Popular, Recreational, and Miscellaneous Mathematics

The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the "small scale" structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the "elementary particles" of mathematics that build up the mathematical universe?

This is a classic collection of mathematical recreations written by W.W. Rouse Ball. It is a comprehensive first source for information about magic squares, Platonic and Archimedian solids, "Knight's Tours" and other chessboard recreations, and just about any other variety of math-related puzzle you could name.

This book will show you how to perform some magical miracles to impress and entertain your friends. But it will also explain the mathematics behind the tricks and how that same mathematics is used in the real world. It also looks at the varied and exciting sorts of jobs that make use of the mathematics powering your magic.

The goal of this book is to help the reader make the transition from being a consumer of mathematics to a producer of it. This is what is meant by ‘pure’ mathematics. While a consumer of mathematics might learn the chain rule and use it to compute a derivative, a producer of mathematics might derive the chain rule from the rigorous definition of a derivative, and then prove more abstract versions of the chain rule in more general contexts (such as multivariate analysis).

Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions and unsolved problems. Readers will discover exciting mathematics topics from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared.

An analysis of novelistic explorations of modernism in mathematics and its cultural interrelations. Persuasively and engagingly, it demonstrates that modernism's relation to contemporary mathematics was often more analogous than adversarial.

What role does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? This is open access book defends the thesis that mathematics contributes to the explanatory power of science by expressing conceptual rules that allow for the transformation of empirical descriptions.

This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. It is appropriate for either It could also be used as a starting point for undergraduate research topics or a place to find a short undergraduate seminar talk. This is a wonderful book that is not only fun to read, but gives the reader new ideas to think about.

This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction.

This book consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

How is life different from 25 or even 10 years ago? Mathematics has profoundly changed our world, from banking & computers to listening to music. This course is designed for those who haven't had college mathematics but would like to understand some of the mathematical concepts behind important modern applications.

This book highlights the societal and internal pressures preteen and early-teen girls often face when they excel in these subjects, and it shows strategies for overcoming barriers to being themselves and doing what they love while still fitting in socially.

This book is an introduction to the language and standard proof methods of mathematics.