Free math and science help for high school and college students

This site is a collection of the math and science notes I use or have used in my high school math and science classes. It has become a sort of electronic textbook, but I hope one that is a bit more direct, helpful and friendlier than many modern textbooks. In translating my written notes to this site, I've tried to fill in some gaps, but in the process I've identified a few more. I'll try to fill those in as I continue to refine. I haven't yet included all of the problem sets and solutions I'd like to. And I continue to put up a lot of video and animations to help you learn math and science.

The site now contains more than 200 html pages that cover math, physics, chemistry and biology.

It's a work in progress. In these pages you'll find explanations that I've tried to keep thorough – but in non text-booky language, lots of solved examples, sample problems with download-able solution sets, and video examples.

I create the vast majority of the drawings, animations and videos on this site from scratch, and it's hard work. I'll strive to respect your intellectual property rights, and I ask you to respect mine.

If you've got any suggestions for how to make this site work better for you our your students, please let me know.

A note about the text on this site

A student of mine did some summer research on dyslexia and reading. He discovered that many people with some degree of dyslexia found it more difficult to read wide columns of text.

To the extent possible, I've taken his advice and converted wide-format text on this site into a narrower 2-column format that is compatible with small devices, with the hope that it might help anyone who struggles in that way. Thanks, Josh!

My teaching philosophy

I love math and science. They provide me with a way of making connections between what would seem to be distinct phenomena. They show me that things everywhere are more the same than they are different (just like people), and to the extent that we can make connections, we can understand a lot about the world around us — what it is and what it might become. Using every means I can think of, I try to pass that wonder and ability to my students.

In high school, we try to move beyond an algorithmic approach to math and science, and ask open-ended questions, or questions for which there may be many paths to a solution, and no one clear starting point. I try to move my students beyond formulas to thinking about what's actually being modeled. I try to encourage them to take risks, even in a world that, for them, increasingly penalizes

the kind of consructive failure that is the very foundation of learning. Albert Einstein once said of math (and I think it's equally true of the sciences),

"Pure mathematics is, in its own way, the poetry of logical ideas."

I think that Einstein, a thinker if there ever was one, would agree that math and science are of no value as tools in society if they aren't wielded by people trained to be ethical, moral citizens. Therefore I support liberal arts education in equal partnership with science, technology, engineering and math. Math and science, poetry, fine arts and music are all more the same than they are different, but only the arts and humanities show us how to balance the tension between technological progress and maintaining a just society.

You can help

This site is a one-person operation and a labor of love. If you can manage it, I'd appreciate anything you could give to help defray the cost of keeping up the domain name, server, search service and my time.

  optimized for firefox by Dr. Jeff Cruzan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. © 2012, Jeff Cruzan. All text and images on this website not specifically attributed to another source were created by me and I reserve all rights as to their use. Any opinions expressed on this website are entirely mine, and do not necessarily reflect the views of any of my employers. Please feel free to send any questions or comments to