How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for t...

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original...

Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth cent...

“Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!”—Scientific AmericanMany people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and br...

A student in a remedial class who couldn't count by twos is now in an academic program a year ahead of her grade level. An entire Grade 3 class, including so-called slow learners, scores over 90% on a Grade 6-7 math test. These are just two of mathematician John Mighton's many success stories since he started JUMP (Junior Undiscovered Math Prodigies), a not-for-profit organization providing free math tutoring for elementary-level students from low income homes. In The Myth of Ability John ...

Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything--quickly--and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these.The ability to guesstimate on your feet is an essential skill to h...

Turn your hard work into top A-Level results with the Cheeky Shortcut Guide to the most common topics for A level maths revision. This workbook features key exam topics for maths with precise and clear points to help you achieve top marks.This guide covers:Coordinate GeometryTrigonometryBasic AlgebraAdvanced AlgebraSequences and SeriesFunctionsDifferentiationIntegrationNumerical MethodsVectors, Lines and Planes

This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world. It is an excellent training resource for high school students who plan to participate in mathematics contests, and a wonderful collection of problems that can be used by teachers who wish to offer their advanced students some challenging nontraditional problems to work on to build their problem solving skills. It is also an excellent source of problems for ...

The Not-So-Scary Guide to Basic Trigonometry eliminates the fear, frustration and anxiety often associated with learning trigonometry. By introducing a new and intuitive technique called a mathematical tripod, author Kevin Hunter is able to do away with traditional, complicated algebraic methods, resulting in better comprehension and less stress. This slim but effective guide is written in a simple, straightforward style designed to make things easy for the average person who may ...

Doing Math with Python shows you how to use Python to delve into high school–level math topics like statistics, geometry, probability, and calculus. You’ll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once you’ve gotten the hang of things.Along the way, you’ll discover new ways to explore math and gain valuable programming skills that you’ll use throughout your study of math and computer science...

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of ...

In this book, Johnny Ball tells one of the most important stories in world history – the story of mathematics.By introducing us to the major characters and leading us through many historical twists and turns, Johnny slowly unravels the tale of how humanity built up a knowledge and understanding of shapes, numbers and patterns from ancient times, a story that leads directly to the technological wonderland we live in today. As Galileo said, 'Everything in the univers...