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The University of Jordan
Accreditation & Quality Assurance Center
COURSE Syllabus
Course Name: Abstract Algebra I
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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1 Course title Abstract Algebra I
2 Course number (0301341)
3 Credit hours (theory, practical) 3
Contact hours (theory, practical) 3
4 Prerequisites/corequisites (0301211)
5 Program title B.Sc.
6 Program code
7 Awarding institution The University of Jordan
8 Faculty Science
9 Department Mathematics
10 Level of course Obligatory Specialization requirement
11 Year of study and semester (s) 3rd year, 1st and 2nd semester
12 Final Qualification B.Sc. in Mathematics
13 Other department (s) involved in teaching the course
None
14 Language of Instruction English
15 Date of production/revision 13.11.2017
16. Course Coordinator:
Dr. Manal Ghanem
17. Other instructors:
18. Course Description:
Groups and subgroups; cyclic groups; permutation groups; isomorphism’s of groups; direct product of groups; cosets, and
Lagrange 's theorem; normal subgroups and factor groups; homomorphisms of groups; the first isomorphism theorems
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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19. Course aims and outcomes:
A- Aims:
1. Write mathematical proofs and reason abstractly in exploring properties of groups.
2. Define, construct examples of, and explore properties of groups, including symmetry groups, permutation groups
and cyclic groups.
3. Determine subgroups, subgroups and factor groups of finite groups.
4. Determine, use and apply homomorphisms between groups.
B- Intended Learning Outcomes (ILOs): Successful completion of the course should lead to the following outcomes:
A. Knowledge and Understanding Skills: Student is expected to
A1) Express and solve problems using the axiom of various algebraic structures.
A2) Describe groups, subgroups and give standard examples.
A3) Determine normal subgroups and factor groups of finite groups.
A4) Describe and explain the properties of mappings including the concept of homomorphisms.
A5) Discuss applications of algebra to other fields of study.
B. Intellectual Analytical and Cognitive Skills: Student is expected to
B1) Become more comfortable with abstract mathematics, and to see both the aesthetic appeal and the practicality of
seeking abstraction;
B2) Makeconjectures, construct logical arguments, and find and correct mistakes in his own and others' mathematical
work.
B3) Read, write and talk about mathematical arguments.
C. Subject- Specific Skills: Student is expected to
C1) Construct groups, subgroups and find homomorphisms between them.
C2) Apply famous theorems in group theory such as Caylay's theorem and Lagrange’s Theorem.
D. Creativity /Transferable Key Skills/Evaluation: Student is expected to
D1) Writing mathematical proofs.
D2) Using mathematical reasoning.
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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20. Topic Outline and Schedule:
Topic Week Instructor Achieved
ILOs
Evaluation
Methods Reference
Group Definition
Chapter 2: pp 40 - 48
1 A1, A2 Exams
Group Properties
Chapter 2: pp 48 – 51
1 A1, A2
Exams
HOMEWORK 1
Chapter 2:
1,3,5,8,12,14,15,17,18,23,25,26,29,30,32,36,37
2 A1, D1, D2
Exams
Order and Subgroups
Chapter 3: pp 56 - 61
2 A2
Exams
Centers & Centralizers
Chapter 3: pp 61- 64
3 A2 Exams
HOMEWORK 2
Chapter 3:
1,2,4,5,6,9,10,12,15,17,21,22,25,27,28,29,35,44,48,50,
51,52
3 A1, D1, B1, D2
Exams
Cyclic Groups (1)
Chapter 4: pp 71 - 75
4 A2 Exams
Cyclic Groups (2)
Chapter 4: pp 75-78
4 A2 Exams
HOMEWORK 3
Chapter 4:
1,2,7,10,11,13,15,16,19,23,27,28,29,35,38,39,47,51,52,
54,56,57,59,61
5 A1, B1, D1, D2
Exams
Permutation Groups (1)
Chapter 5: pp 90 – 99
6 A2, C1 Exams
Even and Odd
Chapter 5: pp 100 - 107
6 A2, B2 Exams
HOMEWORK 4
Chapter 5:
1,2,3,4,6,7,8,14,17,18,19,20,22,24,26,27,32,36,42,45,5
2
7 A1, D2, Exams
Isomorphisms
Chapter 6 pp 115 - 119
8 A4, C1 Exams
Cayley's Theorem
Chapter 6: pp 119 – 122
8 C2 Exams
HOMEWORK 5
Chapter 6: 1,3,7,10,13,15,17,24,25,33
9 A1, B1, D1, D2
Exams
Cosets
Chapter 7: pp 132 - 135
10 A2 Exams
Lagrange's Theorem
Chapter 7: pp 135 - 138
10 C2, A5 Exams
HOMEWORK 6
Chapter 7: 1,14,15,17,18,19,21,22,23,24,25,26,34,37
11 A1, B1, D1, D2
Exams
Direct Products
