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4434Visualizing Statistical Concepts
http://www.merlot.org/merlot/viewMaterial.htm?id=78010
Some great objects for helping to understand social science research methods and statistical processesThe Salem Witchcraft Site
http://www.merlot.org/merlot/viewMaterial.htm?id=554081
An interactive exploration of the Salem witchcraft outbreak of 1692, the Salem Witchcraft Site provides data about certain aspects of the outbreak and demonstrates how this data can be used to further our understanding of events. The website takes a "learn by doing," or "inquiry" approach to learning. It formulates questions about Salem witchcraft, explores solutions, and encourages users to pursue further understanding on their own.In emphasizing a quantitative approach to Salem, the site provides a number of data sets containing information about various aspects of the Salem outbreak, such as the month of the year when "witches" were accused and the communities in which they lived. Instructions are provided to analyze the data so that users can determine for themselves connections not readily apparent in traditional historical sources and books. The statistical analysis includes histograms, scatter plots, pie charts, means, and medians. Users need not perform statistical analyses but can simply follow the discussion.Used selectively or in its entirety, the site is intended for a wide audience: historians, whether as researchers or teachers; students of history and of the Salem witchcraft episode, whether in school or not; and non-historians, such as those who teach or are learning basic statistics or social science methodology.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'CensusScope
http://www.merlot.org/merlot/viewMaterial.htm?id=84539
CensusScope is an easy-to-use tool for investigating U.S. demographic trends, brought to you by the Social Science Data Analysis Network (SSDAN) at the University of Michigan. With eye-catching graphics and exportable trend data, CensusScope is designed for both generalists and specialists.Dr. Stat: an Online Statistics Course for Social Scientists
http://www.merlot.org/merlot/viewMaterial.htm?id=413277
Dr. Stat is an online statistics course for higher education students. Originally designed for students of Psychology, it can be used for any student of Social Sciences and gives a first introduction into statistics, either as a self study tool or as an exercise tool besides another statistics course. It also provides a great resource when working on a resource project.There are 25 lessons about basic subjects such as measurement levels, measures of central tendency, correlation, probability and distributions, and more advanced subjects as hypothesis testing, measures of association and variance analysis. You can follow each lesson separately. All lessons contain a great number of exercises.Students report great enthusiasm for the course. Especially those Social Science students who have trouble with the subject and would like extra practice appreciate the clear straightforward explanations and the exercises.NOTE: The first lesson can be used for free, without registration. All others require an account that costs €7.50. Payment can be done through Paypal.Elementary Calculus: An Approach Using Infinitesimals
http://www.merlot.org/merlot/viewMaterial.htm?id=302292
'This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences.'