Duration: 24 weeks
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; quaternions and rotations.
Formal languages and grammars: formal languages; context-free grammars; specifications in Backus-Naur form; regular grammmars; finite state acceptors.
Fourier Series: Fourier series; sine series; cosine series.
The web site for this course is located at http://www.maths.tcd.ie/~dwilkins/Courses/2BA1/. It contains lecture notes (in PDF format) and assignments from the current year and from previous years.
Textbooks:
M. Piff, Discrete Mathematics, Cambridge University Press.
Jun 25, 2004