### Announcements:

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.

## Lecture Schedule and Assignment (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 Jan 30 Preliminaries (Reading: 0.1, 0.2, Appendices A, B) 0.1-0.3 0.3: 9, 14, 16 0.4: 1(c)(d)(h), 3(d), 8, 9, 10 1.1: 1(e), 10(c)(d), 15, 18(b), 25 Feb 1 Equivalences Principle of Mathematical Induction 0.4, 1.1 Week 2 Feb 15 HW2 Sol Feb 6 Prime factorization. 1.2 1.2: 22, 33(a), 38, 39, 40, 43, 44 1.3: 4, 8(b), 18, 22(d) Feb 8 Integers Modulo n. 1.3 Week 3 Feb 22 HW3 Sol Quiz 1 Sol Feb 13 Permutations. 1.4 1.3: 31, 32 1.4: 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 Feb 20 Groups 2.2, 2.3 2.1: 6, 8, 12, 19 2.2: 10(b), 24, 25, 29(c) 2.3: 5, 13, 22, 23 Feb 22 Subgroups. Cyclic Groups 2.3, 2.4 Week 5 Mar 8 HW5 Sol Feb 27 More on cyclic Groups Homomorphisms 2.4, 2.5 2.4: 4(b)(d), 8(b), 10, 16(d), 20, 26 2.5: 6, 12(e), 13, 22, 30, 38 Mar 1 Isomorphisms. Caylay's Theorem Review 2.5 Week 6 Mar 15 HW6 Sol Mar 6 Midterm 2.6: 3, 4, 11, 13, 18, 19, 20, 23 Mar 8 Cosets and Lagrange's Theorem 2.6 Week 7 Mar 29 HW7 Sol Quiz 2 Sol Mar 13 Dihedral Groups Groups of Motions (Reading) Normal Groups 2.6, 2.7, 2.8 2.6: 26, 27, 29, 34 2.8: 2, 3, 7, 15, 17, 18 Mar 15 More on Normal Groups Simple Groups 2.8 Week 8 Mar 20 Spring Break (no class) Mar 22 Spring Break (no class) Week 9 Apr 5 HW8 Sol Quiz 3 Sol Mar 27 Factor Groups Isomorphism Theorems 2.9, 2.10 2.9: 11, 16, 17, 19, 30, 31 2.10: 7, 8(d), 10, 20 Mar 29 More on Isomorphism Theorems Cauchy's Theorem 8.1, 8.2 Week 10 Apr 12 HW9 Sol 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) Apr 5 Domains, Division Rings and Fields 3.2 Week 11 Apr 19 HW10 Sol Quiz 4 Sol Apr 10 Field of Quotients Ideals. Factor Rings 3.2, 3.3 3.3: 9(c), 17, 29, 33 3.4: 11, 12, 14, 21, 26, 40 Apr 12 Simple Rings. Ring Homomorphisms 3.3, 3.4 Week 12 Apr 26 HW11 Sol Quiz 5 Sol Apr 17 More on Ring Homomorphisms 3.4 4.1: 3, 4, 16(b), 17(a), 21, 36 4.2: 4, 5(c), 9, 10 Apr 19 Polynomials 4.1 Week 13 Not Due HW12 Sol Apr 24 Basic Properties of Polynomials 4.1, 4.2 4.2: 13, 16, 18(e), 23(a), 24 4.3: 5(a), 6(b), 10(a), 13, 20 Apr 26 Factorization of Polynomials 4.2 Week 14 May 1 Factors rings of Polynomials 4.3 May 3 Review