Course Description form
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Course Title
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English Code/No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Abstract Algebra I
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Math 342
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ر 342
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3
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-
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-
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3
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Pre-requisites
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Math 241 & Math 251
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Brief contents, to be posted in university site and documents(4-5 lines):
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Groups and Subgroups: Definition of Groups, groupoids, semigroups and monoids-Elementary Properties of Groups -Permutation groups – Subgroups –Cosets - Lagrange’s Theorem - Homomorphism’s and Quotient Groups - Homomorphism of Groups -Normal Subgroup - Quotient Groups – Isomorphism - Cayley’s Theorem - Isomorphism Theorems - Introduction to Rings - Definition of Rings and Examples – Fields –Subrings - Rings of Polynomials -Rings of Matrices -Rings of Quaternion -Rings of Power Series -Homomorphism between Rings.
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Faculties and departments requiring this course (if any): Faculty of Science/
Department of Mathematics.
Objectives:
1- To introduce the basic concepts of abstract algebra.
2- To develop the students abstract and logical thinking capabilities.
3- To develop the students mathematical ability to handle proofs.
Contents:
I- Groups and Subgroups
· Binary Operations
· Definition of Groups and Examples
· Definitions of groupoids, semigroups and monoids.
· Elementary Properties of Groups
· Group of Integers Modulo n
· Permutation groups
· Subgroups
· Cosets
· Lagrange’s Theorem
II- Homomorphism’s and Quotient Groups
· Homomorphism of Groups
· Normal Subgroup
· Quotient Groups
· Isomorphism
· Cayley’s Theorem
· Isomorphism Theorems
III- Introduction to Rings
· Definition of Rings and Examples
· Fields
· Subrings
· Rings of Polynomials
· Rings of Matrices
· Rings of Quaternion
· Rings of Power Series
· Homomorphism between Rings.
Course Outcomes:
A- Knowledge:
(Specific facts and knowledge of concepts, theories, formula etc.)
On completion of this course, Students should be able to work through abstract notions and handle easily the abstract proofs which enable them from working in the second course in abstract algebra easily.
B-Cognitive Skills:
(Thinking, problem solving )
1- The students acquire the ability to recognize the algebraic structure axioms.
2- The students should be recognize that abstract algebra is not a conceptually well-defined body of material, but a conventional name that refers roughly to one of the several lists of things that mathematicians need to know to be competent, effective and sensible. It is a core subject of theoretical mathematics that studies important algebraic structures, such as groups, rings, fields and so on….
C- Interpersonal skills and responsibilities:
1. Questioning during lecture.
2. Submitting assignments.
3. Group discussions.
4. Recognizing the importance of the team work.
D- Analysis and communication:
(communication, mathematical and IT skills)
Abstract algebra highlights the importance of theoretical mathematics. This course helps the students to understand that It is a core subject of theoretical mathematics that studies important algebraic structures, such as groups, rings, fields and so on…. Which have important applications in many fields such as communication theory, electrical engineering and computer science.
Assessment methods for the above elements: Discussions, Homework,
Periodic tests and final test
Text book:
A First Course In Abstract Algebra, 7th ed.
Author: John B. Fraleigh
Publisher: Addison-Wesley Publishing Co.
Supplementary references
Modern Algebra: An Introduction, 4th ed.
Author: John R. Durbin
Publisher: John Wiley & Sons, Inc.