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prove it: the art of mathematical argument by bruce edwards [pdf]

### Prove It: The Art of Mathematical Argument by Bruce H. Edwards

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Prove It: The Art of Mathematical Argument written by Bruce H. Edwards, Ph.D., Professor of Mathematics, University of Florida.
The goal of this course is to further your understanding and appreciation of calculus. Just as in Understanding Calculus: Problems, Solutions, and Tips, you will see how calculus plays a fundamental role in all of science and engineering.
In the first third of the course, you’ll use the tools of derivatives and integrals that you learned in calculus I to solve some of the great detective stories of mathematics—differential equations. The middle portion of the course will take you to the beautiful world of infinite series and their connection to the functions you have learned about in your studies of precalculus and calculus. Finally, the third part of the course will lead to a solid understanding of key concepts from physics, including particle motion, velocity, and acceleration. Calculus is often described as the mathematics of change. The concepts of calculus—including velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and work—have enabled scientists, engineers, and economists to model a host of real-life situations.
For example, a physicist might need to know the work required for a rocket to escape Earth’s gravitational field. You will see how calculus allows the calculation of this quantity. An engineer might need to know the balancing point, or center of mass, of a planar object. The integral calculus is needed to compute this balancing point. A biologist might want to calculate the growth rate of a population of bacteria, or a geologist might want to estimate the age of a fossil using carbon dating. In each of these cases, calculus is needed to solve the problem. Although precalculus mathematics (geometry, algebra, and trigonometry) also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference between precalculus mathematics and calculus. Precalculus mathematics is more static, whereas calculus is more dynamic.

Book Detail :-
Title: Prove It: The Art of Mathematical Argument
Edition:
Author(s): Bruce H. Edwards
Publisher: The Teaching Company
Series: The Great Courses
Year: 2012
Pages: 168
Type: PDF
Language: English
ISBN: 1598039563,9781598039566
Country: US

The author of this book Professor Bruce H. Edwards has been a Professor of Mathematics at the University of Florida since 1976. He received his B.S. in Mathematics from Stanford University in 1968 and his Ph.D. in Mathematics from Dartmouth College in 1976. From 1968 to 1972, he was a Peace Corps volunteer in Colombia, where he taught mathematics (in Spanish) at Universidad Pedag�gica y Tecnol�gica de Colombia.
Professor Edwards�s early research interests were in the broad area of pure mathematics called algebra. His dissertation in quadratic forms was titled �Induction Techniques and Periodicity in Clifford Algebras.� Beginning in 1978, Professor Edwards became interested in applied mathematics while working summers for NASA at the Langley Research Center in Virginia. This work led to his research in numerical analysis and the solution of differential equations. During his sabbatical year, 1984 to 1985, he worked on two-point boundary value problems with Professor Leo Xanthis at the Polytechnic of Central London. Professor Edwards�s current research is focused on the algorithm called CORDIC that is used in computers and graphing calculators for calculating function values.
Professor Bruce H. Edwards has coauthored a number of mathematics textbooks with Professor Ron Larson of Penn State Erie, The Behrend College. Together, they have published leading texts in calculus, applied calculus, linear algebra, finite mathematics, algebra, trigonometry, and precalculus.
Over the years, Professor Edwards has received many teaching awards at the University of Florida. He was named Teacher of the Year in the College of Liberal Arts and Sciences in 1979, 1981, and 1990. In addition, he was named the College of Liberal Arts and Sciences Student Council Teacher of the Year and the University of Florida Honors Program Teacher of the Year in 1990. He also served as the Distinguished Alumni Professor for the UF Alumni Association from 1991 to 1993. The winners of this two-year award are selected by graduates of the university. The Florida Section of the Mathematical Association of America awarded Professor Edwards the Distinguished Service Award in 1995 for his work in mathematics education for the state of Florida. His textbooks have been honored with various awards from the Text and Academic Authors Association.
Professor Edwards has taught a wide range of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He particularly enjoys teaching calculus to freshman because of the beauty of the subject and the enthusiasm of the students. Professor Edwards has been a frequent speaker at both research conferences and meetings of the National Council of Teachers of Mathematics. He has spoken on issues relating to the Advanced Placement calculus examination, especially on the use of graphing calculators.

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Book Contents :-
Prove It: The Art of Mathematical Argument written by Bruce H. Edwards cover the following topics. '
Course Scope
1. What Are Proofs, and How Do I Do Them?
2. The Root of Proof—A Brief Look at Geometry
3. The Building Blocks—Introduction to Logic
4. More Blocks—Negations and Implications
5. Existence and Uniqueness—Quantifi ers
7. Let’s Go Backward—Proofs by Contradiction
8. Let’s Go Both Ways—If-and-Only-If Proofs
9. The Language of Mathematics—Set Theory
10. Bigger and Bigger Sets—Infi nite Sets
11. Mathematical Induction
12. Deeper and Deeper—More Induction
13. Strong Induction and the Fibonacci Numbers
14. I Exist Therefore I Am—Existence Proofs
15. I Am One of a Kind—Uniqueness Proofs
16. Let Me Count the Ways—Enumeration Proofs
17. Not True! Counterexamples and Paradoxes
18. When 1 = 2—False Proofs
19. A Picture Says It All—Visual Proofs
20. The Queen of Mathematics—Number Theory
21. Primal Studies—More Number Theory
22. Fun with Triangular and Square Numbers
23. Perfect Numbers and Mersenne Primes
24. Let’s Wrap It Up—The Number e
SUPPLEMENTAL MATERIAL
Solutions
Bibliography

Note:-

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