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Professor Alexandru I. Suciu
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MATH 3175 · Group Theory
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Fall 2010
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 Course Information
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Course
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MATH 3175 · Group Theory:
Sec. 1, CRN 14982 and Sec. 2, CRN 15767
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Instructor
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Alex Suciu
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Course Web Site
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www.math.neu.edu/~suciu/MATH3175/ugroup.fa10.html
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Time and Place
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Section 1: Mon, Wed, Th 10:30am-11:35am, in 247 Ryder Hall
Section 2: Mon, Wed, Th 9:15am-10:20am, in 427 Ryder Hall
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Office
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441 LA – Lake Hall
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Phone
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(617) 373-4456
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Email
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a.suciu@neu.edu
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Office Hours
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Mon, Wed 4:30-5:30pm in 441LA, or by appointment
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Teaching Assistant
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Yinbang Lin.
Email: lin.yinb@husky.neu.edu
Phone: x-7055.
Office hours:
Tue 10:00-11:00am, in 551NI, or by appointment.
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Prerequisites:
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MATH 2331 Linear Algebra
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Textbook
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Contemporary Abstract Algebra, 7th Edition,
by Joseph A. Gallian, Brooks/Cole, 2010. ISBN: 0547165099
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Course Description
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The course introduces some of the basic ideas and applications
of group theory. We will study various classes of group (such as
symmetry groups, abelian, cyclic, and permutation groups), and
also subgroups, normal subgroups, cosets, the Lagrange theorem,
group homomorphisms, quotient groups, direct products, group actions
on a set, and the Sylow theorems. The theory will be illustrated
by examples from geometry, linear algebra, number theory, crystallography,
and combinatorics. Further topics will be covered as time permits.
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Grade
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Based on quizzes (40%), midterm exam (20%), and final exam (40%).
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Class Materials
Homework assignments
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Chapter
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Topic
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Pages
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Problems
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0
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Preliminaries
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21–24
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1, 2, 4, 7, 8, 9, 11, 14, 20, 21, 22, 53, 54
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2
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Definition and Examples of Groups
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52
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1, 2, 3, 4, 5, 6, 7, 8
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Elementary Properties of Groups
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52–54
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9, 14, 15, 16, 20, 23, 25, 32, 34
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3
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Finite Groups; Subgroups
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64–67
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1, 2, 3, 10, 12, 18, 19, 20, 23, 26, 30
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Finite Groups; Subgroups
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67–69
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36, 37, 38, 39, 46, 47, 48, 51, 59, 60
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4
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Properties of Cyclic Groups
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81–83
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1–10, 14, 21, 26, 28
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Classification of Sugroups of Cyclic Groups
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83–85
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36, 37, 38, 39, 46, 47, 48, 51, 59, 60
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Cyclic Groups & Supplementary Exercises
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91–93
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1, 2, 3, 9, 18, 22, 23, 34
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5
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Permutation Groups
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113–115
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1–9, 17, 18, 23, 24, 25
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Permutation Groups
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115–117
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27, 28, 31, 33, 43, 58, 59
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6
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Isomorphisms
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133–135
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1–10, 14, 24, 25
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Isomorphisms
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135
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27, 28, 29, 31, 35, 39, 40
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7
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Cosets and Lagrange's Theorem
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149–150
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1–9, 13, 14, 16, 18, 25, 26
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Cosets and Lagrange's Theorem
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150–152
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27, 34, 35, 38, 39, 45, 46, 49
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8
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External Direct Products
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167–170
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1–13, 16 18, 20, 22, 24, 26, 27, 44, 45, 53, 59, 63
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Supplementary Exercises
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174–176
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5, 10, 13, 14, 25, 26, 35
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11
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Fundamental Theorem of Finite Abelian Groups
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226–228
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1, 3, 4, 5, 7, 13, 15, 17, 19, 21
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9
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Normal Subgroups
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193
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1, 2, 3, 4, 5, 6, 8
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Factor Groups
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193–194
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10, 14, 16, 17, 18, 27, 28, 29, 30, 32, 34,
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Factor Groups
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195–197
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37, 38, 40, 45, 46, 49, 50, 51, 53, 54, 65, 66, 68
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10
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Homomorphisms, Kernels, and Images
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211–213
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5, 7–27, 54, 55, 62
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Handouts
Quizzes
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