Pure Mathematics 1 (4th Edition)

Specifications

Book Description

“Pure Mathematics 1” (4th Edition) by J.K. Backhouse, Peter B. Houldsworth, and P.J.F. Horril is a comprehensive textbook that covers fundamental concepts in pure mathematics. Here's an overview of what you can expect from this book:

1. Foundational Topics: The book starts with foundational topics in pure mathematics, providing a solid understanding of key concepts such as sets, logic, and functions. These topics serve as the building blocks for more advanced mathematical concepts covered later in the book.
2. Algebra: The text covers various algebraic topics, including equations, inequalities, polynomials, and algebraic fractions. It presents techniques for solving equations and manipulating algebraic expressions, with a focus on developing problem-solving skills.
3. Geometry: Geometry topics include Euclidean geometry, coordinate geometry, and trigonometry. The book covers properties of geometric shapes, geometric constructions, and applications of geometry in real-world contexts.
4. Calculus: The book introduces the basic principles of calculus, including limits, differentiation, and integration. It covers techniques for finding derivatives and integrals, as well as applications of calculus in areas such as rates of change and optimization.
5. Vectors and Matrices: The text explores vector algebra and matrix algebra, including operations with vectors and matrices, vector spaces, and matrix transformations. It also covers applications of vectors and matrices in geometric problems and systems of linear equations.
6. Sequences and Series: The book discusses arithmetic sequences, geometric sequences, and series. It covers topics such as convergence tests for series, arithmetic and geometric series, and applications of sequences and series in mathematical analysis.
7. Complex Numbers: Complex numbers and their properties are introduced, including operations with complex numbers, the Argand diagram, and the polar form of complex numbers. The book explores applications of complex numbers in solving equations and analyzing functions.
8. Further Topics: Depending on the edition, the book may also cover additional topics such as discrete mathematics, probability, and statistics. These topics provide further depth and breadth to the study of pure mathematics.
9. Exercises and Examples: Throughout the book, there are numerous exercises and worked examples to reinforce learning and develop problem-solving skills. These exercises range from basic drills to more challenging problems, allowing students to practice and apply their understanding of mathematical concepts.

Overall, “Pure Mathematics 1” serves as a comprehensive resource for students studying pure mathematics at the undergraduate level. It provides a solid foundation in fundamental mathematical concepts and techniques, preparing students for more advanced coursework in mathematics and related fields.