TTC课程集 TTC Courses Collection mathematics

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资源信息： 中文名: TTC课程集 英文名: TTC Courses Collection(mathematics) 发行日期: 2010年07月21日 地区: 美国 对白语言: 英语 文字语言: 英文 概述:

The Teaching Company 美国最著名的大学教育课程制作公司之一，专门聘请世界一流大学的顶尖级教授讲授大学程度的各种课程，并推出课程的磁带，录像带，CD，DVD和学习手册，因注重学术性，教育性和娱乐性，符合终身学习的时代观念，在业界享有盛誉。由它推出的课程简称为TTC course。 　这家教育公司应该是美国生产教育类产品的公司中最为厉害的一家了，从它所聘请到的授课教师背景就能看出这一点来，美国高校有50万教授，为它所挑中的人选有5000人，可谓百里挑一，可以说是美国高校中的精英力量，许多教授在各自校园中都获得过“教师奖”，这种头衔对于一个教授的授课能力来讲是很大的一种肯定。主页的左侧全是关于所授课程的介绍，人文、艺术、宗教学科及社会科学的课程占了比较大的比例。 本贴只用来发布数学类课程。虽然不喜欢理工科课程，但本着造福人民，支持教育频道的原则发布理工科类的课程。希望能满足大家的需要。另外，接受斑竹建议，以后再发布课程均按照类别发布。

