Author	Lang, Serge. author
Title	Math Talks for Undergraduates [electronic resource] / by Serge Lang
Imprint	New York, NY : Springer New York : Imprint: Springer, 1999
Connect to	http://dx.doi.org/10.1007/978-1-4612-1476-2
Descript	IX, 121 p. online resource

For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by students who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book. The talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Undergraduates, and even some high school students, will enjoy the talks which cover prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, harmonic and symmetric polynomials, and more in a lively and informal style

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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Number theory
5. Mathematics
6. Number Theory
7. Analysis