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
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]
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]