Mathematics 2A module (MA21001)

This module is part of a series of four modules that includes Mathematics 1A, 1B, 2A, and 2B.

These are the core Mathematics modules in years 1 and 2.

These modules provide a solid foundation in calculus, algebra, and geometry. You will need these for higher-level mathematics modules.

In the algebra part of this module, you will learn about a key structure called a vector space. Some of the simplest vector spaces are subsets of the 3-dimensional space in which we live. There are however many other mathematical sets that share the same structure.

Recognising hidden structure within a mathematical set is a key skill that allows you to take advantage of the structure. These concepts have a wide range of applications. These range from:

• the theories of quantum mechanics
• electrodynamics
• computer science
• optimisation in finance

In the calculus part of this module, you will extend ideas of differentiation, integration and differential equations. These were introduced in mathematics 1A and 1B. These are the foundations for studying many problems in physics, biology, economics and finance.

What you will learn

In this module, you will:

• study techniques to solve selected differential equations with first and second derivative terms. These are called first and second order equations
• learn about a new class of functions called hyperbolic functions. You will discover their use in algebra and calculus
• learn how a vector space is defined
• be introduced to the related concepts: subspaces, span, linear independence, basis and dimension. You will also find out why these are useful
• find out how the scalar product can be generalised to other vector spaces. The scalar project was introduced in mathematics 1B for more conventional geometric problems. You will also find out why this is useful

By the end of this module, you will be able to:

• prove simple results regarding subspaces and related concepts
• make use of underlying vector space structures to carry out calculations in a variety of settings
• find general solutions of some first and second order differential equations. and the particular solutions which satisfy given initial conditions

Assignments / assessment

• coursework (40%)
• final exam (60%)

Teaching methods / timetable

• four hours of lectures weekly
  • key points of the week's content will be discussed
  • lecture notes covering the full module content will be available before classes
  • in-class time will be prioritised for interactive discussion
• two hours of tutorials weekly
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturers and peers