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Modern Algebra I -- Fall 2011

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MTH 450 - 3 - Modern Algebra. Structure of the abstract mathematical systems: fields, rings, groups, with illustrations and applications from number theory. (PR: MTH 230 ; REC: MTH 300)

  • Time and Place: 5:00 - 6:15 pm TR at 513 Smith Hall.
  • Instructor: Peter Saveliev (call me Peter)
  • Office: 742D Smith Hall
  • Office Hours: MW 5:00 - 6:15, T 3:30 - 4:30, or by appointment
  • Office Phone: x4639
  • E-mail: saveliev@marshall.edu
  • Class Web-Page: math01.com
  • Prerequisites: the ability to understand and write proofs.
  • Text: Contemporary Abstract Algebra by Gallian
  • Goals: good familiarity with groups, ability to work in the definition-theorem-proof format, some "mathematical maturity".
  • Evaluation: 2 tests, final exam, weekly homework, quizzes.
  • Grade Breakdown:
    • homework + quizzes: 40%
    • 2 exams: 15% each
    • final exam: 30%
  • Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60

See also Course policy.

1 Chapter 0

Review Linear algebra: course

  • Lectures: Chapter 0
  • Practice exercises: 7,9-11,13,14,18-21,46-49
  • Problems to be submitted: 10,20

2 Chapter 1

  • Lectures: Chapter 1
  • Practice exercises: 1-6,14-17,22
  • Problems to be submitted: 16

3 Chapter 2

  • Lectures: Chapter 2
  • Practice exercises: 1-5,9,11,14,15,17,18,20
  • Problems to be submitted: 14,18
  • Practice exercises: 22-26,29,30,33-36
  • Problems to be submitted: For #16 Sec. 1, quantitatively describe a symmetry of the strip.

4 Chapter 3

  • Lectures: Chapter 3
  • Practice exercises: 1,2,4,6,7,10,14,16,17,19,21-23,29,30,31,33,35,45,46-49,52,53 10
  • Problems to be submitted:

5 Chapter 4

  • Lectures: Chapter 4
  • Practice exercises: 1,4-7,11-14,17-19,22,23,30-36 30
  • Problems to be submitted: 30 and 33

6 Test 1

7 Chapter 5

  • Lectures: Chapter 5
  • Practice exercises: 1-18 10
  • Problems to be submitted: in a finite group, |ab|=|ba|.
  • Practice exercises: 24-26,34,35,38-40,46,54,55 46
  • Problems to be submitted: 40 and 46

8 Chapter 6

  • Lectures: Chapter 6
  • Practice exercises: 1-7
  • Problems to be submitted: 4
  • Practice exercises: 10,22-25,27,28,30,37 10
  • Problems to be submitted:

9 Chapter 7

  • Lectures: Chapter 7
  • Practice exercises: 1-3,7,8,12-15,18-22 22
  • Problems to be submitted:
  • Practice exercises: 24-31,33,38 28
  • Problems to be submitted:

10 Chapter 8

  • Lectures: Chapter 8
  • Practice exercises: 1-17,23-26,31,32 32
  • Problems to be submitted:

11 Chapter 9

  • Lectures: Chapter 9
  • Practice exercises: 1-13,18,20,21 18
  • Problems to be submitted:
  • Practice exercises: 26,27,30-34,44-48,57,59 30
  • Problems to be submitted:

12 Chapter 10

  • Lectures: Chapter 10
  • Practice exercises: 5-19,24-27 24
  • Problems to be submitted:
  • Practice exercises: 34,35,37-39,44-46,52,53 44
  • Problems to be submitted:

13 Test 2

14 Chapter 11

  • Lectures: Chapter 11
  • Practice exercises: 1-17,21,24,25,28-31
  • Problems to be submitted:

15 Chapter 12

  • Lectures: Chapter 12
  • Practice exercises: 1-18,43-50
  • Problems to be submitted:

16 Final exam

Thursday, Dec. 8, 4:30-6:30 same room.

Sample: Group theory: final exam


The transcribed lectures will appear here: Group theory: course.