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4434An Introduction to Complex Numbers
http://www.merlot.org/merlot/viewMaterial.htm?id=434096
This is a free, online textbook/course that teaches about complex numbers. It is a workbook that has exercises through-out, with some of the answers provided as audio files.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/ .Calculus III
http://www.merlot.org/merlot/viewMaterial.htm?id=602707
This free and open online course in Calculus III 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/ . Causal and Statistical Reasoning
http://www.merlot.org/merlot/viewMaterial.htm?id=519785
This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package.”״Does excessive exposure to violent video games cause violent behavior? Does increased gun availability cause more crime or less? This course examines the nature of causal claims and the statistical sorts of evidence used to support them." 'Our material is delivered in three forms - Concept modules, Case studies, and the Causality Lab. The Case Studies are a collection of over one hundred short news pieces (1-3 pages) - that each deal with some study concerned with a causal claim. They are listed in the Syllabus as part of the Appendix - and they can viewed alphabetically or in hierarchy by topical area (e.g. Health, Social Sciences, etc.). You will read several of them as part of the concept modules, but they are interesting in their own right and we urge you to explore them and find your own over the web. If you find a particularly interesting study we have not included, please send us the URL by email <oli-help@lists.andrew.cmu.edu>, and we will try to incorporate the study into the repository.The Causality Lab is a virtual environment to simulate the science of causal discovery. The lab contains a "true" causal model behind the scenes that was created by the instructor (or another student), and your job is to set-up experiments, collect data, create hypotheses, and compare the predicitons from your hypotheses against the data to find the truth. Causality Lab exercises are included as a regular part of the course, but they are also available as a series of stand alone lessons accessible from the Syllabus in Unit 7: Causality Lab Lessons.The "Concept modules" are meant to present the basic concepts and terminology behind Causal and Statistical Reasoning. Each is meant to cover about the same amount of material delivered in a textbook chapter. Each includes text, pictures, movies, simulations, questions for you to answer, and a quiz at the end of the module that you might be assigned to take for credit. They take anywhere between one to five hours to complete. We have grouped the modules into five topical areas: •Area 1: Causal Theories •Area 2: Statistical Evidence: Association and Independence •Area 3: Causal Theories --> Statistical Evidence •Area 4: Statistical Evidence -->Causal Theories: Problems •Area 5: Statistical Evidence -->Causal Theories: Strategies'Computational Discrete Mathematics
http://www.merlot.org/merlot/viewMaterial.htm?id=519846
This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package.”״Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages.״At this point only one of the planned 15 modules is currently available, that on Groups.Elementary Algebra
http://www.merlot.org/merlot/viewMaterial.htm?id=602721
This free and open online course in Elementary Algebra was produced by the WA State Board for Community & Technical Colleges [http://sbctc.edu/].This course is the study of basic algebraic operations and concepts and the structure and use of algebra. This includes the solutions to algebraic equations. factoring algebraic functions, working with rational expressions, and graphing of linear equations.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/ .Empirical Research Methods
http://www.merlot.org/merlot/viewMaterial.htm?id=519833
This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. “The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package.”״Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily available data. Few understand, at a conceptual level, the limitations of regression analysis.The OLI Empirical Research Methods course bridges the gap between the mathematical foundations of regression and its practical application. We teach students how to move from an interesting question about the world to a regression model that, when estimated, meaningfully addresses the question asked. It emphasizes causal analysis as the main research goal and multivariate linear regression as the main statistical tool. We teach a process that involves:1.Formulating a research problem,2.Developing and formalizing hypotheses,3.Collecting data relevant to these hypotheses,4.Analyzing the data using an appropriate regression model, and5.Critically interpreting the results of these analysesA learner who successfully completes our course will be able to do much more than mechanically estimate a regression model with standard statistical software like SPSS or Minitab, or check whether coefficient estimates are “significant” at the .05 or .01 level. They will be able to bring to bear their own scientific imagination in order to use regression as a tool to investigate problems about the real world. They will be able, perhaps not with professional sophistication, but with competence, to do real empirical research.Essentials of Probability and Statistical Inference IV: Algorithmic and NonParametic Approaches
http://www.merlot.org/merlot/viewMaterial.htm?id=327223
This course introduces the theory and application of modern, computationally-based methods for exploring and drawing inferences from data. Covers re-sampling methods, non-parametric regression, prediction, and dimension reduction and clustering. Specific topics include Monte Carlo simulation, bootstrap cross-validation, splines, local weighted regression, CART, random forests, neural networks, support vector machines, and hierarchical clustering. De-emphasizes proofs and replaces them with extended discussion of interpretation of results and simulation and data analysis for illustration. OCW offers a snapshot of the educational content offered by JHSPH. OCW materials are not for credit towards any degrees or certificates offered by the Johns Hopkins Bloomberg School of Public Health. Included here are a syllabus and lectures.