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Sep 6 Math Club: The Classification of Pythagorean Triples, by Keith Conrad (UConn) 5:30pm

Math Club: The Classification of Pythagorean Triples, by Keith Conrad (UConn)

Wednesday, September 6th, 2023

05:30 PM - 06:30 PM

Monteith 111

A Pythagorean triple is a set of positive integers a, b, and c that are the sides of a right triangle. Two well-known examples are (3,4,5) and (5,12,13). There are infinitely many more examples, and in fact there is a formula for all of them.
In this talk, a formula for all Pythagorean triples will be presented and a few derivations of the formula will be given, using both algebra and geometry. One of the derivations has an unexpected connection to integral calculus.

Note: Free refreshments. The talk starts at 5:40.

Contact Information:
Keith Conrad (kconrad@math.uconn.edu)

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Sep 13 Math Club: Combinatorial Triangles 5:30pm

Math Club: Combinatorial Triangles

Wednesday, September 13th, 2023

05:30 PM

Monteith Building

A “combinatorial triangle” is a system of positive integers (or 0) that count something and are convenient to place into a triangular array. The most famous combinatorial triangle is the system of binomial coefficients, but there are many other important examples.
In this week’s meeting, we’ll look together at some specific combinatorial triangles besides the binomial coefficients: Stirling numbers and Eulerian numbers.
Note: Free refreshments.

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Sep 20 Math Club: Infinitude of the Primes, by Asimina Hamakiotes (UConn) 5:30pm

Math Club: Infinitude of the Primes, by Asimina Hamakiotes (UConn)

Wednesday, September 20th, 2023

05:30 PM

Monteith Building

A prime number is a number bigger than 1 that is only divisible by 1 and itself. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
This list never ends: there are infinitely many primes.In this talk, multiple proofs of the infinitude of primes will be presented.
Note: Free refreshments. The talk starts at 5:40.

Contact Information:
Keith Conrad (kconrad@math.uconn.edu)

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Sep 27 Math Club: Euler’s Constant 5:30pm

Math Club: Euler’s Constant

Wednesday, September 27th, 2023

05:30 PM

Monteith Building

This week in the math club, we will look at an important number called Euler’s constant, which is around .57721. We’ll see where it comes from, different ways to estimate it, and some famous unsolved problems about this number.

Note: Free refreshments.

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Oct 4 Math Club: Continued Fractions, by Swati Gaba (UConn) 5:30pm

Math Club: Continued Fractions, by Swati Gaba (UConn)

Wednesday, October 4th, 2023

05:30 PM

Monteith 111

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Oct 11 Math Club: What is...? 5:30pm

Math Club: What is...?

Wednesday, October 11th, 2023

05:30 PM

Monteith 111

At this meeting, Prof. Conrad will answer any question you have about math (except homework questions). This is a chance to find out more about any problems, concepts, examples, historical events, etc. in math that you’ve heard or read about but don’t understand as well as you’d like.

Note: Free refreshments.

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Oct 18 Math Club: What are differential forms? by Paul Tee (UConn) 5:30pm

Math Club: What are differential forms? by Paul Tee (UConn)

Wednesday, October 18th, 2023

05:30 PM

Monteith Building

In calculus, you meet expressions like dx or dxdy inside integrals. What do these mean? They are examples of differential forms and are used all the time in geometry.
In this talk, we will define and motivate the need for differential forms and then indicate how these objects are used in practice, including examples such as Stokes’ theorem and the first variation of surface area, as time permits. A large portion of the talk should be accessible to students who have seen multiple integrals in multivariable calculus, and will serve as a presentation about the way geometers do calculations in local coordinates.

Note: Free refreshments. The talk starts at 5:40.

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Oct 25 Math Club: All about Rubik’s Cube 5:30pm

Math Club: All about Rubik’s Cube

Wednesday, October 25th, 2023

05:30 PM

Monteith 111

Rubik’s Cube is one of the most widely recognized puzzles in the world. At this meeting many facets of the cube will be discussed: its history, how its pieces fit together and move around, math that is related to Rubik’s cube, and methods that can be used to solve the cube.

