Math 31: Topics in Algebra

Fall 2013



Note: Problems marked by a * are optional and do not need to be handed in with the assigned problems. These problems will tend to be (a bit) harder than the average HW problem. If you solve one, write it and let me know so we can talk about it, they are fun to discuss!


Week 1 Class Topic Reading For Homework From
9/16 Set Theory and Induction Section 0 0.1, 0.4, 0.5, 0.7, 0.8, 0.22*
9/17 (x-hour) Proof Writing & (Basic) Number Theory - Handout
9/18 Binary Operations; Introduction to Groups Section 1 1.1a, 1.3(a,c,g), 1.6a
9/20 Groups (Con't) Section 2 2.1(a,c,f,h), 2.3, 2.8
(Solutions)

Week 2
9/23 Fundamental Group Theorems Section 3 3.1,6,9,10,14,17*
9/25 Powers of an Element Section 4 (Through Thm 4.4) 4.3,6,20,22,24
9/27 Cyclic Groups Section 4 (Remainder) 4.9,10,13,16,17,22,25*
(Solutions)

Week 3
9/30 Subgroups Section 5 (up to p.48) 5.1(e,h,i),5,14,16,23,24
10/1 (x-hour) Cyclic Groups and Subgroups Rest of Section 5 5.4,6,7,8,19
10/2 Cyclic Groups and Subgroups; Functions Section 7 6.1(a,b),3,5; 7.4,7
10/4 Bijective Functions; The Symmetric Groups Section 8 to p71 7.9, 7.11
(Solutions)

Week 4
10/7 Symmetric Groups: The Alternating Group Section 8: p66-71 8.1a, 4, 8, 10
10/8 (x-hour) Symmetric Groups 8.2,3,6,13
10/9 Symmetric Groups: Dihedral Groups Section 8: p71-76 8.15, 17
10/11 Cosets Section 9 9.5a,18
(Solutions)

Week 5
10/14 Counting and Lagrange's Theorem Section 10 (to p. 92) 10.3,6,11,13,15
10/15 Exam #1 (6-10PM) -- --
10/16 Counting and Lagrange's Theorem (Con't) Section 10 (to p. 92) 10.5,8,22*
10/18 Normal Subgroups - 11.3,4,8
(Solutions)

Week 6
10/21 Normal Subgroups Section 11 11.15, 16, 17, 20
10/23 Normal Subgroups and Quotient Groups 11.22,23,29
10/25 Homomorphisms & Isomorphism Section 12 12.2, 4(b,g), 5,14
(Solutions)

Week 7
10/28 Homomorphisms & Isomorphisms Section 12 12.4(c,e,f),7,13,15,
10/29 (x-hour) Homomorphisms & Isomorphisms (Con't) Section 12 12.20,22,36(see ex. 27)
10/30 Fundamental Theorem on Group Homomorphisms Section 13 13.2,4,8,10
11/1 Fundamental Theorem on Group Homomorphisms Section 13 13.15,16,19,20
(Solutions)

Week 8
11/4 Fundamental Theorem on Finite Ablelian Groups Section 14 14.1a,e, 4
11/5 Exam #2 (6-10PM) -- --
11/6 No Class - -
11/8 Fundamental Theorem on Finite Ablelian Groups Section 14 14.2,6,7,12
(Solutions)

Week 9
11/11 Rings Section 16 16.1, 2(a,c),3,18
11/13 Subrings - 16.14,15,24,30
11/15 Ideals and Quotient Rings Section 17 (skip thm 17.5,6,8) 17.1(a,c),5,11,18,27,33
(Solutions)

Week 10
11/18
Final Exam
11/26 Final Exam (8-11AM) -- --