The book is a response to the observation that even in mathematics intensive disciplines like computer science, almost all the mathematics taught in the curriculum is from before the 20th century, because a foundation is all there is time for. Kantor, Matousek, and Samal developed a course for PhD students, and this book is an extension of their lecture notes. It introduces six selected areas of mostly 20th-century mathematics for students and other readers who have gone through the usual undergraduate courses and are accustomed to rigorous presentation with proofs. They are measure and integral, high-dimensional geometry and measure concentration, Fourier analysis, the representation of finite groups, polynomials, and topology. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
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Ida Kantor, Charles University, Prague, Czech Republic.
Jiri Matousek, Charles University, Prague, Czech Republic, and ETH, Zurich, Switzerland.
Robert Samal, Charles University, Prague, Czech Republic.
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