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Course Description Course Name : Module Theory Course Code : MT-548 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. ZEYNEP YAPTI ÖZKURT Learning Outcomes of the Course : Knows definition of modules and its properties Knows submodules, quotient modules and homomorphisms has an idea about the structure of free modules Knows the structure of tensor product and properties Create an exact sequence Defines projective, injective and flat modules Has an idea about the structure of modules on principal ideal domain Knows the Rational and Jordan canonical forms Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : YLMT-200 Special Area Course Recommended Optional Programme Components : None Aim(s) of Course : Understand the basic definitions and theorems about modules and associate them with different algebraic structures. Course Contents : Modules, Homomorphisms,submodules and quotient modules. Short exact Sequences. Direct products, tensor product. Free, Projective, injective and flat modules. Modules over Principal Ideal Domains. Jordan and Normal Canonical forms. Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Main Definitions Read the relevant sections in the textbook and solving problems Lectures 2 Quotient modules and Homomorphisms Read the relevant sections in the textbook and solving problems Lectures 3 Direct sums Read the relevant sections in the textbook and solving problems Lectures 4 Free modules Read the relevant sections in the textbook and solving problems Lectures 5 Free modules Read the relevant sections in the textbook and solving problems Lectures 6 Tensor product of modules Read the relevant sections in the textbook and solving problems Lectures 7 Tensor product of modules Read the relevant sections in the textbook and solving problems Lectures 8 Exact Sequences Read the relevant sections in the textbook and solving problems Lectures 9 Projective modules Read the relevant sections in the textbook and solving problems Lectures 10 İnjective modules Read the relevant sections in the textbook and solving problems Lectures 11 Flat Modules Read the relevant sections in the textbook and solving problems Lectures 12 Modules on principal ideal domain Read the relevant sections in the textbook and solving problems Lectures 13 Rational Canonical Forms Read the relevant sections in the textbook and solving problems Lectures 14 Jordan Canonical forms Read the relevant sections in the textbook and solving problems Lectures 15 Exercises solving problems in the relevant sections of the textbook Lectures 16/17 Final Exam Review and Problem Solving Written examination   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Abstract Algebra (DAvid S. Dummit)  Algebra(Thomas Hungerford) Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 50     Homeworks/Projects/Others 10 50 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Aquires sufficient knowledge to enable one to do research over and above the undergraduate level 4 2 Learns theoretical foundations of his/her field thoroughly 5 3 Uses the knowledge in his/her field to solve mathematical problems 5 4 Proves basic theorems in different areas of Mathematics 2 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 2 6 Uses technical tools in his/her field 3 7 Works independently in his/her field requiring expertise 3 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 3 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 3 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 3 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 3 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 5 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 10 4 40     Mid-term Exams (Written, Oral, etc.) 1 4 4     Final Exam 1 4 4 Total Workload: 146 Total Workload / 25 (h): 5.84 ECTS Credit: 6