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

Alex Iosevich

ISBN: 9789393330154 | Year: 2022 | Paperback | Pages: 152 | Language : English

Book Size: 140 X 216 mm | Territorial Rights: Restricted| Series American Mathematical Society

Price: 550.00

About the Book

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.

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Alex Iosevich, University of Missouri, Columbia, Columbia, MO

Table of Contents

  • Biographical information 
  • Thanks 
  • Foreword 
  • Chapter 1. The Cauchy-Schwarz inequality 
    • §1 Notes, remarks and difficult questions
  • Chapter 2. Projections in R[sup(3)]—the elephant makes an appearance!
    • §1. Notes, remarks and difficult questions
  • Chapter 3. Projections in four dimensions
    • §1. Notes, remarks, and difficult questions
  • Chapter 4. Projections and Cubes
    • §1. Notes, remarks and difficult questions
  • Chapter 5. Incidences and matrices
    • §1. Notes, remarks and difficult questions
  • Chapter 6. Basics of grids over finite fields
    • §1. Notes, remarks and difficult questions
  • Chapter 7. Besicovitch-Kakeya conjecture in two dimensions
    • §1. Notes, remarks and difficult questions
  • Chapter 8. A gentle entry into higher dimensions
    • §1. Notes, remarks and difficult questions
  • Chapter 9. Some basic counting, probability and a few twists
    • §1. Notes, remarks and difficult questions
  • Chapter 10. A more involved taste of probability
    • §1. Notes, remarks and difficult questions
  • Chapter 11. Oscillatory integrals and fun that lies beyond
    • §1. Notes, remarks and difficult questions
  • Chapter 12. Integer points and a crash course on Fourier analysis
    • §1. Notes, remarks and difficult questions
  • Chapter 13. Return of the Fourier transform
    • §1. Notes, remarks and difficult questions
  • Chapter 14. It is time to say goodbye
  • Bibliography

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