To promote mathematics among Indigenous learners, we have created a series of stories with mathematical themes. These stories are based on the storytelling tradition of Indigenous peoples. The fact that most of our stories have been translated into several Indigenous languages as well as French is probably the biggest recognition that an author could hope for.

The first story, Small Number Counts to 100 was inspired by narration from Ms. Rina Sinclair of the Siksika Nation. The story can be shown to elementary school students as a counting practice/puzzle or as a pattern recognition problem. For high school students it can be a way to introduce arithmetic progressions, modular addition, or an idea of number systems with a base different than 10.

The book that started it all, now converted to PreTeXt (its third source format).

This book is aimed at mathematics majors, seeing their first course after calculus that stresses theorems and their proofs. It contains a very thorough introduction to the use of the open source system, Sage, for linear algebra. Besides an extensive collection of traditional exercises, there are also reading questions for each of the thirty-seven (daily) sections.

Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Print versions are in black and white to keep costs low; the electronic versions are full-color.

Through direct request to the author by email (boelkinm at gvsu dot edu), a range of ancillary materials are available to faculty, including WeBWorK .def files, activities workbooks (.pdf files that include only the activities along with room for students to write), computer laboratory exercises for chapters 1-4 that use Geogebra, and daily prep assignments to support students reading the text. Both the 2018 HTML and PDF versions include answers to activities and exercises in appendices in the back.

Each section of the text has at least 3 in-class activities to engage students in active learning. The section on the tangent line approximation is representative of the organization and style of other sections in the text: a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on our goals and the structure of the text can be found in the preface.

Active Calculus - single variable has been publicly available since August 2012. The PDF version has been downloaded over 120,000 times since August 2014 (though most users now prefer the HTML version). The author maintains an email list of interested users and communicates a few times a year with updates to the community.

Active Calculus - Multivariable is a free, open-source calculus text that is designed to support an active learning approach in third semester of calculus, including approximately 100 activities and 300 exercises.

Each section of the text has at least 3 in-class activities to engage students in active learning. More information on our goals and the structure of the text can be found at .

Active Prelude to Calculus is designed as a college-level preparatory text for students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. In particular, the text is intended as an appropriate prerequisite base for students who will go on to study from Active Calculus while also encouraging and promoting an active learning approach. The HTML version of the text includes about 150 anonymous, interactive exercises; static versions of those problems are included in PDF and print. In addition, the text offers about 120 activities designed for student engagement in and out of class. Learn more at activecalculus.org/APC.html.

Beginning Algebra Made Useful requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts, and considering ideas that arise more fully in upcoming lessons. Longer assignments that can be used as group projects are included in the text. Group work is encouraged throughout the text; suggestions for orchestrating group work are included.

The text is open access and free for download by students and instructors in .pdf format. In the electronic format, graphics are in full color and there are live html links to resources, software, and applets.

A one semester course in calculus aimed at business students.

The book is designed to follow the recommendations of the MAA CRAFTY committee

In particular the book assumes studnets will have a laptop with Excel for the class.

Examples are heavily drawn for business context and use business notation

The order of the topics has been tweaked to match the preferences of business faculty. (Partial derivatives are before integrals.)

Numerical methods get a heavier emphasis than in a traditional book.

Homework problems are in the process of being converted to WeBWorK

These notes constitute a self-contained sequence for teaching, using an inquiry-based pedagogy, most of the traditional topics of Calculus I, II, & III in classes of up to 40 students.

Calculus I is taught at Portland Community College using a lecture/lab format. The laboratory time is set aside for students to investigate the topics and practice the skills that are covered during their lecture periods. This lab manual serves as a guide for the laboratory component of the course.

A text for a standard first undergraduate differential calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate integral calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate multivariable calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate vector calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A discovery-based approach to linear algebra.

Extended material to cover a second course in linear algebra is being finalized and will be released Summer 2019.

A free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. Also appropriate for an introduction to proofs course with discrete content.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.

While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook:

• 473 exercises, including 275 with solutions and another 109 with hints. Exercises range from easy to quite involved, with many problems suitable for homework.
• Investigate! activities throughout the text to support active, inquiry based learning.
• A full index and list of symbols.
• Consistent and helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.).

