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Discrete and Continuous Mathematics

Mícheál Mac an Airchinnigh
Organization: University of Dublin, Trinity College
Department: Computer Science
Education level


  • To lay a firm foundation for the mathematical skills required in subsequent years of the degree course, with particular emphasis on ensuring that the mathematical pre-requisites for the second year undergraduate (i.e., Senior Freshman) year are met.
  • To assist the students in developing an understanding of the nature of theorem and proof by providing them with the appropriate experiments and equipment.
  • To develop in them an understanding of the use of mathematics in modelling by providing them with good practical modelling experiences.

All relevant information is available online.

The course 1ICT5 Mathematics is a first year (i.e., Junior Freshman) undergraduate course in Discrete and Continuous Mathematics, with most emphasis on the discrete part, for the degree in Information and Communications Technology. The students all have a common mathematical foundation of the classical sort.

A primary objective of this course is to try to answer the question: What is Mathematics for us as ICT students? On a more practical note the experimental nature of doing mathematics is strongly emphasized and it is here that Mathematica plays a major role.

The choice of the number theory component proved to be a highly significant one for four reasons:

  • It was new for all students and hence everyone found themselves on a "level playing field"; this facilitated the hard job of evaluating the students' mathematical ability during and at the end of the year.
  • It is an excellent field in which to carry out experiments with Mathematica (much as might have been done in the past with pencil and paper).
  • There are some very important applications in Information and Communications Technology, viz., cryptography, error-detecting codes, pseudorandom numbers, etc.
  • There are accessible open problems which can be explored.

Due to the innovative nature of doing experimental mathematics, course materials are constantly reviewed and updated.

A variety of elementary topics are taken from, in order:
  • Number Theory
  • Combinatorics
  • Graph Theory
  • Algebra
  • Automata Theory
  • Calculus

*Applied Mathematics > Computer Science
*Mathematics > Discrete Mathematics > Coding Theory