**Student Mathematical Library**

Volume: 39;
2007;
136 pp;
Softcover

MSC: Primary 05; 11; 28; 30; 40; 42; 52;

Print ISBN: 978-0-8218-4397-0

Product Code: STML/39

List Price: $32.00

Individual Price: $25.60

**Electronic ISBN: 978-1-4704-1217-3
Product Code: STML/39.E**

List Price: $32.00

Individual Price: $25.60

#### Supplemental Materials

# A View from the Top: Analysis, Combinatorics and Number Theory

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*Alex Iosevich*

This book is based on a capstone course that
the author taught to upper division undergraduate students with the
goal to explain and visualize the connections between different areas
of mathematics and the way different subject matters flow from one
another. In teaching his readers a variety of problem solving
techniques as well, the author succeeds in enhancing the readers'
hands-on knowledge of mathematics and provides glimpses into the world
of research and discovery. The connections between different
techniques and areas of mathematics are emphasized throughout and
constitute one of the most important lessons this book attempts to
impart. This book is interesting and accessible to anyone with a basic
knowledge of high school mathematics and a curiosity about research
mathematics.

The author is a professor at the University of Missouri and has
maintained a keen interest in teaching at different levels since his
undergraduate days at the University of Chicago. He has run numerous
summer programs in mathematics for local high school students and
undergraduate students at his university. The author gets much of his
research inspiration from his teaching activities and looks forward to
exploring this wonderful and rewarding symbiosis for years to
come.

#### Table of Contents

# Table of Contents

## A View from the Top: Analysis, Combinatorics and Number Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Biographical information vii8 free
- Thanks ix10 free
- Foreword xi12 free
- Chapter 1. The Cauchy-Schwarz inequality 116 free
- Chapter 2. Projections in R[sup(3)]—the elephant makes an appearance! 924
- Chapter 3. Projections in four dimensions 1732
- Chapter 4. Projections and Cubes 2742
- Chapter 5. Incidences and matrices 3954
- Chapter 6. Basics of grids over finite fields 4762
- Chapter 7. Besicovitch-Kakeya conjecture in two dimensions 5368
- Chapter 8. A gentle entry into higher dimensions 5974
- Chapter 9. Some basic counting, probability and a few twists 6580
- Chapter 10. A more involved taste of probability 87102
- Chapter 11. Oscillatory integrals and fun that lies beyond 97112
- Chapter 12. Integer points and a crash course on Fourier analysis 109124
- Chapter 13. Return of the Fourier transform 123138
- Chapter 14. It is time to say goodbye 133148
- Bibliography 135150
- Back Cover Back Cover 1154

#### Readership

Undergraduate students interested in analysis, combinatorics, number theory, and geometry.

#### Reviews

...a tremendous asset and an endless source of inspiration...

`STML/56`

`MBK/75`

...a tremendous asset and an endless source of inspiration...

`STML/56`

`MBK/75`

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