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MIT OpenCourseWare: Mathematics
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The Massachusetts Institute of Technology, with funding from the William and Flora Hewlett Foundation, the Andrew W. Mellon Foundation, and MIT, has launched this "large-scale, Web-based electronic publishing initiative." The website posts lecture notes, problem sets, and other materials from courses across the MIT campus. This section highlights MIT's undergraduate and graduate program in Mathematics. Courses are listed by title and include topics such as Differential Analysis, Linear Algebra, and Statistical Inference. The materials serve as valuable resources for educators, students, or anyone interested in learning more about these topics.

Subject:
Education
Educational Technology
Mathematics
Material Type:
Full Course
Lesson Plan
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Date Added:
11/08/2006
Masses & Springs
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CC BY
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A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.

Subject:
Physical Science
Physics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Kathy Perkins
Michael Dubson
The Mortenson Family Foundation
Wendy Adams
Date Added:
04/26/2006
Math For Our World
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CC BY-SA
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This course is based on the text Math in Society, edited by David Lippman, Pierce College Ft Steilacoom, and on the text Using Excel, by Noreen Brown, Barbara Lave, Julie Romey, Mary Schatz, and Diane Shingledecker. The modules in this course have been adapted and edited by Gail Poitrast to fit the learning objectives of Math 502. This course is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent. Emphasis is placed on the applicability of the mathematics. The use of Excel is also explored, as it is a learning objective for Math 502.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Granite State College
Author:
Gail Poitrast
Date Added:
01/26/2021
Mathematical Exposition, Spring 2005
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This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Carberry, Emma
Date Added:
01/01/2005
Mathematical Statistics, Spring 2016
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CC BY-NC-SA
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This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Peter Kempthorne
Date Added:
01/01/2016
Mathematics for Elementary Teachers
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CC BY-SA
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This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.

The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:

• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.

• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).

• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.

Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
University of Hawaii
Provider Set:
Pressbooks
Author:
Michelle Manes
Date Added:
08/13/2020
The Mathematics of Nutrition Science
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CC BY-NC-SA
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The Mathematics of Nutrition Science is a workbook designed to integrate and contextualize developmental mathematics into an introductory college level Nutrition class. Definitions and skills from Community College Level Elementary Algebra and Quantitative Literacy courses are explained through examples analyzing the nutritional content of different foods. The book contains exercises for students to practice these skills, and also to reflect on the concepts through short writing assignments aligned with developmental English. These materials could be used by Nutrition course instructor in many different ways, and are designed to be self-contained and require minimal mathematical instruction.

Subject:
Life Science
Nutrition
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
Queensborough Community College
Author:
Jennifer Maloy
Jonathan Cornick
Lana Zinger
Date Added:
03/03/2017
The Mathematics of Rhythm
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CC BY-NC-SA
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Using the free software Supercollider, you can create create music using computer coding. This text and lesson provide instructional videos, downloadable files, and step by step instructions for coding in the unique language. SuperCollider is a platform for audio synthesis and algorithmic composition, used by musicians, artists, and researchers working with sound. It is free and open source software available for Windows, macOS, and Linux.

Subject:
Creative and Applied Arts
Music Production
Material Type:
Module
Provider:
University of Baltimore
Author:
Elliott Grabill
Harvey Sky
Kristin Conlin
Date Added:
05/10/2021
Math for Trades: Volume 1
Unrestricted Use
CC BY
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The Math for Trades: Volume 1 textbook represents the building blocks for math training. The book includes whole numbers, fractions, decimals, and percents. The material is presented from a trades perspective with easy-to-understand examples and video explanations accompanying questions. The goal of this volume is to get students prepared for the more advanced topics that they will encounter during their trades math education.

Subject:
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Author:
Chad Flinn
Mark Overgaard
Date Added:
03/11/2021
Math for Trades: Volume 2
Unrestricted Use
CC BY
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The Math for Trades: Volume 2 textbook continues where the first volume left off. Volume 2 increases the challenge with topics such as converting units and working with equations, perimeter, area, and volume. Once again the material is presented from a trades perspective with easy-to-understand examples and videos explanations accompanying questions. The goal of this volume is to take the material you learned in Math for Trades: Volume 1 and apply it to more advanced topics that you may encounter during your trades training.

