Course Name
Code
Semester
Theory
(hour/week)
Application/Laboratory
(hour/week)
Local Credits
ECTS
Abstract Algebra
MATH 306
Spring
3
0
3
6

Prerequisites
None

Course Language
English
Course Type
Required
Course Level
First Cycle
Course Coordinator -
Course Lecturer(s)
Course Assistants
Course Objectives To provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics and to study of certain structures called groups, rings, fields and some related structures.
Course Learning Outcomes The students who succeeded in this course;
  • will be able to define algebraic structures.
  • will be able to construct substructures.
  • will be able to analyze a given structure in detail.
  • will be able to develop new structures based on given structures.
  • will be able to compare structures.
Course Content In this course, the basic pillars of modern mathematics will be introduced and analyzed. These structures include groups, rings, fields, any mapping between them and their substructures.

 

Week Subjects Related Preparation
1 Groups and subgroups, definitions, examples. “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 11:67.
2 Permutations, cosets “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 75:96.
3 Lagrange's theorem, products “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 96:114.
4 Homomorphisms “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 125:151.
5 Group actions “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 154:165.
6 Rings and fields “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 167:184.
7 Fermat's and Euler's theorems “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 184:197.
8 Factorization “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 198:220.
9 Ideals, factor rings “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 237:245.
10 Prime ideals, maximal ideals “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 245:254.
11 Gröbner bases “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 254:264.
12 Field extensions “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 265:282.
13 Algebraic extensions “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 283:293.
14 Finite fields “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley, 300:305.
15 Review
16 Review of the Semester  

 

Course Notes / Textbooks “A First Course in Abstract Algebra” by J.B. Fraleigh, Addison Wesley.
References “Abstract Algebra: A first course” by D. Saracino, Waveland.“Topics in Algebra” by I.N. Herstein, Wiley.“Algebra” by M. Artin, PrenticeHall.“Basic Abstract Algebra” by P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul, CUP.“Introduction to Abstract Algebra” by J.D.H. Smith, CRC.

 

Semester Requirements Number Percentage of Grade
Attendance/Participation
-
-
Laboratory
-
-
Application
-
-
Field Work
-
-
Special Course Internship (Work Placement)
-
-
Quizzes/Studio Critics
-
-
Homework Assignments
3
20
Presentation/Jury
-
-
Project
-
-
Seminar/Workshop
-
-
Midterms/Oral Exams
2
40
Final/Oral Exam
1
40
Total
6
100

PERCENTAGE OF SEMESTER WORK
5
60
PERCENTAGE OF FINAL WORK
1
40
Total 6 100

 

Course Category

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

 

#
 Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods,
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

 X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

 X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

 X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

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

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
16
3
48
Laboratory
-
-
-
Application
-
-
-
Special Course Internship (Work Placement)
-
-
-
Field Work
-
-
-
Study Hours Out of Class
15
1
15
Presentations / Seminar
-
-
-
Project
-
-
-
Homework Assignments
3
5
15
Quizzes
-
-
-
Midterms / Oral Exams
2
20
40
Final / Oral Exam
1
30
30
    Total Workload
148