On successful completion of this module, students will be able to
justify, with reasoned logical argument, basic properties
of mathematical objects that are specified as sets,
relations on sets, functions between sets, and/or monoids;
analyse simple context-free grammars to determine the
formal languages that they generate, and construct
specifications of context-free grammars and finite
state machines that generate and/or determine formal
languages, given specifications of such formal languages;
recognize, identify and justify properties of
undirected graphs that are networks consisting of
vertices together with edges joining pairs of vertices;
apply standard algorithms in order to determine
spanning trees in connected graphs;
determine solutions to certain types of homogeneous
and inhomogeneous linear ordinary differential equations
of degree at least two, where the coefficients of the
differential equation are constants and the forcing function
is typically constructed from polynomial, exponential
and/or trigonometric functions;
apply procedures founded in the algebra of vectors
in three-dimensional space in order to solve
simple geometrical problems;
calculate quantities in modular arithmetic using methods,
justified on the basis of theorems explicitly presented
and proved within the module, that have relevance to the
implementation of public key cryptographic systems
such as the Rivest-Shamir-Adelman (RSA) public key
cryptosystem.
Module Content
Specific topics addressed in this module include the following:
The Principle of Mathematical Induction
Sets, Relations and Functions
Introduction to Abstract Algebra
Introduction to Formal Languages and Context-Free Grammars
Introduction to Graph Theory
Algorithms for computing Minimal Spanning Trees
Spanning Trees in Connected Graphs
Ordinary Differential Equations
Vectors
Introduction to Number Theory and Cryptography
Lecture notes, assignments, worked solutions to problems
from previous years and further information relevant
to the module are available from the module webpage at
http://www.maths.tcd.ie/~dwilkins/Courses/MA2C03/.
Module Prerequisite
Module CS1001 (Mathematics I), or an equivalent module
developing the necessary mathematical skills in areas such
as calculus and linear algebra.
Assessment Detail
This module will be examined in a 3 hour examination in Trinity
term. Also students should complete a small number of assignments during
the academic year. The final grade at the annual examination session will
be a weighted average over the examination mark (90%) and the continuous
assessment mark (10%). The final grade at the supplemental examination
session will be wholly determined by the supplemental examination paper.