Evan Dummit's Repository of Problem Sets


Main. Teaching. Personal. Sets. Handouts/Talks.

As the page title indicates, this is a repository of some problems sets I've completed over the past several years, in pdf format. Depending on my mood and level of boredom, there may or may not be more files than actually listed here; feel free to try to find them. (No comments on my typesetting programs, please.)


Note -- The author makes no claims as to any of the following:
(1) That any given solution is correct
(2) That any given solution is complete
(3) That any given solution is clear
(4) That any given solution is elegant

Caveat lector, cheating only hurts yourself, etc., etc., etc.
I have marked some of the known mistakes. If anyone finds more, please let me know and I'll note them here.


Obligatory copyright notice:
Solutions are copyright me, Evan Dummit. Problems are copyright their authors.
No individual or group has permission to repost, modify, or distribute these files without my express consent.

--- Newer problem sets (UW-Madison courses) ---

Math 752 (Algebraic Topology II, Hatcher Topology chs. 3-4):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions
  3. Set #3 , Solutions
  4. Set #4 , Solutions
  5. Set #5 , Solutions
  6. Set #6 , Solutions
  7. Final , Solutions
Math 844 (Elliptic Curves + Modular Forms, Silverman AEC chs. 1-8 + Diamond FCMF ch. 1):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions 
  3. Set #3 , Solutions 
  4. Set #4 , Solutions 
  5. Set #5 , Solutions


--- Older problem sets (Caltech courses) ---
[Senior Year]
Math 105 (Elliptic Curves, Silverman AEC chs. 1-6):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions 
  3. Sets #3+4 , Solutions 
Math 130a (Algebraic Geometry - Varieties; Hartshorne ch. 1):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions 
  3. Set #3 , Solutions 
  4. Set #4 , Solutions 
  5. Problems.
Math 151a (Algebraic Topology 1; Hatcher chs. 1-2):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions 
  3. Set #3 , Solutions 
  4. Midterm , Solutions
  5. Set #4 , Solutions 
  6. Set #5 , Solutions
  7. Set #6 , Solutions 
  8. Final , Solutions 
  9. Problems.


[Junior year]
Math 109abc (Introduction to Topology and Geometry):
  1. Math 109a (Intro to Topology): Armstrong.
  2. Set #1 , Solutions 
  3. Set #2 , Solutions 
  4. Set #3 , Solutions 
  5. Set #4 , Solutions 
  6. Set #5 , Solutions
  7. Set #6 , Solutions 
    1. Problem #3: The map f is not continuous at 2/3. (Thanks to V F for pointing this out.)
  8. Set #7 , Solutions 
  9. Set #8 , Solutions 
  10. Set #9 , Solutions
  11. Final .
  12. Math 109b (Differential Geometry of Curves and Surfaces): Do Carmo.
  13. Set #1 , Solutions 
  14. Set #2 , Solutions 
  15. Set #3 , Solutions 
  16. Set #4 , Solutions 
  17. Set #5 , Solutions
  18. Set #6 , Solutions 
  19. Set #7 , Solutions 
  20. Set #8 , Solutions 
  21. Math 109c (Differential Topology of Manifolds): Guillemin-Pollack.
  22. Set #1 , Solutions 
  23. Set #2 , Solutions 
  24. Set #3 , Solutions 
  25. Set #4 , Solutions 
  26. Midterm , Solutions 
  27. Set #5 , Solutions
  28. Set #6 , Solutions 
  29. Set #7 , Solutions 
  30. Set #8 , Solutions 
Math 110abc (Analysis) :
  1. Math 110a: Real Analysis, Rudin R+CA + Folland.
    (Note: Due to a copyright claim, I have removed the problem sets, to which I do not hold the copyright.)
  2. Set 1 Solutions 
  3. Set 2 Solutions 
  4. Set 3 Solutions 
  5. Set 4 Solutions 
  6. Math 110b: Complex Analysis, Rudin R+CA + Ahlfors.
  7. Set 1 Solutions 
  8. Set 2 Solutions 
  9. Set 3 Solutions 
  10. Set 4 Solutions 
  11. Math 110c: Functional and Harmonic Analysis, Rudin R+CA + Reed-Simon.
  12. Set 1 Solutions 
  13. Set 2 Solutions 
  14. Set 3 Solutions 
  15. Set 4 Solutions 
Math 160a (Algebraic Number Fields, Marcus):
  1. Set #1 , Solutions 
  2. Set #2 , Solutions 
  3. Set #3 , Solutions 
  4. Set #4 , Solutions 
  5. Set #5 , Solutions


