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.
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ABCD algebra angle sum Archimedes arithmetic axes axiom base binary bit pattern Brahmi numerals calculation called Cayley table centre chapter circle circuit column coordinates cyclic group decimal diagram dice dimensional equal equation Euler's formula Euler's Theorem example Exercise factors figure fraction full adder gate given gives gradient Greek group of order Hexadecimal hexagon inputs integers inverse logic magic square mathematical induction mathematician mathematics matrix Mayan mid point multiplication negative numbers nines complements number system octal output parallel parallelogram pentagon perfect fifth Pick’s Theorem place value polygon position probability Proof propositional calculus Prove Pythagoras Pythagorean triple radius rectangle represented result rotation side Solution Splinge Splodge square statement straight line subtraction Sudoku Suppose symbol symmetry total number transformation triangle truth set truth table Vert vertex vertices write zero