Prepare for success in mathematics with DOING MATHEMATICS: AN INTRODUCTION TO PROOFS AND PROBLEM SOLVING! By discussing proof techniques, problem solving methods, and the understanding of mathematical ideas, this mathematics text gives you a solid foundation from which to build while providing you with the tools you need to succeed. Numerous examples, problem solving methods, and explanations make exam preparation easy.

If someone told you that mathematics is quite beautiful, you might be surprised. But you should know that some people do mathematics all their lives, and create mathematics, just as a composer creates music. Usually, every time a mathematician solves a problem, this gives rise to many oth ers, new and just as beautiful as the one which was solved. Of course, often these problems are quite difficult, and as in other disciplines can be understood only by those who have studied the subject with some depth, and know the subject well. In 1981, Jean Brette, who is responsible for the Mathematics Section of the Palais de la Decouverte (Science Museum) in Paris, invited me to give a conference at the Palais. I had never given such a conference before, to a non-mathematical public. Here was a challenge: could I communicate to such a Saturday afternoon audience what it means to do mathematics, and why one does mathematics? By "mathematics" I mean pure mathematics. This doesn't mean that pure math is better than other types of math, but I and a number of others do pure mathematics, and it's about them that I am now concerned. Math has a bad reputation, stemming from the most elementary levels. The word is in fact used in many different contexts. First, I had to explain briefly these possible contexts, and the one with which I wanted to deal.

Children Doing Mathematics provides a reliable and up to date review of the substantial recent work in children' mathematical understanding. The authors also present important new research on children's understanding of number, measurement, arithmetic operation and fractions both in and out of school. The central theme of Children Doing Mathematics is that there are crucial conditions for children's mathematical learning. Firstly, children have to come to grips with conventional mathematical systems. Secondly, but equally important, they have to be able to present mathematical knowledge in a way that solves problems. The book also discusses how mathematical activities and knowledge involve much more than what is currently viewed as mathematics in the school curriculum. Most recent work illustrates how children can be successful in mathematical activities outside school whereas they fail in similar activities in the classroom. Through these two underlying themes the authors bring together discussions on conventional mathematical learning and on real life mathematical success. In so doing, they also highlight new and better ways of analysing children's abilities and of advancing their learning in school.

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. Learn how to: –Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots –Explore set theory and probability with programs for coin flips, dicing, and other games of chance –Solve algebra problems using Python’s symbolic math functions –Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set –Write programs to find derivatives and integrate functions Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. You’ll write an inequality solver, plot gravity’s effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 "darts" at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more. Whether you’re interested in math but have yet to dip into programming or you’re a teacher looking to bring programming into the classroom, you’ll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math. Uses Python 3

Rediscovering Mathematics is aimed at a general audience and addresses the question of how best to teach and study mathematics. The book attempts to bring the exciting and dynamic world of mathematics to a non-technical audience. With so much focus today on how best to educate the new generation and make mathematics less rote and more interactive, this book is an eye-opening experience for many people who suffered with dull math teachers and curricula. Rediscovering Mathematics is an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics. By focusing on problem solving, and discouraging rote memorization, the book shows how to learn and teach mathematics through investigation, experimentation, and discovery. Rediscovering Mathematics is also an excellent text for training math teachers at all levels. Topics range in difficulty and cover a wide range of historical periods, with some examples demonstrating how to uncover mathematics in everyday life, including: number theory and its application to secure communication over the Internet, the algebraic and combinatorial work of a medieval mathematician Rabbi, and applications of probability to sports, casinos, and gambling. Rediscovering Mathematics provides a fresh view of mathematics for those who already like the subject, and offers a second chance for those who think they don't.

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

This book discusses some ways of doing mathematical work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians--all depend on mathematics, what will work out and what won't. And the mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The causes studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, the stability of matter, the Ising model, and the Langlands Program in number theory and representation theory. Contents: Convention: How Means and Variances are Entrenched as Statistics; Subject: The Fields of Topology; Appendix: The Two-Dimensional Ising Model of a Ferromagner; Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis; Analogy; A Syzygy Between a research Program in Mathematics and a Research Program in Physics, Each of Which is Itself an Analogy; Mathematics in Concreto. Readership: Mathematicians, Physicists, philosophers and historians of science.

Bring joy and energy to math learning without adding to your already-packed schedule! Here are 150 fun and engaging math activities suitable for kindergartners to 5th graders, with math-themed ideas for all four Morning Meeting components: greeting, group activity, sharing, and morning message. Use these games, songs, chants, hands-on experiments, and more to inspire students' interest in math and help them practice skills. Each activity includes easy how-to steps; relevant NCTM content and process standards; specific math skills addressed; materials needed (all require few or no materials); tips on preparing students for success; math vocabulary to emphasize; and variations and extensions.

"Making Mathematics with Needlework will inspire mathematicians, mathematics educators, and crafters; every chapter has an overview as well as sections on mathematics and mathematics education and detailed instructions for completing the chapter's project. All readers will be able to understand the overview sections, as they include introductions to the various fiber arts as well as summaries of the mathematical content. While the mathematics sections are written for mathematicians, the authors have made a special effort to make their work accessible to lay readers by providing definitions of mathematical terms and many diagrams. The project sections are written for crafters, so that non-mathematician readers can have a tangible experience with mathematical concepts."--BOOK JACKET.

Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see 'an identity in a manifold presentation of profiles,' as the phenomenologists would say.This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an 'ugly' first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude.