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"No doubt: The most powerful lesson learned from our traditional lessons in math is to hate math (or at least to be very, very suspicious of it)." --DLH

The material is especially important for people who need to discover the value of mathematics for the fast-moving age in which we live ... and, for course, its value in a chosen career path.


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Here is what one of our learners says about this math program:

i am very sorry i did not see this website earlier when I had to take college algebra. Here I can take my time and understand it better. It is so simple when you take the time rather than having someone breathing down your neck and hurrying you. Algebra or any form of math takes time, especially when you aren't using it every day. I am grateful for the site. Thanks!

lovely

Now for a brief word from one of our sponsors ...

David L. Heiserman

I didn't actually dislike math through the primary and secondary grades. It's more like I was passive about it. I completed the work, usually paid attention in class, and got decent grades--not really great grades, but a bit above average. The passive nature of my early math education is reflected by an incident in a high school plane geometry class. The teacher was an older, near-retirement guy whose vision was getting really bad. So one day, around six or eight of us decided to have a party during class. We each brought a bottle of Coke (still in the greenish bottles in the late 1950s), and a handful of peanuts. Luckily, someone thought to bring a bottle opener. Yes, we opened our Cokes, passed the peanuts around, and enjoyed a party while that faithful old math teacher droned on about the areas of triangles or some such thing.

I had joined the Navy immediately after graduation from high school. It was during that time that I completed correspondence courses in college algebra and trigonometry. Why? I had gotten a serious opportunity for a full-ride college scholarship, and thought I might be able to get a bit ahead by passing some proficiency exams in math, and going straight to calculus. My plan worked, at least the start-up part. The problem was that I was taking engineering physics at the same time. Too much for someone who was clueless about good study habits. So I switch my major to psychology.

I was doing okay with the psych courses, and didn't need any more math except one semester of statistics. And I flunked it! Now, that's just wrong! So I had to repeat the stat course ... and I flunked again. So much for college. I gathered up my stuff and simply walked away from school and my full scholarship.

I have never made amends with statistics. I've had to mess around with mean, median, mode, and the bell curve from absolute necessity. And just last week, I finally got an intuitive grasp of the standard deviation. It seems that the whole world that interests me is embracing more concepts requiring statistical analysis. So I will probably have to get my head straight and get with the program. Maybe I should write a book about it.

My first post-college job was managing and teaching basic electronics at a franchise radio and TV repair school. It was fun and I learned a lot about electronics--about one day ahead of my classes. But the math bug made a nest in my soul about that time. Whereas I'd spent most of my life with a passive attitude toward math, I became intensely interested in the derivation of some equations for the transport of ions across semi-permeable membranes. It was a recent development in biophysics; but more important for me, it demonstrated the mindset that drives mathematicians--applied mathematicians, in this case. The discovery was already done, and the guy got a Nobel Prize for it. I was just driven to go through the process of deriving that equation from what was known about ions and semi-permeable membranes.

It is a fantastic feeling to see a problem that needs to be solved, knowing it is just a bit beyond your grasp at the moment. Doing math, theoretical and applied, is quite inexpensive and no one cares how many degrees you are using for wallpaper. It's the results that matter. Perfect freedom.

I eventually solved the problem. A year or so later, I was back at my university, but as a lab technician in pharmacology. One of the profs was conducting graduate-level courses in nerve cell conduction; and, being more of a pharmacologist than biophysicist, he needed help with explaining ion transport. So he offered me several hours of graduate credit to take his classes and actively participate when the topic of the week was ion transport. So I flunk out of undergraduate school, but accumulate some 4.0 GPA graduate work. Go figure.

My next step in my math life was to take a part-time position teaching trigonometry at a private business college. That was fun! I was back into teaching and learning a lot of cool new things about trigonometry. I did not have proper credentials for teaching at an accredited college, even a private one. But it seems there was a shortage of college-level math teachers in the area, so the requirements were waived. I enjoyed teaching and apparently the students enjoyed my classes. Someone must have been impressed because I eventually conducted courses in analytic geometry and calculus.

I had taught myself the fascinating subject of analytic geometry, as it was called in those days. I think they call it something like algebraic geometry these days and have lumped it into something called pre-calculus. But no matter what they want to call it, combining trig, geometry, elementary calculus, and perhaps some ... whatever. It's fun to learn, fun to play with, and fun to teach.

One day I got an offer I couldn't refuse--teaching ordinary differential equations at a state college. This was just three nights a week, but I would do about anything to teach ODE. It was an amazing and fulfilling experience. I got there with no formal credentials, but with experience, a network of people who knew my work, a love for math, and a knack for teaching. (Incidentally, I was teaching myself the material about a week ahead of the class. So I was acutely aware of what was going on in the minds of my students who were likewise facing the material for the first time. It was a very productive synergy.).

After leaving classroom teaching altogether and forever, I had more time for my freelance writing. I did one rather unusual math book, Experiments in Four Dimensions. It was basically about geometric translations in four dimensions. Now that isn't a strange thing these days--translations in four dimensions is a required skill for game developers. Anyway, I am proud of the topic and the algorithm I developed for viewing 4-dimensional objects in 2-dimensional space (on a sheet of paper). However, I am embarrassed with the way I implemented it. Maybe I will revise it someday, leaving out all of the unnecessary solution procedures and assuming the reader has access to a computer.

Note: It occurred to me just a moment ago--while finishing the previous paragraph--that it would be so much fun to do coordinates for 3D projections and construct ball-and-stick models of four-dimensional objects as they would appear in three-dimensional space.

The moral of the story here is that the best ideas usually come when actively engaged in the subject ... and not from formal brainstorming sessions. Don't get all wrapped up and led astray by popular attempts to systemize creativity. That's like trying to milk the grass before feeding it to the cow.

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This page, like any lifelong learning venture, is never done. This is a lifelong "work in progress."


David L. Heiserman, Editor

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Revised: June 06, 2015