Prior experience with Rubik’s cube is not required.
Note: Free refreshments.

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Nov 1 Math Club: Computing the Gaussian integral, by Iddo Ben-Ari (UConn) 5:30pm

Math Club: Computing the Gaussian integral, by Iddo Ben-Ari (UConn)

Wednesday, November 1st, 2023

05:30 PM

Monteith 111

The Gaussian integral is the improper integral \(\int_^\infty e^ \, dx\), which turns out to be \(\sqrt\). This appears in probability theory as a normalization constant for the Gaussian distribution, in Stirling’s formula estimating \(n!\), in the Laplace method for estimating integrals, and elsewhere. In this talk, I will discuss these applications and will present several ways to evaluate the integral.

Note: Free refreshments. The talk starts at 5:40.

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Nov 8 Math Club: Undergraduate Research Opportunities in Math 5:30pm

Math Club: Undergraduate Research Opportunities in Math

Wednesday, November 8th, 2023

05:30 PM

Monteith 111

The math club is hosting a panel discussion on undergraduate mathematics research opportunities. The panelists will discuss how to become involved in mathematics research as an undergraduate and what the research process is like.
Note: Free refreshments.

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Nov 15 Math Club: Integrality of Binomial Coefficients, by Rachel Bailey (UConn) 5:30pm

Math Club: Integrality of Binomial Coefficients, by Rachel Bailey (UConn)

Wednesday, November 15th, 2023

05:30 PM

Monteith 111

Binomial coefficients, defined as \[ \binom = \frac\] when \(k = 0, 1, \ldots, n\), can be found in many areas of mathematics, including probability, orthogonal polynomials and most notably combinatorics, due to their common interpretation as the number of ways to select \(k\) items from \(n\) items without attention to the order of selection. However, from their definition as a ratio, it is not at all clear that \(\binom\) is actually an integer rather than just a fraction.
In this talk, I will prove that binomial coefficients are always positive integers. If you don’t believe me the first time, then you’ll have two more opportunities to be convinced because I will prove this fact in three different ways using techniques from calculus, algebra, and, unsurprisingly, combinatorics.
Note: Free refreshments. The talk starts at 5:40.

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Nov 29 Math Club: Uses of Complex Numbers in Mathematics, by Keith Conrad (UConn) 5:30pm

Math Club: Uses of Complex Numbers in Mathematics, by Keith Conrad (UConn)

Wednesday, November 29th, 2023

05:30 PM

Monteith 111

Complex numbers have the form \(x+yi\) where \(x\) and \(y\) are real numbers and \(i^2 = -1\). They were originally created during the 1500s in the study of polynomial roots and were shrouded in mystery. Later on, it turned out that complex numbers show up in much of mathematics: algebra, geometry, analysis, combinatorics, number theory, dynamical systems, and so on.
In this talk, we will review some basic features of complex numbers and then show how they are used in several different branches of mathematics.
Note: Free refreshments. The talk starts at 5:40.

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Past talks in or after Spring 2019 are accessible through the UConn Events Calendar (search on “math club”). A list of math club talks prior to Spring 2019 can be found here.

Contact us: You can reach the math club by email at the address uconnmathclub@gmail.com.

Officers: The president and secretary is Keegan Reck, and the vice-president and treasurer is Jason Dai. The faculty advisor is Keith Conrad.

Interested in joining? The math club is open to all registered UConn students. We have a group page on UConntact, on Twitter, and on Discord. Please go to our UConntact page and click on the Join Organization button.

Interested in a topic? If you are a UConn student who wants to hear a talk about some part of mathematics, especially one which may not be in a regularly offered course, write to the email address above and hopefully we can find a suitable speaker to address your interests.

Videos Check out some past math club talks on the math department’s You Tube channel: Nick Juricic’s talk on differentiation under the integral sign on Sept. 30, 2020, Keith Conrad’s talk on patterns that don’t last on Sept. 9, 2015, and Jon Hanke’s talk on the geometry of projective space on April 4, 2012. Other videos are available on the UConn math department’s YouTube Channel.

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