What you will study
Exploring mathematics offers both a way in to honours-level mathematics and deeper insights into the mathematics that supports other areas of study. It rounds off the suite of modules designed to provide a rich and enlightening introduction to mathematical ideas and techniques.
This module builds on the approach and design of our OU level 1 module Using mathematics (MST121), extending the mathematical concepts and techniques (to cover more calculus, for example), the range of applications, and use of the module software. It looks at questions underlying some of the methods from MST121, such as why particular patterns occur in mathematical solutions, and how you can be confident that a result is true. It introduces the role of reasoning in mathematics, and offers opportunities to investigate mathematical questions for yourself. By the end of the module you will have encountered many of the topics that are developed in later mathematics modules, in particular in our main OU level 2 modules Pure mathematics (M208), and Mathematical methods, models and modelling (MST210). It also provides a good mathematical basis for modules in physics and engineering.
There are four sections, with each of the first three revisiting and developing the ideas introduced in the corresponding section in MST121. An important theme that runs through the module is mathematical reasoning.
Work on numbers and sequences is extended to Fibonacci and related sequences; that on circles is extended to the study of other conic sections. There is further exploration of the properties of functions and matrices, including applications in transformation geometry. The computer is used to help with important ideas of iteration in discrete mathematics. The ideas of calculus are extended to include more sophisticated techniques of differentiation and integration and use in the approximation of functions using Taylor series.
The last section of the module introduces important mathematical ideas, such as complex numbers, number theory and groups, that are built on in later modules. It concludes with a chapter on the role of proof in mathematics.
The module also develops more general skills such as communication of mathematical ideas, which will be useful in studying later modules.
You will learn
Successful study of this module should improve your skills in:
communicating mathematical ideas clearly and succinctly
working with abstract concepts
constructing logical arguments
finding solutions to problems
using a computer algebra software package.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.