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#2: Functions and Relations
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This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given
an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.

Subject:
Functions
Material Type:
Reading
Author:
Brent Yorgey
Date Added:
10/21/2020
APEX Calculus
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APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

Subject:
Calculus
Material Type:
Textbook
Provider:
APEX: Affordable Print and Electronic TeXtbooks
Author:
Brian Heinold
Dimplekumar Chalishajar
Gregory Hartman
Troy Siemers
Date Added:
01/01/2014
APEX Calculus: UND Edition
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This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free.

Subject:
Calculus
Material Type:
Textbook
Provider:
University of North Dakota
Author:
Gregory Hartman
University of North Dakota Mathematics Department
Date Added:
07/01/2017
APEX PreCalculus
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This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.

Subject:
Calculus
Material Type:
Textbook
Author:
Amy Givler Chapman
Jessica Libertini
Meagan Herald
Date Added:
12/05/2019
Abstract Algebra: Theory and Applications
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This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Subject:
Algebra
Material Type:
Textbook
Provider:
University of Puget Sound
Author:
Thomas Judson
Date Added:
01/01/2016
Active Calculus
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CC BY-NC-SA
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Active Calculus is different from most existing calculus texts in at least the following ways: the text is 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 java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Mathematics
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matt Boelkins
Steve Schlicker
Date Added:
12/05/2019
Active Calculus 2.0
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Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

Subject:
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matt Boelkins
Steve Schlicker
Date Added:
11/18/2021
"Active Calculus 2.0" by Matthew Boelkins, David Austin et al.
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CC BY-NC-SA
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Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

Subject:
Calculus
Material Type:
Textbook
Author:
Austin David
Boelkins Matthew
David Austin
Matthew Boelkins
Schlicker Steven
Steven Schlicker
Date Added:
08/28/2020
"Active Calculus 2.1" by Matthew Boelkins, David Austin et al.
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ctive Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; there are live WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

Subject:
Calculus
Material Type:
Textbook
Author:
Austin David
Boelkins Matthew
David Austin
Matthew Boelkins
Schlicker Steven
Steven Schlicker
Date Added:
08/28/2020
Active Calculus Multivariable
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Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are 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 java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Subject:
Calculus
Material Type:
Textbook
Provider:
Grand Valley State University
Author:
David Austin
Matthew Boelkins
Steven Schlicker
Date Added:
07/01/2018
Active Prelude to Calculus
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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.

There are links to interactive Desmos activities, interactive applets, and even some interactive Javascript graphics embedded in the text. These features are best accessed in HTML. In addition, all of the graphics are full-color in the electronic versions. To keep costs low, the bound, print version for sale on Amazon is in black and white.

Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes its importance in calculus. The reader will find that the text requires them to engage actively with the material, to view topics from multiple perspectives, and to develop a deep conceptual understanding of ideas. Many courses at the high school and college level with titles such as college algebra, precalculus, and trigonometry serve other disciplines and prepare students for courses other than calculus. As such, these prerequisite classes frequently contain wide-ranging material that, while mathematically interesting and important, isn't necessary for calculus. Perhaps because of these additional topics, certain ideas that are essential in calculus can be under-emphasized or ignored. In Active Prelude to Calculus, one of our top goals is to keep the focus narrow on the following most important ideas. See more about the motivating forces behind the text in the Our Goals section of the text's preface. Students who will use the text are especially encouraged to read the Students! Read This! section of the preface.

Instructors are strongly encouraged to have their students use the Activities Workbook. This workbook is simply a PDF document that has a single activity per page along with room for students to record their work and thinking. Instructors can provide students with the PDF, have their bookstore or copy center create coursepacks for students to purchase for a small fee, or purchase a bound workbook directly from Amazon. To acquire a PDF copy of the Activities Workbook, please contact the author directly: boelkinm at gvsu dot edu.

Active Prelude to Calculus was first made publicly available in January 2019. The text is free and open-source; the source code can be found on GitHub.

Subject:
Mathematics
Calculus
Material Type:
Textbook
Author:
Matthew Boelkins
Date Added:
12/02/2021
Advanced High School Statistics
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CC BY-SA
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This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss

View our video tutorials here:
openintro.org/casio
openintro.org/TI

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
OpenIntro
Author:
Christopher Barr
David Diez
Leah Dorazio
Mine Cetinkaya-Rundel
Date Added:
12/05/2019
Advanced Problems in Mathematics: Preparing for University
Unrestricted Use
CC BY
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This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Open Book Publishers
Author:
Stephen Siklos
Date Added:
12/05/2019
Agent-Based Evolutionary Game Dynamics
Unrestricted Use
CC BY
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This book is a guide to implement simple agent-based evolutionary models using NetLogo.

Subject:
Mathematics
Material Type:
Textbook
Author:
Luis R. Izquierdo
Segismundo S. Izquierdo
William H. Sandholm
Date Added:
12/05/2019
Algebra and Trigonometry
Unrestricted Use
CC BY
Rating

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Subject:
Algebra
Trigonometry
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
David Lippman
Jay Abramson
Jean-Marie Magnier
Melonie Rasmussen
Nicholas Belloit
Rachael Gross
Rick Norwood
Valeree Falduto
Date Added:
01/29/2015
Algorithms
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CC BY-SA
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This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Wikibooks
Date Added:
06/15/2019
Applied Calculus
Unrestricted Use
CC BY
Rating

An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text.

Subject:
Calculus
Material Type:
Textbook
Author:
Dale Hoffman
David Lippman
Shana Calaway
Date Added:
08/28/2020
Applied Calculus
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Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Subject:
Calculus
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Dale Hoffman
David Lippman
Shana Calaway
Date Added:
06/13/2019