This course constitutes a mathematically rigorous introduction to sets, functions, counting, induction, equivalence relations, recursion, elementary graph theory, finite state machines, and languages.

These materials were designed to introduce concepts of logic and discrete mathematics via carefully picked problems that test understanding of definitions. Another source of exercises is required at this time.

Throughout the book, we incorporate applications to motivate new topics. We present ideas using verbal, numerical, and graphical tools. We use graphs extensively to illustrate algebraic techniques and to help students visualize relationships between variables. In the Homework Problems we break up skills practice into smaller sets of exercises and combine them with conceptual questions, graphing, and applications of various types.

We have included a number of features to encourage student participation.

• The reading is broken into small segments by using boxes around Examples, definitions, and rules, and flags including Caution, Look Closer, and Look Ahead.
• We want students to learn how to read a math book, so we have included Reading Questions that mirror the content of the lesson. For example, the first Reading Question is A numerical quantity that changes over time or in different situations is called a __________ . Ideally, students would answer these questions before class, perhaps through an on-line homework system.
• Each section ends with a Skills Warm-Up (with answers) for students to complete on their own. The Skills Warm-Up problems review an arithmetic or algebraic technique needed for the Lesson that follows.
• Because choosing appropriate scales for the axes is a time-consuming task for beginning students, the text includes labeled grids for most of the graphing exercises. Ready-made grids allow students to consider a wider range of examples (with harder numbers) and to focus on the properties of the graphs, such as intercepts and slope, and on interpreting the information given by the graph. If students are using technology to create graphs, the grids can help them choose an appropriate window.

Chapter Reviews include a Summary, Review Questions for writing or discussion, and a set of Review Problems. Answers to odd-numbered Homework problems are provided, as well as a Glossary of mathematical terms.

The textbook is accompanied by an Activities Workbook that provides a Lesson for each section in the book. These Lessons consist of Activities for students to complete in groups or with guidance from the instructor; or they can be used as support for a lecture format. Each Lesson ends with a Wrap-Up and a set of Homework Preview exercises.

An Instructor's Manual for the text is also available. The Manual contains objectives and teaching notes for each section of the text, as well as suggested concept questions and topics for writing or discussion. The teaching notes include suggestions for using the Activities booklet and how to structure class time.

A computer homework system for Elementary Algebra is available through xyzhomework.

An inquiry-based introduction to game theory.

Appropriate for a non-majors quantitative reasoning course or an extra topics course at the secondary level.

Includes discussion questions on game theory in popular culture.

Complete instructor's guide available by request.

This document provides an environment in which a student may enhance their understanding of the ideas in linear algebra by working examples often too tedious to do by hand. We use Cocalc (SageMath) as the computational tool of choice.

This document is not intended as a textbook, but a companion guide to a textbook. It is also important to note that the emphasis is on providing functionality, not necessarily a robust discussion of topics.

These notes are not intended as a textbook for a first or second course in linear algebra, though they assume the reader has seen the material in a basic linear algebra course. The intent is provide a review of basic material as prerequisite to taking a more advanced course which requires a knowledge of linear algebra.

These notes will undertake a review of many basic topics from a typical first course, often taking the opportunity to interleave more advanced concepts with simpler ones when convenient. It will refresh the reader's memory of definitions, structural results, core examples, and provide some computational tools to help the reader come to a deeper appreciation of the ideas first met perhaps a long time ago.

A one-semester modern approach to Linear Algebra, at a 2nd year level.

Uses real vector spaces and linear maps to introduce abstract mathematical thinking (definitions, thereoms and proofs).

The style is conversational, the material is elementary, but the approach offers a glimpse of higher mathematics.

Notable features include: multivariable calculus (multivariable polynomials, polynomial vector fields, gradient, divergence, double integrals, etc.) as examples of vector spaces and linear maps, as well as studying differential equations from a linear algebra point of view.

A follow-up second semester course also incorporates the differential geometry of surfaces (tangent spaces, the shape operator) into linear algebra.

Includes numerous videos, images, Geogebra apps, JSXGraph apps, SageMath worksheets, as well as Tutorials.

This is a set of class notes I developed for the first discrete course at Wichita State University.

