Study Skills in Mathematics – Reading

Academic material needs to be read for understanding, not entertainment: satisfaction and enjoyment will follow.

You are at university to read for a degree – you will need to do some reading as well as attending lectures! Don’t put it off until later … it will never get done if you do. Buy all the first and second level core books yourself (perhaps second-hand – you’ll be able to sell them on later), but share/borrow more advanced books. The syllabuses (available from your VLE or web pages) usually contain reading lists. You will rarely need to read the whole book but you will need to know where to find the information you need. Very few modules follow a book completely in set order, so learn to use the contents and index pages effectively.

Mathematics, science and technology modules generally require far less reading than most other subjects. They stress mastery of a few concepts instead. On the other hand, books can and do help by giving an alternative view, extra examples, different proofs etc. Seek to understand, rather than memorise, facts. The only exceptions here are that you do need to memorise a few key formulae and all definitions (exactly); for example, you may need to memorise the definition of continuity. That’s only a start though – you still need to understand and be able to apply each part of the definition.

Books do not read themselves! Buy a book that your existing knowledge will allow you to understand, even if it is “elementary”, and study it. Do not ignore less advanced books, such as maths books for engineers, which are often a good start, since they stress the main points and give lots of examples. They tell you HOW to apply a technique, which is necessary but not sufficient. You will need to follow this with the more advanced set books which will tell you WHY a technique works and give you the detail and level of treatment required. Advanced texts may look good on your bookshelf but are of most use later when you have already studied the topics covered in class and want a reference text for e.g. project work.

There is a good deal of elementary mathematics material on the web; the best place to start is


Understanding content rich material

For content-rich material with a lot of facts/data, it may help to scan the relevant sections first to get the gist of them, and see in broad terms the logical structure of the content i.e. what depends on what, what follows from what, etc. However, scanning and speed reading are unlikely to work for concept-rich material, such as pages of mathematics, unless you already know quite a lot about the material already. You can also try blanking out some of the material with a sheet of paper, to focus your attention. Dyslexic people sometimes find coloured filters placed over the page are helpful.

Read the relevant section carefully, concentrating on the main ideas and subsidiary points. Jot down the main pointers in the argument very briefly. Study the diagrams carefully. Note that it is unrealistic to expect to read more than a few pages of content-rich material or new mathematics at one sitting, unless you are already familiar with the general topic and are revising. If you get stuck you should; go back a few pages to see what you are missing, have another look at the contents page to see where your reading is leading and where it came from, and finally seek help from your lecturer. Make some notes about the material to aid your understanding, but do not simply copy things from the book which you don’t understand or to have as a record of the material (use a scanner or photocopier for that if you do not have the book). File the notes you have made with other notes from the same topic. Use post-it notes rather than highlighter pens to mark text, so that you can change your mind later.

Do something with what you have read!

Rather than endlessly re-reading in the hope that it will go in somehow, try a few of questions, noting anything you are not clear about so that you can ask people (friends, staff, maths support staff etc.). You need to get your hands dirty with the content – if you really do this, then it will go in. There’s no other way – learning does require engagement and it’s generally pretty hard. Concentrate on what is relevant for your purpose, as it is inefficient to read a whole book when all you need is information from a chapter. Set manageable targets for your reading, e.g. a section each time. Keeping your purpose in mind is especially important when using the web; there is always another tempting link to follow and you could end up wasting a lot of time.

Writing well

Being able to write well by naturally and consistently using correct grammar, expanding your vocabulary and even spelling correctly doesn’t come easily. Certainly you could be taught this, but this ultimately is pointless unless you do most of the work by acting on the feedback given in all your modules and being selective about what you read. It needs be learned, and you can do this yourself by ensuring you read some quality material every week. Read what you are interested in so that you learn additional content beyond your course, but also you will develop a better writing style ‘by osmosis’. The New Scientist and The Economist are certainly worth reading, as are quality newspapers like the Times, Telegraph or Guardian. If all you read is the tabloid press, then that’s how you’ll write; note that tabloid journalists are professional and highly-educated writers, but their brief will be to simplify the vocabulary and usually dumb down the story to make it accessible to their intended readership.

The advantages of being able to write convincingly go well beyond getting better marks; your employment prospects will be very substantially enhanced. Note that degrees and jobs in social sciences like economics will obviously contain lots of writing, but even in STEM careers like maths or computer science where you might not expect a lot, you’ll need to be able to communicate clearly and concisely. You will, at the very least, have clients who will need documentation, but you will also be called on to produce reports for the company’s senior management and more widely, even for the general public. This is particularly true in statistics where what is communicated is rarely just about the numbers (often these just form the appendix) and usually comprises a clear and sometimes extended report or discussion on the numbers meaning and validity.

About the Study Skills for Mathematics pages

These pages were originally created by Martin Greenhow.

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Study Skills in Mathematics by Martin Greenhow is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Study Skills in Mathematics – Introduction

Study Skills in Mathematics – Time Management

Study Skills in Mathematics – Lectures

Study Skills in Mathematics – Reading

Study Skills in Mathematics – Projects and Essays

Study Skills in Mathematics – Using Charts and Graphs

Study Skills in Mathematics – Problem Sheets

Study Skills in Mathematics – Experiments

Study Skills in Mathematics -Presentations

Study Skills in Mathematics – Revision

Study Skills in Mathematics – Exams

Study Skills in Mathematics – Help

Study Skills in Mathematics – Postgraduate Research