| Course Name: | ABSTRACT ALGEBRA II |
| Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
| MATH 302 | 2 | 6 | 3 | - | 3 | 5 |
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| Name of Lecturer(s)-Academic Title: | Sanhan Khasraw - |
| Teaching Assistant: | - |
| Course Language: | English |
| Course Type: | Main |
| Office Hours | 13:30-14:30, Wednesday |
| Contact Email: | [email protected]
Tel:xxx
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| Teacher's academic profile: | PhD in Mathematics, 2015, University of Birmingham, United Kingdom.
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| Course Objectives: | Abstract algebra is often a student’s first exposure to the world of pure mathematics. While this course has many applications, abstract algebra is mainly a study of mathematical structure. Thus, you will need to orient yourself to look for mathematical patterns that arise simply from the definitions of the objects that we will be studying. This is a level of abstraction that will be new to most of you, and you need to be aware coming into this year that it will be a different way of thinking than you are used to. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures |
| Course Description (Course overview): | introduction to ring theory, ideals, ring homeomorphisms, divisibility, polynomial rings, Modules, Projective and injective modules, fields, field extensions, algebraic extensions, field of rational functions, Integral domains and field, Kronecker's theorem, finite fields. |
COURSE CONTENT| Week | Hour | Date | Topic | | 1 |
3 |
3-7/2/2019 |
Normal subgroups and quotient groups. | | 2 |
3 |
10-14/2/2019 |
Commutator subgroups and homomorphisms |
| | 3 |
3 |
17-21/2/2019 |
Kernel of a homomorphism and isomorphic groups. | | 4 |
3 |
24-28/2/2019 |
Isomorphism theorems. |
| | 5 |
3 |
3-7/3/2019 |
p-groups and Cauchy theorem. | | 6 |
3 |
26-28/3/2019 |
Sylow subgroups. |
| | 7 |
3 |
31/3-4/4/2019 |
Simple groups, examples | | 8 |
3 |
7-11/4/2019 |
Sylow subgroups. |
| | 9 |
3 |
14-18/4/2019 |
Midterm Exam | | 10 |
3 |
21-25/4/2019 |
Divisors of zero and integral domain. |
| | 11 |
3 |
28/4-2/5/2019 |
Subrings, characteristics of the rings and center of rings. | | 12 |
3 |
5-9/5/2019 |
Homomorphisms, Kernel and isomorphic rings. |
| | 13 |
3 |
12-16/5/2019 |
Ideals and quotient rings. | | 14 |
3 |
19-23/5/2019 |
Maximal and prime ideals and Principal ideal rings. |
| | 15 |
3 |
26-30/5/2019 |
Isomorphism theorems, division rings and fields | | 16 |
3 |
9-13/6/2019 |
Final Exam |
| | 17 |
3 |
16-20/6/2019 |
Final Exam |
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COURSE/STUDENT LEARNING OUTCOMES | | | 1 | To develop understanding of algebraic structures as abstractions of more familiar number systems. | | 2 | To acquire ability to work with concepts of groups, rings, and fields. | | 3 | To develop the deeper understanding of algebra needed to teach high school algebra. | | 4 | To develop awareness and appreciation of formal axiomatic systems and their applications. |
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COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
(Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | P | | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | | | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | A | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | P | | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | | | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | | | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
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| Prerequisites (Course Reading List and References): | Calculus, Linear Algebra and Foundation of Mathematics.
1. An introduction to modern abstract algebra, David M. Burton(1967) |
| Student's obligation (Special Requirements): | 1. Students have an obligation to arrive on time and remain in the classroom for the duration of scheduled classes and activities. 2. Students have an obligation to write, homeworks, tests and final examinations at the times scheduled by the teacher or the College. Students have an obligation to inform themselves of, and respect, College examination procedures. 3. Students have an obligation to show respectful behaviour and appropriate classroom deportment. Should a student be disruptive and/or disrespectful, the teacher has the right to exclude the disruptive student from learning activities (classes) and may refer the case to the Director of Student Services under the Student Code of Conduct. 4. Electronic/communication devices (including cell phones, mp3 players, etc.) have the effect of disturbing the teacher and other students. All these devices must be turned off and put away. Students who do not observe these rules will be asked to leave the classroom. |
| Course Book/Textbook: | An introduction to modern abstract algebra, David M. Burton(1967) |
| Other Course Materials/References: | 1- A First Course in Abstract Algebra, Fraleigh, 1982.
2- Topics in Algebra, Herstein, 1975. Abstract Algebra, Dummit and Foote, 2004. |
| Teaching Methods (Forms of Teaching): | Lectures, Excersises, Presentation, Assignments |
COURSE EVALUATION CRITERIA
| Method | Quantity |
Percentage (%) | | Attendance | 1 | 5 | | Participation | 1 | 5 | | Quiz | 2 | 5 | | Homework | 2 | 5 | | Midterm Exam(s) | 1 | 30 | | Final Exam | 1 | 40 |
| Total | 100 |
Examinations: Essay Questions, Multiple Choices, Short Answers |
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Extra Notes:
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ECTS (ALLOCATED BASED ON STUDENT) WORKLOAD| Activities | Quantity | Duration (Hour) | Total Work Load | | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | | | 0 | | Hours for off-the-classroom study | | | 0 | | Study hours for the Midterm Exam | | | 0 | | Study hours for the Final Exam | | | 0 | | Other | | | 0 | | ECTS | | | 0 | | | | 0 | | | | 0 | | Total Workload | 0 | | ECTS Credit (Total workload/25) | 0 |
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