**Student Mathematical Library**

Volume: 75;
2015;
343 pp;
Softcover

MSC: Primary 14; 20; 28; 43; 52; 54; 55;

Print ISBN: 978-1-4704-2261-5

Product Code: STML/75

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-2623-1
Product Code: STML/75.E**

List Price: $49.00

Individual Price: $39.20

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#### Supplemental Materials

# Mathematics++: Selected Topics Beyond the Basic Courses

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*Ida Kantor; Jiří Matoušek; Robert Šámal*

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.

#### Readership

Graduate students and research mathematicians interested in theoretical computer science and discrete mathematics.

#### Reviews & Endorsements

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, ZMATH

This 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

#### Table of Contents

# Table of Contents

## Mathematics++: Selected Topics Beyond the Basic Courses

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Chapter 1. Measure and integral 114
- Chapter 2. High-dimensional geometry and measure concentration 3952
- Chapter 3. Fourier analysis 8598
- Chapter 4. Representations of finite groups 141154
- Chapter 5. Polynomials 173186
- Chapter 6. Topology 235248
- Index 333346
- Other titles in this series 345358
- Back Cover Back Cover1359