| School/Faculty/Institute |
Faculty of Education |
| Course Code |
MATH 333 |
| Course Title in English |
Abstract Algebra |
| Course Title in Turkish |
Abstract Algebra |
| Language of Instruction |
EN |
| Type of Course |
Lecture |
| Level of Course |
Select |
| Semester |
Spring |
| Contact Hours per Week |
| Lecture: 2 |
Recitation: |
Lab: 1 |
Other: |
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| Estimated Student Workload |
136 hours per semester |
| Number of Credits |
5 ECTS |
| Grading Mode |
Standard Letter Grade
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| Pre-requisites |
MATH 139 - Introduction to Discrete Mathematics
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| Co-requisites |
None |
| Expected Prior Knowledge |
Introduction to Discrete Mathematics |
| Registration Restrictions |
Only Undergraduate Students |
| Overall Educational Objective |
To produce features of mathematical information and to identify the basic structure of the mathematical information and procedure. |
| Course Description |
Abstract Algebra: Definition of a group, subgroups, permutation groups, homomorphism, cyclic groups, cosets, normal subgroups, quotient groups, definition of a ring, subrings, ideals.
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Course Learning Outcomes and Competences
Upon successful completion of the course, the learner is expected to be able to:
1) exhibit improved reading, writing, and questioning skills in Abstract Algebra;
2) utilize defining, hypothesizing, generalizing, proving, manipulating, and computing processes relevant to Abstract Algebra;
3) use inductive and deductive reasoning skills necessary for their educational profession;
4) demonstrate relational understanding of abstract algebra by knowing the purpose of abstract algebra and why abstract algebra works;
5) appreciate abstract algebra as a coherent body of knowledge and as a human accomplishment.
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| Program Learning Outcomes/Course Learning Outcomes |
1 |
2 |
3 |
4 |
5 |
| 1) Has a broad understanding of economics with a deep exposure to other social sciences and mathematics. |
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| 2) Demonstrates knowledge and skills in understanding the interactions of different areas of economics. |
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| 3) Displays a sound comprehension of microeconomic and macroeconomic theory. |
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| 4) Applies economic concepts to solve complex problems and enhance decision-making capability. |
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| 5) Uses quantitative techniques to analyze different economic systems. |
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| 6) Applies theoretical knowledge to analyze issues regarding Turkish and global economies. |
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| 7) Demonstrates proficiency in statistical tools and mainstream software programs to process and evaluate economic data. |
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| 8) Behaves according to scientific and ethical values at all stages of economic analysis: data collection, interpretation and dissemination of findings. |
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| 9) Uses written and spoken English effectively (at least CEFR B2 level) to exchange scientific information. |
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| 10) Exhibits individual and professional ethical behavior and social responsibility. |
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| 11) Displays learning skills necessary for further study with a high degree of autonomy |
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Relation to Program Outcomes and Competences
| N None |
S Supportive |
H Highly Related |
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Program Outcomes and Competences |
Level |
Assessed by |
| 1) |
Has a broad understanding of economics with a deep exposure to other social sciences and mathematics. |
N |
|
| 2) |
Demonstrates knowledge and skills in understanding the interactions of different areas of economics. |
N |
|
| 3) |
Displays a sound comprehension of microeconomic and macroeconomic theory. |
N |
|
| 4) |
Applies economic concepts to solve complex problems and enhance decision-making capability. |
N |
|
| 5) |
Uses quantitative techniques to analyze different economic systems. |
N |
|
| 6) |
Applies theoretical knowledge to analyze issues regarding Turkish and global economies. |
N |
|
| 7) |
Demonstrates proficiency in statistical tools and mainstream software programs to process and evaluate economic data. |
N |
|
| 8) |
Behaves according to scientific and ethical values at all stages of economic analysis: data collection, interpretation and dissemination of findings. |
H |
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| 9) |
Uses written and spoken English effectively (at least CEFR B2 level) to exchange scientific information. |
H |
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| 10) |
Exhibits individual and professional ethical behavior and social responsibility. |
H |
|
| 11) |
Displays learning skills necessary for further study with a high degree of autonomy |
H |
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| Prepared by and Date |
LEYLA PARLAR ATEŞ , |
| Course Coordinator |
BENGİ BİRGİLİ |
| Semester |
Spring |
| Name of Instructor |
VOLKAN YALÇIN |
Course Contents
| Week |
Subject |
| 1) |
Introduction to groups |
| 2) |
Groups |
| 3) |
Finite and cyclic groups |
| 4) |
Permutation groups |
| 5) |
Isomorphisms |
| 6) |
Cosets, Lagrange's Theorem |
| 7) |
Midterm |
| 8) |
Direct products |
| 9) |
Normal subgroups, quotients |
| 10) |
Homomorphisms |
| 11) |
Finite Abelian groups |
| 12) |
Rings and Ideals |
| 13) |
Ring homomorphisms |
| 14) |
Polynomial rings, factorization and divisibility |
| 15) |
Final Examination Period |
| 16) |
Final Examination Period |
| Required/Recommended Readings | Required Textbooks:
Contemporary Abstract Algebra, 9th Edition, Joseph Gallian. Brooks/Cole, 2016,
ISBN-13: 978-1305657960.
Abstract Algebra: Theory and Applications, 2017 Edition, Thomas W. Judson, Orthogonal Publishing L3C, ISBN-13: 978-1944325053.
Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, 2nd Edition, David Joyner, Johns Hopkins University Press, 2008, ISBN-13: 978-0801890130.
Abstract Algebra, 3rd Edition, David S. Dummit, Richard M. Foote, John Wiley and Sons, Inc., ISBN 978-0-471-43334-7.
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| Teaching Methods | Flipped Classroom model will be used while teaching this course. Learners will gain first exposure to new course material outside of class, usually via reading or watching lecture videos/audios, and then class time will be used to assimilate that prior mathematical knowledge through problem-solving or classroom discourse.
Learners will access key Abstract Algebra content individually or in small groups prior to class time, generate their questions, underline the points that they find most difficult or hardly understand, and then meet face-to-face in the larger group with similar misunderstandings to explore content through active learning and engagement strategies.
Learners will take the responsibility of their own learning, and study core content either individually or in groups before class and then apply mathematical knowledge and skills to a range of activities using higher order thinking.
Lecturing is still important but there will be a greater focus on gaining significant learning opportunities through facilitating active learning of mathematics, engaging students in the use of mathematical language, guiding learning, correcting misunderstandings and providing timely feedback, etc.
In the Flipped Classroom setting, there will be a greater focus on concept exploration, meaning making, and demonstration or application of mathematical knowledge face-to-face.
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| Homework and Projects | The course is of an abstract nature compared to most other courses; comprehension of the mathematical arguments and a careful reading of the lecture notes or the textbook are important. It should be noted that an important part of the homework assigned is reading the required textbook. This is a study habit that many students are not accustomed to, but is essential to thoroughly understanding the course. Students should attempt to solve all of the questions at the end of each chapter, and regularly keep in touch with the instructor about questions that they cannot solve. Homework will not be graded or corrected. Learners are strongly recommended to have the suggested textbook in order to fully understand the course and successfully solve the problems in the worksheets. |
| Laboratory Work | None |
| Computer Use | Computers will be used both in pre-class activities and student projects. |
| Other Activities | None |
| Assessment Methods |
| Assessment Tools |
Count |
Weight |
| Attendance |
1 |
% 25 |
| Project |
1 |
% 10 |
| Midterm(s) |
1 |
% 25 |
| Final Examination |
1 |
% 40 |
| TOTAL |
% 100 |
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| Course Administration |
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Information Package / Course Catalogue