What makes this unique is that it includes complete worked examples as videos, complete solutions to exercises, and an embedded discussion forum powered by Discourse.

In the past, I've used this as my platform for my online course. For the COVID-19 Fall Hybrid-Online-Experience, I will be using this to flip my class, having this be the first point of contact for the material and running lectures.

We cover:

• Math objects
• Propositional Logic
• Basic concepts of proof
• Basic number theory, specifically applying proof techniques and building to RSA encryption
• Sequences, recursion, and induction
• Basic counting

The five chapters are logic and sets, financial math, statistics, probability and the math of democracy (United States). Additional sections can be used from David Lippman's Math In Society. There are video lectures in each section of the book and corresponding fill-in notes. Group activity pages are also available under resources. A MyOpenMath course shell is available. We emphasize spreadsheets in the financial math chapter and also include the formulas. We use spreadsheets and GeoGebra in the statistics chapter except in the normal section we use the onlinestatbook.com normal calculator and spreadsheets.

The United States democracy chapter includes apportionment, voting methods, popular vote, electoral college and electoral power, gerrymandering and how to measure it and federal debt and deficit. The gerrymandering section focuses on how to calculate the efficiency gap.

The culturally responsive features are diverse names, gender pronouns and sexual orientations throughout the book. Each chapter begins with the biography of an underrepresented mathematician or economist who contributed to that subject. In the apportionment section we include the racial context of the formation of the United States, including race-based chattel slavery and the genocide of Native Americans. A timeline of major events runs parallel to the apportionment method timeline. Hamilton, Jefferson and Webster's relationship to slavery is discussed. The names in the examples for this section are the names of civil rights leaders and Black victims of police brutality.

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. Version 3 of this book is almost identical to Version 2.1. The main change is that the preview activities in Version 2.1 have been renamed to beginning activities in Version 3. This was done to emphasize that these activities are meant to be completed before starting the rest of the section and are not just a short preview of what is to come in the rest of the section.

The primary goals of the text are to help students:

• Develop logical thinking skills;

• develop the ability to think more abstractly in a proof-oriented setting;

• develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples;

• develop the ability to read and understand written mathematical proofs;

• develop talents for creative thinking and problem solving;

• improve their quality of communication in mathematics, which includes improving writing techniques, reading comprehension, and oral communication in mathematics;

• better understand the nature of mathematics and its language.

• Another important goal of this text is to provide students with material that will be needed for their further study of mathematics.

Important features of the book include: Emphasis on writing in mathematics; instruction in the process of constructing proofs; and an emphasis on active learning.

Screencasts designed for use with the book can be found on YouTube.

Note to Instructors: Please contact Ted Sundstrom at mathreasoning@gmail.com for information about instructor resources such as solutions to the preview activities and solutions to the exercises. In your email, please include the name of your institution (school, college, or university), the course for which you are considering using the text, and a link to a website that can be used to verify your position at your institution.

Mathématiques et algorithmes is an open-access textbook written in French and designed for use in a one-semester introduction to algorithms from the mathematician's viewpoint. It only assumes basic knowledge in calculus as a prerequesite: good highschool students should understand this material. Also, this digital textbook is fueled with Python code and Sage interacts to help students experiment with algorithms. Topics covered include root finding, polynomial interpolation, numerical integration and number theory.

The text employs a variety of applications to motivate mathematical thinking. Each chapter opens with a problem of historical or contemporary significance highlighting the material in the chapter. We have also provided a set of more challenging Projects at the end of each chapter.

Function notation is introduced in Chapter 1 and is used consistently in subsequent chapters treating the various families of functions. We study functions using algebraic, numerical, graphical, and verbal methods, and work to establish the connections between these approaches. We want students to learn to write an algebraic expression from a verbal description, recognize trends in a table of data, and extract and interpret information from the graph of a function. Many students have trouble progressing from a point-wise understanding of graphs to a more global view. By taking advantage of graphing utilities, we can examine a large number of examples and study them in detail, and we can consider more realistic models.

An in-text Exercise or Checkpoint, with answers, follows each Example, allowing students to try out new concepts and skills as they are presented. Each Section Summary includes a list of new Vocabulary words that can be found in the Glossary, a brief review of new Concepts introduced in the section, a short set of Study Questions for students to test their understanding of the material, and a list of mastery Skills and the appropriate Homework Problems for practicing each skill.

