BSc (Honours) Mathematics: pathway

Stage 1

You’ll begin Stage 1 with the compulsory module Discovering mathematics (MU123)Discovering mathematics::This key introductory Level 1 course provides a gentle start to the study of mathematics. It will help you to integrate mathematical ideas into your everyday thinking and build your confidence in using and learning mathematics. You’ll cover statistical, graphical, algebraic, trigonometric and numerical concepts and techniques, and be introduced to mathematical modelling. Formal calculus is not included and you are not expected to have any previous knowledge of algebra. The skills introduced will be ideal if you plan to study more mathematics courses, such as Using mathematics (MST121). It is also suitable for users of mathematics in other areas, such as computing, science, technology, social science, humanities, business and education.undergraduate.qualification.pathways.Q31-2,module,MU123,,1 (30 credits), which introduces and helps integrate key ideas from statistics, algebra, geometry and trigonometry into your everyday thinking to build your confidence in learning and using mathematics.

You’ll follow this with three compulsory 30-credit modules: Using mathematics (MST121)Using mathematics::This broad, enjoyable introduction to university-level mathematics assumes some prior knowledge, as described on our MathsChoices website. The course shows how mathematics can be applied to answer some key questions from science, technology, and everyday life. You will study a range of fundamental techniques, including calculus, recurrence relations, matrices and vectors and statistics, and use integrated specialist mathematical software to solve problems. The skills of communicating results and defining problems are also developed. This is not a course for beginners – at the MathsChoices website (mathschoices.open.ac.uk) there are quizzes, sample material and advice to help you determine if this course is right for you.undergraduate.qualification.pathways.Q31-2,module,MST121,,1, Introducing statistics (M140)Introducing statistics::Today, more than ever, statistics is part of our lives. From this key introductory course you will learn how to use basic statistical tools and quantitative methods that are useful in business, government, industry, medicine, the economy, and most academic subjects. Topics covered include: summarising data; examining relationships; randomness and sampling distributions; probability; testing hypotheses; and estimation. Using data from a range of applications, you’ll learn practical statistical techniques and fundamental principles, as well as using software and a calculator to analyse data. The skills introduced will be ideal if you plan to study more mathematics courses. This course is also suitable for students of other subjects who need a basic knowledge of statistics.undergraduate.qualification.pathways.Q31-2,module,M140,,1 and Exploring mathematics (MS221)Exploring mathematics::Exploring mathematics builds on the concepts and techniques in Using mathematics (MST121) and uses the same software. It looks at questions underlying some of those techniques, 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 and offers opportunities to investigate mathematical problems. Together with Using mathematics this course will give you a good foundation for higher-level mathematics, science and engineering courses. Even if you don't intend to study further, you will gain a good, university-level understanding of the nature and scope of mathematics.You are advised to be confident with the content of Using mathematics (MST121), or equivalent from elsewhere, before commencing study of this course.undergraduate.qualification.pathways.Q31-2,module,MS221,,1. Together, they provide a broad introduction to various topics in pure and applied mathematics and statistics. You’ll develop a variety of skills including problem solving, how to develop and present a mathematical argument and how to represent and interpret statistical data. These are the key skills required for higher level study in mathematics.

Note: you will normally need to achieve a certain standard in Stage 1 mathematics before progressing to Stage 2.

Stage 2

At Stage 2 you’ll develop your skills and knowledge in the following areas:

• Pure mathematics (M208)Pure mathematics::Pure mathematics is one of the oldest creative human activities and this course introduces its main topics. Group Theory explores sets of mathematical objects that can be combined – such as numbers, which can be added or multiplied, or rotations and reflections of a shape, which can be performed in succession. Linear Algebra explores 2- and 3-dimensional space and systems of linear equations, and develops themes arising from the links between these topics. Analysis, the foundation of calculus, covers operations such as differentiation and integration, arising from infinite limiting processes. To study this course you should have a sound knowledge of relevant mathematics as provided by the appropriate Level 1 study.undergraduate.qualification.pathways.Q31-2,module,M208,,1 (60 credits) – formal proof, abstract structures, linear algebra, analysis, group theory
• Mathematical methods and models (MST209)Mathematical methods and models::Solve real problems by finding out how they are transformed into mathematical models and learning the methods of solution. This course covers classical mechanical models as well as some non-mechanical models such as population dynamics; and methods including vector algebra, differential equations, calculus (including several variables and vector calculus), matrices, methods for three-dimensional problems, and numerical methods. Teaching is supported and enhanced by use of a computer algebra package. To study this course you should have a sound knowledge of relevant mathematics as provided by the appropriate Level 1 study.undergraduate.qualification.pathways.Q31-2,module,MST209,,1 (60 credits) – differential equations, linear algebra, vector calculus
• Mathematical modelling (MSXR209)Mathematical modelling::Mathematics is enjoyable and creative in its own right, but can also be a powerful tool for solving real problems. This course, which includes a residential week, introduces mathematical modelling and other techniques such as data and sensitivity analysis within the framework of group-learning. You'll learn to use mathematical software and acquire presentation and group-working skills. You'll also be expected to put together a short technical report. Most of the work will be collaborative, carried out in small groups with a tutor. You should have an understanding of applied mathematics and mechanics to successfully study this course.undergraduate.qualification.pathways.Q31-2,module,MSXR209,,1 (10 credits) – computer algebra software, methods of Newtonian mechanics, practical elements of mathematical modelling.

You’ll also continue to broaden your experience in the use of appropriate mathematical software and in explaining and communicating mathematical ideas to others.

Stage 3

At Stage 3 you’ll study a selection from a range of more advanced mathematical topics currently including: complex analysis, graphs and networks, optimization, groups, metric space theory, number theory, waves, diffusion, variational principles, computer algebra, chaos, mathematical methods, fluid mechanics, quantum physics, and electromagnetism.