Welcome!
All students interested in mathematics are invited to attend the club’s events, such as talks aimed at students, problem-solving sessions, and panel discussions. The talks generally will not require a background beyond calculus and a little linear algebra. Free refreshments will be provided.
Events this semester
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Sep
4
Math Club: What’s the deal with the power series of tan x, by Keith Conrad (UConn) 5:30pm
Math Club: What’s the deal with the power series of tan x, by Keith Conrad (UConn)
Wednesday, September 4th, 2024
05:30 PM
Monteith 419
Calculus courses present the derivatives of all the basic trigonometric functions, but they present the power series of sin \(x\) and cos \(x\) while ignoring the power series of the other trigonometric functions. Why is that?
In this talk we will discuss the power series of tan \(x\), whose coefficients turn out to have connections to the binomial theorem and combinatorics.
Note: Free refreshments. The talk starts at 5:40.
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Sep
11
Math Club: Differentiation under the integral sign, by Nicholas Juricic 5:30pm
Math Club: Differentiation under the integral sign, by Nicholas Juricic
Wednesday, September 11th, 2024
05:30 PM
Monteith 419
The two main techniques of integration taught in calculus courses are integration by substitution and integration by parts. This talk will describe and illustrate a third technique of integration, almost never taught in math courses, called differentiation under the integral sign. It can handle integrals that appear inaccessible to simpler methods. The physicist Richard Feynman had great affection for differentiation under the integral sign, writing once “I caught on how to use that method, and I used that one damn tool again and again.”
Some familiarity with calculating partial derivatives from multivariable calculus will be assumed.Note: Free refreshments. The talk starts at 5:40.
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Sep
18
Math Club: The random graph and 0-1 laws, by Reed Solomon (UConn) 5:30pm
Math Club: The random graph and 0-1 laws, by Reed Solomon (UConn)
Wednesday, September 18th, 2024
05:30 PM
Monteith 419
A random infinite graph is formed by starting with a countably infinite set of vertices and then flipping a coin for each pair of vertices to determine whether or not to place an edge between those vertices. This talk is about the kinds of graphs you get by this process and it will illustrate a nifty connection between probability, graph theory, and logic.
Note: Free refreshments. The talk starts at 5:40.
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Sep
25
Math Club: Stirling’s formula, by Matt Lamoureux (UConn) 5:30pm
Math Club: Stirling’s formula, by Matt Lamoureux (UConn)
Wednesday, September 25th, 2024
05:30 PM
Monteith 419
The factorials \(n! = 1 \cdot 2 \cdot 3 \cdots n\), which count how many ways \(n\) objects can be arranged, show up anywhere that rearrangements have to be counted, such as combinatorics, probability, thermodynamics, statistical mechanics, and quantum mechanics. The numbers \(n!\) grow very rapidly, e.g., 100! has 158 digits. For applications in chemistry, \(n!\) may occur for \(n\) on the order of Avogadro’s number (about \(6.02 \times 10^\)), for which an exact factorial calculation is out of the question. When exact values are computationally inaccessible, it’s natural to seek approximations to the values.Stirling’s formula is the standard way to estimate \(n!\) when \(n\) is large. In this talk we will see what Stirling’s formula is and how to derive it using tools from calculus.
Note: Free refreshments. The talk starts at 5:40.
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Oct
2
Math Club: Quantum mechanics as a deformation of classical mechanics, by Dion Mann (UConn) 5:30pm
Math Club: Quantum mechanics as a deformation of classical mechanics, by Dion Mann (UConn)
Wednesday, October 2nd, 2024
05:30 PM
Monteith 419
A new mathematical description of a physical theory should be consistent with an earlier description of the theory in settings where the earlier one has been well-tested by experiments. This often means that the earlier mathematical description is a limiting case of the new one at certain parameter values or that the new description is a “deformation” of the old one.
As a prototypical example, the ancient idea of a flat Earth is a limiting case of the more accurate sphere model when we look at a sphere up close. We also can interpret quantum mechanics as a deformation of classical mechanics via a mathematical technique called “deformation quantization.” Here, quantum mechanics involves Planck’s constant \(\hbar\) and its limiting behavior as \(\hbar \to 0\) leads us back to classical mechanics. This talk will give an introduction to what deformation quantization is all about.
The talk will assume the audience has seen partial derivatives and eigenvalues.
Note: Free refreshments. The talk starts at 5:40.
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Oct
9
Math Club: Why should we care about a new proof of the Pythagorean Theorem, by Alvaro Lozano-Robledo (UConn) 5:30pm
Math Club: Why should we care about a new proof of the Pythagorean Theorem, by Alvaro Lozano-Robledo (UConn)
Wednesday, October 9th, 2024
05:30 PM
Monteith 419
The Pythagorean Theorem is old news. Pythagoras was born in 570 BC but, in fact, we know proofs of “his” theorem that are much, much older than Pythagoras himself. Nowadays there are over 350 different proofs of the Pythagorean theorem in print, and yet many rejoiced when two high-school students from New Orleans, Ne’Kiya Jackson and Calcea Johnson, discovered a new proof of the theorem in 2023. However, is this theorem relevant today? Why is there such an emphasis on this particular theorem? Why would anyone be excited about a new proof of a theorem that already has over 350 proofs? Why are new proofs of old theorems interesting? More importantly, do you know a proof of this theorem?In this talk we will discuss all of these questions, and present a few proofs along the way, including the recent one by Jackson and Johnson.Note: Free refreshments. The talk starts at 5:40. -
Oct
16
Math Club: Commuting polynomials, by Georgia Harbor-Collins (UConn) 5:30pm
Math Club: Commuting polynomials, by Georgia Harbor-Collins (UConn)
Wednesday, October 16th, 2024
05:30 PM
Monteith 419
Composition of functions usually depends on the order in which it is done: $f(g(x))$ usually is not \(g(f(x))\). Sometimes, however,
\(f(g(x)) = g(f(x))\) for all \(x\). We then say \(f(x)\) and \(g(x)\) commute.In this talk, we will see how polynomials can satisfy \(f(g(x)) = g(f(x))\). It turns out that there are only two interesting ways this can happen, and one way
has an unexpected relationship to trigonometry.Note: Free refreshments. The talk starts at 5:40.
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Oct
23
Math Club: TBA, by TBA 5:30pm
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Oct
30
Math Club: TBA, by TBA 5:30pm
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Nov
6
Math Club: TBA, by TBA 5:30pm
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Nov
13
Math Club: TBA, by TBA 5:30pm
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Nov
20
Math Club: TBA, by TBA 5:30pm