TTC Video - High School Level - Geometry (30 lectures, 30 minutes/lecture) Course No. 105 Taught by James Noggle Pendleton Heights High School, Pendleton, Indiana M.Ed., Ball State University For over 30 years James Noggle has been letting his students in on a secret at the 在过去的30多年里，James Noggle 一直让他在印第安纳州Pendleton高中的学生 high school in Pendleton, Indiana. 参与一个秘密。 He makes geometry feel like a long, cool drink as he guides you through the mysteries 他让你领会线，面，角，归纳与演绎，平行线以及面，三角形及多边形的神秘。而通过这 of lines, planes, angles, inductive and deductive reasoning, parallel lines and planes, 些，使几何学起来感觉像夏日里一大杯清凉的冷饮。 triangles, polygons, and more. In this course taught by award-winning teacher James Noggle, you develop the ability to read, write, think, and communicate about the concepts of geometry. As your comprehension and understanding of the geometrical vocabulary increase, you will have the ability to explain answers, justify mathematical reasoning, and describe problem-solving strategies. The language of geometry is beautifully expressed in words, symbols, formulas, postulates, and theorems. These are the dynamic tools by which you can solve problems, communicate, and express geometrical ideas and concepts. Connecting the geometrical concepts includes linking new theorems and ideas to previous ones. This helps you to see geometry as a unified body of knowledge whose concepts build upon one another. And you should be able to connect these concepts to appropriate real-world applications. Mr. Noggle relies heavily on the blackboard and a flipchart on an easel in his 30 lectures. Very little use is made of computer-generated graphics, though several physical models of geometric objects are used throughout the lectures. Upon completion of Geometry, you should be able to: 1. State and apply postulates and theorems related to points, lines, planes, and angles and use symbols to name and draw representations of them. 2. State and apply components of deductive reasoning to investigate relationships, solve problems, and prove statements. 3. State and apply postulates and theorems involving parallel lines and convex polygons to solve related problems and prove statements using deductive reasoning. 4. State and apply postulates and theorems related to congruent polygons to prove triangles and/or their corresponding parts congruent. 5. State and apply definitions, properties, and postulates to identify different quadrilaterals and prove statements about them. 6. State and apply components of logic and indirect proof to investigate inequities in triangles. 7. State and apply definitions, properties, postulates, and theorems related to similar polygons to prove triangles similar using deductive reasoning and to deduce information about segments or angles. 8. State and apply properties, postulates, and theorems related to right triangles to deduce relationships and solve for missing information in diagrams. 9. State and apply definitions, properties, postulates, and theorems about circles and terms related to circles to solve problems and prove statements using deductive reasoning. 10. Use compass, straight edge, and previously learned relationships to construct simple geometric figures. 11. State and apply formulas for finding area and volume for plane figures. 12. State and apply formulas for finding surface area and volume for simple solids. How We Found the SuperStar Teachers of the High School Classroom by Tom Rollins, Founder of The Teaching Company The dream that got me to quit my job as Chief Counsel to a U. S. Senate Committee, sell all my possessions, and move into an attic so I could start The Teaching Company was this: to let every student in America learn from the best teacher in the country. How could we find the stars of the high school classroom? We sent a letter to every teacher listed in Who’s Who among American High School Teachers. (Teachers are included if they are nominated as outstanding by a student listed in Who’s Who among American High School Students.) We explained to the teachers that we were looking for the SuperStars of the American High School classroom, and that the only way we could judge this at a distance would be for the teachers to send us videotapes of their classroom teaching. In these days of the portable video camera, asking all of these teachers to send us a sample of their work did not seem unreasonable. But then all of the tapes arrived. It took me two days just to open all of them. And it took months in front of the VCR in my office to watch all of the entries we had received. Was it tough to watch all of them? Of course. But the reward when a great teacher came along was worth the wait. I remember a late Saturday night, marching dutifully through a big box of videocassettes, when I put in the tape of James Noggle, a geometry teacher from Pendleton, Indiana. He was explaining to his class the calculation of the volumes of pyramids and cones and the ways in which these were similar. The lesson was carefully planned: he knew exactly when to use the formulas on the board, when to use a three-dimensional model, and how to introduce pi into the formula. And I thought to myself, "If I’d had you for high school math, Mr. Noggle, I would have stayed with my boyhood ambitions in science and medicine rather than becoming a lawyer." I had the same reaction when I saw Murray Siegel (named by Kentucky Educational Television as the Best Math Teacher in America) on quadratic equations, and Frank Cardulla (recipient of the Presidential Award for Science Teaching) on atomic theory. Lin Thompson’s lecture on the Vikings was so good that when Lin came to town to tape the course several people at the company rearranged their work schedules to be in the studio audience for his lectures. And so on. These were folks who could explain math, science, and history in a way that intrigues you, draws you in, and makes the solution-finding as exciting as finishing a good novel. And they are the people who can fulfill a dream I had long ago—to make the best teachers in America available to every student. Full size: 5.2Gb. 1.Fundamental Geometric Concepts 2.Angles and Angle Measure 3.Inductive Reasoning and Deductive Reasoning 4.Preparing Logical Reasons for a Two-Column Proof 5.Planning Proofs in Geometry 6.Parallel Lines and Planes 7.Triangles 8.Polygons and Their Angles 9.Congruence of Triangles 10.Variations of Congruent Triangles 11.More Theorems Related to Congruent Triangles 12.Median, Altitudes, Perpendicular Bisectors, and Angle Bisectors 13.Parallelograms 14.Rectangles, Rhombuses, and Squares 15.Trapezoids, Isosceles Trapezoids, and Kites 16.Inequalities in Geometry 17.Ratio, Proportion, and Similarity 18.Similar Triangles 19.Right Triangles and the Pythagorean Theorem 20.Special Right Triangles 21.Right-Triangle Trigonometry 22.Applications of Trigonometry in Geometry 23.Tangents, Arcs, and Chords of a Circle 24.Angles and Segments of a Circle 25.The Circle as a Whole and Its Parts 26.The Logic of Constructions through Applied Theorems (Part I) 27.The Logic of Constructions through Applied Theorems (Part II) 28.Areas of Polygons 29.Prisms, Pyramids, and Polyhedra 30.Cylinders, Cones, and Spheres

Discrete Mathematics Course No. 1456 (24 lectures, 30 minutes/lecture) 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. Course Lecture Titles 1. What Is Discrete Mathematics? 2. Basic Concepts of Combinatorics 3. The 12-Fold Way of Combinatorics 4. Pascal's Triangle and the Binomial Theorem 5. Advanced Combinatorics—Multichoosing 6. The Principle of Inclusion-Exclusion 7. Proofs—Inductive, Geometric, Combinatorial 8. Linear Recurrences and Fibonacci Numbers 9. Gateway to Number Theory—Divisibility 10. The Structure of Numbers 11. Two Principles—Pigeonholes and Parity 12. Modular Arithmetic—The Math of Remainders 13. Enormous Exponents and Card Shuffling 14. Fermat's "Little" Theorem and Prime Testing 15. Open Secrets—Public Key Cryptography 16. The Birth of Graph Theory 17. Ways to Walk—Matrices and Markov Chains 18. Social Networks and Stable Marriages 19. 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