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443411.124 Introduction to Education: Looking Forward and Looking Back on Education (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=883727
An introductory course on teaching and learning science and mathematics in a variety of K-12 settings. Topics include education and media, education reform, the history of education, simulations, games, and the digital divide.Geometry
http://www.merlot.org/merlot/viewMaterial.htm?id=734974
This is a free online course offered by the Saylor Foundation.'“Everything is numbers.” This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show “NUMB3RS.” If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, “six degrees of separation (or Kevin Bacon)” kind of way.Geometry is the study of space (for now, mainly two-dimensional, with some three-dimensional thrown in) and the relationships of objects contained inside. It is one of the more relatable math courses, because it often answers that age-old question, “When am I ever going to use this in real life?” Look around you right now. Do you see any triangles? Can you spot any circles? Do you see any books that look like they are twice the size of other books? Does your wall have paint on it?In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a three-dimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.These are just some of the topics you will be learning. As you will quickly see, everything is not just numbers; it is also relationships. Even nature itself knows this. What did the little acorn say when it grew up? “Gee, I’m a tree!”'Introduction to Pitch Systems in Tonal Music
http://www.merlot.org/merlot/viewMaterial.htm?id=571045
This series is one part of UC Irvine's Musicianship 15 ABC sequence for music majors. An understanding of music notation and basic musical terms is helpful but not required for these presentations. The math involved is basic. Pitch systems use mathematics to organize audible phenomenon for creative expression. The cognitive processes we develop through exposure to music comprise a kind of applied mathematics; our emotional responses to musical nuance grow out of a largely unconscious mastery of the patterns and structures in music. This series of presentations covers the basic mathematics and cognitive phenomenon found in the tonal system used in Western music and much of the music of the world. Over the course of several presentations we will explore basic concepts of pitch and frequency, the organizing rules of tonal systems, and the mathematical construction of basic scales and chords. The reasoning and purpose of equal temperament, the standard tuning system for tonal music, will be explored in this context. Presentations will include graphics and computer applications designed specifically to illustrate these concepts.1.050 Engineering Mechanics I
http://www.merlot.org/merlot/viewMaterial.htm?id=680810
This subject provides an introduction to the mechanics of materials and structures. You will be introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of materials and structures and you will learn how to solve a variety of problems of interest to civil and environmental engineers. While there will be a chance for you to put your mathematical skills obtained in 18.01, 18.02, and eventually 18.03 to use in this subject, the emphasis is on the physical understanding of why a material or structure behaves the way it does in the engineering design of materials and structures.12.010 Computational Methods of Scientific Programming (MIT)
http://www.merlot.org/merlot/viewMaterial.htm?id=884339
This course introduces programming languages and techniques used by physical scientists: FORTRAN, C, C++, MATLAB®, and Mathematica. Emphasis is placed on program design, algorithm development and verification, and comparative advantages and disadvantages of different languages.2.24 Ocean Wave Interaction with Ships and Offshore Energy Systems (13.022)
http://www.merlot.org/merlot/viewMaterial.htm?id=591464
The subject introduces the principles of ocean surface waves and their interactions with ships, offshore platforms and advanced marine vehicles. Surface wave theory is developed for linear and nonlinear deterministic and random waves excited by the environment, ships, or floating structures. Following the development of the physics and mathematics of surface waves, several applications from the field of naval architecture and offshore engineering are addressed. They include the ship Kelvin wave pattern and wave resistance, the interaction of surface waves with floating bodies, the seakeeping of ships high-speed vessels and offshore platforms, the evaluation of the drift forces and other nonlinear wave effects responsible for the slow-drift responses of compliant offshore platforms and their mooring systems designed for hydrocarbon recovery from large water depths. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.022. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.24.Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=555337
Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.In addition to the videos, there are summary slides and practice problems complete with an audio narration by Professor Strang. You can find these resources to the right of each video.This resource is also available on Highlights for High School.About the InstructorProfessor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. StrangAcknowledgementsSpecial thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.Calculus 1 (I)
