The Beginnings and Evolution of AlgebraThe elements of algebra were known to the ancient mesopotamians at least 4000 years ago. Today, algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? An illuminating read for historians of mathematics and working algebraists looking into the history of their subject. |
Contents
Chapter 1 Elements of algebra in ancient Babylonia | 1 |
Chapter 2 Ancient Greek geometric algebra | 11 |
Chapter 3 The birth of literal algebra | 35 |
Chapter 4 Algebra in the Middle Ages in the Arabic East and in Europe | 49 |
Chapter 5 The first achievements of algebra in Europe | 67 |
Chapter 6 Algebra in the 17th and 18th centuries | 91 |
Chapter 7 The theory of algebraic equations in the 19th century | 109 |
Common terms and phrases
addition ancient applied Arabic arbitrary arithmetic associated Babylonians base Book calculus called century classes coefficients commutative complex complex numbers composition connection considered construction contains cubic curves defined definition denoted determinate Diophantus discovery divisible domain elements equal equation equivalent Euler example expressed extension factors field Figure formula functions fundamental Galois Gauss geometric geometric algebra given idea ideal important integers introduced known later letters linear literal magnitudes mathematicians mathematics means method multiplication namely negative numbers obtained operations period permutations polynomial positive possible powers prime problem proof propositions proved quadratic equations radicals rational reduced respect result ring roots rules segments showed side solution solvable solve square subgroup substitution symbols takes theorem theory transformation triangle unknown values Viète wrote