Course Contents BS Mathematics 7th Semester
Course Code: MATH 401Course Title: Functional Analysis I
Credit
Hours: 3 + 0
Metric Spaces
- Review of metric spaces
- Convergence in metric spaces
- Complete metric spaces
- Completeness proofs
- Dense sets and separable spaces
- No-where dense sets
- Normed linear spaces
- Banach spaces
- Convex sets
- Quotient spaces
- Equivalent norms
- Linear operators
- Linear functional
- Finite dimensional normed space
- Continuous or bounded linear operators
- Dual spaces
- Definition and examples
- Orthonormal sets and bases
- Annihilators, projections
- Hilbert space
- Linear functional on Hilbert spaces
- Reflexivity of Hilbert spaces
Recommended Books:
- Curtain RF, Pritchard AJ, Functional Analysis in Modern Applied Mathematics, Academic Press, New York
- Friedman A, Foundations of Modern Analysis, 1982, Dover Publications
- Kreyszig E, Introductory Functional Analysis with Applications, John Wiley, New York
- Rudin W, Functional Analysis, 1973, McGraw Hill, New York
Course Contents BS Mathematics 5th (E)
Course Title: Algebra II Course Code: MATH 301
Credit
Hours: 3 + 0
- Definition and examples of groups
- Abelian group
- Subgroups lattice, Lagrange’s theorem
- Relation between groups
- Cyclic groups
- Groups and symmetries, Cayley’s theorem
- Complexes and coset decomposition of groups
- Centre of a group
- Normalizer in a group
- Centralizer in a group
- Conjugacy classes and congruence relation in a group
- Normal subgroups
- Proper and improper normal subgroups
- Factor groups
- Fundamental theorem of homomorphism
- Cauchy’s theorem for Abelian and non-Abelian group
- Sylow theorems
- Definition and example of rings
- Special classes of rings
- Fields
- Ideals and quotient rings
- Ring homomorphisms
- Prime and maximal ideals
- Field of quotients
- Allenby RBJT, Rings, Fields and Groups: An Introduction to Abstract Algebra, 1983, Edward Arnold
- J. B. Fraleigh, A First Course in Abstract Algebra, 7th edition, (Addison-Weseley Publishing Co., 2003)
- Macdonald ID, The Theory of Groups, 1975, Oxford Clarendon Press, Ma., USA
- P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, (Cambridge University Press, 1986)
- Vijay K. Khanna, S K Bhambri, A Course in Abstract Algebra(2nd Revised Edition) Vikas Publishing House PVT LTD.
- H. Marshall, The Theory of Groups, (Macmillan, 1967)
- Humphreys, J.F.: A Course in Group Theory (Oxford University Press, 2004)
- Lederman, W.: Introduction to Group Theory (Cambridge University Press, 1987).
- Burton, D.E.: A First Course in Rings and Ideals (Addision Wesley Pub. Co., 1968).