The text frequently refers students to the appropriate section of Appendix A, Algebra Skills Refresher. We hope that this Appendix will be useful both to individual students and to instructors who want to provide just-in-time parallel support for their classes.

An Activities Workbook is available from xyztextbooks. The Workbook provides a Lesson for each section in the book, consisting of Activities for students to complete in groups or with guidance from the instructor; or they can be used as support for a lecture format. Each Lesson ends with a Wrap-Up and a set of questions for discussion.

An Instructor's Manual for the text is also available. The Manual contains objectives and teaching notes for each section of the text, as well as suggested concept questions and topics for writing or discussion. The teaching notes include suggestions for using the Activities booklet and how to structure class time.

A computer homework system for the text is also available through xyzhomework.

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

ORCCA is available as an interactive eBook, as a downloadable PDF (in B/W or color), and as a printed/bound copy.

The materials begin with linear equations in two variables and extends through trigonometry. The materials can be used in various ways, particularly in online courses.

The material was written with review in mind, but there is enough detail that it would be useful for new students as well. All exercises in the content areas are fully keyed, with no steps excluded. The supplemental problem sets only include answers; they are not fully keyed. While video instruction is useful for many, there are also learners who prefer written exposition, hence the redundancy in presentation of material.

A text for a standard first undergraduate in mathematical proof. Included are a substantial collection of problems with complete hints, and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

Precalculus is taught at Mt. Hood Community College over two 10-week courses. This text aims to address all learning outcomes from the first course, suitable for use in a single 10-week term.

For flexibility, students who have encountered elements of triangle trig in previous courses may be able to skip all or part of Chapters 1 through 3. Students preparing for technical courses may not need much of the material after Chapter 6 or 7. Chapters 9 and 10 cover vectors and polar coordinates, optional topics that occur in some trigonometry courses but are often reserved for precalculus.

Chapter 1 reviews only the most basic facts about triangles and circles that students will need to begin their study of trigonometry, and may be omitted or assigned as homework. Other facts about functions and angles are introduced when they are needed.

Chapter 2 introduces the three (not six) basic trig ratios, and considers angles in the first quadrant only. This initial simplicity allows students to focus on the fundamental concepts without simultaneously trying to master a welter of peripheral detail.

Chapter 3 introduces reference angles for the second quadrant in order to study obtuse triangles and the Laws of Sines and Cosines. Reference angles are covered again in more generality in Chapter 4.

Chapter 4 considers angles as rotations in preparation for the graphs of sine and cosine. Applications of periodic functions in this chapter are functions of degrees only. Radians come later, after students have some experience with sinusoidal graphs.

Chapter 5 begins with a section on algebraic manipulations with trig ratios, a skill that is often neglected but can engender endless confusion for students. We solve equations both graphically and analytically, and we use graphs as well as algebra to verify trigonometric identities.

Chapter 6 introduces radians and the circular functions of real numbers. Most of this chapter and Chapter 7 revisit basic skills such as analyzing graphs and solving equations, but working now in radians rather than degrees.

Chapter 8 studies identities and their use in more detail, including the sum and difference formulas and the double angle identities. Inverse trig functions are included here, and the three reciprocal trig functions.

Chapters 9 and 10 cover ancillary topics; typical trigonometry courses may include one or more of these topics: vectors, polar coordinates, and complex numbers.

Each Example in the book is followed by a similar Exercise for students to test their understanding. Each Section concludes with a Summary, a set of Study Questions, and a list of Skills to be addressed in the Homework. A Summary and a set of Review Problems follows each chapter. Chapters 1 through 8 include Activities for students to work through some of the main ideas. We have described the use of a graphing calculator, but other graphing utilities can easily be substituted.

Understanding Linear Algebra is an open-source, open-access textbook designed for use in a one-semester introduction to linear algebra that does not assume calculus as a prerequisite. There is an emphasis on conceptual thinking, motivating applications, and computation using the open-source software Sage. The text supports active learning by including preview activities and several in-class activities for each of its 22 sections.

Material for a second semester follow-up course is in development and will be published in May 2020.

This is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Rob Beezer has contributed complementary material using the open source system, Sage.

