Product Description

This text provides a self-contained introduction to Pure Mathematics. The style is less formal than in most text books and this book can be used either as a first semester course book, or as introductory reading material for a student on his or her own. An enthusiastic student would find it ideal reading material in the period before going to University, as well as a companion for first-year pure mathematics courses. The book begins with Sets, Functions and Relations, Proof by induction and contradiction, Complex Numbers, Vectors and Matrices, and provides a brief introduction to Group Theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with Continuity and Functions, or hat you have to do to make the calculus work Geoff Smith's book is based on a course tried and tested on first-year students over several years at Bath University. Exercises are scattered throughout the book and there are extra exercises on the Internet.

Product Details

• Amazon Sales Rank: #39205 in Books
• Published on: 1998-02-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 216 pages

Customer Reviews

Great introduction for undergrads.
Geoff Smith takes a light-hearted yet suitably rigorous approach to the "pure core" of any undergraduate maths program. In addition to dealing with Sets, functions/mappings, Complex numbers, elementary linear algebra in the form of vectors and matrices, group theory and sequences and series (the basis for any course on analysis) this is the only book I've seen with a section on how to write a formal proof. Many introductory level texts teach us how to use proof by induction or contradiction, but Smith goes on to speak about style, form and other things which are so difficult to get undergraduates to do! The book closes with two constructions of the reals and introduces the p-adic numbers. While not suitable for a more advanced course in either analysis or algebra, it provides an excellent introduction to both, as well as a good companion to some other text. With an associated web page providing occasional updates and additions to the material covered, as well as suggestions for further reading, this book will stand you in good stead for further maths courses. All in all, highly recomended - get one today!

A great bridge betwen pure maths at school and university
I bought this for one of my children to try to explain what 1st year University pure maths was about. It is written in an amusing style and I finally read in it what I had waited 30 years to have confirmed: that hyperbolic functions arise geometrically from drawing triangles on hyperbolae!

Another highly recommended book of this sort is Martin Liebeck's A concise introduction to pure mathematics