CoursePlan_221424_57.docx

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Zarqa University Instructor: Dr. Aliaa Burqan

Faculty of Science Lecture’s time: 1- 2 S, T, T

Department: Mathematics Semester: First

Course title: Abstract Algebra 1 Office Hours: 10 - 11 S, T, T

Course description:

This Course is devoted to study groups and subgroups, examples of groups, properties of group, important groups, normal subgroup, factor group, rings, ideals, integral domain, field and isomorphism.

Aims of the course:

Upon completion of this course, the student should be able to

1.

Understand definitions, examples, and theorems pertaining to groups and rings.

2.

Follow and to construct a formal mathematical proof using each of the following methods: a direct proof, a proof by contradiction and a proof by induction.

3.

Demonstrate an understanding of the relationship of abstract algebra to other branches of mathematics and to related fields.

4.

Independently explore related topics using resources other than the text

.

Intended Learning Outcomes: (ILOs)

A.

Knowledge and Understanding A1. Concepts and Theories:

1. Define and illustrate the concept of group, subgroup, order of group, order of element, cyclic group, center of group, normal subgroup, factor group.

2. Define and illustrate the concept of permutation group, cycle notation, disjoint cycles, even and odd permutation and Dihedral group.

3. Define and illustrate the concept of external direct product.

4. Define and illustrate the concept of homomorphism and isomorphism.

5. Define and illustrate the concept of ring, integral domain, field and ideal, A2. Contemporary Trends, Problems and Research:

1. Comprehend properties pertaining to groups and rings.

2. Comprehend the meaning of isomorphism.

A3. Professional Responsibility:

1. Reach to properties of groups(rings) via basic theorems in abstract algebra.

2. Prove some basic theorems in abstract algebra.

B.

Subject-specific skills B1. Problem solving skills:

1. Find and determine the most important properties of a group (ring) 2. Find the kernel and range of a homomorphism.

B2. Modeling and Design:

Computing the order, inverse and centralizer of an element by using the Cayley table.

B3. Application of Methods and Tools:

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C.

Critical-Thinking Skills C1.Analytic skills:

Reach to algebraic properties of a group(ring) by analyzing basic information about this group(ring).

C2.Strategic Thinking:

Reach to new results by combining different theorems.

C3. Creative thinking and innovation:

Constructing a proof of theorems.

D.

General and Transferable Skills (other skills relevant to employability and personal development) D1. Communication:

Effectively communicate in the field of mathematics by conducting discussions and participating in class, asking questions intended to encourage the exchange of ideas in class.

D2.Teamwork and Leadership:

Fostering an ability to work together in teams, engaging in group work, and to develop skills motivating others to accomplish goals.

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Course structures:

Week Credit

Hours ILOs Topics Teaching

Procedure

Assessment methods

1

11\10-15\10 3 ^{A1, B1}

Introduction, Definition and Examples of Groups

Lectures, cooperative learning and discussion

Homework's , Quiz and Exams

2

18\10-22\10 3 ^{A1, A2}

Properties of Groups

Lectures, cooperative

learning and discussion Homework's , Quiz and Exams

3

25\10-29\10 3 ^{A1, B1, B2}

Order, Subgroups

4

1\11-5\11 3 A1, B1, B2,

C1,C2

Center, Centralizers, Cyclic Groups

5

8\11-12\11 3 A1, A2, C1,

C2,C3

Cyclic Groups

6

15\11-19\11 3 A1, A2, A3,

B1,B2

Permutation Groups

7 22\11-26\11

3 ^{A1, A2, B1}

Even and Odd Permutations, Dihedral Group

8 29\11-3\12

3 A1, A3, C1,

C2, C3

Cosets and Lagrange's Theorem

9

6\12-10\12 3 A1, A2, B1,

B2

External Direct Products, Normal Subgroups

10

13\12-17\12 3 A1, A3, B1,

C2

Normal Subgroups and Factor Groups

11 20\12-24\12

3 A1, A2, B1,

C3

Group Homomorphism

12

27\12-31\12 3 ^{A1, A2, B1}

Introduction to Rings

13 3\1-7\1

3 A1, A2, B1,

C1

Integral Domains, Ideals and Factor Ring

14

10\1-14\1 3 A1, A2, B1

Ring Homomorphism

References:

A.

Main Textbook:

Contemporary Abstract Algebra, Joseph Gallian, 7

^th

Edition, BROOKS\COLE

B.

Supplementary Textbook(s):

A First Course in Abstract Algebra, John Fraleigh.

Assessment Methods:

Methods Grade Date

First Exam 25 15\11\2015

Second Exam 25 20\12\2015

Final Exam 50

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