A function's derivative is not more complex than the function itself and can be simpler: polynomials and trig functions have polynomial and trig derivatives, and logarithmic functions have rational function derivatives. But integrating can lead to functions that are far more complex than the original function. Why is that?

The goal of this talk is to explain why you "can't integrate" functions such as \(e^{-x^2}\) and arc length integrals on the graph of \(y = x^3\). We will start by explaining what such impossibility results are saying as well as what they are \(not\) saying, and then discuss theorems of Chebyshev and Liouville that impose strong restrictions on integrals that have a "nice" formula.


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TBA

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One corollary of the Mean Value Theorem is that any function on \(\mathbf R\) whose derivative is zero everywhere must be constant. This can be viewed as a statement regarding the existence and uniqueness of solutions to the Ordinary Differential Equation (ODE) \(f'(x)=0\).

In this talk, we will leverage this fact to solve the sorts of ODEs which arise often when doing physics. The motivating example will be the Driven Simple Harmonic Oscillator. We may also mention relations to quantum mechanics and harmonic analysis. No previous knowledge of differential equations, linear algebra or physics is necessary.

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TBA

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I will give a brief introduction to the motivations, concepts, and properties of distributions, which generalize the notion of functions \(f(x)\) to allow derivatives of discontinuities, “delta” functions, and other nice things. In the land of distributions, everything is infinitely differentiable, exchanging limits and derivatives is always okay, and no vague infinities are involved in delta functions. Distributions are central to understanding Fourier transforms, partial differential equations, and many applications of calculus to physics and engineering, but were only formalized in the 1950s. Although this is ultimately a deep subject, the key ideas should be accessible to anyone who has mastered basic calculus.

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TBA

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I will demonstrate (and explain!) some magic tricks based on fascinating and not-very-well-known mathematical principles.


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TBA

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TBA

Note: Join the meeting at https://uconnvtc.webex.com/meet/mathclub

TBA

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TBA

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If you are considering graduate school in mathematics or related areas after college, come to this panel discussion where you will hear from members of the UConn math department about their experiences planning for and applying to graduate school. The discussion will then be opened to answer your questions. A packet containing a suggested reading list and some general advice will be provided too.


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