Spring 2024
General Information
Syllabus and Homeworks
Exams
Syllabus
Below is the tentative syllabus for MAT 312/AM 351. It is subject to change.
Homeworks for every week should be handed to your recitation instructor during the recitation next week (e.g., homework for week 1 should be handed during recitation in week 2). It will be graded and returned to you the following week.
| Week | Sections covered | Homework |
| Jan 22 - 26 | 1.1: Euclid's algorithm | Textbook, Section 1.1, Exercises 1, 2, 3, 4, 5, 6, 7 |
| Jan 29 - Feb 2 | 1.2: Induction, 1.3: Unique Factorization |
HW2 |
| Feb 5 - 9 | 1.4: Congruences, 1.5: Linear congruences |
HW3 |
| Feb 12 - 16 | 1.6: Euler theorem and Public Key Crypto | HW4 |
| Feb 19 - 23 | 1.6 continued 4.1: Permutations |
|
| Feb 26 - March 1 | review; midterm 1 4.2: sign of permutation |
HW 5: 4.1: #4, #5; 4.2: #1, #6, #9, 13. Optional problem: 4.2#10 |
| Mar 4 - 8 | 4.3: groups 5.1: subgroups |
HW6 |
| Mar 11 - 15 | Sping break | |
| Mar 18 - 22 | 5.1, 5.2: Cosets and Lagrange Theorem | HW7 |
| Mar 25 - 29 | Normal subgoups and quotient groups | HW8 |
| Apr 1 - 5 | 5.4: error-correcting codes; | HW9 |
| Apr 8 - 12 | Review; midterm 2 |
|
| Apr 15 - 19 | 6.1,6.2: Polynomials, divisibility, Euclid's algorithm | HW10 |
| Apr 22 - 26 | 6.3: irreducible polynomials, factorisation 6.4: polynomial congruences |
HW11 |
| Apr 29 - May 3 | 6.4: polynomial congruences |