SE 353. Basic Structure of Mathematics
(3 - 1 - 0 - 0 - 4)
Finite and Infinite Sets: Finite sets, Countable sets, Uncountable sets. Groups and Symmetry: Groups, Subgroups, Lagrange theorem, Normal subgroups, Quotient groups, Group actions, Homomorphisms, Group of symmetry - rigid motion group, finite subgroups of the rotation group, symmetric group. Metric Spaces: Open sets, Closed sets, Sequences, Continuity, Complete metric spaces, Contraction principle and applications, Connectedness and compactness. Fractals: Metric space of fractals and its completeness, Iterated function systems, Attractor, Algorithms to generate fractals. Topology of Surfaces: Euler's theorem, Construction of surfaces by identification: Torus, mobius strip, Klein bottle.
- REFERENCES:
- M. Artin, Algebra, Prentice Hall, 1994
- B. Mendelson, An Introduction to Topology, C.B.S. Publishers, New Delhi
- M.A. Armstrong, Basic Topology, Springer-Verlag, 1978
- M.F. Barnsley, Fractals Everywhere, II ed., Academic Press, 1993
- G.F. Simmons, Introduction to Topology and Modern Analysis, Tata Mc-Graw Hill International Ltd.
- Concerned Department: Mathematics