems. E.g. P=NP, Graph Homomorphism, Ramsey (5,5,), etc.

At 2nd year ans above, it is likely many already have heard of Monty Hall,C Cardinal Infinities, and Mandelbrot(although this could be included if you hedge your bet with a split between dynamical systems and graph theorg).

If these are not present in course work:

• Galois Theory: an overview of what it accomplished with an emphasis on history.
• Group actions and counting if not emphasized too deeply in the standard course.
• Interaction between the geometry of principal fiber bundles and the physics of Yang Mill's theory. Weyl's crazy idea and how it led to our modern theory of classical fields.
• What is representation theory? (I wish I knew all, but I'll settle for more, of the answers to this question)
• What are spinors? On the representation of the Lorentz group and how a bit of imagination finds supersymmetry.

Really most graduate math classes condensed into a best-of talk without proofs can be very interesting. Also, this might serve to motivate students to take such classes if that is an option

( or for non-graduate math possessing institution, such talks can help give students a better sense of the big world of math beyond the core course work. Naturally,attending a JMM or similar math meet is even better in this regard )

Basic topological ideas and knot theory are surprisingly accesible because they treat objects concretely representable in three space, via planar diagrams, and via actual physical models. (Basic ideas like isotopy can be illustrated with computer generated simulations.) Combinatorial methods in knot theory (knot polynomials, grid diagrams) can be learned and used without understanding their (sometimes quite deep) topological content. Students who know a bit of group theory can be shown connections with the braid group. There are numerous popular and undergraduate level accounts of knot theory, and most are full of examples that could be adapted to a classroom presentation.

Linear optimization as used in oil refineries (or even midstream movements and trading).

Anything dealing with statistics in business.

Matching algorithms (of mates or medschool students).

Additional to the above:

molecular or crystallographic symmetries. (BTW, if you approach it from the chemical or visual standpoint, rather than abstract algebra, it will be easier to understand and more interesting/applied.)

Here's another cool topic, gambling skill: https://www.youtube.com/watch?v=658xlubwnDc

And another (more fluffy, but fun) is the fourth dimension in art: https://en.wikipedia.org/wiki/Fourth_dimension_in_art

Bottom line, keep it fun. DON'T be afraid to be relevant or to have some non pure math in there. You are not trying to teach a course in a seminar. You are trying to get some interest, that maybe pays of later.

Many fine probability topics could be suitable, depending on background and interest. A few such topics:

• Random walk, culminating with the law of the iterated logarithm
• The law of large numbers, or the central limit theorem
• If not covered: The Laplace approximation for integrals
• Extreme value theory

Some other topics:

5: Matrices: The Perron-Frobenius theorem for nonnegative matrices, with application "the Google matrix" 6: Simulation: Some examples of mcmc ... 7: Error-correcting codes ...

One might consider organizing a seminar with the theme:

Mathematical Insights Into Fairness Questions

Examples of such questions in recent news involve

a. Fair ways to share diminished amounts of water in the Colorado River due to drought conditions

b. School choice

c. Improved ways to conduct primary elections when there are many candidates

d. Rent sharing systems

e. Medicine costs

Mathematical topics would include vertex/edge graph theory, solving difference equations (recursions),linear programming and other optimization methods, ham sandwich ideas, etc. Both continuous and discrete mathematical ideas come into play.

This approach might help students see how mathematics affects their daily lives.

• $\begingroup$ +1 for the last (important) sentence. Mathematics is useful in daily life. Unfortunately, too few know enough to appreciate it. $\endgroup$ –  user21820 Commented Mar 10, 2023 at 6:35

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How do I prepare a slide talk presentation for conference in mathematics?

I am a graduate student in mathematics. I am preparing to give a 20-minute short talk for a conference. I am looking at some beamer presentations this one and this one . Neither of these slides neither have any references, nor any numbering of definitions, theorems, propositions, lemmas etc.

I have some few questions in mind:

• Is it normal to omit proof of the main results?
• Is it normal to omit numberings of theorems, lemmas, propositions, etc.?
• Why don't people use \begin{theorem}... \end{theorem} for theorems and the same for lemmas, and propositions?

Besides that, what would be the best way to present a short 20-minute conference talk?

• mathematics
• presentation

• 22 Your talk is only 20 minutes long. Putting proofs into a beamer talk most likely results in losing the audience, especially, if proofs use more than one slide and if the audience has to remember formulae from previous slides. Similar for numberings of theorems. –  Marktmeister Commented May 23, 2022 at 14:31
• 3 And just to complete the picture, I'll add to all the good advice that you've already gotten: Keep in mind that at some conferences there's even the option to use blackboards instead of slides. –  Jochen Glueck Commented May 23, 2022 at 20:37
• 2 I am thankful to all for giving me valuable suggestions. All the answers are just equally excellent. –  learner Commented May 24, 2022 at 2:53
• 3 The Notices of the American Mathematical Society has a column dedicated to advice for early-career scholars—I recommend checking it out for articles like this one by Bryna Kra that directly addresses your question. Indeed, you might ask your advisor to sponsor you for a student membership to the AMS and other professional societies. –  Greg Martin Commented May 24, 2022 at 7:24
• 4 As someone who works in a math department: in this field, you can get away with anything. Want yo just present your paper in beamer format, no changes to content? People do it. Want to have an extremely didactic (skipping proofs) presentation? people do it. There is no norm. My advice (from a non mathematician like me) is to try to get to the most people in the audience. –  Ander Biguri Commented May 24, 2022 at 10:24

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Math Talk: Preparing Your Conference Presentation

If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan . And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of the summer, I thought about some of the best and the worst math talks I have witnessed. And I said to myself: “Self, you have surely seen the worst!” But why? Why do so many mathematicians give truly disastrous talks? Maybe we should talk about talks a bit.

