This document provides a summary of 10 books accessible to AS and higher-level math students.
The books cover a wide range of mathematical topics including proofs of theorems, mathematical physics, geometry, number theory, cryptography, and the history of mathematics. They utilize an engaging and accessible writing style with examples, illustrations, puzzles and anecdotes to communicate complex mathematical concepts to readers with a variety of expertise levels. Many of the books provide intellectual stimulation and insight into the beauty and applications of mathematics.
This document provides a summary of 10 books accessible to AS and higher-level math students.
The books cover a wide range of mathematical topics including proofs of theorems, mathematical physics, geometry, number theory, cryptography, and the history of mathematics. They utilize an engaging and accessible writing style with examples, illustrations, puzzles and anecdotes to communicate complex mathematical concepts to readers with a variety of expertise levels. Many of the books provide intellectual stimulation and insight into the beauty and applications of mathematics.
This document provides a summary of 10 books accessible to AS and higher-level math students.
The books cover a wide range of mathematical topics including proofs of theorems, mathematical physics, geometry, number theory, cryptography, and the history of mathematics. They utilize an engaging and accessible writing style with examples, illustrations, puzzles and anecdotes to communicate complex mathematical concepts to readers with a variety of expertise levels. Many of the books provide intellectual stimulation and insight into the beauty and applications of mathematics.
This document provides a summary of 10 books accessible to AS and higher-level math students.
The books cover a wide range of mathematical topics including proofs of theorems, mathematical physics, geometry, number theory, cryptography, and the history of mathematics. They utilize an engaging and accessible writing style with examples, illustrations, puzzles and anecdotes to communicate complex mathematical concepts to readers with a variety of expertise levels. Many of the books provide intellectual stimulation and insight into the beauty and applications of mathematics.
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Ten books accessible to AS and Higher students
1089 and all that: A Journey into Mathematics It Must be Beautiful David Acheson Graham Farmelo (editor) Oxford University Press, 2002, ISBN 0198516231 Granta Books, 2003, ISBN 1862075557 A mathematician’s account of the maths that’s intrigued The essays in this book cover a wide range of the and interested him, it is written in a highly accessible and scientific research of the twentieth century. The main entertaining style, with plenty of puzzles and illustrations. content is in the field of mathematical physics but It communicates the buzz the author gets from maths as chemistry, environmental science and human behaviour well as introducing many mathematical ideas. Something are also included. The book is very readable and can be to curl up and read or just dip into. enjoyed by students with little mathematical or scientific expertise. The essays are seasoned with anecdotes and Fermat’s Last Theorem short biographies of some of the major scientific Simon Singh personalities of the last hundred years. Fourth Estate, 2002, ISBN 1841157910 Polyominoes Simon Singh’s very readable bestseller focuses on Solomon Golomb Andrew Wiles’ proof of Fermat’s Last Theorem, and also Princeton University Press, 1996, ISBN 0691024448 manages to touch on most of the puzzles that have occupied mathematicians over the centuries. The Daily Polyominoes are shapes made by joining squares edge Mail likened it to a chronicle of an obsessive love affair. to edge. You'll have seen tetrominoes if you've played the game Tetris. This book looks at the mathematics behind also by Simon Singh these shapes. You'll be introduced to proofs by colouring, The Code Book: The Secret History of Codes and which will convince you that you'll never be able to tile a 5 Code-breaking by 4 rectangle with the 5 tetrominoes, and how to create Fourth Estate, 2000, ISBN 1857028899, £9.99 fault-free tilings using dominoes. There's a jigsaw using Flatland: A Romance Of Many Dimensions the 1285 enneominoes (nine squares) but what if, instead Edwin Abbott of squares, you used equilateral triangles? Or cubes? ... Kessinger, 2004, ISBN 0760755876 The Magical Maze This fresh and original mind-expanding book, easily Ian Stewart accessible to layman and mathematician alike, was first Phoenix Press, 1998, ISBN 0753805146 published in 1884. An enduring classic, in story form, it Very readable collection of diverse mathematical topics explores how it might be to live in worlds of other such as the Monty Hall problem, optimisation and chaos. dimensions. The worlds are inhabited by characterful This book places maths in a real life context. Some of the geometric forms whose activities paint a satirical picture mathematics will be familiar to AS students but most will of Victorian Society and, at the same time, illuminate and find something new and stimulating in this book. deepen our understanding of dimensions. The book has the virtues of being short, entertaining and illuminating, a also by Ian Stewart (see also overleaf) combination not always found in Maths books! From Here to Infinity Oxford Paperbacks, 1996, ISBN 0192832026 How to Take a Penalty Rob Eastaway and John Haigh The Penguin Dictionary of Curious and Interesting Robson Books, 2005, ISBN 1861058365 Numbers David Wells This book shows how mathematics can help improve Penguin, 1997, ISBN 0140261494 performance in athletics, darts, football, snooker and tennis, among other sports. It does this, as well as giving This book takes the form of a numerical dictionary much more information about the mathematics of sport, starting with -1 and i and ending with Graham's number. in a lively and accessible fashion. The entries give mathematical properties and historical facts. Many concepts, such as Fermat and Catalan by Rob Eastaway and Jeremy Wyndham numbers, are explained. Tables of common sequences How Long is a Piece of String? are included. This book is ideal for dipping into, by GCSE Robson Books, 2003, ISBN 1861056257 as well as AS students. Find out why 13 is lucky, why 28 Why do Buses Come in Threes? is perfect and about the first uninteresting number. Robson Books, 2006, ISBN 1861058624 Uncle Petros and Goldbach’s Conjecture In Code: A Mathematical Adventure Apostolos Doxiadis Sarah Flannery and David Flannery Faber & Faber, 2000, ISBN 0571202039 Profile Books, 2001, ISBN 1861972717 This novel is a delightful story of the search for a solution Sarah was a teenage mathematician who wrote, with her to a famous problem and of the possible pitfalls in a father’s help, about her childhood with daily puzzles set research project that is too restricted in its outlook. There by her father, which led to a love of problem solving and is a wonderful mix of humour, pathos and maths. also to knowledge of cryptology that won her international recognition. It includes problems to solve (with solutions) and an easy-to-follow explanation of her work. Ten more advanced works The Book of Numbers The Mathematical Universe: An Alphabetical Journey John Conway and Richard Guy Through the Great Proofs, Problems, & Personalities Springer, 2006, ISBN 038797993X William Dunham This book presents a highly idiosyncratic but immensely John Wiley & Sons, 1990, ISBN 0471176613 stimulating choice of properties of numbers – not just This book offers incisive profiles of the great integers, though there are plenty of those, but fractions, theorems, conundrums, disputes, and unsolved real numbers, complex numbers, infinite numbers, and mysteries that have shaped mathematics. Dunham Conway's own most important contribution to doesn’t just state the theorems, he gives the original mathematics: surreal numbers. He approaches the topic proofs in ways accessible to A level students. in his inimitable manner, stripping away much of the Insights include how Euler used the binomial detail to reveal the structure of his argument with unusual theorem in his work on partitions and how clarity. You will see, among other things, how geometric Archimedes calculated the surface area of a sphere. visualization can help with number properties, why also by William Dunham Fibonacci numbers occur in nature, and how to do Euler, the Master of us all arithmetic with infinite numbers. Many of the book's gems MAA, 1999, ISBN 0883853280, £22.99 are easy to pick up and admire with bare hands; others demand perseverance and more mathematical Mathematics: A Very Short Introduction sophistication, but with correspondingly rich rewards. Timothy Gowers Oxford Paperbacks, 2002, ISBN 0192853619 Does God Play Dice? The author captures the essence of maths and gives a Ian Stewart feel for how maths is approached beyond school level. Penguin, 1997, ISBN 0140256024 Many advanced ideas are introduced in a clear and A very accessible introduction to the exciting field of accessible style which relates theoretical concepts to chaos, it gives an insight into the mathematics behind practical applications. fractals as well as many other situations in which you can find chaotic behaviour. Maths for the Mystified Michael J de Smith e: The Story of a Number Troupador, 2006, ISBN 1905237812 Eli Maor From irrational numbers to fractional dimensions, from Princeton University Press, 1998, ISBN 0691058547 image processing to credit card security, this book is a A chronological tale of the development of e. Starting with treasury of the most exciting maths and its application to Napier and progressing to Newton, Leibniz and the today’s sophisticated world. Accurate yet accessible to Bernouillis, it discusses logarithms, series, areas and the lay reader, the book’s content ranges from delightful curves. Applications in mechanics, geometry and music anecdotes to serious insights and applications. The are included. author does not side-step the mathematical reasoning but instead lucidly explores and explains it. Four Colours Suffice Robin Wilson The Millennium Problems Penguin, 2003, ISBN 014100908X Keith Devlin If your experience of proof in mathematics is always Granta Books, 2005, ISBN 1862077355 algebraic or geometric, it is difficult to imagine how you In May 2000 the Clay Foundation in the United States could prove that any map needs at most four colours so offered $1 000 000 for the solution of the seven most that no adjoining regions have the same colour. This difficult mathematical problems today, known as the book explains the ideas clearly and gives a fascinating Millennium Problems. Keith Devlin offers a very clear account of this problem, posed in 1852 and solved in description of the background to these problems and 1976. Even if the four colour proof is complicated, the describes in simple terms exactly what they are. This is a proof that five colours suffice is beautiful. very readable book that gives a good insight into the frontiers of mathematics. The Man Who Knew Infinity: A Life of the Genius Ramanujan The Music of the Primes Robert Kanigel Marcus du Sautoy Abacus, 1992, ISBN 0349104522 Harper Perennial, 2004, ISBN 1841155802 Srinivasa Ramanujan, born in India in 1887, was from an Great mathematics and a great read, as the author early age fascinated with mathematics. Largely self- describes the quest for the truth about the Riemann taught, a letter to G. H. Hardy at Cambridge University Hypothesis, one of the most famous unsolved questions led to him spending most of the rest of his short life in maths, and describes many interesting episodes en working there. This is the story of his life, giving the route. This book’s high reputation is well deserved. reader an insight into his extraordinary mathematical vision and how his ideas continue to fascinate the mathematical world. This booklist was compiled by the Post-16 Subcommittee of the Teaching Committee of The Mathematical Association (www.m-a.org.uk) and published in April 2007.