Information Package / Course Catalogue
| Elementary Mathematics Education | |||||
| Bachelor | Length of the Programme: 4 | Number of Credits: 240 | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF: Level 6 |
Ders Genel Tanıtım Bilgileri
| 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 | Seçiniz | ||||
| Semester | Spring | ||||
| Contact Hours per Week |
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| Estimated Student Workload | 136 hours per semester | ||||
| Number of Credits | 5 ECTS | ||||
| Grading Mode | Standard Letter Grade | ||||
| Pre-requisites |
MATH 139 - Introduction to Discrete Mathematics |
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| Expected Prior Knowledge | Introduction to Discrete Mathematics | ||||
| Co-requisites | None | ||||
| 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. | ||||
| Course Description in Turkish | Grup tanımı, alt gruplar, permütasyon grupları, homomorfizma, devirli gruplar, kalan sınıfları, normal alt grupları, bölüm grupları, halka tanımı, alt halkalar, idealler. |
Course Learning Outcomes and CompetencesUpon 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. |
| Program Learning Outcomes/Course Learning Outcomes | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1) Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | |||||
| 2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | |||||
| 3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | |||||
| 4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | |||||
| 5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | |||||
| 6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | |||||
| 7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | |||||
| 8) Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | |||||
| 9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | |||||
| 10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | |||||
| 11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | |||||
| 12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | |||||
| 13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | |||||
| 14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. |
Relation to Program Outcomes and Competences
| N None | S Supportive | H Highly Related |
| Program Outcomes and Competences | Level | Assessed by | |
| 1) | Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | S | Participation,Project |
| 2) | Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | N | |
| 3) | Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | H | Exam,Participation,Project |
| 4) | Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | S | Project |
| 5) | Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | N | |
| 6) | Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | S | Project |
| 7) | Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | H | Participation,Project |
| 8) | Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | S | Select,Participation,Project |
| 9) | Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | S | Project |
| 10) | Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | S | Participation,Project |
| 11) | Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | S | Project |
| 12) | Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | N | |
| 13) | Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | N | |
| 14) | Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. | N |
| Prepared by and Date | LEYLA PARLAR ATEŞ , |
| Course Coordinator | BENGİ BİRGİLİ |
| Semester | Spring |
| Name of Instructor | Asst. Prof. Dr. İLKER ARSLAN |
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. | ||||||||||||||||||
| 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. | ||||||||||||||||||
| 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 |
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| Course Administration |
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ECTS Student Workload Estimation
| Activity | No/Weeks | Hours | Calculation | ||||
| No/Weeks per Semester | Preparing for the Activity | Spent in the Activity Itself | Completing the Activity Requirements | ||||
| Course Hours | 14 | 2 | 3 | 2 | 98 | ||
| Project | 2 | 3 | 2 | 10 | |||
| Midterm(s) | 1 | 10 | 1 | 11 | |||
| Final Examination | 1 | 15 | 2 | 17 | |||
| Total Workload | 136 | ||||||
| Total Workload/25 | 5.4 | ||||||
| ECTS | 5 | ||||||