It is an introductory course on commutative algebra, based on the book of M. F. Atiyah and I. G. Macdonald, titled “Introduction to commutative algebra”. This course aims to cover the following topics. 1. Rings and ideals 2. Rings and Modules of fractions 3. Primary decomposition 4. Integral Dependence and valuations 5. Noether Normalization 6. Chain conditions 7. Noetherian and Artinian rings 8. The Nullstellensatz and Spec of a ring 9. Zariski topology on Spec of a ring 10. Graded rings and modules 11. Dimension theory
Commutative Algebra -1 (MATH 546)
2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Ayesha Asloob Qureshi aqureshi@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Interactive,Project based learning
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Programs\Type | Required | Core Elective | Area Elective |
Computer Science and Engineering - With Bachelor's Degree | * | ||
Computer Science and Engineering - With Master's Degree | * | ||
Computer Science and Engineering - With Thesis | * | ||
Cyber Security - With Bachelor's Degree | * | ||
Cyber Security - With Master's Degree | * | ||
Cyber Security - With Thesis | * | ||
Data Science - With Thesis | * | ||
Electronics Engineering and Computer Science - With Bachelor's Degree | * | ||
Electronics Engineering and Computer Science - With Master's Degree | * | ||
Electronics Engineering and Computer Science - With Thesis | * | ||
Electronics Engineering - With Bachelor's Degree | * | ||
Electronics Engineering - With Master's Degree | * | ||
Electronics Engineering - With Thesis | * | ||
Energy Technologies and Management-With Thesis | * | ||
Industrial Engineering - With Bachelor's Degree | * | ||
Industrial Engineering - With Master's Degree | * | ||
Industrial Engineering - With Thesis | * | ||
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis | * | ||
Leaders for Industry Computer Science and Engineering - Non Thesis | * | ||
Leaders for Industry Electronics Engineering and Computer Science - Non Thesis | * | ||
Leaders for Industry Electronics Engineering - Non Thesis | * | ||
Leaders for Industry Industrial Engineering - Non Thesis | * | ||
Leaders for Industry Materials Science and Engineering - Non Thesis | * | ||
Leaders for Industry Mechatronics Engineering - Non Thesis | * | ||
Manufacturing Engineering - Non Thesis | * | ||
Manufacturing Engineering - With Bachelor's Degree | * | ||
Manufacturing Engineering - With Master's Degree | * | ||
Manufacturing Engineering - With Thesis | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) | * | ||
Mathematics - With Bachelor's Degree | * | ||
Mathematics - With Master's Degree | * | ||
Mathematics - With Thesis | * | ||
Mechatronics Engineering - With Bachelor's Degree | * | ||
Mechatronics Engineering - With Master's Degree | * | ||
Mechatronics Engineering - With Thesis | * | ||
Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) | * | ||
Physics - Non Thesis | * | ||
Physics - With Bachelor's Degree | * | ||
Physics - With Master's Degree | * | ||
Physics - With Thesis | * |
CONTENT
OBJECTIVE
To understand the basics of commutative ring theory
Update Date:
ASSESSMENT METHODS and CRITERIA
Percentage (%) | |
Final | 40 |
Midterm | 40 |
Quiz | 20 |
RECOMENDED or REQUIRED READINGS
Textbook |
Introduction to Commutative Algebra by Michael Atiyah and I. G. Macdonald |