To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.
Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure.
The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory?
Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Master Math: Geometry and the Master Math series as a whole are clear, concise, and yet comprehensive reference sources. They are designed to allow quick access to clearly presented and easy-to-understand explanations of concepts, principles, definitions, examples, and applications. This book was written for students, teachers, tutors, and parents, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and pertinent examples. It provides everything a high school or first year college student needs to know including: explanation of deductive reasoning, how to perform proofs, definitions, theorems, and postulates, Examples pertaining to points, lines, plans, angles, and ratios, coverage on triangles, quadrilaterals, polygons, and much more
The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein.
Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.
Calculus For Dummies is intended for three groups of readers:
- Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
- Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
- Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth.
This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:
- Real-world examples of calculus
- The two big ideas of calculus: differentiation and integration
- Why calculus works
- Pre-algebra and algebra review
- Common functions and their graphs
- Limits and continuity
- Integration and approximating area
- Sequences and series
Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression.
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Budgeting and personal finance, planning for retirement, buying a house, estimating travel and leisure expenses, estimating costs of home repair: modern life presents us with an array of calculations we need to make but may not know how. Now, with his trademark wry humor and simple language, Darrell Huff explains how to figure: the likely outcome of different investments; how much home insurance is enough; whether it makes more sense to buy or lease a new car; the most efficient way to save for future needs, from vacations to college tuition; air-conditioning and heating requirements for a new house; how many rolls of wallpaper you will need for a particular room; and much more. Here are tips for getting the most out of a modest pocket calculator or home computer to make tedious calcuations easy, a handy chapter on Math in a Hurry, and even tips on improving your chances in tennis, horse racing, and blackjack.
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you're looking for an in-depth treatment of the entire subject matter or occasional reinforcement of key algebra concepts, this is the place to find it.
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.