The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

These notes are not intended as a first or second course in abstract algebra, though they assume the reader has seen the material in a basic abstract algebra course.

These notes will undertake a review of many topics from a typical first course, often taking the opportunity to interleave more advanced concepts with simpler ones when convenient. There is an emphasis on ring theory, especially as preparation for a course in field theory. The notes will refresh the reader's memory of definitions, structural results, and core examples to help the reader come to a deeper appreciation of the ideas first met perhaps a long time ago.

This text was designed for an IBL approach to MATH A305 Introduction to Geometries at the University of Alaska Anchorage. Its purpose in the mathematics baccalaureates at UAA is to cover geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry.

Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite. The students have typically taken high school geometry.

I am currently working to replace the problems that support each proof with interactive WeBWorK problems. In the meantime I would be happy to share the problem sets over email.

An undergraduate, introductory, inquiry-based learning course in undergraduate real analysis on the real line.

This is a text with more than enough material for a one-semester introduction to combinatorics. The original target audience was primarily computer science majors, but the topics included make it suitable for a variety of different students. Topics include:

• Basic enumeration: strings, sets, binomial coefficients
• Recursion and mathematical induction
• Graph theory
• Partially ordered sets
• Additional enumeration techniques: inclusion-exclusion, generating functions, recurrence relations, and Polya theory
• Graph algorithms: minimum weight spanning trees, Dijkstra's algorithm, network flows

For some sections, embedded SageMath Cells are used to provide assistance with computations.

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially, but not exclusively, on the part of combinatorics that mathematicians refer to as "counting." The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on.

There are six chapters as well as an appendix with three additional topics:

1. What is Combinatorics?
2. Applications of Induction and Recursion in Combinatorics and Graph Theory.
3. Distribution Problems.
4. Generating Functions.
5. The Principle of Inclusion and Exclusion.
6. Groups Acting on Sets.

Many of problems have hints, which can be found in the back of the book (for the pdf and print versions) or linked directly from the problem (in the online version).

Exploring Combinatorial Mathematics is a free and open source textbook suitable for an upper level undergraduate or Master's level discrete math or combinatorics course, especially if the intended audience is pre-service or in-service secondary teachers. The text borrows material from Bogart's Combinatorics through Guided Discovery and Levin's Discrete Mathematics: an Open Introduction, falling somewhere between these in terms of difficulty.

This book was written specifically to be used as the textbook for the Master's level Discrete Mathematics course at the University of Northern Colorado. This course is part of a MA in Mathematics with a Teaching Emphasis. Most of the students in the course are current secondary math teachers. This intended audience has influenced the style and content of the book in a few important ways.

First, we acknowledge that not everyone reading this book will be immediately familiar with the content of a standard undergraduate discrete mathematics course. Little is assumed about the reader's previous work in the subject, beyond a general understanding of how abstract mathematics proceeds, as well as some basic ability with mathematical proof. For the reader completely unfamiliar with these and the basic objects of mathematical study (sets and functions), background material is included in an Appendix.

Topics have been selected to illustrate larger concepts of interest to secondary teachers. We have put an emphasis on understanding simple concepts deeply and in more than one way. Although some topics intersect secondary curriculum, most of the questions here are at a higher level. Still, the problem solving strategies and big ideas illustrated by our questions have applications to secondary mathematics. This emphasis is quite different than other mid level discrete and combinatorics textbooks, since we are not preparing our readers to begin a career in research mathematics.

While this course is not a course on teaching mathematics, we have tried to model good pedagogical practice. As you will see, almost all of the textbook consists of Activities and Exercises that guide students to discover mathematics for themselves. This will require quite a bit more work both from students and instructors, but we strongly believe that the best way to learn mathematics is by doing mathematics. Most of all, discovering mathematics is fun.

Our focus in this book is the study of algebraic structures called groups. Along the way, we will explore rigorous mathematical notions of similarity and difference: When can we consider two objects to be more or less the same? When are they fundamentally different? For instance, consider two houses that have exactly the same construction, but are painted different colors. Are they the same house? No. But viewed structurally (as opposed to aesthetically) they are the same. This means that if we know certain information about one of the houses (say, how far the bathroom is from the kitchen) we know the same information about the other house. However, knowing that the first house is painted yellow does not tell us anything about the second house's color. We explore an analogous idea in mathematics, namely, the concept of isomorphism.

