PMAT 32063

>< Type/ Status : Elective
>< Title : Graph Theory and Abstract Algebra
>< Pre-requisites : PMAT 11025
>< Objectives :
At the end of this course, the student will acquire the rudiments of graph theory and basic algebraic structures.
>< Course Content :

Graph Theory: Graphs and Multigraphs, Subgraphs, Matrices and graphs, Isomorphic and homeomorphic Graphs, Planar graphs, Kuratowski's theorem.

Group Theory: Groups and subgroups, Normal subgroups, Factor groups, Group Homomorphisms.

Rings: Rings and subrings, Characteristic of a ring, Ideals, Quotient Rings, Integral Domains, Euclidean Domains.
Fields: Finite and infinite fields, Field of fractions.

>< Methodology : A combination of lectures, tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests, presentations and end of course examination
>< Recommended Reading :
1. Fraleigh, J.B. (1994). A first Course in Abstract Algebra, Addison Wesley.
2. Khanna, V.K. & Bhambri S.K. (1999). A Course in Abstract Algebra,Vikas, India.
3. Singh, S. & Zameeruddin Q. (1997). Modern Algebra, Vikas, India.
4. Cohn, P.M. (1974). Algebra, John Wiley, New York.
5. Johnsonbaugh, R. (1990). Discrete Mathematics, Macmillan.
6. West, D. B. (2002). Introduction to Graph Theory, Prentice Hall, India.

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