02221nmm a2200301 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001600139245007400155260004800229300003100277505066700308653001600975653003400991653001801025653001601043653001801059653001301077710003401090041001901124989003801143856007401181082001001255520065401265EB000618629EBX0100000000000000047171100000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814612147621 aLang, Serge00aMath Talks for UndergraduateshElektronische Ressourcecby Serge Lang aNew York, NYbSpringer New Yorkc1999, 1999 aIX, 121 pbonline resource0 aWeierstrass 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 aMathematics aGlobal analysis (Mathematics) aNumber theory aMathematics aNumber Theory aAnalysis2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -2004 uhttp://dx.doi.org/10.1007/978-1-4612-1476-2?nosfx=yxVerlag3Volltext0 a512.7 aFor 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