Pure Mathematics by J.K. Backhouse and S.P.T. Houldsworth remains a definitive resource for A-Level and pre-university mathematics students. First published decades ago, the series is praised for its clear explanations, rigorous pedagogy, and extensive graded exercises. Core Content Overview
Most "free" PDFs of Backhouse circulating on file-sharing sites and student forums are:
Pearson has a modern ebook version under a different ISBN (978-0582353875). It is not free, but it is legal, searchable, and contains the full content. You can rent it for 180 days for approximately $30-40. pure mathematics by jk backhouse pdf full
– If a PDF isn’t essential, purchasing a used hardcopy can be cost‑effective. Websites like AbeBooks, Alibris, or Amazon’s used‑book marketplace often list earlier editions for a few dollars.
Below is a of the style you’ll find in the book (this is created by me, not copied from the text). Pure Mathematics by J
| Part | Chapter(s) | Main Themes | |------|------------|-------------| | | 1. Logic & Proof, 2. Set Theory, 3. Functions & Relations | Formal logical language, propositional and predicate logic, methods of proof (direct, contrapositive, contradiction, induction), basic set operations, cardinalities, mappings. | | II. Number Theory | 4. Integers, 5. Divisibility, 6. Congruences, 7. Prime Numbers | Euclidean algorithm, Bézout’s identity, fundamental theorem of arithmetic, modular arithmetic, Chinese remainder theorem, Fermat’s little theorem, Euler’s theorem. | | III. Algebra | 8. Groups, 9. Rings, 10. Fields, 11. Polynomials | Definitions and examples, substructures, homomorphisms, Lagrange’s theorem, cyclic groups, isomorphism theorems, integral domains, factorisation, field extensions. | | IV. Linear Algebra | 12. Vector Spaces, 13. Linear Transformations, 14. Matrices | Basis, dimension, linear independence, rank–nullity theorem, eigenvalues/eigenvectors, diagonalisation, inner product spaces. | | V. Real Analysis | 15. Real Numbers, 16. Sequences & Series, 17. Continuity, 18. Differentiation, 19. Integration | Completeness of ℝ, limits, Cauchy sequences, power series, epsilon‑delta definitions, mean value theorem, Riemann integral, fundamental theorem of calculus. | | VI. Further Topics | 20. Metric Spaces, 21. Topology (basic), 22. Complex Numbers | Metric definitions, open/closed sets, compactness, connectedness, complex arithmetic, Argand diagram, De Moivre’s theorem. |
To illustrate the depth of the book, let’s examine a representative exercise and its solution strategy (fully paraphrased, not reproduced). First published decades ago, the series is praised
: You can find various editions available for borrowing or viewing on the Internet Archive .