Games that show how mathematics can solve the apparently unsolvable. This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.

A look at the extraordinary ways the brain turns thoughts into actions—and how this shapes our everyday lives Why is it hard to text and drive at the same time? How do you resist eating that extra piece of cake? Why does staring at a tax form feel mentally exhausting? Why can your child expertly fix the computer and yet still forget to put on a coat? From making a cup of coffee to buying a house to changing the world around them, humans are uniquely able to execute necessary actions. How do we do it? Or in other words, how do our brains get things done? In On Task, cognitive neuroscientist David Badre presents the first authoritative introduction to the neuroscience of cognitive control—the remarkable ways that our brains devise sophisticated actions to achieve our goals. We barely notice this routine part of our lives. Yet, cognitive control, also known as executive function, is an astonishing phenomenon that has a profound impact on our well-being. Drawing on cutting-edge research, vivid clinical case studies, and examples from daily life, Badre sheds light on the evolution and inner workings of cognitive control. He examines issues from multitasking and willpower to habitual errors and bad decision making, as well as what happens as our brains develop in childhood and change as we age—and what happens when cognitive control breaks down. Ultimately, Badre shows that cognitive control affects just about everything we do. A revelatory look at how billions of neurons collectively translate abstract ideas into concrete plans, On Task offers an eye-opening investigation into the brain’s critical role in human behavior.

Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem. Features A collection of the world’s best mathematical puzzles Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.

This book consists of 200 difficult puzzles of a variety of different types focussing on maths and numerical reasoning. Questions include mathematical grid puzzles such as killer Sudoku and numerical crosswords, as well as maths-based logic and pattern puzzles. Puzzle artworks and full-colour illustrations are included throughout.

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.

Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.