This textbook offers a comprehensive undergraduate course in real analysis in one variable.
Taking the view that analysis can only be properly appreciated as a rigorous theory the book
recognises the difficulties that students experience when encountering this theory for the
first time carefully addressing them throughout. Historically it was the precise description
of real numbers and the correct definition of limit that placed analysis on a solid foundation.
The book therefore begins with these crucial ideas and the fundamental notion of sequence.
Infinite series are then introduced followed by the key concept of continuity. These lay the
groundwork for differential and integral calculus which are carefully covered in the following
chapters. Pointers for further study are included throughout the book and for the more
adventurous there is a selection of nuggets exciting topics not commonly discussed at this
level. Examples of nuggets include Newton's method the irrationality of pi Bernoulli numbers
and the Gamma function. Based on decades of teaching experience this book is written with the
undergraduate student in mind. A large number of exercises many with hints provide the
practice necessary for learning while the included nuggets provide opportunities to deepen
understanding and broaden horizons.
