Posted by: Alexandre Borovik | May 18, 2011

Help! Are there any GOOD A-level mathematics textbooks?

Indeed, can anyone recommend GOOD A-level mathematics textbooks? I mean REALLY GOOD, the ones that can act as model of a good textbook?

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  1. The most comprehensive way to learn maths post-GCSE is to completely ignore advice from any government guided program or curricular. Instead, get into the mind-set of learning for the sake of learning.

    This brings me to book [1], which should be a standard textbook imho. In my school, they didn’t have many copies of this, and the few that were available were older than me. Maths doesn’t change as time goes on, so everything in this book is still relevant. What I liked about this one is that it gives you something extra and isn’t limited by what will be on the exam. Thanks to this one, I can inverse 3×3 matricies in less than half a page of A4.

    Unlike [1], Book [2] covers just the bits found in the further maths course. This is the model of a good text book that you’re looking for. A lot of the content in an FM course comes as self contained ideas* and this book reflects that as it guides the reader through each concept from introduction, to competency.

    Book [3] is probably a book to avoid. All of A-level is summarised in chapter 1 since this is a degree level textbook. However, if you can get hold of this one, then it serves as a very good source of revision material before the exam.
    This is what real text books start to look like, no fancy gimmicks or jokes like [4], but one that builds upon ideas developed in previous sections. This is something that you don’t read, you reference it.

    For some light reading, look for the works of Martin Gardner. A fantastic puzzle maker including the classic [5].

    * eg. You don’t need to know Cartesian coordinates to learn polar coordinates.






  2. Now that there exist other, superior methods of learning, I’d like to ask more generally – are there good textbooks?

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