[Sophomore Year]
Math 6ac (Introduction to Discrete Mathematics):
  1. Math 6a (Discrete Mathematics).
  2. Set #1 , Solutions 
  3. Set #2 , Solutions 
  4. Set #3 , Solutions 
  5. Set #4 , Solutions 
  6. Set #5 , Solutions
  7. Set #6 , Solutions 
  8. Set #7 , Solutions 
  9. Set #8 , Solutions 
  10. Set #9 , Solutions 
  11. Set #10 , Solutions 
  12. Math 6c (Intro to Formal Logic).
  13. Set #1 , Solutions 
  14. Set #2 , Solutions 
  15. Set #3 , Solutions 
  16. Set #4 , Solutions 
  17. Set #5 , Solutions
  18. Set #6 , Solutions 
  19. Set #7 , Solutions 
  20. Set #8 , Solutions 
  21. Set #9 , Solutions 
  22. Set #10 , Solutions 
Math 108abc (Introduction to Analysis):
  1. Math 108a (Intro Real Analysis): Rudin PMA, Carothers.
  2. Set #1 , Solutions 
  3. Set #2 , Solutions 
  4. Set #3 , Solutions 
  5. Set #4 , Solutions 
  6. Midterm , Solutions
  7. Set #5 , Solutions
  8. Set #6 , Solutions 
  9. Set #7 , Solutions 
  10. Set #8 , Solutions 
  11. Final , Solutions
  12. Math 108b (Intro Measure Theory): Carothers.
  13. Set #1 , Solutions 
  14. Set #2 , Solutions 
  15. Set #3 , Solutions 
  16. Set #4 , Solutions 
  17. Set #5 , Solutions
  18. Set #6 , Solutions 
  19. Set #7 , Solutions 
  20. Set #8 , Solutions 
  21. Math 108c (Intro Complex Analysis): Greene-Krantz.
  22. Set #1 , Solutions 
  23. Set #2 , Solutions 
  24. Set #3 , Solutions 
  25. Set #4 , Solutions 
  26. Midterm .
  27. Set #5 , Solutions
  28. Set #6 , Solutions 
  29. Set #7 , Solutions 
  30. Set #8 , Solutions 
Math 120abc (Abstract Algebra):
  1. Math 120a: Groups and Rings, Hungerford.
  2. Set #1 , Solutions 
  3. Set #2 , Solutions 
  4. Set #3 , Solutions 
  5. Set #4 , Solutions 
  6. Set #5 , Solutions
  7. Set #6 , Solutions 
  8. Set #7 , Solutions 
  9. Set #8 , Solutions 
  10. Math 120b: Rings and Modules, Hungerford.
  11. Set #1 , Solutions 
  12. Set #2 , Solutions 
  13. Set #3 , Solutions 
  14. Set #4 , Solutions 
  15. Set #5 , Solutions
  16. Set #6 , Solutions 
  17. Set #7 , Solutions 
  18. Set #8 , Solutions 
  19. Math 120c: Fields and Galois Theory, Lang.
  20. Set #1 , Solutions 
  21. Set #2 , Solutions 
  22. Set #3 , Solutions 
  23. Set #4 , Solutions 
  24. Set #5 , Solutions
  25. Set #6 , Solutions 


[Freshman Year]
Math 5abc (Introduction to Abstract Algebra):
  1. Math 5a (Groups): Dummit-Foote chs. 1-6.
  2. Set #1 , Solutions 
  3. Set #2 , Solutions 
  4. Set #3 , Solutions 
  5. Set #4 , Solutions 
  6. Set #5 , Solutions
  7. Set #6 , Solutions 
  8. Set #7 , Solutions 
  9. Set #8 , Solutions 
  10. Math 5b (Rings, Modules, Vector Spaces): Dummit-Foote chs. 7-12.
  11. Set #1 , Solutions 
  12. Set #2 , Solutions 
  13. Set #3 , Solutions 
  14. Set #4 , Solutions 
  15. Set #5 , Solutions
  16. Set #6 , Solutions 
  17. Set #7 , Solutions 
  18. Set #8 , Solutions 
  19. Math 5c (Fields, Galois Theory, Representation Theory): Dummit-Foote chs. 13-14 + 18-19.
  20. Set #1 , Solutions 
  21. Set #2 , Solutions 
  22. Set #3 , Solutions 
  23. Set #4 , Solutions 
  24. Set #5 , Solutions
  25. Set #6 , Solutions 
  26. Set #7 , Solutions 
  27. Set #8 , Solutions