Course Title: Groups Theory Course Code: MTH4223-3
Program: BSc. in Mathematics Department: Mathematics
College: Jamoum University College
Institution: Umm Al-Qura University
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Table of Contents
A. Course Identification ... 3
6. Mode of Instruction (mark all that apply) ... 3
B. Course Objectives and Learning Outcomes ... 3
1. Course Description ... 3
2. Course Main Objective ... 3
3. Course Learning Outcomes ... 4
C. Course Content ... 5
D. Teaching and Assessment ... 5
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods ... 5
2. Assessment Tasks for Students ... 6
E. Student Academic Counseling and Support ... 6
F. Learning Resources and Facilities ... 6
1.Learning Resources ... 7
2. Facilities Required ... 7
G. Course Quality Evaluation ... 8
H. Specification Approval Data ... 8
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A. Course Identification
1. Credit hours: 4 2. Course type
a. University College Department ✔ Others
b. Required Elective ✔
3. Level/year at which this course is offered: Level 8/ year 3 4. Pre-requisites for this course (if any):
Introduction to Group Theory MTH3221-4
5. Co-requisites for this course (if any):
6. Mode of Instruction (mark all that apply)
No Mode of Instruction Contact Hours Percentage
1 Traditional classroom Four hours/week %100
2 Blended 0 0
3 E-learning 0 0
4 Distance learning 0 0
5 Other 0 0
7. Contact Hours (based on academic semester)
No Activity Contact Hours
1 Lecture 30
2 Laboratory/Studio 0
3 Tutorial 0
4 Others (specify) 0
Total 30
B. Course Objectives and Learning Outcomes
1. Course Description
Group theory is an essential part of modern mathematics. This course is an advanced in group theory.
This is an advanced course of group theory which contains the following topics, as Revision of the concept of groups and group actions on sets, (Cayley’s Theorem as an application) and Burnside counting argument and Orbit Stabilizer Theorem as a consequence of group action. Sylow Theorems are an essential part of the course. Then composition series, nilpotent and solvable groups, free abelian groups and free groups, simplicity of the alternating group and the projective special linear group, and the fundamental theorem of finitely generated abelian groups. The course, will emphasize both the theory and the examples.
2. Course Main Objective
This course will provide a common mathematical foundation for students in all of the
programs, drawing upon the full range of undergraduate courses in mathematics. In addition, it will permit students to build upon and share knowledge already acquired while pointing out areas in which additional study may be needed. In addition, it will develop the communication skills and understanding of the process of doing mathematics necessary for graduate-level study.
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3. Course Learning Outcomes
CLOs Aligned
PLOs 1 Knowledge and Understanding: by the end of this course, the
student is expected to be able to
1.1 Identify groups, group actions and Sylow Theorems, nilpotent and solvable groups.
1.2 Identify different methods of recognize finitely generated abelian groups.
1.3 Present basic concepts and properties of simple groups.
1.4 State the basic rules of semidirect product of two groups 1.5 Describe Burnside counting argumentand its applications 1.6 Define direct and semidirect product of groups.
1.7 State and recognize simple, nilpotent, solvable groups.
2 Skills: by the end of this course, the student is expected to be able to 2.1 Compare between nilpotent and non-nilpotent groups.
2.2 Use methods of Burnside counting argument and its applications 2.3 Apply algebraic structures on projective PSL special linear groups and
their subgroups.
3 Values: by the end of this course, the student is expected to be able to
3.1 Prepare for success in disciplines which rely on simple group theory as part of mathematics, which is the key to understand most of
mathematical subjects. (An is a simple group for n not equal 4.) 3.2 Interpret free groups and free abelian groups.
3.3 Evaluate fundamental concepts of groups, cyclic groups, normal subgroups, and the interrelationship between group action of p-groups 3.4 Generalize mathematical concepts in problem-solving through Sylow
theorems of new material and modeling which are related to group theory.
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C. Course Content
No List of Topics Contact
Hours 1 Revision of the concept of groups and group actions on sets, Cayley’s
Theorem as application
4
2 Finite p-groups and Sylow’s Theorems 6
3 Simple Groups and Simplicity of An, PSL 4
4 Direct and Semidirect Product of groups and compositions series. 4
5 Free Abelian Groups and Free Groups 4
6 Fundamental Theorem of finitely generated Abelian groups 4
7 Finite Nilpotent and Soluble Groups 4
Total 30
D. Teaching and Assessment
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods
Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and Understanding
1.1
Identify groups, group actions and Sylow Theorems, nilpotent and solvable groups.
Lecture and Tutorials Exams, quizzes
1.2 Identify different methods of recognize finitely generated abelian groups.
Lecture and Tutorials Exams, quizzes 1.3 Present basic concepts and properties
of simple groups.
Lecture and Tutorials Exams, quizzes 1.4 State the basic rules of semidirect
product of two groups
1.5 Describe Burnside counting argument and its applications
Lecture and Tutorials Exams, quizzes 1.6 Define direct and semidirect product of
groups and composition series
Lecture and Tutorials Exams, quizzes 1.7 State and recognize simple, nilpotent,
solvable groups.
