This is a problem based module that will reinforce and introduce the techniques involved in a variety of problem-solving situations across mathematics, including calculus, algebra, combinatorics, geometry and mechanics. Each week students will bring to bear their mathematical skills and develop them further in order to solve a number of problems that are varied in nature and difficulty. Moreover students will learn to write mathematical arguments that explain why their calculations allow the question to be fully answered. Some historical background to the mathematics will feature in discussion of the problems and their solutions.
Syllabus:
Topics that will be featured in the problem sets include:
Differentiation and Integrations methods
Solutions of equations (including use of complex numbers)
Familiarity and exploitation of the properties of trigonometric and other transcendental functions
Kinematics and problems involving vector quanitites
Euclidean geometry
Elementary number theory
Discrete counting and probablity problems
Problems requiring a mixture of mathematical ideas.
(c) On completion of the course, students will:
Be adept at solving general mathematical problems that arise in which the student does not know in advance what specific mathematical skills are needed;
Be able to justify through mathematical argument how a given mathematical calculation leads to solution of a problem;
Become sure-footed in the use of algebraic techniques that arise throughout mathematics.
Syllabus:
Topics that will be featured in the problem sets include:
Differentiation and Integrations methods
Solutions of equations (including use of complex numbers)
Familiarity and exploitation of the properties of trigonometric and other transcendental functions
Kinematics and problems involving vector quanitites
Euclidean geometry
Elementary number theory
Discrete counting and probablity problems
Problems requiring a mixture of mathematical ideas.
(c) On completion of the course, students will:
Be adept at solving general mathematical problems that arise in which the student does not know in advance what specific mathematical skills are needed;
Be able to justify through mathematical argument how a given mathematical calculation leads to solution of a problem;
Become sure-footed in the use of algebraic techniques that arise throughout mathematics.