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THIRD CYCLE - DOCTORATE DEGREE
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
MATHEMATICS DEPARTMENT
1441 Mathematics
Course Information
Course Learning Outcomes
Course's Contribution To Program
ECTS Workload
Course Details
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COURSE INFORMATION
Course Code
Course Title
L+P Hour
Semester
ECTS
MAT 614
MODULE THEORY
3 + 0
2nd Semester
7,5
COURSE DESCRIPTION
Course Level
Doctorate Degree
Course Type
Elective
Course Objective
To present the concepts of module theory.
Course Content
Modules and submodules, module homomorphisms, direct sums and products of modules, free modules, projective and injective modules, prime and maximal submodules, Noetherian and Artinian modules.
Prerequisites
No the prerequisite of lesson.
Corequisite
No the corequisite of lesson.
Mode of Delivery
Face to Face
COURSE LEARNING OUTCOMES
1
To learn the concepts of module and submodule.
2
To learn isomorphism theorems and use them to solve problems.
3
To understand the relations between ring and module theories.
4
To become aware of different module structures.
COURSE'S CONTRIBUTION TO PROGRAM
PO 01
PO 02
PO 03
PO 04
PO 05
PO 06
PO 07
PO 08
LO 001
LO 002
LO 003
LO 004
Sub Total
Contribution
0
0
0
0
0
0
0
0
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities
Quantity
Duration (Hour)
Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)
14
3
42
Hours for off-the-classroom study (Pre-study, practice)
14
7
98
Assignments
1
5
5
Mid-terms
1
15
15
Final examination
1
35
35
Total Work Load
ECTS Credit of the Course
195
7,5
COURSE DETAILS
Select Year
All Years
2022-2023 Spring
2021-2022 Spring
2019-2020 Fall
2018-2019 Fall
Course Term
No
Instructors
Details
2022-2023 Spring
1
CANAN CELEP YÜCEL
Details
2021-2022 Spring
1
CANAN CELEP YÜCEL
Details
2018-2019 Fall
1
CANAN CELEP YÜCEL
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Course Details
Course Code
Course Title
L+P Hour
Course Code
Language Of Instruction
Course Semester
MAT 614
MODULE THEORY
3 + 0
1
Turkish
2022-2023 Spring
Course Coordinator
E-Mail
Phone Number
Course Location
Attendance
Prof. Dr. CANAN CELEP YÜCEL
ccyucel@pau.edu.tr
FEN A0201
%70
Goals
To present the concepts of module theory.
Content
Modules and submodules, module homomorphisms, direct sums and products of modules, free modules, projective and injective modules, prime and maximal submodules, Noetherian and Artinian modules.
Topics
Weeks
Topics
1
Groups
2
Groups
3
Rings
4
Rings
5
Module definition and Examples
6
Submodules
7
Module homomorphisms and Isomorphism Theorems
8
Direct sums and products of modules
9
midterm
10
Exact Sequence
11
Free Modules
12
ProjectiveModules
13
Injective Modules
14
general review
Materials
Materials are not specified.
Resources
Course Assessment
Assesment Methods
Percentage (%)
Assesment Methods Title
Final Exam
50
Final Exam
Midterm Exam
50
Midterm Exam
L+P:
Lecture and Practice
PQ:
Program Learning Outcomes
LO:
Course Learning Outcomes
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Home Page
About University
Name And Address
Acedemic Authorities
General Discription
Academic Calendar
General Admission Requirements
Recognition of Prior Learning
General Registration Procedures
ECTS Credit Allocation
Academic Guidance
Information For Students
Cost Of Living
Accommodation
Meals
Medical Facilities
Facilities for Special Needs Students
Insurance
Financial Support for Students
Student Affairs
Learning Facilities
International Programs
Language Courses
Internships
Sports Facilities and Leisure Activities
Student Associations
Practical Information for Mobile Students
Degree Programmes