2.0 Skills
2.1 Compare between nilpotent and non- nilpotent groups.
Lecture and Individual or group work
Exams, quizzes 2.2 Use methods of Burnside counting Lecture and Individual Exams, quizzes
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Code Course Learning Outcomes Teaching Strategies Assessment Methods argument and its applications or group work
2.3 Apply algebraic structures on projective PSL special linear groups and their subgroups.
Lecture and Individual or group work
Exams, quizzes
3.0 Values
3.1 Prepare for success in disciplines which rely on simple group theory as part of mathematics, which is the key to understand most of mathematical subjects. (An is a simple group for n not equal 4.)
Lecture and Individual or group work
Exams, quizzes
3.2 Evaluate fundamental concepts of groups, cyclic groups, normal subgroups, and the interrelationship between group action of p-groups
Lecture and Individual or group work
Exams, quizzes
3.3 Evaluate fundamental concepts of groups, cyclic groups, normal subgroups, and the interrelationship between group action and permutation representation.
Lecture and Individual or group work
Exams, quizzes
3.4 Generalize mathematical concepts in problem-solving through Sylow theorems of new materials and modeling which are related to group theory.
Lecture and Individual or group work
Exams, quizzes
2. Assessment Tasks for Students
# Assessment task* Week Due Percentage of Total
Assessment Score
1 Midterm Exam 6th %25
2 Quizes and homeworks During semester %25
3 Final exam End of semester %50
*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)
E. Student Academic Counseling and Support
Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice:
All faculty members are required to be in their offices outside teaching hours. Each member allocates at least 4 hours per week to give academic advice to students and to better explain the concepts seen during the lectures.
Students are required to complete the homework problems. Students are welcome to work together on homework. However, each student must turn in his or her own assignments, and no copying from another student's work is permitted. Deadline extensions for homework will not be given. Students are encouraged to discuss with professor about homework problems.
F. Learning Resources and Facilities
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1.Learning Resources
Required Textbooks
1- A course in group theory by John S. Rose: Publisher:
Cambridge University Press Language: English Pages: 318 ISBN 10: 0521214092 ISBN 13: 9780521214094, Year (1978)
2- Abstract Algebra by D. Dummit and R. Foote; Publisher:
Wiley; 3 edition (July 14, 2003) Language: English ISBN-10:
0471433349 ISBN-13: 978-0471433347
3-Basic Abstract Algebra by: P. B. Bhattacharya, S. K. Jain, S. R.
Nagpaul, Cambridge University Press, Jum. II 21, 1415 AH - Mathematics - 487 pages ISBN: 0-521-46081-6 and 0-521-46629- 6
3- Algebra by Thomas W. Hungerford, Edition: 8th Publisher:
Springer Language: English Pages: 504 / 265 ISBN 10:
0387905189 ISBN 13: 9780387905181, Year:(2003) 4- A course in group theory by John F. Humphreys, publisher:
Oxford University Press Language: English Pages: 292 ISBN 10: 0198534590 ISBN 13: 9780198534594 Series: Oxford science publications Year (1996)
Essential References Materials
1- A First Course in Abstract Algebra, 7th Edition 7th edition, by John B. Fraleigh; Publisher: Pearson; 7 edition (November 16, 2002) ISBN-10: 0201763907: ISBN-13: 978-0201763904
2- Modern Algebra: An Introduction 6th Edition, by John R. Durbin;
Publisher: Wiley; 6 edition (December 31, 2008) ISBN-10: 0470384433 ISBN-13: 978-0470384435.
3 – Theory and Problems of Abstract Algebra by Frank Ayres and Lloyd R. Jaisingh, Schaum’s Outlines Series. Second Edition.
Electronic Materials
- (http://www.math.niu.edu/~beachy/abstract_algebra/study_guide/co ntents.html)
- https://en.wikipedia.org/wiki/group_theory - https://en.wikipedia.org/wiki/Algebraic_structure - http://mathworld.wolfram.com/GroupTheory.html http://mathworld.wolfram.com/topics/GroupTheory.html Other Learning
Materials None
2. Facilities Required
Item Resources
Accommodation
(Classrooms, laboratories, demonstration rooms/labs, etc.)
Large classrooms that can accommodate more than 30 students
Technology Resources
(AV, data show, Smart Board, software, etc.)
Data Show, Smart Board Other Resources
(Specify, e.g. if specific laboratory equipment is required, list requirements or
attach a list)
None
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G. Course Quality Evaluation
Evaluation
Areas/Issues Evaluators Evaluation Methods
Effectiveness of teaching and assessment
Students Direct
Quality of learning resources Students Direct Extent of achievement of
course learning outcomes
Faculty Member Direct
Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)
Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)
H. Specification Approval Data
Council / Committee Council of the Mathematics Department
Reference No.
Date
