Introductory Mathematics
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This text provides a lively introduction to pure mathematics. It 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. The book features numerous exercises of varying difficulty throughout the text.
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We use the language of sets when doing mathematics. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
We use the language of sets when doing mathematics. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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29 of 30 people found the following review helpful
Format:Paperback
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!
3 of 3 people found the following review helpful
Format:Paperback
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
Another highly recommended book of this sort is Martin Liebeck's A concise introduction to pure mathematics
2 of 2 people found the following review helpful
Format:Paperback
This book is a perfect introduction to analysis, a maths text with a sense of humour and clear, often entertaining explanations of sometimes hard-to-grasp concepts.
Can't recommend this enough. I found its lighter tone perfect for when the going got too tough (or, to be precise, dull) in other more "formal" texts.
Can't recommend this enough. I found its lighter tone perfect for when the going got too tough (or, to be precise, dull) in other more "formal" texts.
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