Название: Algebra & Geometry: An Introduction to University Mathematics, 2nd Edition
Автор: Mark V. Lawson
Издательство: Chapman and Hall/CRC
Год: 2021
Страниц: 425
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

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.

The aim of this book is to provide a bridge between school and university mathematics centred on algebra and geometry. Apart from pro forma proofs by induction at school, mathematics students usually meet the concept of proof for the first time at university. Thus, an important part of this book is an introduction to proof. My own experience is that aside from a few basic ideas, proofs are best learnt by doing and this is the approach I have adopted here. In addition, I have also tried to counter the view of mathematics as nothing more than a collection of methods by emphasizing ideas and their historical origins throughout. Context is important and leads to greater understanding. Mathematics does not divide into watertight compartments. A book on algebra and geometry must therefore also make connections with applications and other parts of mathematics. I have used the examples to introduce applications of algebra to topics such as cryptography and error-correcting codes and to illustrate connections with calculus.

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