There are some commonalities in all the good talks I have seen. Below I list a few characteristics of a good talk:

• The presenter is clear and audible : This is obvious. If the audience cannot hear you, you are toast.
• The presentation was prepared on a computer : Some old-school mathematicians will disagree with me. Chalk, they will say, is the ultimate communicator. And racking my brain, I too can recall an excellent chalk talk, one that was given by Lauren Williams (UC Berkeley) a while back. It is true that good chalk talks are easier to follow as they are paced more naturally; the presenter is somewhat constrained by her own writing speed which almost always works to the advantage of the audience. However it is also true that good chalk talks are VERY hard to do. So unless you are one of the naturals (and perhaps even then), I’d vote for a Beamer presentation any time.
• The slides are legible : This means that you are using a sensible font size and are not packing in too much information in one slide.
• The content in each slide is interesting but not too interesting : You want the audience to have a reason to look at you, the presenter, the conveyor of the Ultimate Truth about Exponential Sums and Polynomial-Growth Groups with Finitely Many Nilpotents. A humorous slide every now and then, perhaps one every twenty minutes, might be acceptable.
• The slides contain visual and tabular information as much as possible : To contradict immediately with what I said above, I propose that you aim to include as much visual material in your talk as is feasible for your topic. Graphs, figures, tables, and any other content that describes your math in a visual way will go a long way toward making your talk comprehensible and interesting. We all know that striking mathematical imagery adds value and visual insight to most advanced mathematics.
• The talk was not put together in the last five minutes : Ok, so, it is true that many talks are indeed put together at the last minute, I mean, the night before the actual event. But if you want to make this talk work well, you have to start early. You have to put your thoughts together onto paper (or preferably an electronic medium) much earlier. You want to start brainstorming: What needs to be in this talk? What is the minimum background the audience should have and what definitions and background results should you provide? What motivating examples would be best to start with? Is there one good sample case that you can use through the whole talk? What are the best figures to use? And then you want to have some time to put the slides together. Make sure things flow right, and that your overall presentation has a narrative coherence to it. Then you want to let it sit for a while and simmer, while you go play your favorite video game, and then come back to it with fresh eyes to see if it really works well. Then you have to practice. More on that later. But just like in cooking, slow and steady wins the race, or at least makes a delicious meal more likely.

The web is full of great suggestions about how to prepare successful presentations. Some are clearly intended for non-academic audiences, but they may still have some good ideas for you to ponder. And some of these may seem to be focusing exclusively on Powerpoint, and almost all math people will immediately roll their eyes at that, but the perspective gained from giving a good presentation in one context does carry over to other contexts; see for instance Jeana Mastrangeli’s article PowerPoint Unveils Coordinate Confusion for some great tips learned from a job in the industry that carry over well to the academic context. And you can find more tips on academic blogs and other sites for an academic audience, for instance on general presentation tips , on how not to use Powerpoint in the academic context . on how to give a fabulous academic presentation , and more specifically on how to create a presentation out of a completed paper .

Now besides these general-purpose advice articles, you might wish to know just what is out there on math talks specifically. If so, you should check out these AMS-sanctioned suggestions on presenting papers . A great resource for good advice on anything math-related is Terence Tao’s blog , and as expected he has some substantive things to say about how to give a good math talk . Another great resource for the fundamentals of giving a good math talk is Technically Speaking , an NSF-funded project aiming to improve the oral communication skills of STEM undergraduates. Though intended mainly for undergraduate math majors, the short videos on this site are eye-opening for most people, and not only for those who are new to giving math talks.

Friends and colleagues may have more pointed suggestions; my favorite is a list by Bill Ross (University of Richmond) . I totally agree with him in all the specifics, in particular about not including any proofs in a 20-minute talk. If you insist that your proof is the most elegant and the most intellectually satisfying proof on earth, then bring along copies of your paper to share with your audience after the talk. If you really really really have to, and if you are ok with upsetting Bill, then go ahead and do include an outline of the proof in one slide, but please do not spend more than a tenth of your time on this outline (about as much as a slide deserves).

Now if you are speaking at a specialized session (with the caveat that not all AMS special sessions are as specialized as you might think), and if you have a lot more time than 20 minutes, you might want to focus on your proof a bit more. This is understandable. Proof is the heart of what most academic mathematicians do, so it is natural that you want to share your life’s work with your colleagues. Just be aware that you might lose some of your audience when you do that. It is unavoidable. But it may be worth it. You will probably even have people come up to you later on and ask you detailed questions about one of your technical lemmas, to leave you convinced that at least some of those people with the closed eyes had indeed been awake, for at least some of the time.

