An introduction to many mathematical topics applicable to quantitative finance that teaches how to “think in mathematics” rather than simply do mathematics by rote.
An analysis of Newton’s mathematical work, from early discoveries to mature reflections, and a discussion of Newton’s views on the role and nature of mathematics.
The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, In addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the "obvious" concepts they have taken for granted earlier.
Historians of science have usually assumed that the mathematicians of the Renaissance took up where prior mathematicians had left off. This important work argues that during the sixteenth century, a crucial change in the concept of number took place which distinguishes ancient and modern mathematics once and for all.
The author regards Francois Vieta as "the true founder of modern mathematics" and demonstrates that to this development of symbolic algebra corresponds a fundamental change in the concept of the number.
"'It takes all the running you can do to keep in the same place,'" remarks the Red Queen to Alice in Lewis Carroll's Through the Looking Glass. "'If you want to get somewhere else, you must run at least twice as fast as that!' It is surely a part of [Carroll's] genius that he has this dialogue take place between two females," Lynn Osen notes dryly, "for nowhere is this metaphor more applicable than it is for women in mathematics." Yet despite the prejudice against intellectual women through almost all ages, there have always been those with the courage a
The papers in this volume cluster about the following topics: the location of the zeros of polynomials and other analytic functions; the approximation of analytic functions by polynomials in which the location of zero is restricted (these papers represent some of Pólya's most influential work); the behavior of the zeros of successive derivatives; the zeros of functions defined by trigonometric integrals; and the signs of derivatives and their analytic character.
The first volume of Pólya's papers deals with singular points of analytic functions and with other broadly related topics, such as conformal mappings, entire functions, and the rate of growth of analytic functions. The papers are arranged in chronological order, but the editor, in his introduction, shows that they fall into four main sets of topics.
The first is concerned with properties of a function (in particular, the location and nature of its singular points) as deduced from the properties of the coefficients in its power series.
This book consists of notes for a second-year graduate course in advanced topology given by Professor George Whitehead at MIT. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory. The book emphasizes (relative) CW-complexes, which the author believes to be the natural setting for obstruction theory, and follows the spirit of J. H. C. Whitehead's "combinatorial homotopy."
An introduction to many mathematical topics applicable to quantitative finance that teaches how to “think in mathematics” rather than simply do mathematics by rote.
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.
An analysis of Newton’s mathematical work, from early discoveries to mature reflections, and a discussion of Newton’s views on the role and nature of mathematics.
