Mathematics

Steven Goldberg, “Mathematical Elegance: An Approachable Guide to Understanding Basic Concepts”

Rudolf Taschner, “Game Changers: Stories of the Revolutionary Minds behind Game Theory”

Hung-Hsi Wu, “Teaching School Mathematics: Algebra”

Raju, “Cultural Foundations Of Mathematics, Volume X Part 4”

V.A. Ditkin, A.P. Prudnikov, “Operational Calculus in Two Variables and Its Applications (Dover Books on Mathematics)”

Steven Goldberg, “Mathematical Elegance: An Approachable Guide to Understanding Basic Concepts”

ISBN: 1412854644 | 2015 | EPUB | 108 pages | 602 KB

The heart of mathematics is its elegance; the way it all fits together. Unfortunately, its beauty often eludes the vast majority of people who are intimidated by fear of the difficulty of numbers. Mathematical Elegance remedies this. Using hundreds of examples, the author presents a view of the mathematical landscape that is both accessible and fascinating.

At a time of concern that American youth are bored by math, there is renewed interest in improving math skills. Mathematical Elegance stimulates students, along with those already experienced in the discipline, to explore some of the unexpected pleasures of quantitative thinking. Invoking mathematical proofs famous for their simplicity and brainteasers that are fun and illuminating, the author leaves readers feeling exuberant–as well as convinced that their IQs have been raised by ten points.

A host of anecdotes about well-known mathematicians humanize and provide new insights into their lofty subjects. Recalling such classic works as Lewis Carroll’s Introduction to Logic and A Mathematician Reads the Newspaper by John Allen Paulos, Mathematical Elegance will energize and delight a wide audience, ranging from intellectually curious students to the enthusiastic general reader.

Rudolf Taschner, “Game Changers: Stories of the Revolutionary Minds behind Game Theory”

ISBN: 1633883736 | 2017 | EPUB | 237 pages | 1 MB

In this lively history of game theory, a gifted math educator and science writer explains for lay readers the uses and value of this innovative yet easy-to-understand approach to mathematical modeling. Essentially, game theory interprets life as a game with mathematical rules. By following the rules, decisions can be calculated that result in the greatest benefit for all participants.

The author takes the reader from the 17th century through the Cold War to today’s age of turbo capitalism. Along the way he introduces such leading contributors as Blaise Pascal in the 17th century, who invented the theory of probability; Ludwig Wittgenstein in the 20th century, who conceived of the world as a play of words; John Nash (the subject of A Beautiful Mind) in the 1950s, who laid the foundation of modern game theory; and today’s practitioners who apply the theory to global finance and military strategy.

As the author shows, game theory is more than a type of cost-benefit analysis; ultimately, it is a quest for meaning.

Hung-Hsi Wu, “Teaching School Mathematics: Algebra”

2016 | ISBN-10: 1470427214 | 283 pages | PDF | 2 MB

This is a systematic exposition of introductory school algebra written specifically for Common Core era teachers. The emphasis of the exposition is to give a mathematically correct treatment of introductory algebra. For example, it explains the proper use of symbols, why “variable” is not a mathematical concept, what an equation is, what equation-solving means, how to define the slope of a line correctly, why the graph of a linear equation in two variables is a straight line, why every straight line is the graph of a linear equation in two variables, how to use the shape of the graph of a quadratic function as a guide for the study of quadratic functions, how to define a parabola correctly, why the graph of a quadratic function is a parabola, why all parabolas are similar, etc. This exposition of algebra makes full use of the geometric concepts of congruence and similarity, and it justifies why the Common Core Standards on algebra are written the way they are.

Raju, “Cultural Foundations Of Mathematics, Volume X Part 4”

2007 | ISBN-10: 8131708713 | 480 pages | PDF | 21 MB

Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE: Project of History of Science, Philosophy and Culture in Indian Civilization Volume X Part 4

V.A. Ditkin, A.P. Prudnikov, “Operational Calculus in Two Variables and Its Applications (Dover Books on Mathematics)”

ISBN: 0486818497 | 2017 | EPUB | 176 pages | 55 MB

A concise monograph by two Russian experts provides an account of the operational calculus in two variables based on the two-dimensional Laplace transform. Suitable for advanced undergraduates and graduate students in mathematics, the treatment requires some familiarity with operational calculus in one variable.

Part One of the two-part approach presents the fundamental theory in two chapters, examining the two-dimensional Laplace transform and offering basic definitions and theorems of the operational calculus in two variables and its applications. Part Two presents tables of formulae for various categories of functions, including rational and irrational functions; exponential and logarithmic functions; cylinder, integral, and confluent hypergeometric functions; and other areas.