Bui's Maths Book Vol. 1: a Compendium of Mathematical Invention

Bui?s Maths Book is in two volumes. Volume 1 contains 15 chapters and volume 2 contains 13 chapters.

Chapter 1 introduces the number systems invented by the Babylonians, the Egyptians, the Greeks, the Chinese, the Etruscans, the Maya and the Hindus and Chapter 2 shows how Euclid?s axioms quickly build up into a theory of plane geometry. Chapters 3 and 4 concern Pythagoras?s theorem and his ideas on the musical scale and a number of results based upon the Pythagoras diagram. Chapters 5 to 8 show how the binary and hexadecimal number systems with the algebra of George Boole can be applied the design of computer logic circuits. Chapter 9 illustrates a mathematical approach to problem solving by discussing how to find the length of a roll of paper, how to stop a table from wobbling, how to make a snooker ball return to its starting position and how to design a football. Chapter 10 concerns topology and Chapter 11 deals with Descartes coordinate geometry. Chapters 12 and 13 deal with matrices, transformations and the theory of groups. Chapter 14 uses mathematical induction to sum series and prove the binomial theorem and Chapter 15 discusses probability.

Volume 2 continues the story with chapters on sequences and series, Fibonacci, trigonometry, areas and volumes, Ceva, Menelaus and Morley, circles, special relativity, complex numbers, calculus and conics. There are many solved examples and exercises, all with answers. It should appeal both to the general reader and to the mathematics specialist.