Throughout, we provide readers with many mathematical proofs, as well as specific examples demonstrating more general ideas.

Motivated by questions in cosmology, the text investigates hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

It is written for students who have taken vector calculus, and intended to be suitable as a one-semester course or as a guide to independent study in non-Euclidean geometry and the geometry of surfaces.

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.

This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.

This free, online text is designed for a one-semester undergraduate mathematics course that combines an introduction to group theory with an introduction to modern geometries using the Kleinian paradigm.

The chapter on groups develops the basic theory of groups and homomorphisms, culminating with group actions. The chapter on geometry makes use of group symmetries in the basic theory of Möbius, hyperbolic, elliptic, and projective geometries.

The text is designed for active engagement, with carefully structured exercises throughout.

The text assumes prerequisite courses in calculus, linear algebra, and experience with proof writing.

Materials for teaching linear algebra using Team-Based Inquiry Learning, part of the NSF-funded TBIL Resource Library.

This book explores several non-Euclidean geometries, in each case providing a short introduction accompanied by interactive GeoGebra applets. The emphasis is therefore on explicit models of these geometries, including in particular taxicab, elliptic, and hyperbolic geometry. Suitable for self-study or to accompany an undergraduate course, although there are no unsolved exercises. Currently available online only, with a CC license.

An undergraduate course on differential equations aimed at engineers and applied sciences. Covers undergraduate ODEs including linear and nonlinear systems and very basic PDE theory. Also includes an appendix on basic linear algebra. Usable for one or two semester sequences.

The PreTeXt code for this project is automatically generated from the LaTeX source code, and uses some custom tags, therefore it requires a custom xsl (see the github repository) to build the HTML version.

In this book, we take an inquiry-oriented approach to ring theory, in the style of Marshall, Odell, and Starbird's Number Theory Through Inquiry, which serves as inspiration for the first chapter. No proofs or solutions are given; instead, the theorems and exercises are carefully chosen and sequenced to provide sufficient scaffolding for students to supply the proofs.

In chapters 2 and 3, students are introduced to fields, rings, and ideals, with aim of understanding the structural properties required for preserving unique factorization. In chapter 4, ideals and homomorphisms are explored.

The textbook focuses on modeling, an early introduction to systems, and systems of linear equations. More specifically, the order of topics covered is first-order differential equations, systems of differential equations, linear systems, second-order linear equations, nonlinear systems, and the Laplace transform. There is more than enough material for a one-semester course. There are many interactive Sage cells in the HTML version of the book.

This is the first computer science textbook authored with PreTeXt. It has been used in the classroom two semesters (2016/17 AY) at Sonoma State University and Santa Rosa Jr. College. I and the PreTeXt developers would very much appreciate hearing your feedback about the formats used to display the various elements in the book. And of course, I welcome any comments you have about the content, especially any errors that your find. I maintain a log of corrections in Errata so you can see if any sections you have already read may have been changed.

Topics include forces and moments; equilibrium of particles, rigid bodies, and structures; centroids and moments of inertia.

This short expository note was authored in PreTeXt early in the development of PreTeXt itself (Summer 2013). The LaTeX output required very few adjustments to be acceptable to the journal's editorial processes.

The XML source has been updated to reflect early changes in PreTeXt, and the HTML output was last built in March 2015. As of early 2020 the online version seems to still be rendering just fine, a testimony to certain fundamental technical decisions.

The purpose of Sound Writing is to help you develop a range of techniques that you can use to succeed as an academic writer. As you'll soon discover (if you have not discovered already), academic writing is a practice with its own conventions and expectations. Academic inquiry is about using the best possible evidence to grapple with contested issues. Academic writing places special emphasis on rigorous use of evidence to substantiate claims, on clear and specific theses, and on the framing of arguments within scholarly contexts. These traits distinguish academic writing from most popular writing (the type of writing that one finds on blogs, in newspapers and magazines, and on Facebook). Though it is possible to discuss academic writing as a coherent entity, academic writing is also diverse and reflects writers' own personal, disciplinary, and sub-disciplinary biases. (Take a look at the example student essays included in the Resources section of this book.) In Sound Writing, we hope to provide you with the essentials of university writing so that you can write with as little stress and as much success as possible. Inside this book, you'll find a breakdown of research, composition, and revision processes; strategies for overcoming common writing challenges; advice from faculty members; a guide to APA-, Chicago-, and MLA-style citations; and much more.

