MATH 4320 Introduction to Algebra
Spring 2009
Course Information
Introduction to abstract algebra and number theory.
Topics include group theory, group actions, rings, commutative rings,
polynomial rings, factorization, fields, and quotient fields, finite fields, Galois theory.
syllabus
Time: M W 1:25 p.m. - 2:15 p.m.
Classroom: MLT 224
Instructor: Seonhee Lim
E-mail:slim@math.cornell.edu email
Office: Malott 593
Office Hours: M 4:30 p.m. - 5:30 p.m. W 4:20 p.m. - 5:20 p.m., and by appointment.
Teaching assistant: Alexander Landraitis
E-mail:acl73@cornell.edu email
Office: Malott 218
Office Hours: TH 1:30 p.m. - 2:30 p.m. F 3:00 p.m. - 4:00 p.m., and by appointment.
Textbook: J. Rotman, A First Course in Abstract Algebra with Applications, 3rd edition (Chapter 1, 2, 3, 5)
Assignments
- Homework 1 : Section 1.3 #49, 51, 54, 55, 60, 67, Section 1.4 #73, 74 (due Jan. 26)
- Homework 2 : Section 1.5 #80, 87, 89, 92, 95, Section 2.1 #13, 17 Section 2.3 #36 (i)-(v) (due Feb. 2)
Extra (also due Feb. 2) : 72x is congruent to 27 modulo 39. Is there a solution x? Find all the solutions.
- Homework 3 : Section 2.2 # 27, 30, 34, Section 2.3 #36 (v)-(x), 39(ii), 43(ii), 44, 48, 49, (due Feb. 9)
- Homework 4 : Section 2.4 #52 (iv),(vi)-(xi), 53, 57, 60, 63, Section 2.5. 71, 72, 73, 75,
Extra: Show that any subgroup of a cyclic group is a cyclic group.
(due Feb. 16)
- Homework 5 : Section 2.5. #64. (v), (vii), (x), 67 (iii), 86, Section 2.6 #98, 100, 107, 108, 113 (due Feb. 23)
- Homework 6 : Section 2.6 : 2.111 (show it only for n=2), Section 2.7 2.114 (iii)-(xi), 2.116, 2.134, 2.136,
1. Show that S_n can be generated by two elements. 2. Show that the group A_n contains a subgroup isomorphic to S_{n-2}. (due Mar. 9)
- Homework 7 : Section 3.1 : 3.1(ii),(v),(vi), 3.7, 3.9, 3.10, 3.15, Section 3.2 : 3.17(iii),(v),(vi),(vii), 3.19, 3.20, 3.25, 3.27 (due Mar. 23)
- Homework 8 : Section 3.3: 3.29 (iii), (iv), (vii), 3.30, 3.35, 3.38, 3.39, (due Mar. 27)
- Homework 9 : Section 3.4 : 3.41 (vii)-(x), 3.43, 3.48, 3.52(i), 3.55 Section 3.5 :3.72, 3.75, 3.76 (due Apr. 3)
- Homework 10 : Section 3.5 : 3.69, Section 3.6 : 3.82 (ii), (v), Section 3.7 : 3.88, 3.91 (due Apr. 10)
- Homework 11 : Section 3.7 : 3.87 (vii), (viii), Section 3.8 : 3.93, 3.100, 3.104 (due Apr. 17)
- Homework 12 : Section 3.8 : 3.92 (ix) (Give a counterexample.) (xi) (Write the polynomial you are using to construct such a field.) 3.97, 3.98, 3.103, Section 7.1 : 7.2, 7.7, 7.16 (due Apr. 24)
- Homework 13 : Section 5.2 : 5.15 (ii), (iii), 5.22 (iii),(iv), 5.23 (due May. 1)
Exams
- First prelim : February 27th, 2009 (Friday) 1:25pm-2:15pm, in class.
(materials covered : Section 1.3-1.5, 2.2-2.7)
- Second prelim : Take home exam April 3rd - April 17th (on Chapter 2-3).
- Final exam : May 15th, 2009 (Friday) 2pm-4:30pm at MLT 253 (on Chapter 2, 3 and 7.1).
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