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Course Info

About this Course

This subject consists of three main topics: Groups, Rings and Fields. The properties of groups, rings and fields will be discussed with emphasis on the algebraic structures and homomorphisms.

Course Syllabus

Groups and Subgroups
1.1) Definitions and Properties
1.2) Binary Operations
1.3) Isomorphic Binary Structures
1.4) Abelian Group
1.5) Finite and Infinite Groups
1.6) Subgroups
1.7) Cyclic Groups

Permutations, Cosets and Direct Product
2.1) Groups of Permutations
2.2) Orbits, Cycles and Alternating Groups
2.3) Cosets and Theorem of Lagrange
2.4) Direct Product and Finitely Generated Abelian Group

Homomorphisms and Factor Groups
3.1) Homomorphisms
3.2) Normal Subgroups
3.3) Factor Groups
3.4) Fundamental Homomorphism Theorem

Rings and Fields
4.1) Definition of Rings and Fields
4.2) Integral Domains

Frequently Asked Questions

Q1 : What is the Pre-Requisite for this subject
A1 : There is no Pre-Requisite for this subject

Q2 : Is there any other Reading list?
A2 : Joseph Gallian 2016, Contemporary Abstract Algebra, 8 Ed., Cengage Learning [ISBN: 9781305657960] CTI Reviews 2016, Abstract Algebra, 3 Ed., Cram101 Textbook Reviews [ISBN: 9781619054493] Shahriar Shahriari 2017, Algebra in Action: A Course in Groups, Rings, and Fields, 1st Ed., American Mathematical Society; 1st edition (August 16, 2017) [ISBN: 978-147042849] Gregory T. Lee 2018, Abstract Algebra: An Introductory Course, 1st Ed., Springer Undergraduate Mathematics Series [ISBN: 978-331977648]