Math and science help for high school and college students

This site is a collection of the math and science notes I have used in my high school math and science classes. It has become a sort of constantly-evolving electronic textbook, but I hope one that is a bit more direct, helpful and friendlier than many 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 try to fill those in as I continue to refine. For each of more than 230 subjects in math, physics, chemistry and biology, you'll find explanations, worked examples, practice problems with answers animations and video.

I enjoy hearing your feedback as long as it's specific and constructive. For the most part I try to make corrections when necessary as soon as possible. Just let me know if I've missed something.

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 certain aspects of dyslexia found it more difficult to read wide columns of text than narrow.

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.

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 constructive 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.

About learning math and science

One of the most valuable pieces of advice I can offer you as a student of math and science is that, while often you'll feel like you've learned a hundred different things in just a few weeks, it's likely that you haven't. You've learned a few key concepts and a bunch of ways to use them. If you can remember the simple principles, looking for things that different subjects have in common more than their differences, it will take you a long way. You'll begin to learn by analogy.

More things are the same in math and science than different.



Dyslexia is a learning disorder that involves difficulty reading due to problems identifying speech sounds and learning how they relate to letters and words (decoding). Also called reading disability, dyslexia affects areas of the brain that process language.

People with dyslexia have normal intelligence and usually have normal vision.

Excerpted from Mayo Clinic



An analogy is a comparison between two things, usually for the purpose of explanation or clarification.

Learning by analogy can be a powerful tool. "I don't know anything about that, but it looks similar to something I do understand, so perhaps I can begin to draw some conclusions ..."

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