What Inspires My Teaching and My Writing
I believe strongly that every person can learn (and do) mathematics. Despite the abstract and inaccessible field mathematics is often perceived as, we are all mathematicians at heart. We are all pattern seekers (think about the clothes you wear most often; I bet you’ll spot a pattern) and finding patterns is at the heart of mathematics.
What I’ve just done is to deploy the first of the three main approaches I use to help teach mathematics:
Reveal the hidden mathematics behind everyday events and activities.
Create opportunities to interact with mathematics.
Simplify the teaching of mathematics.
Once you realize that mathematics is all around you, including in the everyday things and events you experience, the subject becomes much less abstract, much more accessible, and much more personally relevant. This was the approach I took in my first two books, Everyday Calculus and The Calculus of Happiness. Everyday Calculus focuses on revealing the hidden calculus behind everyday events and activities (e.g., making breakfast); The Calculus of Happiness focuses on uncovering the mathematics behind health, personal finance, and love. As these books show, math is not only relevant and accessible, but empowering too.
Because a central theme of my writing is to reveal the hidden mathematics all around you, I often create interactive applets and figures intended to help you engage directly with mathematics and not just observe it or be made aware of its presence. Creating these opportunities to interact with mathematics is my second main approach to teaching math. I’ve created a growing list of interactive math applets that help you engage with mathematics and illustrate some of the concepts and applications I discuss in my writing. The list of applets is archived on the Interactive Math Applets page.
The final approach I use in my quest to help every person learn and enjoy math is to simplify its teaching. We don’t need thousand-page tomes to learn calculus, for example. In fact, the essence of calculus can be described in just 7 pages. That’s what I did in the first chapter of Calculus Simplified (you can download that chapter for free on the site), which teaches the first semester in a college-level calculus course in about 100 pages without any prior knowledge of trigonometric, logarithmic, or exponential functions. It does this by distilling the subject to its essence, giving the reader choices about what content they’d like to learn, and keeping the exposition concise. I do something similar in Calculus 2 Simplified, where I give the reader the option to learn Calculus 2 via a "sequences first" approach, which requires far fewer prerequisites to start compared to the standard approach (which requires knowledge of integration right away).
Beyond the books I have written, check out the Math Articles page to read my other writing, including my articles on The Huffington Post.