Math Talks for Undergraduates / Edition 1

Math Talks for Undergraduates / Edition 1

by Serge Lang
     
 

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

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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:
9.21(w) x 6.14(h) x 0.38(d)
Age Range:
18 Years

Table of Contents

Foreword
Prime Numbers1
The abc Conjecture18
Global Integration of Locally Integrable Vector Fields32
Approximation Theorems of Analysis49
Approximation Theorems of Analysis49
Examples: Weierstrass Approximation, Fourier Series, Harmonic Functions on the Disc, Harmonic Functions on the Upper Half Plane53
The Heat Kernel on the Real Line62
The Heat Kernel on the Circle65
Theta Series and the Convolution Product70
The Poisson Summation Formula and Functional Equation of the Zeta Function72
Theta Functions and Complex Doubly Periodic Functions75
Bruhat-Tits Spaces79
The Semi Parallelogram Law80
The Space of Positive Definite Matrices85
The Metric Increasing Property of the Exponential Map93
Historical Notes97
Harmonic and Symmetric Polynomials101
A Positive Definite Scalar Product103
Harmonic Polynomials105
Symmetric Polynomials107

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