Titlebook: Math Talks for Undergraduates; Serge Lang Book 1999 Springer Science+Business Media New York 1999 Fourier series.calculus.integration.prim

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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.978-1-4612-7157-4978-1-4612-1476-2

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ble 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

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Harmonic and Symmetric Polynomials,rmonic polynomials and the symmetric polynomials, provide a fertile ground to illustrate concepts from linear algebra, not to speak of the calculus involved with partial derivatives. When dealing with polynomials, however, the analysis side of things is mostly illusory.

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The , Conjecture,cluding myself. It came as a surprise when R. C. Mason in 1983 discovered a new, very interesting fact about polynomials [Ma 83]. Even more remarkable, this fact actually had been already discovered by another mathematician, W. Stothers [Sto81], but people had not paid attention and I learned of Sto

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Global Integration of Locally Integrable Vector Fields,on calculus of several (actually two) variables. No knowledge of complex analysis is assumed. Some basic knowledge about partial derivatives, is taken for granted, but no more than what is in [La 87], Chapter VIII, §4. A more complete treatment will be found in [La 97], Chapters XV and XVI.