# 0301341 - Faculty of Science

```University of Jordan
Faculty of Science
Department of Mathematics
Course Outline
Course code and name: 0331341 Abstract Algebra I
Credit hours: 3
Prerequisite: 0301211 Fundamentals of Mathematics
Course description and objectives:
Upon completion of this course, the student should be able to
1. Write mathematical proofs and reason abstractly in exploring
properties of groups and rings.
2. Define, construct examples of, and explore properties of groups,
including symmetry groups, permutation groups and cyclic groups.
3. Determine subgroups and factor groups of finite groups.
4. Determine, use and apply homomorphism's between groups.
5. Understand definitions, examples, and theorems pertaining to
groups.
Tests &amp; evaluations
exams and a final exam, using the scheme
Course contents and schedule
Topic
Introduction
Number of
lectures
1
Group Definition
Chapter 2: pp 40 - 48
2
Group Properties
Chapter 2: pp 48 – 51
1
HOMEWORK 1
Chapter 2: 1,3,5,8,12,14,15,17,18,19,26, 39
Order and Subgroups Chapter 3: pp 57 - 61
1
Centers&amp;Centralizers Chapter 3: pp 61- 64
2
1
HOMEWORK 2
Chapter 3: 1,2,4,6,7,8,9,10,12,18,20,23,26,27, 30,33,51,59
1
Cyclic Groups (1)
Chapter 4: pp 72 - 75
1
Cyclic Groups (2)
Chapter 4: pp 75-80
2
Chapter 4:
1,2,3,7,9,10,11,13,14,19,23,28,29,31,33,38,40,45,49,53,60,62,64
Permutation Groups (1) Chapter 5: pp 95 – 103
HOMEWORK 3
Even and Odd
1
2
Chapter 5: pp 103 - 112
1
Chapter 5: 1,2,3,4,6,7,8,9,12,17,18,23,24,27,28,32,34,42,44,45,48
1
Isomorphisms
Chapter 6 pp 122 - 126
2
Cayley's Theorem
Chapter 6: pp 126 – 133
1
HOMEWORK 5
Cosets
Chapter 6: 1,3,6,7,10,17,24,25
Chapter 7: pp 138 - 141
1
Chapter 7: pp 141 - 144
2
Chapter 7: 1,2,3,8,14,18,20,22,23
1
Chapter 8: pp 154 - 160
2
HOMEWORK 7
Chapter 8: 3,4,5,6,7,8,9,10,11,14,16,17,18,20,24,25,29,30,31,32
1
Normal Subgroups
Chapter 9: pp 178 - 181
2
Internal Direct Product Chapter 9: pp 181 – 184
1
HOMEWORK 4
Lagrange's Theorem
HOMEWORK 6
Direct Products
2
HOMEWORK 8
Homomorphisms
Chapter 9: 1,4,5,7,10,12,14,16,19,20,48
Chapter 10: pp 200 – 206
1
First Isomorphism
Theorem
Chapter 10: pp 206 – 211
1
Chapter 10: 9,11,15,21,24,31
1
Homework 9
Text book
Contemporary Abstract Algebra, J. Gallian (Houghton-Mifflin).
References
- Abstract Algebra, David S. Dummit and Richard M. Foote.
- Topics in Algebra, I. N. Herstein.
- Abstract Algebra: An Introduction, Thomas W. Hungerford.
- A first course in Abstract Algebra, Fraleigh
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