Spring-2022. Math H113. Honors Introduction to Abstract Algebra . TuTh 12:30-2:00, 2 Evans
Instructor: Alexander Givental
Office hours: Th 3-4 in 701 Evans, and Mon 11:30-12:30 on Zoom
Text: The whole book
Lectures on Groups,
Rings, and Fields by Alexander Givental
Also, Topics in Algebra by I. N. Herstein
2nd edition can be recommended (but not required, and will not be really
Grading: Final 30%, quizzes 30%, hw 40% (these details are
still to be discussed and might be subject to change because of COVID constraints)
More precisely: Each individual hw or quiz scores below the score on the final will be dropped (together with their share in the total percentage), and the relative weight of hw / quizzes / final recalculated accordingly.
Homework: To be posted to this website weekly, due on Tue in class
or by email before the start of the lecture
Quizzes: Typically 1 question for 5 minutes at the start of each Thursday
lecture (but not during the first two weeks, when we are on zoom)
HW1, due Tue, Jan. 25: Read Lectures 1 and 2. Solve Exercises 2,4,5,9. Answers to HW1
HW2, due Tue, Feb. 1: Read Lectures 3 and 4. Solve exercises 12,13.
Answers to HW2
QZ1, on Th, Feb. 3: At the start of the lecture we will have a
5-min/ 1-question quiz on the material of Lecture 4.
HW3, due Tue, Feb. 8: Read Lectures 5 and 6. Solve exercises 17, 28, 30,33. Answers to HW3
QZ2, on Th, Feb. 10: on the material of lecture 5.
HW4, due Tue, Feb. 15: Read Lectures 7 and 8. Solve exercises 42, 45, 47, 51. Answers to HW4
QZ3, on Th, Feb. 17: Cycle structure of permutations.
HW5, due Tue, Feb. 22: Read Lectures 9 and 10. Solve exercises 58, 60, 62, 65. Answers to HW5
QZ4, on Th, Feb. 24: Direct products of groups.
HW6, due Tue, Mar. 1: Read Lectures 11 and 12. Solve exercises 72, 80, 81, 82. Answers to HW6
QZ5, on Th, Mar. 3: Quaternions.
HW7, due Tue, Mar. 8: Read Lectures 13 and 14. Solve exercises 95, 110,
111 (take for granted that in polynomial rings, factorization into irredcibles is unique), 112. Answers to HW7
QZ6, on Th, Mar. 10: Euclidean rings
HW8, due Tue, Mar. 15: Read Lectures 15, 16. Solve exercises 118, 121, 127, 130. Answers to HW8
QZ7, on Th, Mar. 17: Gaussian integers
HW9, due Tue, Mar. 29: Read Lecture 17. Solve exercises 135, 138, 143, 145. Answers to HW9
QZ8, on Th, Mar. 31: Waring's algorithm.
HW10, due Tue, Apr. 5: Read Lectures 18, 19. Solve exercises 149, 151, 158, 159. Answers to HW10
QZ9, on Th, Apr. 7: Straightedge and compass constructions.
HW11, due Tue, Apr. 12: Read lectures 20, 21. Solve exercises 160, 161, 173, 177. Answers to HW11
QZ10, on Th, Apr. 14: Multiple roots.
HW12, due Tue, Apr. 19: Read lectures 22, 23. Solve exercises 180, 182,
189, 190. (Beware: this hw is volumous but important; don't neglect it ---
this is your chance to understand Galois theory.) Answers to HW12
QZ11, on Th, Apr. 21: Cyclotomic polynomials. CANCELLED
HW13, due Tue, Apr. 26: Read lectures 24, 25, and Appendix II.
Solve exercises: 197, 198, 202, 203. Answers to HW13
QZ12, on Th, Apr. 28: Solvable groups. CANCELLED
HW14, due Tue, May 3: Read lectures 26, 27. Solve exercises: 204, 205,
211, 213. Answers to HW14
On the history of Cardano's formula (discussed in lecture 27) I highly
recommend the following (truly spectacular) presentation by
Sample final exam 1
Sample final exam 2
Those who want to refresh their knowledge of complex numbers and/or determinants
are welcome to read (among many other available sources)
Section 2 of Chapter 1 and Section 3 of Chapter 2 respectively of my own book
Linear Algebra (which, were the author not seeking eternal fame,
could have been titled "Linear Algebra Done Wrong") currently accessible online