Mathematics++: Selected Topics Beyond the Basic Courses (Student Mathematical Library) by Ida Kantor (PDF)

Description

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications-some quite surprising-in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

User’s Reviews

Editorial Reviews: Review The book under review contains six chapters that can be read independently, each one surveying one mathematical topic. … It is carefully written, and it is better than a collection of lecture notes. Such books are needed for students, as a complement to the standard textbooks and to present more specialized applications of classical mathematics. The reviewer wishes there were many more such books. –Athanase Papadopoulos, ZMATHThis book has its origins, we are told, in the authors’ experiences teaching graduate students in computer science, who needed background in certain mathematical topics. Since these topics were not covered in the basic courses that these students had taken, the authors undertook to introduce them in courses spanning several semesters, the lecture notes of which, suitably expanded, became this text. … I like expository books, because I think, particularly in these days of increasing specialization, that they serve a valuable purpose, not only for students but also professionals who want to see what’s going on in other areas, or who need some background in one area for research in another. This book is a fine example of that genre. –Mark Hunacek, MAA Reviews About the Author 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The authors note that this text was written with graduate level CS students in mind…let me tell you something, any graduate level student in the mathematical sciences could profit from careful study of this book. The contents are a beautiful twist of pure and applied mathematics. Somehow the authors have found the ability to rigorously construct Fourier theory from the theory of characteristics of finite abelian groups, and in the same binding explore algebraic geometry, with a wonderful condensed chapter on measure theory…why not do a little topology as well? The book is deep. Seriously. A first or second year graduate student would do well to carry it with them at all times, with frequent breaks for vigorous discussion. There are so many gems you might be blinded by prolonged exposure. Also can highly recommend Thirty-three Miniatures by one of the authors – this is how math is supposed to be!

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