Duration:
Number of lectures per week: 3
Assessment: Assignments counting 10%
End-of-year Examination: One three hour examination
Description:
The Principle of Mathematical Induction.
Sets and functions: power sets; binary relations; congruences; equivalence relations; partial orders and lattices; Cartesian products; functions between sets; inverse functions; injective, surjective and bijective functions; partial mappings.
Graphs: incidence and adjacency matrices, complete graphs, bipartite graphs; connectedness and components; Euler trails; Hamilton paths; forests and trees; directed graphs.
Algebraic structures: semigroups, monoids and groups; homomorphisms and isomorphisms.
Grammars: phrase structure and Chomsky hierarchy; Languages: context free and regular; Machines: finite state acceptors
Fourier Series: orthonormal functions, Euler coefficients, half-range expansions, truncated series approximation.
Textbooks:
M. Piff, Discrete Mathematics, Cambridge University Press.
Judith L. Gersting, Mathematical Structures for Computer Science, W. H. Freeman.
D. J. Cooke & H. E. Bez, Computer Mathematics, Cambridge University Press.
R. P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley.
W. E. Boyce & R. C. DiPrima, Elementary Differential Equations, John Wiley.
Nov 8, 2000