Chapters in this book

1. Frontmatter i
2. CONTENTS vii
3. PREFACE xi
4. ACKNOWLEDGMENTS xv
5. INTRODUCTION: WHAT THIS BOOK IS ABOUT 1
6. PART ONE. FINITE SUMS
7. CHAPTER 1. PROEM 11
8. CHAPTER 2. SUMS OF TWO SQUARES 22
9. CHAPTER 3. SUMS OF THREE AND FOUR SQUARES 32
10. CHAPTER 4. SUMS OF HIGHER POWERS: WARING’S PROBLEM 37
11. CHAPTER 5. SIMPLE SUMS 42
12. CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA 50
13. PART TWO. INFINITE SUMS
14. CHAPTER 7. INFINITE SERIES 73
15. CHAPTER 8. CAST OF CHARACTERS 96
16. CHAPTER 9. ZETA AND BERNOULLI 103
17. CHAPTER 10. COUNT THE WAYS 110
18. PART III. MODULAR FORMS AND THEIR APPLICATIONS
19. CHAPTER 11. THE UPPER HALF-PLANE 127
20. CHAPTER 12. MODULAR FORMS 147
21. CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE? 160
22. CHAPTER 14. CONGRUENCE GROUPS 179
23. CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED 186
24. CHAPTER 16. MORE THEORY OF MODULAR FORMS 201
25. CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS 213
26. BIBLIOGRAPHY 225
27. INDEX 227