Algebra & Geometry

"Algebra and geometry successfully meets its aims. It has a reassuringly large overlap with familiar ideas from school mathematics but reappraises them in a
readable yet rigorous manner. It introduces readers to the style of abstract reasoning that will be the staple of pure mathematics courses at university. It also includes
plenty of nuggets that can be savoured after a first reading (such as the construction of the real numbers via equivalence classes of Cauchy sequences of rationals, and the proofs of the generalised associativity and Cantor-Schroeder-Bernstein theorems). I shall happily recommend this book to prospective undergraduate mathematicians and warmly welcome it to the growing shelf of recent bridging texts."
- The Mathematical Gazette, July 2023

"This book aims to provide a bridge between school mathematics and university mathematics centred on themes from algebra and geometry. In doing so, it seeks to build on intuitions already developed, making them rigorous through an introduction to formal proofs, as well as pointing the way ahead to new ideas that will be met in the years ahead.
[. . .] Algebra and geometry successfully meets its aims. It has a reassuringly large overlap with familiar ideas from school mathematics but reappraises them in a readable yet rigorous manner. It introduces readers to the style of abstract reasoning that will be the staple of pure mathematics courses at university. It also includes plenty of nuggets that can be savoured after a first reading (such as the construction of the real numbers via equivalence classes of Q-Cauchy sequences of rationals, and the proofs of the generalised associativity and Cantor-Schroeder-Bernstein theorems). As such, I shall happily recommend this book to prospective undergraduate mathematicians and warmly welcome it to the growing shelf of recent bridging texts."
- The Mathematical Gazette

"This is an excellent mathematics book on introductory algebra and geometry. It's written for early year university students, but it's not your dull everyday textbook. It's both an easy and an enjoyable read, almost like a book on popular science, but all the while actually teaching you the material. What struck me most, in addition to the broad perspective on mathematics and clear eyed view of the material presented, was the way it brought out wider vistas to ponder over. These things along with the links made between the topics covered will give students a feeling of real accomplishment and, dare I say it, power. This is really a fine book for students and self-learners alike."
-Samuel L. Braunstein, Professor at University of York

"This book introduces the basic ideas that underpin algebra and geometry at degree level.It rewards the student with a true feel for university mathematics and so, as the student progresses through the subject, it is likely to acquire the status of an old and trusted friend. As its contents become ever more familiar, the owner will value it as a prized possession."
-Peter Higgins, Professor at Essex University and the author of Mathematics for the Curious