This book provides an introduction to University maths courses and therefore bridges the gap between high-school and University-level maths. The style is less formal than in most text books and the book could be used as material for an introductory course (one semester) to analysis, or as preliminary reading material for the student who has opted for a science degree.

As may be gathered from the table of contents, the book starts with
Sets, Functions and Relations, Proof by induction and *reductio
ad absurdum*, Complex numbers, Vectors and Matrices and a short
introduction to group theory. A grasp of such topics should facilitate
the approach to delta-epsilon analysis and tackling the hard problems
of continuity and limits. Exercises and problems are found throughout
the book and the author has even provided additional exercises at the
following web address: http://www.maths.bath.ac.uk/~masgcs/book1/.
The book is written in a lively style and makes interesting reading
for those who want to use it.

(translated from the Italian by Anna Beria).

Geoff Smith | Introductory Mathematics: Algebra and Analysis | group pub forum