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Preface To All

HTML, PDF, and print

This book is available as an eBook, a free PDF, or printed and bound. All versions offer the same content and are synchronized such that cross-references match across versions. They can each be found at

There are some differences between the eBook, PDF, and printed versions.

  • The eBook is recommended, as it offers interactive elements and easier navigation than print. It requires no more than internet access and a modern web browser.

  • A PDF version can be downloaded and then accessed without the internet. Some content is in color, but most of the colorized content from the eBook has been converted to black and white to ensure adequate contrast when printing in black and white. The exceptions are the graphs generated by WeBWorK.

  • Printed and bound copies are available online. Up-to-date information about purchasing a copy should be available at Contact the authors if you have trouble finding the latest version online. For each online sale, all royalties go to a PCC Foundation account, where roughly half will fund student scholarships, and half will fund continued maintenance of this book and other OER.

Copying Content

The graphs and other images that appear in this manual may be copied in various file formats using the eBook version. Below each image are links to .png, .eps, .svg, .pdf, and .tex files that contain the image.

Mathematical content can be copied from the eBook. To copy math content into MS Word, right-click or control-click over the math content, and click to Show Math As MathML Code. Copy the resulting code, and Paste Special into Word. In the Paste Special menu, paste it as Unformatted Text. To copy math content into source, right-click or control-click over the math content, and click to Show Math As TeX Commands.

Tables can be copied from the eBook version and pasted into applications like MS Word. However, mathematical content within tables will not always paste correctly without a little extra effort as described above.


The HTML version is intended to meet or exceed web accessibility standards. If you encounter an accessibility issue, please report it.

  • All graphs and images should have meaningful alt text that communicates what a sighted person would see, without necessarily giving away anything that is intended to be deduced from the image.

  • All math content is rendered using MathJax. MathJax has a contextual menu that can be accessed in several ways, depending on what operating system and browser you are using. The most common way is to right-click or control-click on some piece of math content.

  • In the MathJax contextual menu, you may set options for triggering a zoom effect on math content, and also by what factor the zoom will be. Also in the MathJax contextual menu, you can enable the Explorer, which allows for sophisticated navigation of the math content.

  • A screen reader will generally have success verbalizing the math content from MathJax. With certain screen reader and browser combinations, you may need to set some configuration settings in the MathJax contextual menu.

Tablets and Smartphones

PreTeXt documents like this book are “mobile-friendly.” When you view the HTML version, the display adapts to whatever screen size or window size you are using. A math teacher will always recommend that you do not study from the small screen on a phone, but if it's necessary, the eBook gives you that option.

WeBWorK for Online Homework

Most exercises are available in a ready-to-use collection of WeBWorK problem sets. Visit to see a demonstration WeBWorK course where guest login is enabled. Anyone interested in using these problem sets should contact the project leads.

Odd Answers

The answers to the odd homework exercises at the end of each section are not contained in the PDF or print versions. As the eBook evolves, they may or may not be contained in an appendix there. In any case, odd answers are available somewhere. Check to see where.

Interactive and Static Examples

Traditionally, a math textbook has examples throughout each section. This textbook uses two types of “example”:


These are labeled “Example.” Static examples may or may not be subdivided into a “statement” followed by a walk-through solution. This is basically what traditional examples from math textbooks do.


These are labeled “Checkpoint,” not to be confused with the exercises that come at the end of a section that might be assigned for homework, etc. In the HTML output, active examples have WeBWorK answer blanks where a reader could try submitting an answer. In the PDF output, active examples are almost indistinguishable from static examples, but there is a WeBWorK icon indicating that a reader could interact more actively using the eBook. Generally, a walk-through solution is provided immediately following the answer blank.

Some HTML readers will skip the opportunity to try an active example and go straight to its solution. Some readers will try an active example once and then move on to the solution. Some readers will tough it out for a period of time and resist reading the solution.

For readers of the PDF, it is expected that they would read the example and its solution just as they would read a static example.

A reader is not required to try submitting an answer to an active example before moving on. A reader is expected to read the solution to an active example, even if they succeed on their own at finding an answer.

Interspersed through a section there are usually several exercises that are intended as active reading exercises. A reader can work these examples and submit answers to WeBWorK to see if they are correct. The important thing is to keep the reader actively engaged instead of providing another static written example. In most cases, it is expected that a reader will read the solutions to these exercises just as they would be expected to read a more traditional static example.