Serge Lang

Math Talks for Undergraduates (eBook, PDF)

• Format: PDF

Produktbeschreibung

For many years, Serge Lang has given talks on selected items in mathematics which could be extracted at a level understandable by those who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book covering such topics as: prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, and harmonic and symmetric polynomials. Each talk is written in a lively and informal style meant to engage any reader looking for further insight into mathematics.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 121
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461214762
• Artikelnr.: 44179953

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

"This new book of its very prolific author is based on talks delivered by him at European and North American universities. It takes the form of simulated discussions: expositions are combined with students'questions and remarks. The material is chosen to be accessible with minimal prerequisites and of interest to a broad mathematically oriented audience. ... The text is written in a lively light style with an adequate degree of precision. Even for more advanced readers it provides pleasant reading, showing how to popularise mathematics."
EMS Newsletter, Vol. 37, Sept. 2000