This text will cover all of the usual topics in the typical first semester course in Calculus, as taught in American colleges. However the topics are arranged to reflect the history of the topic, rather than its logical structure in order to use history to illuminate the progression of ideas and concepts. The current version is being written in LaTeX. However the authors will be starting a conversion to PreTeXt in the near future. The text will be published under a Creative Commons license by the Open SUNY Textbook (OST) program and projected to be completed no later than December 2020.

Warning: The version at the URL above is the authors' working draft, not a final version. It is thus subject to change without notice.

Introductory material in each of logic, set theory, graph theory, and combinatorics.

Includes worksheets for in-class activities suitable for a partially-flipped classroom.

The text begins with fundamentals such as invariant subspaces, refelctors, projectors, and positive semi-definite matrics. A chapter on matrix decompositions includes LU, QR, SVD, and Cholesky, with Schur planned. Canonical forms is mostly about Jordan canonical form, with plans for rational form. The final two chapters are applications and further topics.

Notation agrees with, and cross-references point to, the author's A First Course in Linear Algebra.

AAFT is organized into three parts: (1) An Introduction to Groups and Rings, (2) Topics in Group Theory, and (3) Topics in Ring and Field Theory. The first part introduces the key concepts of both groups and rings. Instructors may then taylor the course by selecting topics from parts (2) and (3). AFTA was developed from the open source textbook Abstract Algebra: Theory and Applications. AAFT is still in development.

Une approche géométrique à l'algèbre linéaire avec de nombreux exemples dynamiques et interactifs.

La théorie est présentée à la fois d'une manière intuitive (se basant sur la géométrie) et rigoureuse.

A theorem sequence for an inquiry-based introductory topology course.

The initial version of this book, available March 2020, contains supplemental material for the Dartmouth course Engs31/CoSc56. Topics include: Boolean logic; electronics and logic gates; computer-assisted tools for design capture, simulation, and synthesis; prototyping with discrete components and with programmable logic (FPGAs); top-down modular and register transfer level (RTL) design with bottom-up construction and physical testing; interfacing with peripheral devices (SPI, UART). Other topics will be filled in over time to cover an entire course.

The only prerequisite is an introduction to programming. Basic electronics are taught as they are needed. To serve both engineering and computer science students, I emphasize the differences between VHDL, a hardware description language, and software languages like C or Python. Practical examples and lab assignments use the Xilinx Vivado tool set, Xilinx Artix7 FPGA, and Digilent Basys3 development board.

These are the notes for the edX course Programming for High Performance to be launched in late May 2019. This course uses matrix-matrix multiplication to illustrate how algorithms and architectures need to interact if high performance is to be attained.

Lecture notes for a third-year course in linear algebra.

Contains a mixture of theoretical and computational content.

Computations are done in Sage cells using the SymPy Python library.

Based on Linear Algebra with Applications, by Keith Nicholson.

The text will be structured in stand-alone modules, each related to a single social justice topic. Each module will begin with an overview of the topic, historical context, and a discussion of current questions and concerns related to the topic. This section may include particular case studies related to the topic, articles discussing the topic, and other resources. This section will followed by discussion prompts for faculty to use in helping students explore the issue.

The mathematical content will follow. Each topic will be paired with 2--4 mathematical topics which will help the reader to ask questions and build understanding about the social justice topic being discussed. These mathematical topic sections will stand alone, and may be repeated in multiple places throughout the text (for example, a section on exponential growth may be included in the module on climate change as well as the module on predatory lending).

Each module will end with homework exercises related to the social justice and mathematics topics, longer prompts intended to support more extensive explorations of the topics, and reflection questions to encourage students to consider what they’ve learned.

Music Theory for the 21st-Century Classroom is an openly-licensed online four-semester college music theory textbook. This text differs from other music theory textbooks by focusing less on four-part (SATB) voiceleading and more on relating harmony to the phrase.