Mathematics - Course Outline
The University of Cambridge offers an undergraduate course in Mathematics. The course is well built and incorporates theories as well as practical exercises. The Mathematics course outlines are given as follows.
In the first two years, students concentrate on the basic tools they need to mathematics at deeper levels with an equal combination of applied and pure mathematics.
The first year of the course introduces students to the basic of higher mathematics, which may include:
Pure Mathematics: algebraic systems (like groups) and exact analysis
Applied Mathematics: mathematical methods like Special Relativity, vector calculus and Newtonian dynamics
Students who take Mathematics with Physics may also cover, for instance, electromagnetism, kinetic theory and Fourier analysis.
Part First 'B'
In the part first 'B', students choose, under the close supervision of their Director of Studies, from a wide range of seventeen papers options available to them. In this phase of the course, the topics become deeper and broader and are classified as applicable, applied and pure; however, there are strong associations between the different areas. For example:
- The pure side is divided into analysis and algebra.
- Algebra does not mean tedious manipulation of letters of the alphabet. Algebra is the study of systems of objects like groups that obey certain rules. These rules explain the symmetries that underline most areas of physics and mathematics.
- In analysis, the foundation of calculus is assessed comprising the theory of functions of a complex variable
- The applied side includes theoretical physics and mathematics methods
- The purpose of the mathematics methods is to establish techniques for solving a series of problems without much focus upon rigorous justification
- Theoretical Physics introduces students to the pillars of contemporary physics: quantum electromagnetism. There is a paper on fluid dynamics that is studied for physical importance as well as its mathematical elegance.
- Applicable mathematics consists of optimization and statistics, for example, choosing the best route through a network. The fundamental ideas of data analysis are introduced. Here, students need to take a paper in Optimization because of its tidy mathematical treatment of familiar problems.
There are some optional computational projects, evaluated by programmes and note books submitted before the exam in the summer. Students use computers to solve mathematical problems.
The third year offers students an opportunity to unfold their mathematical interests and use the skills they have achieved. Students have a broad choice of topics including:
- Number Theory
- Algebraic Topology
- Stochastic Financial Models
- Coding and Cryptography
- Principles of Quantum Mechanics
- Logic and Set Theory
Students also have option of studying computational projects.
In the forth year, part third, students have more than eighty courses to choose from including all areas of theoretical physics and mathematical and are motivated to complete a mathematical project or essay chosen from a similar wide range of topics.