## Mathematics 2 University of London

If you are studying this subject, you will already have studied (or be concurrently studying) 05A Mathematics 1 or you will have a qualification which allowed you exemption from that course due to its equivalence. This subject builds upon Mathematics 1. Everything in Mathematics 1 is essential to Mathematics 2. So, although Mathematics 2 is formally a separate subject, it is best thought of as an extension of Mathematics 1. Given this, it is essential that you have a good understanding of Mathematics 1. In this subject guide, we will briefly review some of the important ideas and techniques from Mathematics 1 that we shall need for

Mathematics 2, but you should refer to the Mathematics 1 guide and the textbooks if you feel the need to refresh yourself on some of the more basic Mathematics 1 topics.

In Mathematics 2, we explore further some topics introduced in Mathematics 1 and we study some more applications to the social sciences, particularly economics. In particular, we investigate further the applications of differentiation and integration, and functions of several variables: we shall see some new applications and also some new techniques.

This subject also introduces some important new topics: for example, we shall meet new techniques for solving linear equations, and we introduce differential and difference equations.

This half course may not be taken with 76 Management mathematics, 173 Algebra or 174 Calculus.

## Studying mathematics

I make a number of points in the introductory chapter of the 05A Mathematics 1 guide about the nature of studying mathematics, and these are worth repeating here.

The study of mathematics can be very rewarding. It is particularly satisfying to solve a problem and know that it is solved. Unlike many of the other subjects you will study, in the mathematics subjects, there is always a right answer. Although there may be only one right (final) answer, there could be a number of different ways of obtaining that answer, some more complex than others. Thus, a given problem will have only one ‘answer’, but many ‘solutions’ (by which we mean routes to finding the answer). Generally, a mathematician likes to find the simplest solution possible to a given problem, but that does not mean that any other solution is wrong. (There may be different, equally simple, solutions.)

With mathematical questions, you first have to work out precisely what it is that the question is asking, and then try to find a method (hopefully a nice, simple one) which will solve the problem. This second step involves some degree of creativity, especially at an advanced level. You must realise that you can hardly be expected to look at every mathematics problem and write down a beautiful and concise solution, leading to the correct answer, straight away. For obvious reasons, teachers, lecturers, and textbooks rarely give that impression: they present the solution right there on the page or the blackboard, with no indication of the time a student might be expected to spend thinking — or of the dead-end paths he or she might understandably follow — before a solution can be found. It is a good idea to have scrap paper to work with so that you can try out various methods of solution. You must not get frustrated if you can’t solve a problem immediately. As you proceed through the subject, gathering more experience, you will develop a feel for which techniques are likely to be useful for particular

problems. You should not be afraid to try different techniques, some of which may not work, if you cannot immediately recognise which technique to use.