The History of Mathematics: A Brief Course
Format: PDF / Kindle (mobi) / ePub
Praise for the Second Edition
"An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential."
This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed.
Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include:
- Material arranged in a chronological and cultural context
- Specific parts of the history of mathematics presented as individual lessons
- New and revised exercises ranging between technical, factual, and integrative
- Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book)
- An emphasis on geography, culture, and mathematics
In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.
a/2 + MN, we see that the latter sum is the sum of all the squares MN2 inside KOC (which is the same as the sum of all the squares DE2 inside AHK) plus a times the sum of all the lines MN inside KOC (which is a3/8), plus another a3/8 for the sum of the squares a2/4 of the lines inside the square HBOK. Altogether then, the sum of the squares of the lines inside ABC is twice the sum of the squares of the lines inside AHK, plus a3/4. Since the sum of the squares of the lines inside AHK is one-eighth
Leibniz Although Leibniz wrote a full treatise on combinatorics, which provides the mathematical apparatus for computing many probabilities in games of chance, he did not himself gamble. But he did analyze many games of chance and suggest modifications of them that would make them fair (zero-sum) games. Some of his manuscripts on this topic have been analyzed by De Mora-Charles (1992). One of the games he analyzed is known as quinquenove. This game is played between two players using a pair of
(f(x + ct) + f(x − ct))/2 is a solution of the one-dimensional wave equation that is valid for all x and t, and y(0, t) = 0 = y(L, t) for all t, then f(x) must be an odd function of period 2L. 42.2. Show that the problem X ” (x) − λX(x) = 0, Y ” (y) + λY(y) = 0, with boundary conditions Y(0) = Y(2π), Y′ (0) = Y′ (2π), implies that λ = n2, where n is an integer, and that the function X(x)Y(y) must be of the form (cnenx + dne−nx)(an cos (ny) + bn sin (ny)) if n ≠ 0. 42.3. Show that Fourier series
8.1 Sources 8.2 General Features of Greek Mathematics 8.3 Works and Authors Questions Chapter 9: Greek Number Theory 9.1 The Euclidean Algorithm 9.2 The Arithmetica of Nicomachus 9.3 Euclid's Number Theory 9.4 The Arithmetica of Diophantus Problems and Questions Chapter 10: Fifth-Century Greek Geometry 10.1 “Pythagorean” Geometry 10.2 Challenge No. 1: Unsolved Problems 10.3 Challenge No. 2: The Paradoxes of Zeno of Elea 10.4 Challenge No. 3: Irrational Numbers and Incommensurable
Apollonius' purely synthetic arguments with analytic arguments, based on the algebraic notation we are familiar with. All this labor has no doubt made Apollonius more readable. On the other hand, Apollonius' work is no longer current research; and from the historian's point of view, this kind of tinkering with the text only makes it harder to place the work in proper perspective. Nevertheless, one can fully understand the decision to use symbolic notation, since the mathematical language in which