Looking for further personal study of Mathematics

[-Daniel-]

I'm a student from the UK who has just finished my A-levels. I am looking for further study materials/advice on how to get into more mathematics. I did not study Further Mathematics at A-level, I only completed a single Mathematics A-level. I am interesting in developing my pure mathematics skills for the future and would appreciate any guidance on texts/materials that would enable me to self-teach to a higher level.

 

[bda23]

Hi Daniel, a great decision! The two fields I would recommend to anyone, on which most of advanced mathematics (and also physics) is based, allows you to develop problem solving skills and conceptual understanding are Analysis and Linear Algebra. For analysis, try "A First Course in Real Analysis" by Protter and Morrey. It is not door-stopper size, but covers a lot of material. The book is very self-contained, the explanations are very good and the exercises useful. Other, thicker books exist, too, which may be very good (e.g. Introduction to Calculus and Analysis by John and Courant), but a book that is too thick may get difficult working through at some point, and for someone starting out in the subject a slightly shorter book may be better (not spending 200 pages on every chapter). For linear algebra, I really don't know, but there are a lot of good books out there.