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;
|
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. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | X | |
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
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 |
Semester Activities | Number | Weigthing |
Participation | ||
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 10 | 20 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
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 |
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
Study Hours Out of Class | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 10 | 3 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 2 | 15 | |
Final Exams | 1 | 30 | |
Total | 180 |
# | 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