University Mathematics — Year 3

Bachelor Year 3 (Age 20–21)

1. 1 Group Theory 12 solved exercises
2. 2 Rings and Arithmetic 12 solved exercises
3. 3 Modules over a Principal Ideal Domain 12 solved exercises
4. 4 Field Extensions and Galois Theory 12 solved exercises
5. 5 Representations of Finite Groups 12 solved exercises
6. 6 General Topology 12 solved exercises
7. 7 Complete Spaces: Baire, Ascoli, Stone–Weierstrass 12 solved exercises
8. 8 Banach Spaces and the Fundamental Theorems 12 solved exercises
9. 9 Measure Theory 12 solved exercises
10. 10 The Lebesgue Integral 12 solved exercises
11. 11 Product Measures, Fubini, Change of Variables 12 solved exercises
12. 12 The Lp Spaces 12 solved exercises
13. 13 Hilbert Spaces 12 solved exercises
14. 14 The Fourier Transform 12 solved exercises
15. 15 Compact Operators and the Spectral Theorem 12 solved exercises
16. 16 Holomorphic Functions 12 solved exercises
17. 17 Laurent Series and the Residue Theorem 12 solved exercises
18. 18 Conformal Maps and the Riemann Mapping Theorem 12 solved exercises
19. 19 Ordinary Differential Equations 12 solved exercises
20. 20 Submanifolds of ℝn 12 solved exercises
21. 21 Differential Forms and Stokes’ Theorem 12 solved exercises
22. 22 Probability: Foundations and the Law of Large Numbers 12 solved exercises
23. 23 Characteristic Functions and the Central Limit Theorem 12 solved exercises

23 chapters — 23 online so far, and more publishing regularly. The complete book is already available as a free PDF you can read online.