The Heart of Mathematics addresses the big ideas of mathematics (many of which are cutting edge research topics) in a non-computational style intended to be both read and enjoyed by students and instructors, as well as by motivated general readers. It features an engaging, lively, humorous style full of surprises, games, mind-benders, and all without either sacrificing good mathematical thought or relying on mathematical computation or symbols. The authors are award-winning authors, holding awards such as: Distinguished Teaching Award (Burger, from the Mathematical Association of America); Chauvenet Prize (the best expository mathematics writer in the world, Burger, from the MAA) and many others.

The Heart of Mathematics: An invitation to effective thinking (Textbooks in Mathematical Sciences)

Science & Math

MICHAEL STARBIRD

Edward B. Burger

Mathematics

Springer-Verlag Telos

Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

Number Theory Through Inquiry (AMS/MAA Textbooks, 9)

David C. Marshall

Edward Odell

American Mathematical Society

Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning--of mathematics and beyond--joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.

Topology Through Inquiry (AMS/MAA Textbooks, 58)

Francis Su

Lecture Transcript and Course Guidebook: Parts 1 and 2

Change and Motion: Calculus Made Clear (The Great Courses Teaching That Engages the Mind, Parts 1 an by Michael Starbird (2001) Paperback

The Teaching Company

The world of mathematics contains some of the greatest ideas of humankind-ideas comparable to the works of Shakespeare, Plato, and Michelangelo. These mathematical ideas can add texture, beauty, and wonder to your life. Most importantly, you don't have to be a mathematician to have access to this world.A Mathematical Journey: The Joy of Thinking is a course about fun, aesthetics, and mystery-about great mathematical ideas that arise from puzzles, observations of everyday life, and habits of curiosity and effective thinking. It is as much about learning to think abstractly as it is about what we traditionally think of as mathematics. You explore the fourth dimension, coincidences, fractals, the allure of number, and geometry, and bring these weighty notions back down to earth to see how they apply to your own life. Rather than focusing on adding figures or creating equations (in fact, there are fewer numbers than you might expect), this course enables you to uncover and grasp insightful strategies for approaching, enjoying, and understanding the world around you.

The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas, Parts 1 and 2 (The Great Courses Lecture Transcript and Course Guidebook)

Who was the greatest baseball hitter of all time? What is a guilt-free way to get someone to admit to cheating? Which hospital has the best outcome for a given procedure? When is it a good idea to buy a product's extended warranty? How does a tax assessor calculate the market value of a house? These questions all involve the interpretation of statistics. This course is your introduction to a vitally important subject in today's data-driven society. In 24 half-hour lessons, you will explore the principles and methods that underlie the study of statistics. You will sharpen your understanding of basic statistical vocabulary and learn how to extract meaning from data, all while using no more than basic algebra. Statistical information is truly everywhere. You can't look at a newspaper without seeing statistics on virtually every page. You can't talk about the weather forecast without invoking statistics. Statistics obviously arises in business and social science, and even enters the arts in endeavors such as analyzing manuscripts. And you'd better not go to a casino without understanding statistics! When you gain an understanding of how statistics works, you can make it work for you in a variety of life-changing ways.

Meaning from Data: Statistics Made Clear

Statistics Made Clear. Gathering information from Data

The Great Courses Meaning From Data: Statistics Made Clear Part 1 and 2

The Teaching Co.

Calculus. The word has the power to strike fear in the hearts of many people. But it doesn't have to be daunting or inaccessible, even if you aren't a "math person." The 24 lessons of this course will teach you to grasp the power and beauty of calculus, even if you only have a basic understanding of algebra and geometry. Award-winning professor of mathematics Michael Starbird of the University of Texas at Austin is your able guide, committed to opening the door to this powerful subject and making its concepts accessible to all. While calculus has made it possible for humans to build bridges across miles of river, take spaceships to the moon, and predict the patterns of population change around the world, it can be boiled down to just two ideas - the derivative and the integral - both of which arise from simple analysis of motion. In fact, a 1,300-page calculus textbook contains 1,298 pages of examples of these two concepts. You will begin with a discussion of a car driving down a road, discussing its speed and position and their relationship to each other. This simple example begins your exploration of a fascinating and not at all intimidating mathematical subject that will keep you spellbound. You will be able to apply these powerful insights to any situation that changes over time: economics, astronomy, and even baseball. By the end of the course, you will be seeing calculus everywhere you look and finally feel confident that you have gained an appreciation of this powerful mathematical subject.

Change and Motion: Calculus Made Clear, 2nd Edition

The Great Courses

This is an introduction to the concepts of calculus in a way which is understandable to those without a technical background. These are the lecture transcripts &amp; course guidebooks of Professor Michael Starbird of the University of Texas at Austin. There are 24 lectures divided into two books, Part 1 &amp; Part 2.

Change and Motion: Calculus Made Clear, 2nd Edition (Part 1 & 2)

Geometry has long been recognized as a gateway to the highest realms of human thought. These 24 lectures introduce you to the terms, concepts, and astonishing power of geometry. You'll discover the important role this profound mathematical field plays in everything from algebra and calculus to art and architecture. Professor Starbird believes there's no excuse for a dull course on mathematics, a philosophy he pursues throughout these lectures. You'll consider intriguing applications of geometry, including conic sections (the shapes produced by the intersection of a plane and a cone), non-Euclidean geometries (which accurately reflect phenomena in physics and other disciplines), and topology (the branch of mathematics that deals with shapes that retain their identity after twisting and stretching). No other area of mathematics is so richly endowed with interesting examples as geometry, which appeals to both the intellect and the eye. All of geometry's many applications make use of the bedrock concepts of axioms, theorems, and proofs. You'll discover that these traditional techniques are not ends in themselves but tools for gaining new insights. According to Euclid, There is no royal road to geometry. Now there is Professor Starbird's road, which is a delightful and invigorating journey through one of the most glorious inventions of the human mind.

Mathematics from the Visual World

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Books by MICHAEL STARBIRD