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Math Talks for Undergraduates [Hardcover]

Serge Lang
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Table of Contents

Prime Numbers.- The abc Conjecture.- Global Integration of Locally Integrable Vector Fields.- Approximation Theorems of Analysi.- Approximation Theorems of Analysis.- Examples: Weierstrass Approximation, Fourier Series, Harmonic Functions on the Disc, Harmonic Functions on the Upper Half Plane.- The Heat Kernel on the Real Line.- The Heat Kernel on the Circle.- Theta Series and the Convolution Product.- The Poisson Summation Formula and Functional Equation of the Zeta Function.- Theta Functions and Complex Doubly Periodic Functions.- Bruhat-Tits Spaces.- The Semi Parallelogram Law.- The Space of Positive Definite Matrices.- The Metric Increasing Property of the Exponential Map.- Historical Notes.- Harmonic and Symmetric Polynomials.- A Positive Definite Scalar Product.- Harmonic Polynomials.- Symmetric Polynomials.

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