Preparing for University Mathematics

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Subject: Maths » A-level Maths
Last updated: 19/06/2018
Tags: maths tutor caterham, maths tutor coulsdon, maths tutor croydon, maths tutor epsom, maths tutor reigate

Even when the A-level exams are over, prospective university Maths students cannot afford to take the whole summer off. Mathematics requires frequent practice in order to develop and maintain skills. The diligent student will start their university preparation work no more than 1-2 weeks after their final A-level exam. 

What kind of mathematics can prepare a student for university? University Maths is typically more abstract than school Maths, with concepts that are thinly covered at A-level - such as mathematical proofs - being critical at the university stage. Fortunately, there are a number of good resources that can be used as a basis for self-study in the run-up to university Maths courses. 

One of my favourite Maths books of any level is "How To Think Like A Mathematician: A Companion to Undergraduate Mathematics" by Kevin Houston. This book covers a wide variety of topics, including:

  • study skills for mathematicians
  • how to think logically
  • definitions, theorems and proofs
  • techniques of proof
  • foundational maths such as modular arithmetic

Reading the Kevin Houston book is a great start to a summer of preparation for undergraduate Maths courses. 

Whilst "How To Think Like A Mathematician" covers the basics of abstract reasoning, another area to consolidate during the summer would be Precalculus, which includes many of the methods that are covered at GCSE and A-level Maths, and a lot more mathematical tools beside those that the student would have previously encountered. 

A great book for Precalculus is "Schaum's Outline Of Precalculus" (2nd Edition) which has plenty of worked examples and exercises for a prospective undergraduate to expand their mathematical toolkit. It could be read in parallel with "How To Think Like A Mathematician", but a cleverer way to use the Precalculus book is to use it to follow Dr Kevin Houston's advice of constructing one's own examples and proofs. This may be difficult to do at first reading, so the summer could be used to cover "Schaum's Outline of Precalculus" twice - once at a superficial level in which the student does exactly those exercises shown, and then at a deeper level in which the student applies the techniques of proof from Dr Kevin Houston's book, to develop more abstract exercises from the material in the Schaum's book. 

This can be a quite complicated endeavour, but direction from a mathematics tutor should improve the student's chances of success.  

Another resource that can be used for preparing for university maths is the book "Bridging the Gap to University Mathematics" by Martin Gould and Edward Hurst. This book was written by university Maths students, for students who are about to begin their undergraduate studies. This book covers more Precalculus material than Dr Kevin Houston's book, but less Precalculus than the Schaum's Outline. It does dip into mathematical proofs, but only midway through the book, and in a less extensive fashion than Dr Kevin Houston's book.

If you can afford only one book, I would recommend Dr Kevin Houston's book. If you can afford two, I would recommend both that and the Precalculus book from Schaum's. I found the third book a little too verbose and too thin on details for my liking, but if you have covered the first two books comfortably and have the time, I would suggest at least reading through a library version of the Martin Gould and Edward Hurst book.

Nyasha Madavo A-level Maths Tutor (Croydon)

About The Author

I help students to learn in a way that is tailored to their interests within a particular subject. A Cambridge graduate, I have degrees in Economics and mathematical Computer Science. I have professional experience in Finance.

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