Coming back to the practice issue: I won’t suggest that you need 10,000 hours of practice , but it is always a good idea to do a complete run-through of your talk beforehand. Especially if you have not yet given over thirty talks in your career, you need to practice. Even if you have been a celebrated teaching assistant for years, even if you have taught your own classes for a couple years with no serious blunder, if you have not stood in front of a mathematical audience to talk about your work for over thirty times, then you have to practice. Find someone to listen to you. And time yourself. Everybody understands and nobody will blame you if you are nervous during your talk, but almost everyone will be quite annoyed if you go over time. Conference regulars in each subdiscipline know who gives great talks and who always goes over time. You can guess whose talks are well attended and whose are avoided like the dusty reruns of a decade-old reality show.

Keep in mind that you also do not want to be late to your own talk. So find out where the talk is, and visit the room before the day of your talk. If the organizers requested it, it helps to send them a copy of your talk ahead of time (another reason why it is a good idea to prepare your slides before the night before your talk!); this ensures that the transitions between speakers will not cost you precious time.

Now after all that hard work, it is still possible that you could go to your conference room on the day of your talk and then face this:

So sit back, relax, and just try to enjoy the conference. The talk, if well-prepared, will almost certainly be a good one, and if not, there will surely be a chance for a do-over.

Gizem Karaali is associate professor of mathematics at Pomona College and a founding editor of the Journal of Humanistic Mathematics . Since May 2013, she is also the associate editor of the Mathematical Intelligencer .

6 Responses to Math Talk: Preparing Your Conference Presentation

Thank you for this post, Gizem. Excellent points. Just because something “should be obvious” doesn’t mean that it is. For example, I went to a talk at the last JMM by a well-known number theorist who decided that he didn’t need the microphone. He does have a booming voice, at least for the first half of each sentence. But I missed most of the punchlines, as I was two-thirds of the way back in a typical mid-sized conference center space with lousy acoustics. The in crowd, meaning the organizers and presenters of that session, could all hear what he said, bunched as they were up front. At least several of the rest of us were frustrated. So organizers and moderators: to make sure that talks are accessible to all in the room, please insist that all speakers use the mike. Speakers, use the mike, and if still in doubt, start the talk with “those in the back, raise your hand if you can hear me clearly.” (“Can you hear me?” won’t get a response from those who can’t.)

Who made the cartoon?

The cartoon is from “Piled Higher and Deeper” by Jorge Cham (www.phdcomics.com). This should be clearer in the body of the post now. Thanks for the inquiry (= gentle prod to correct attribution).

Very insightful remarks… Enjoyed reading. I also think if the presenter gives out a fairly detailed and clear abstract to the audience before the talk, it helps run the proceeds more smoothly. A handout during the talk summarizing the main points would not hurt either.

Here is another good summary: http://blogs.lse.ac.uk/impactofsocialsciences/2015/02/20/how-to-win-at-academic-presentations/

Making a presentation on these events will ensure that you attract the right kind of attention for your career moves. Our blog post today will focus on 5 vital steps that will help you sail through any academic or professional conference. These steps are equally applicable to national as well as international academic conferences.

To know more click on the link given below: http://www.texilaconference.org/blog/5-steps-to-prepare-for-an-academic-conference/

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Course info, instructors.

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

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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.

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2024 Putnam Seminar

Po-shen loh, carnegie mellon, attendance form, course description.

Course Number

Course assistants, additional activities considered to be part of the course, levels and expectations, detailed syllabus.

	Introduction
	Polynomials / /
	Number theory / /
	Calculus / / No Tue
	Functional equations No Sun / / No Tue
	Inequalities / /
	Convergence / /
	Fall Break
	Recursions No Sun / /
	Linear algebra / /
	Combinatorics / / No Tue
	Integer polynomials / /
	Probability / /
	Thanksgiving Break / No Tue
	Geometry / /
	Competition from 10:00am – 1:00pm and 3:00pm – 6:00pm, in Baker A51.

Course Policies

since 28 August 2024.

University of Notre Dame

Department of Mathematics

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Topology Seminar; Ishan Banerjee - The Ohio State University

Time: Tue Sep 17, 2024, 2:30 pm - 3:30 pm

Location: 359 Hurley Bldg

Speaker: Ishan Banerjee The Ohio State University Will give a Topology Seminar entitled: Monodromy and vanishing cycles for curves in surfaces Abstract: This talk will be about the monodromy group associated to a family of algebraic curves in an algebraic surface as a subgroup of the mapping class group. I will start by surveying some older results in this area about the image of monodromy in the symplectic group. I will then discuss joint work with Nick Salter, where we describe the precise image of monodromy in the mapping class group in the special case of complete intersections. Date: 09-17-2024 Time: 2:30 pm Location: 258 Hurley

Download Poster [PDF, 149k]

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

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Triangle Topology Seminar

New constructions and invariants of exotic 4-manifolds, speaker(s): lisa piccirillo (university of texas), ncsu, sas 4201.

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