ECTS - Abstract Algebra
Abstract Algebra (MATH331) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Abstract Algebra | MATH331 | 5. Semester | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | The course is designed to provide necessary backgrounds in Abstract Algebra. In this course students will learn the general concepts of abstract algebra. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Groups: subgroups, cyclic groups, permutation groups, Lagrange Theorem, normal subgroups and factor groups, homomorphisms, isomorphism theorems, rings and fields: subrings, integral domains, ideals and factor rings, maximal and prime ideals, homomorphisms of rings,field of quotients, polynomial rings, principal ideal domain (PID), irreducibility of |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Introduction to Groups (Symmetries of a Square, The Dihedral Groups: pg 31-37) Groups: Definition of group and Abelian group, basic examples (42-49) | pp. 31-37, 42-49 |
| 2 | Elementary properties of Groups (uniquness of identity, cancellation, uniquness of inverse element, inverse of the product: 50-53) Finite groups; Subgroups: Order of a Group, order of an element, definition of subgroup and basic examples (59-66) | pp. 50-53, 59-66 |
| 3 | Cyclic Groups (73-82) Permutation groups (94-112) | pp. 73-82, 94-112 |
| 4 | Isomorphisms: Definition and examples,Cayley’s Theorem, Properties of Isomorphism (120-128 skip automorphisms but the definition) Cosets and the Lagrange Theorem: Definition, Properties of Cosets, Lagrange Theorem (137-141 up to Fermat’s Little Theorem) | pp. 120-128, 137-141 |
| 5 | External Direct Product: Definitions and Examples, Properties of Direct Product (153-157), Applications* Normal subgroups and Factor Groups (177-184), Internal Direct Products (187-190) | pp. 153-157, 177-184, 187-190 |
| 6 | Group Homomorphisms: Definitions, Examples, Properties of Homomorphisms, The First Isomorphism Theorem (199-207) Fundamental Theorem of Finite Abelian Groups (217-225) | pp. 199-207,217-225 |
| 7 | Rings: Definition of Ring and examples, properties of ring, Uniqueness of Unity and Inverses, Definition of subring, Subring test (235-240) | pp. 235-240 |
| 8 | Integral Domains: Definition of zero-divisors and integral domain with examples, Cancellation Theorem, Definition of Field, Finite Integral Domains are Field, Z_p is a field, (248-251) Ideals and Factor Rings: Definition, Ideal Test, Existance of Factor Rings, Examples (261-265) | pp. 248-251, 261-265 |
| 9 | Prime Ideals and Maximal Ideals (266-268) Ring Homomorphisms: Definitions with examples, properties of ring homomorphisms, First Isomorohism Theorem for Rings (278-284) | pp. 266-268, 278-284 |
| 10 | Field of Quotients(284-285) Polynomial Rings (291-294) The Division Algorithm and Consequences: Division Algorithm for F[x], The Remainder Theorem, The Factor Theorem (294-297) | pp. 284-285,291-294, 294-297 |
| 11 | Principal Ideal Domain (PID), F[x] is a PID (297-298) | pp. 297-298 |
| 12 | Factorization of Polynomials: Definition of Irreducible and reducible polynomials, Reducibility test for degrees 2 and 3, Content of a Polynomial, Primitive Polynomial, Gauss Lemma (303-306) Irreducibility Test: Mod p irreducibility test, Eisenstein’s Criterion (306-311) | pp. 303-306, 306-311 |
| 13 | Divisibility in Integral Domains:Irreducibles, Primes (320-323), Unique Factorization Domains (326-329), | pp. 326-329 |
| 14 | Euclidean Domains (329-333) | pp. 329-333 |
Sources
| Course Book | 1. Contemporary Abstract Algebra, by Joseph A. Gallian |
|---|---|
| Other Sources | 2. A First Course in Abstract Algebra, by John B. Fraleigh |
| 3. Fundamentals of Abstract Algebra, by D.S. Malik, John M. Morderson, M.K. Sen , McGraw-Hill |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 55 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 8 | 32 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 16 | 32 |
| Prepration of Final Exams/Final Jury | 1 | 22 | 22 |
| Total Workload | 142 | ||