Advanced Algebra I (110.401)

Spring 2017


[Course Syllabus]

[Lecture Schedule and Assignment]


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  

Midterm Solution

Final Exam Solution