http://www.merlot.org/merlot/viewMaterial.htm?id=731684
This is a free online course offered by the Saylor Foundation.'Calculus can be thought of as the mathematics of CHANGE. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT. Solving an Algebra problem, like Y = 2X + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt where t is elapsed time and X0 is the initial deposit. But with compounded interest, now things get complicated for algebra as the rate R is now itself a function of time with Y = X0+ R(t)t. Now we have a rate of change which itself is changing. Calculus “to the rescue,” as Isaac Newton introduced the world to mathematics specifically designed to handle “those things that change.” Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences, including physical, biological, social, economic, and engineering. However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will learn in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for future courses you might take. This course is divided into four learning sections, or units, plus a reference section, or Appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding “limits” could not be more important as that topic really begins the study of calculus. The third unit will introduce and explain derivatives. With derivatives we are now ready to handle all those “things that change” mentioned above. The fourth unit makes “visual sense” of derivatives by discussing derivatives and graphs. Finally, the fifth unit provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over.'Calculus I
http://www.merlot.org/merlot/viewMaterial.htm?id=602672
This free and open online course in Calculus 1 was produced by the WA State Board for Community & Technical Colleges [http://sbctc.edu].Calculus is the mathematics of CHANGE and almost everything in our world is changing.Calculus is among the most important and useful developments of human thought, and, even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful and beautiful and useful set of ideas and techniques You will see the fundamental ideas of this course over and over again in future courses in mathematics, the sciences (physical, biological and social) as well as in economics, engineering and others.But calculus is an intellectual step up from your previous mathematics courses. Many of the ideas are more carefully defined, and they have both a functional and a graphical meaning Some of the algorithms are more complicated, and in many cases you will need to decide on the appropriate algorithm to use. And there is a huge variety of applications, too many to be able to discuss each one in class in detail.This module is part of the Open Course Library, a collection of shareable course materials created for faculty to use in their classes. As part of the Open Course Library this content is licensed under the Creative Commons Attribution License which means that you are free to reuse the course in its entirety, edit it and use a your own modified version, or pick out only pieces which can be incorporated into your own course, as long as you credit the original author for their work.To access all materials for this course you may download either the ANGEL export file or the IMS Common Cartridge file. While the ANGEL file is specific to that system, the Common Cartridge file is compatible with many learning management systems. More information on Common Cartridge is available at http://www.imsglobal.org/cc/.Calculus II
http://www.merlot.org/merlot/viewMaterial.htm?id=602690
This free and open online course in Calculus II was produced by the WA State Board for Community & Technical Colleges [http://sbctc.edu/].Calculus is the mathematics of CHANGE and almost everything in our world is changing. Calculus is among the most important and useful developments of human thought, and, even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful and beautiful and useful set of ideas and techniques.You will see the fundamental ideas of this course over and over again in future courses in mathematics, the sciences (physical, biological and social) as well as in economics, engineering and others. But calculus is an intellectual step up from your previous mathematics courses. Many of the ideas are more carefully defined, and they have both a functional and a graphical meaning Some of the algorithms are more complicated, and in many cases you will need to decide on the appropriate algorithm to use. And there is a huge variety of applications, too many to be able to discuss each one in class in detail.This module is part of the Open Course Library, a collection of shareable course materials created for faculty to use in their classes. As part of the Open Course Library this content is licensed under the Creative Commons Attribution License which means that you are free to reuse the course in its entirety, edit it and use a your own modified version, or pick out only pieces which can be incorporated into your own course, as long as you credit the original author for their work.To access all materials for this course you may download either the ANGEL export file or the IMS Common Cartridge file. While the ANGEL file is specific to that system, the Common Cartridge file is compatible with many learning management systems. More information on Common Cartridge is available at http://www.imsglobal.org/cc/ .