Chapters in this book

1. Frontmatter i
2. Contents v
3. Preliminaries
4. 1. Introduction 3
5. 2. Basic Math and Logic* 6
6. 3. Set Theory* 14
7. Real Numbers
8. 4. Least Upper Bounds* 27
9. 5. The Real Field* 35
10. 6. Complex Numbers and Euclidean Spaces 46
11. Topology
12. 7. Bijections 61
13. 8. Countability 68
14. 9. Topological Definitions* 79
15. 10. Closed and Open Sets* 90
16. 11. Compact Sets* 98
17. 12. The Heine-Borel Theorem* 108
18. 13. Perfect and Connected Sets 117
19. Sequences
20. 14. Convergence* 129
21. 15. Limits and Subsequences* 138
22. 16. Cauchy and Monotonic Sequences* 148
23. 17. Subsequential Limits 157
24. 18. Special Sequences 166
25. 19. Series* 174
26. 20. Conclusion 183
27. Acknowledgments 187
28. Bibliography 189
29. Index 191