Abstract Algebra SP15

Welcome to an undergraduate course in Abstract Algebra (MTH232).

ANNOUNCEMENTS:

 

Course Module: Abstract Algebra SP15

Lecture # 1: Sets, functions and equivalence relation.

Lecture # 2: Properties of Integers

Lecture # 3: The integers modulo n

Lecture # 4: Groups

Lecture # 5: Dihedral group, The Quaternion group, Klein-4 group

Lecture # 6: Symmetric/Permutation Group

Lecture # 7: Homomorphism and Isomorphism

Lecture # 8: Subgroups, Centralizer, Normalizer and Centre

1st Sessional Examination Spring 2015

Lecture # 9: Cyclic Groups

Lecture # 10: The structure of cyclic groups up to isomorphism

Lecture # 11: The subgroups of cyclic groups

Lecture # 12: Coset decomposition and Lagrange’s Theorem

Lecture # 13: Direct Product of Groups

Lecture # 14: Fundamental Theorem of Finite Abelian Groups

Lecture # 15: Normal Subgroups, Factor/ Quotient groups

Lecture # 16: Computations in factor groups

Lecture # 17: Isomorphism Theorems

Second Sessional Examnation SP15

Lecture # 18: Cayley’s Theorem

Lecture # 19: Alternating groups

Lecture # 20: Conjugacy classes and class equation

Lecture # 21: Sylow’s Theorem

Lecture # 22: Applications of Sylow’s Theorems

Lecture # 23: Rings and their types

Lecture # 24: Fields, Integral domains, polynomial rings

Lecture # 25: Ring Homomorphisms, ideals and Quotient rings

Lecture # 26: Maximal and Prime ideals

 

Assignment # 1: Sets, Functions and Equivalence relation, Properties of Integers, The integers modulo n.

Solution Assignment # 1

Assignment # 2: Groups, Dihedral group, Symmetric group, The Quaternion group, Klein-4 group, Permutation groups, Homomorphism and Isomorphism, Subgroups, Centralizer, Normalizer and Centre.

Solution: Assignment # 2

Assignment # 3: Cyclic group, the structure of cyclic groups up to isomorphism, subgroups of cyclic groups

Solution Assignment # 3

Assignment # 4: Coset decomposition and Lagrange’s Theorem, Direct product of groups, Fundamental Theorem of finite abelian groups, Normal Subgroups, Factor/Quotient groups, Computations in factor groups, Isomorphism Theorems

Solution Assignment # 4

Quiz # 1: Sets, Functions and Equivalence relation, Properties of Integers, The integers modulo n.

Quiz # 3

 

DEADLINES:

Assignment # 1 due date: 6 March 2015 

Assignment # 2 due date: 17 March 2015 New

Assignment # 3 due date: 3 April 2015 New

Assignment # 4 due date: 28 April 2015 New

NOTE: The lectures, assignments and quizzes above are loosely based on the following text books:

 D. S. Dummit & R. M. Foote, Abstract Algebra, 3rd Edition, John Wiley & Sons, Inc.
 I. N. Herstein, Abstract Algebra, 3rd Edition, Prentice-Hall.
 John B. Fraleigh, A First Course in Abstract Algebra, 7th Edition, Addison-Wesley.

Leave a Reply

Your email address will not be published. Required fields are marked *