Reviews

From The Assayer:

Excellent for the novice Math student by jsprpl
Content: better than 80%
Writing: better than 90%

I encountered this book while browsing through www.eevl.ac.uk . It's goal is to prepare you for your first encounter with analysis. It is divided into three chapters. The first is about set theory, the second about the real number system and the third about vector spaces. I have to say I only read the first chapter and part of the second (yet). 'Basic Concepts...' has a very 'clean' feeling to it. The text seems structured and to the point without losing any detail. The book doesn't waste your time trying to translate basic concepts into layman's terms from which you will have to 'recover' at a later stage and are better understandable when served 'straight up'. For example in the second chapter you are immediately introduced to the field axioms and not, as other texts do, to 'properties of numbers' only to be told a year later that, 'by the way', these are referred to as the axioms of an ordered field. There is a strong focus on making the student familiar with the proper notation right from the start. For example quantifiers are introduced very early where as other texts seem to take hundreds of pages to get there even though quantifiers are very useful even to the most novice of math students. The author helps you in seeing that the right notation makes mathematics clearer and thus easier to understand, that notation is something useful not something to break your head over. I like to see 'Basic Concepts...' as a toolbox in which you can find the basic tools to start studying analysis. It doesn't leave you in fear of what's to come but with a feeling of preparedness. Which probably is a wrong feeling ;-) This book comes highly recommended. It is probably useful as well to those already deep into their analysis study to occasionally 'unconfuse' themselves about some of the basic concepts.

The above review is copyrighted by its author, and is copylefted under the following license: Open Publication License 1.0 without options A or B.

From The National Science Digital Library Scout Report for Mathematics, Engineering, and Technology:

The Trillia Group: Basic Concepts of Mathematics [pdf]

Math students will find this online textbook to be a valuable study aid to complement their lecture notes and standard class text. It is intended to help students, especially those majoring in mathematics, make the transition from standard math classes to more rigorous, advanced topics and abstract theory. Spanning over 200 pages, the text covers "basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields," and Euclidean spaces. The book is not free to everyone, so it is important to read the terms and conditions before downloading.

Recognition

From EEVL: The Internet Guide to Engineering, Mathematics, and Computing:

Elias Zakon's Basic Concepts of Mathematics is an EEVL Key Site.