FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 460 | Course Introduction and Application Information

Course Name
Additional Topics in Algebra
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 460
Fall/Spring
3
0
3
6

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives To continue introducing additional topics of algebra, and to extend the basic structures introducted in abstract algebra course.
Learning Outcomes The students who succeeded in this course;
  • will be able to analyze algebraic structures.
  • will be able to introduce isomorphism theorems.
  • will be able to use important results to identify structures such as Sylow theorems, p-groups,simple groups,topological groups.
  • will be able to apply Gröbner basis techniques to multivariate polynomials.
  • will be able to apply group actions to counting problems.
Course Description The focus of the course will be the applications of abstract structures such as group actions, Sylow theorems, Gröbner bases, Galois theory, homology computations. This course is a complement of abstract algebra and enables students to understand abstract notions as solid structures.

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Recollections: Definitions of group, ring and field “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 11:305.
2 Advanced group theory “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 307:321.
3 Sylow theorems “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 321:327.
4 Applications of Sylow theorems “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 327:333.
5 Free groups and group presentations “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 333:354.
6 Group actions “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 154:161.
7 Applications of group actions: Counting “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 161:165.
8 Gröbner bases “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 254:264.
9 UFDs, EDs “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 389:413.
10 Automorphisms, isomorphisms “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 415:431.
11 Splitting fields, separable extensions “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 431:448.
12 Galois theory, illustrations, insolvability “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 448:475.
13 Homology groups “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 355:363.
14 Computations and applications “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841, 363:379.
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

“A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 2nd Edition, 1976. ISBN-13: 978-0201019841

Suggested Readings/Materials

“Abstract Algebra: A first course” by D. Saracino, Waveland, Waveland Pr Inc, 2nd Edition, 2008. ISBN-13: 978-1577665366

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
40
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
12
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
3
42
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
10
3
30
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
15
30
Final Exam
1
30
30
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

2

To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.

X
3

To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.

X
4

To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.

X
5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

6

To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.

7

To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.

8

To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.

9

To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.

10

To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.

X
11

To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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