Subject:
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Author:
Chad Flinn
Mark Overgaard
Date Added:
06/18/2021
Math in Society
Unrestricted Use
CC BY
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The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics than expressions and equations.

The core course is a complete, ready to run, fully online course, featuring 9 topics: Problem solving, voting theory, graph theory, growth models, consumer finance, collecting data, describing data, probability, and historical counting. Additional optional topics are provided. The course materials can easily be used with a face-to-face course.

Each topic features:

Readings from a complete textbook, available in printed form for ~$15, or online for free. A playlist of videos, corresponding to the examples in the text. Exercises available in the book, or algorithmically generated online homework and quizzes are available on WAMAP.org (for Washington faculty) or MyOpenMath.com (for everyone else). Writing assignments, requiring the students to think beyond calculations. For many topics, some in-class activities and paper quizzes are available.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Author:
David Lippman
Date Added:
08/13/2020
Math in Society
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CC BY-SA
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Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).

Subject:
Mathematics
Material Type:
Textbook
Author:
David Lippman
Date Added:
08/13/2020
Maze Game
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CC BY
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Learn about position, velocity, and acceleration in the "Arena of Pain". Use the green arrow to move the ball. Add more walls to the arena to make the game more difficult. Try to make a goal as fast as you can.

Subject:
Physical Science
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
Sam Reid
Wendy Adams
Date Added:
10/30/2006
Measure and Integration, Fall 2003
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Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.

Subject:
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Viaclovsky, Jeffrey Alan
Date Added:
01/01/2003
Modeling, Functions, and Graphs: Algebra for College Students
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Mathematics, as we all know, is the language of science, and fluency in algebraic skills has always been necessary for anyone aspiring to disciplines based on calculus. But in the information age, increasingly sophisticated mathematical methods are used in all fields of knowledge, from archaeology to zoology. Consequently, there is a new focus on the courses before calculus. The availability of calculators and computers allows students to tackle complex problems involving real data, but requires more attention to analysis and interpretation of results. All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking.

Subject:
Mathematics
Material Type:
Textbook
Provider:
American Institute of Mathematics
Author:
Katherine Yoshiwara
Date Added:
01/27/2019
Modelling
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Modelling is about understanding the nature: our world, ourselves and our work. Everything that we observe has a cause (typically several) and has the effect thereof. The heart of modelling lies in identifying, understanding and quantifying these cause-and-effect relationships.

A model can be treated as a (selective) representation of a system. We create the model by defining a mapping from the system space to the model space, thus we can map system state and behaviour to model state and behaviour. By defining the inverse mapping, we may map results from the study of the model back to the system. In this course, using an overarching modelling paradigm, students will become familiar with several instances of modelling, e.g., mechanics, thermal dynamics, fluid mechanics, etc.

Subject:
Engineering
Material Type:
Assessment
Homework/Assignment
Lecture
Lecture Notes
Provider:
Delft University of Technology
Provider Set:
Delft University OpenCourseWare
Author:
Dr. Y. Song
Date Added:
03/07/2016
Modern Navigation, Fall 2006
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Introduces the concepts and applications of navigation techniques using celestial bodies and satellite positioning systems such as the Global Positioning System (GPS). Topics include astronomical observations, radio navigation systems, the relationship between conventional navigation results and those obtained from GPS, and the effects of the security systems, Selective Availability, and anti-spoofing on GPS results. Laboratory sessions cover the use of sextants, astronomical telescopes, and field use of GPS. Application areas covered include ship, automobile, and aircraft navigation and positioning, including very precise positioning applications.

Subject:
Career and Technical Education
Maritime Science
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Herring, Thomas
Date Added:
01/01/2006
Molarity
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CC BY
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What determines the concentration of a solution? Learn about the relationships between moles, liters, and molarity by adjusting the amount of solute and solution volume. Change solutes to compare different chemical compounds in water.

Subject:
Chemistry
Physical Science
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Chris Malley
Julia Chamberlain
Kathy Perkins
Kelly Lancaster
Robert Parson
Date Added:
02/20/2012