Chapter 8: pp 149 - 161
12 A2, C1 Exams
HOMEWORK 7
Chapter 8: 1,2,3,5,6,7,8,9,10,11,15,16,17,26,37
12 A1, B1, B2, D2
Exams
Normal Subgroups
Chapter 9: pp 171 - 181
13 A3, C1 Exams
Internal Direct Product
Chapter 9: pp 181 – 184
13 A2, C1 Exams
HOMEWORK 8 14 A1,B1,B2 Exams
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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Chapter 9:
1,4,10,15,16,20,30,32,36,40,43,44,45,50,51,56,57, , D2
Homomorphisms
Chapter 10: pp 192 – 198
15 A4, C1 Exams
HOMEWORK 9
Chapter 10: 7,9,10,12,14,15,19,22,27
15 A1, B1, B2, B3, D1, D2
Exams
21. Teaching Methods and Assignments:
Development of ILOs is promoted through the following teaching and learning methods: In order to succeed in this course, each student needs to be an active participant in learning – both in class and out of class.
- Class time will be spent on lecture as well as discussion of homework problems and some group work.
- To actively participate in class, you need to prepare by reading the textbook and doing all assigned homework
before class (homework will be assigned each class period, to be discussed the following period).
- You should be prepared to discuss your homework (including presenting your solutions to the class) at each class
meeting - your class participation grade will be determined by your participation in this.
- You are encouraged to work together with other students and to ask questions and seek help from the professor,
both in and out of class.
- You are encouraged to visit the webpage: http://www.d.umn.edu/~jgallian/
for more practicing, and problem solving.
22. Evaluation Methods and Course Requirements:
Opportunities to demonstrate achievement of the ILOs are provided through the following assessment methods and requirements:
ILO/s Learning Methods Evaluation Methods Related ILO/s to the program
A1,
A2,A3,A4,A5 Lectures Exams
A4, A6, C2, D1
B1,B2,B3
C1, C2, D1,
D2, D3
23. Course Policies:
1. The student is not allowed to take the course and its pre-requisite in the same time.
2. Attendance is absolutely essential to succeed in this course. You are expected to attend every class; please notify your
instructor if you know you are going to be absent. All exams must be taken at the scheduled time. Exceptions will be
made only in extreme circumstances, by prior arrangement with the instructor.
3. If a student is absent for more than 10% of lectures without an excuse of sickness or due to other insurmountable
difficulty, then he/she shall be barred from the final examination also he/she will get a failing grade in this course.
4. Medical certificates shall be given to the University Physician to be authorized by him. They should be presented to the
Dean of the Faculty within two weeks of the student’s ceasing to attend classes.
5. Test papers shall be returned to students after correction. His/her mark is considered final after a lapse of one week
following their return.
6. Solutions for the exams questions and marks will be announced at the webpage of the instructor:
http://eacademic.ju.edu.jo/m.ghanem/default.aspx
7. Cheating is prohibited. The University of Jordan regulations on cheating will be applied to any student who cheats in
exams or on homeworks.
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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24. Required equipment:
Data Shows
25. References:
A- Required book (s), assigned reading and audio-visuals:
J. Gallian Contemporary Abstract Algebra, (Houghton-Mifflin).
B- Recommended books, materials, and media:
- David S. Dummit and Richard M. Foote. Abstract Algebra,
- I. N. Herstein Topics in Algebra,.
- Thomas W. Hungerford Abstract Algebra: An Introduction,.
- J. Fraleigh A first course in Abstract Algebra,
26. Additional information:
Name of Course Coordinator: Dr. Manal Ghanem Signature: ------------------------- Date: 13/11/2017
Head of curriculum committee/Department: Signature: ---------------------------------
Head of Department: Dr. Baha AlZalq Signature: ---------------------------------
Head of curriculum committee/Faculty: Signature: ---------------------------------
Dean: Signature: ---------------------------------
Copy to: Head of Department
Assistant Dean for Quality Assurance Course File
The University of Jordan Course Syllabus Accreditation and Quality Assurance Center
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