Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications.

The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra.

New to the second edition

  • Several updated chapters, plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers
  • Includes fifteen short ‘essays’ that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material
  • Expanded references
  • Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035

section I|128 pages


chapter 2Chapter 1|8 pages

The Nature of Mathematics

chapter Chapter 2|20 pages


chapter Chapter 3|62 pages


chapter Chapter 4|36 pages

Algebra Redux

section II|254 pages


chapter 130Chapter 5|40 pages

Number Theory

chapter Chapter 6|16 pages

Complex Numbers

chapter Chapter 7|40 pages


chapter Chapter 8|72 pages


chapter Chapter 9|40 pages


chapter Chapter 10|20 pages

The Principal Axes Theorem

chapter Chapter 11|24 pages

What are the Real Numbers?