School of Mathematics
Course 239(2BA1) - Mathematics for SF Computer Scientists 1999-2000 (SF Computer Science and CS Linguistics & a Language )
Lecturer: Dr. N. H. Butimore
Requirements/prerequisites: 135 (1BA1) - A course in calculus and linear algebra.

Number of lectures per week: 3

Assessment: Assignments counting 15%

End-of-year Examination: One three hour examination


  1. Finite induction; sets; partial orders and lattices; equivalence relations and Fermat's Little Theorem.
  2. Mappings: partial, total, injective, surjective, bijective, invertible and Boolean

  3. Graphs: complete, bipartite, Euler, Hamilton paths; Directed graph: adjacency matrix, finite relations; Trees: binary, height and nodes

  4. Algebraic structures: semigroups, monoids and groups; Homomorphisms and isomophisms.

  5. Grammars: phrase structure and Chomsky hierarchy; Languages: context free and regular; Machines: finite state acceptors

  6. Ordinary Differential Equations: higher order, initial and boundary value problems
  7. Fourier Series: orthonormal functions, Euler coefficients, half-range expansions, truncated series approximation.


  1. M. Piff, Discrete Mathematics, Cambridge University Press.
  2. Judith L. Gersting, Mathematical Structures for Computer Science, W. H. Freeman.

  3. D. J. Cooke & H. E. Bez, Computer Mathematics, Cambridge University Press.

  4. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley.

  5. W. E. Boyce & R. C. DiPrima, Elementary Differential Equations, John Wiley.

May 13, 1999