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.

# 434 Results

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

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

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.

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 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 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 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.

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.

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

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

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

Learning and Understanding Mathematical Concepts in the Areas of Water Distribution and Water Treatment

- Subject:
- Mathematics
- Hydrology
- Material Type:
- Textbook
- Provider:
- College of the Canyons
- Author:
- Michael Alvord
- Regina Blasberg
- Date Added:
- 12/05/2019

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 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

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

This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.

- Subject:
- Mathematics
- Geometry
- Material Type:
- Textbook
- Provider:
- Global Text Project
- Author:
- Jurg Nievergelt
- Klaus Hinrichs
- Date Added:
- 01/01/2011

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.

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

Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.

Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom’s MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book’s source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book.

Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- M.T. Keller
- W.T. Trotter
- Date Added:
- 01/01/2017