Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.
Have you ever wondered how your GPS can find the fastest way to your destination, selecting one route from seemingly countless possibilities in mere seconds? How your credit card account number is protected when you make a purchase over the Internet? The answer is algorithms. And how do these mathematical formulations translate themselves into your GPS, your laptop, or your smart phone? This book offers an engagingly written guide to the basics of computer algorithms.
In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception—the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space—were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence.
The classical view of concepts in psychology was challenged in the 1970s when experimental evidence showed that concept categories are graded and thus cannot be represented adequately by classical sets. The possibility of using fuzzy set theory and fuzzy logic for representing and dealing with concepts was recognized initially but then virtually abandoned in the early 1980s. In this volume, leading researchers—both psychologists working on concepts and mathematicians working on fuzzy logic—reassess the usefulness of fuzzy logic for the psychology of concepts.
Volume 2 of Musimathics continues the story of music engineering begun in Volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform.
Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton’s work that has not been tightly connected to Newton’s actual practice: his philosophy of mathematics.
In problem solving, as in street fighting, rules are for fools: do whatever works—don’t just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.
Robert Reitano’s Introduction to Quantitative Finance offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. This manual provides solutions to the Practice Exercises in the text.
This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems.
Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming.