Syllabus updated
Purpose of Course: The aim of the course is to introduce students to the basic abstract algebraic structures such as groups, rings and fields. Students will be expected to read the text and comprehend proofs, as well as to do problems involving both computations and proofs.
Credit hours: 4
Prerequisites: Grade of C or better
in Math 215 and Grade of C or better in Math 320.
Text: J. Gallian,
Contemporary Abstract Algebra, 5th edition.
Grading:
Hour Exams (2) 50%
Homework 10%
Final Exam 40%
Homework: Homework listed for each week is due on Friday of that week at the beginning of class. No late homework accepted. Several lowest grades will be dropped. Solutions to listed homework will be posted on the course homepage.
The listed homework does not cover all of the important topics of the course and it does not allow for enough practice. It is suggested that you do as many of the odd numbered problems as you can. Their solutions can be found in the back of the text book.
Academic Honesty: Students are expected to be thoroughly familiar with the University's policy on academic integrity. See page 56 of the 2001-2003 Undergraduate Catalog. The University has instituted serious penalties for academic dishonesty. We have encouraged you to work with your classmates on homework. Regarding homework, quizzes, hour exams, and the final examination: Copying work to be submitted for grade, or allowing your work to be submitted for grade to be copied, is considered academic dishonesty.
Students with Disabilities: It is University policy that students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS); phone number 312-413-2103.
Course Topics
A brief review of sets, mappings
and equivalence relations.
Properties of integers.
Groups: Subgroups, homomorphisms, cyclic
groups, permutations, matrix groups, cosets,
Lagrange's Theorem, normal subgroups and factor groups.
Rings: Integral domains, homomorphisms,
ideals, factor rings, polynomial rings, factorization of polynomials.
Fields: Finite extensions and their connection with polynomial rings,
construction of finite extensions, application to geometric constructibility problems.
Chapters 1-4, all pages
Chapter 5, p.93-108; Ch 6, p.118-125, p.129; Ch 7, p.134-140;
Chapter 8, p.150-156; Ch 9, p.172-179; Ch 10, p.194-205
Chapter 12, p.229-234; Ch 13, p.240-246; Ch 14, p.253-260;
Ch 15, p.270-277; Ch 16, p.283-290; Ch 17, p.295-305
Chapter 20, p.344-349; Ch 21, p.361-366
Chapter 23, p.384-388
Week Date
Pages
Problems and Comments
1
08/23 0: 3--7
23: 2, 6, 16
08/25 0: 7--14
24: 18
08/27 0: 14--23
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2
08/30 1: 31--37
24: 22, 48; 37: 10, 14
09/01 2: 42--50
09/03 2: 50--52
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3
09/06 **** holiday, no classes
*****
09/08 3:
58--60
09/10 3: 60--62
Homework #3 on Course Homepage
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4
09/13 3: 62--67
09/15 4: 73--75
09/17 4: 75--77
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5
09/20 4: 77--82
09/22 5: 93--98
09/24 5:
98--103
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6
09/27 5: 103--108
09/29 6:
118--122
10/01 6:
122--123
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7
10/04 6: 123--124
10/06 6:
124--125
10/08
TEST I
(covers Chapters 0--5 on syllabus)
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8
10/11 7: 134--138
10/13 8:
150--153
10/15 8:
154--156
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9
10/18 9: 172--174
10/20 9: 174--179
10/22 10: 194--197
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10 10/25
10: 198--205
10/27 12: 229--234
10/29 13: 240--243
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11 11/01
13: 244--246
11/03 14: 253--256
11/05 14: 257--260
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12 11/08
15: 270--277
11/10 16: 283--286
11/12 16: 286--290
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13 11/15
17: 295--300
11/17 17: 300--305
11/19
TEST II
(covers Chapters 6--15 on syllabus)
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14 11/22
20: 344--346
11/24 20: 346--349
11/26
**** holiday, no
classes *****
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15 11/29
21: 361--363
12/01 21: 363--366
12/03 23: 383--387
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16 12/ Final
Examination Monday 12/06/04 1PM--3PM BH308
The syllabus for the final examination is Chapters 0 --- 16 as
indicated above. Also see Commentary
for the Final Examination . You will have plenty
of written materials to draw on at this point. There will be 8 multiple
part questions on the final.
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Last updated December