School of Mathematics School of Mathematics
Course 2BA1 - Mathematics for SF Computer Scientists 2002-2003 (SF Computer Science and CS Linguistics & a Language )
Lecturer: Dr. D. R. Wilkins
Requirements/prerequisites: 1BA1 - A course in calculus and linear algebra.

Duration: 24 weeks

Number of lectures per week: 3

Assessment: Assignments counting 10%

End-of-year Examination: One three hour examination

Description:

  1. The Principle of Mathematical Induction.

  2. 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.

  3. Graphs: incidence and adjacency matrices; complete graphs; bipartite graphs; connectedness and components; Euler trails; Hamilton paths; forests and trees; directed graphs.

  4. Algebraic structures: semigroups, monoids and groups; homomorphisms and isomorphisms; quaternions and rotations.

  5. Formal languages and grammars: formal languages; context-free grammars; specifications in Backus-Naur form; regular grammmars; finite state acceptors.

  6. Ordinary Differential Equations: second order differential equations, initial and boundary value problems.

  7. 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:

Jan 24, 2003

File translated from TEX by TTH, version 2.70.
On 24 Jan 2003, 16:40.