This resource may be used as a primary source for a general education/quantitative reasoning (QR) math course delivered in the inquiry based learning style. It may also be used to supplement a QR course with occasional in-class active learning activities.

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

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.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

This course was originally developed for the Open Course Library project.  The text used is Math in Society, edited by David Lippman, Pierce College Ft Steilacoom.  Development of this book was supported, in part, by the Transition Math Project and the Open Course Library Project. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.

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.

The goal of this video lesson is to teach students about new and exciting ways of holding an election that they may not be aware of. Students will learn three different methods of voting: plurality, instant runoff, and the Borda count. They will be led through a voting experiment in which they will see the weakness of plurality when there are three or more candidates. This lesson will show that not every voting system is perfect, and that each has its strengths and weaknesses. It will also promote thought, discussion, and understanding of the various methods of voting.

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.

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).

This art history video discussion examines Henri Matisse's "Luxe, calme et volupte", 1904, oil on canvas, 37 x 46 inches (Musee d'Orsay, Paris). Painted while the artist stayed with the pointillist painter, Signac, at his home in Saint-Tropez on the Cote d'Azur. Matisse's title comes from Charles Baudelaire's poem, L'invitation au voyage (Invitation To A Voyage) from his collection, The Flowers of Evil. Luxe, calme et volupte translates just as it sounds in English, Luxury, calm, and voluptuous(ness).

This art history video discussion examines Henri Matisse's "The Piano Lesson", 1916 (The Museum of Modern Art).

This art history video discussion looks at Henri Matisse's "The Red Studio", oil on canvas, 1911 (MoMA).

Students leach organic matter from soil to create a water sample with high dissolved organic matter content (DOM), and then make filters to see if the DOM can be removed. They experience the difficulties of removing DOM from water, and learn about other processes that might make DOM removal more effective.

Students play the role of engineers as they test, design and build Mentos(TM) fountains a dramatic example of how potential energy (stored energy) can be converted to kinetic energy (motion). They are challenged to work together as a class to optimize the design of the basic soda/candy geyser made by the teacher. To do this, three research teams each investigate how a different variable nozzle shape, soda temperature, number of candies affects fountain height. They devise and run experimental tests to determine the best variable values. Then they combine their results to design the highest fountain to compete head-to-head with the teacher's geyser design.

Students learn how to find the maximum power point (MPP) of a photovoltaic (PV) panel in order to optimize its efficiency at creating solar power. They also learn about real-world applications and technologies that use this technique, as well as Ohm's law and the power equation, which govern a PV panel's ability to produce power.

This lesson explores the drag force on airplanes. The students will be introduced to the concept of conservation of energy and how it relates to drag. Students will explore the relationship between drag and the shape, speed and size of an object.

Students revisit Bernoulli's Principle (Lesson 1 of the Airplanes unit) and learn how engineers use this principle to design airplane wings. Airplane wings create lift by changing the pressure of the air around it. This is the first of four lessons exploring the four key forces in flight: lift, weight, thrust and drag.

In this lesson, students will study how propellers and jet turbines generate thrust. This lesson focuses on Isaac Newton's 3rd Law of Motion, which states that for every action there is an equal and opposite reaction.

The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.