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Discrete Mathematics 24 Video
Video Lectures | Xvid 640×480 29.97fps | MP3 – 128Kbps | 24 lectures, 30 minutes per lecture | 4.52 GB
Taught by Arthur T. Benjamin | Harvey Mudd College | Ph.D., The Johns Hopkins University
Welcome to Discrete Mathematics, a subject that is off the beaten track that most of us followed in school but that has vital applications in computer science, cryptography, engineering, and problem solving of all types.
Most of the mathematics taught after elementary school is aimed at preparing students for one subject—calculus, which is the mathematics of how things grow and change continuously, like waves in the water or clouds in the sky. Discrete mathematics, on the other hand, deals with quantities that can be broken into neat little pieces, like pixels on a computer screen, the letters or numbers in a password, or directions on how to drive from one place to another.
While continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting.
Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra.
Problems, Proofs, and Applications
Discrete mathematics covers a wide range of subjects, and Professor Benjamin delves into three of its most important fields, presenting a generous selection of problems, proofs, and applications in the following areas:
* Combinatorics: How many ways are there to rearrange the letters of Mississippi? What is the probability of being dealt a full house in poker? Central to these and many other problems in combinatorics (the mathematics of counting) is Pascal’s triangle, whose numbers contain some amazingly beautiful patterns.
* Number theory: The study of the whole numbers (0, 1, 2, 3, …) leads to some intriguing puzzles: Can every number be factored into prime numbers in exactly one way? Why do the digits of a multiple of 9 always sum to a multiple of 9? Moreover, how do such questions produce a host of useful applications, such as strategies for keeping a password secret?
* Graph theory: Dealing with more diverse graphs than those that plot data on x and y axes, graph theory focuses on the relationship between objects in the most abstract sense. By simply connecting dots with lines, graph theorists create networks that model everything from how computers store and communicate information to transportation grids to even potential marriage partners.
Learn to Think Mathematically
Professor Benjamin describes discrete mathematics as “relevant and elegant”—qualities that are evident in the practical power and intellectual beauty of the material that you study in this course. No matter what your mathematical background, Discrete Mathematics will enlighten and entertain you, offering an ideal point of entry for thinking mathematically.
In discrete math, proofs are easier and more intuitive than in continuous math, meaning that you can get a real sense of what mathematicians are doing when they prove something, and why proofs are an immensely satisfying and even aesthetic experience.
The applications featured in this course are no less absorbing and include cases such as these:
* Internet security: Financial transactions can take place securely over the Internet, thanks to public key cryptography—a seemingly miraculous technique that relies on the relative ease of generating 1000-digit prime numbers and the near impossibility of factoring a number composed of them. Professor Benjamin walks you through the details and offers a proof for why it works.
* Information retrieval: A type of graph called a tree is ideal for organizing a retrieval structure for lists, such as words in a dictionary. As the number of items increases, the tree technique becomes vastly more efficient than a simple sequential search of the list. Trees also provide a model for understanding how cell phone networks function.
* ISBN error detection: The International Standard Book Number on the back of every book encodes a wealth of information, but the last digit is very special—a “check digit” designed to guard against errors in transcription. Learn how modular arithmetic, also known as clock arithmetic, lies at the heart of this clever system.
Deepen Your Understanding of Mathematics
Professor Benjamin believes that, too often, mathematics is taught as nothing more than a collection of facts or techniques to be mastered without any real understanding. But instead of relying on formulas and the rote manipulation of symbols to solve problems, he explains the logic behind every step of his reasoning, taking you to a deeper level of understanding that he calls “the real joy and mastery of mathematics.”
Dr. Benjamin is unusually well qualified to guide you to this more insightful level, having been honored repeatedly by the Mathematical Association of America for his outstanding teaching. And for those who wish to take their studies even further, he has included additional problems, with solutions, in the guidebook that accompanies the course.
With these rich and rewarding lectures, Professor Benjamin equips you with logical thinking skills that will serve you well in your daily life—as well as in any future math courses you may take.
About Your Professor
Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College, where he has taught since 1989. He earned a B.S. from Carnegie Mellon University in 1983 and a Ph.D. in Mathematical Sciences from The Johns Hopkins University in 1989.
Professor Benjamin’s teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA’s Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. Most recently, the MAA named Professor Benjamin the 2006–2008 George Pólya Lecturer.
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Directory: TTC – Joy of Mathematics
01. The Joy of Math—The Big Picture.avi
02. The Joy of Numbers.avi
03. The Joy of Primes.avi
04. The Joy of Counting.avi
05. The Joy of Fibonacci Numbers.avi
06. The Joy of Algebra.avi
07. The Joy of Higher Algebra.avi
08. The Joy of Algebra Made Visual.avi
09. The Joy of 9.avi
10. The Joy of Proofs.avi
11. The Joy of Geometry.avi
12. The Joy of Pi.avi
13. The Joy of Trigonometry.avi
14. The Joy of the Imaginary Number i.avi
15. The Joy of the Number e.avi
16. The Joy of Infinity.avi
17. The Joy of Infinite Series.avi
18. The Joy of Differential Calculus.avi
19. The Joy of Approximating with Calculus.avi
20. The Joy of Integral Calculus.avi
21. The Joy of Pascal’s Triangle.avi
22. The Joy of Probability.avi
23. The Joy of Mathematical Games.avi
24. The Joy of Mathematical Magic.avi
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TTC VIDEO – High School Basic Math
Murray H. Siegel
This course introduces the student to the basic concepts of mathematics as well as the fundamentals of more complicated areas. Basic Math is designed to provide students with an understanding of arithmetic and to prepare them for Algebra I and beyond.
Dr. Murray H. Siegel has a Ph.D. in Mathematics Education. Kentucky Educational Television honored him as “the best math teacher in America.”
He has a gift and evident passion for explaining mathematical concepts in ways that make math seem clear and obvious rather than arbitrary and murky.
From the basics of multiplication to decimals and fractions and the operations of geometry, he is the master of the skillful metaphor and the well-wrought example……..
01. Introduction and a Review of Addition and Subtraction
02. Multiplication and Division
03. Long Division
04. Introduction to Fractions
05. Adding Fractions
06. Subtracting Fractions
07. Multiplying Fractions
08. Dividing Fractions, Plus a Review of Fractions
09. Adding and Subtracting Decimals
10. Multiplying and Dividing Decimals
11. Using the Calculator
12. Fractions, Decimals, and Percents
13. Percent Problems
14. Ratios and Proportions
15. Exponents and the Order of Operations
16. Adding and Subtracting Integers
17. Multiplication and Division of Integers, and an Introduction to Square Roots
18. Negative and Fractional Powers
19. Geometry I
20. Geometry II
21. Graphing in the Coordinate Plane
22. Number Theory
23. Number Patterns I
24. Number Patterns II
28. Problem-Solving Techniques
29. Solving Simple Equations
30. Introduction to Algebra I
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