5/15: Course grades posted to SIS. Have a great summer!

5/15: Final exam solution posted.

5/3: Reminder: The final exam is on Friday May 12, 9am-12 noon, in Maryland 114.

5/3: Extra office hours for the final exam: Wednesday May 10, 2-3:30pm and Thursday May 11, 2-5pm.

3/14: No office hours today (school closed). There will be class tomorrow.

3/2: Homework solutions 4 is posted.

2/28: Extra office hour for midterm: Friday March 3, 3-4:30pm.

2/28: Reminder: The midterm is on Monday March 6.

2/7: TA's office hour: Wednesday 3-4pm.

1/23: The first meeting is on Monday January 30.

(This is tentative schedule. Check here frequently for updates.)

(Homework and quiz solutions provided by TA)

Date |
Topic |
Sections |
Homework |
Due Date |
HW Solutions(selected problems) |

Week 1 | Feb 8 |
HW1 Sol |
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Jan 30 | Preliminaries (Reading: 0.1, 0.2, Appendices A, B) |
0.1-0.3 | 0.3: 9, 14, 160.4: 1(c)(d)(h), 3(d), 8, 9, 101.1: 1(e), 10(c)(d), 15, 18(b), 25 |
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Feb 1 | Equivalences Principle of Mathematical Induction |
0.4, 1.1 | |||

Week 2 | Feb 15 |
HW2 Sol |
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Feb 6 | Prime factorization. | 1.2 | 1.2: 22, 33(a), 38, 39, 40, 43, 441.3: 4, 8(b), 18, 22(d) |
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Feb 8 | Integers Modulo n. | 1.3 | |||

Week 3 | Feb 22 |
HW3 SolQuiz 1 Sol |
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Feb 13 | Permutations. | 1.4 | 1.3: 31, 321.4: 5, 13(d), 14, 16, 23, 26, 27, 28 |
||

Feb 15 | More on Permutations Binary Operations |
1.4, 2.1 | |||

Week 4 | Mar 1 |
HW4 Sol |
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Feb 20 | Groups | 2.2, 2.3 | 2.1: 6, 8, 12, 192.2: 10(b), 24, 25, 29(c)2.3: 5, 13, 22, 23 |
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Feb 22 | Subgroups. Cyclic Groups | 2.3, 2.4 | |||

Week 5 | Mar 8 |
HW5 Sol |
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Feb 27 | More on cyclic Groups Homomorphisms |
2.4, 2.5 | 2.4: 4(b)(d), 8(b), 10, 16(d), 20, 262.5: 6, 12(e), 13, 22, 30, 38 |
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Mar 1 | Isomorphisms. Caylay's Theorem Review |
2.5 | |||

Week 6 | Mar 15 |
HW6 Sol |
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Mar 6 | Midterm |
2.6: 3, 4, 11, 13, 18, 19, 20, 23 |
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Mar 8 | Cosets and Lagrange's Theorem | 2.6 | |||

Week 7 | Mar 29 |
HW7 SolQuiz 2 Sol |
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Mar 13 | Dihedral Groups Groups of Motions (Reading) Normal Groups |
2.6, 2.7, 2.8 | 2.6: 26, 27, 29, 342.8: 2, 3, 7, 15, 17, 18 |
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Mar 15 | More on Normal Groups Simple Groups |
2.8 | |||

Week 8 | |||||

Mar 20 | Spring Break (no class) |
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Mar 22 | Spring Break (no class) |
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Week 9 | Apr 5 |
HW8 SolQuiz 3 Sol |
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Mar 27 | Factor Groups Isomorphism Theorems |
2.9, 2.10 | 2.9: 11, 16, 17, 19, 30, 312.10: 7, 8(d), 10, 20 |
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Mar 29 | More on Isomorphism Theorems Cauchy's Theorem |
8.1, 8.2 | |||

Week 10 | Apr 12 |
HW9 Sol |
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Apr 3 | Basic Properties of Rings | 3.1 | 3.1: 7, 22, 23, 25, 26, 36(b)3.2: 7, 14, 16, 18, 22, 29(a)(b)(c) |
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Apr 5 | Domains, Division Rings and Fields | 3.2 | |||

Week 11 | Apr 19 |
HW10 SolQuiz 4 Sol |
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Apr 10 | Field of Quotients Ideals. Factor Rings |
3.2, 3.3 | 3.3: 9(c), 17, 29, 333.4: 11, 12, 14, 21, 26, 40 |
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Apr 12 | Simple Rings. Ring Homomorphisms | 3.3, 3.4 | |||

Week 12 | Apr 26 |
HW11 SolQuiz 5 Sol |
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Apr 17 | More on Ring Homomorphisms | 3.4 |
4.1: 3, 4, 16(b), 17(a), 21, 364.2: 4, 5(c), 9, 10 |
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Apr 19 | Polynomials | 4.1 | |||

Week 13 | Not Due |
HW12 Sol |
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Apr 24 | Basic Properties of Polynomials | 4.1, 4.2 | 4.2:
13, 16, 18(e), 23(a), 244.3: 5(a), 6(b), 10(a), 13, 20 |
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Apr 26 | Factorization of Polynomials | 4.2 | |||

Week 14 | |||||

May 1 | Factors rings of Polynomials | 4.3 | |||

May 3 | Review |