Math Talks for Undergraduates / Edition 1

Math Talks for Undergraduates / Edition 1

by Serge Lang
     
 

ISBN-10: 0387987495

ISBN-13: 9780387987491

Pub. Date: 06/24/1999

Publisher: Springer New York

For many years Serge Lang has given talks to undergraduates on selecte d items in mathematics which could be extracted at a level understanda ble by students who have had calculus. Written in a conversational to ne, 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 stud ents in

Overview

For many years Serge Lang has given talks to undergraduates on selecte d items in mathematics which could be extracted at a level understanda ble by students who have had calculus. Written in a conversational to ne, 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 stud ents in seminars run by the students themselves. Undergraduates, and e ven some high school students, will enjoy the talks which cover prime numbers, the abc conjecture, approximation theorems of analysis, the s emi-parallelogram law and Bruhat-Tits spaces, harmonic and symmetric p olynomials, and more in a lively and informal style.

Product Details

ISBN-13:
9780387987491
Publisher:
Springer New York
Publication date:
06/24/1999
Edition description:
1999
Pages:
121
Product dimensions:
6.10(w) x 9.25(h) x 0.01(d)
Age Range:
18 Years

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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