Algebra & Geometry: An Introduction to University Mathematics

Algebra & Geometry: An Introduction to University Mathematics 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 solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra.

• 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.

Mark V. Lawson is a professor in the Department of Mathematics at Heriot-Watt University. Prof. Lawson has published over 70 papers and has given seminars on his research work both at home and abroad. His research interests focus on algebraic semigroup theory and its applications. In 2017, he was awarded the Mahoney-Neumann-Room prize by the Australian Mathematical Society for one of his papers.