I registered for a trigonometry class at my school last week. I recognize it’s a basic level of math, but my high school academic success was pathetic, and I’ve been paying for it ever since. Anyway, I am excited. It has been ten years since I took my BSU math class (college algebra), sixteen years since I took trigonometry (and earned C’s, if I remember), and eight years since I took any kind of class that required mathematics (algebra based physics). My mathematical mind is in disrepair, a rusty car engine that may be salvaged with proper maintenance.
My long-term goal, by the way, is to take one math class per semester until I am taking the highest level that this 2-year school offers (calculus, differential equations, and linear algebra) so that I can eventually understand some quantum physics and chemistry.
I am curious to see what ten years of philosophy has done to my mind, and how I will think differently about the mathematical concepts. The mind I inhabit now works differently than it did ten years ago. I dominated my college math and science classes in ways I never dreamed of in high school, but I am much busier now and further removed from my last math experience.
The first line of my textbook’s chapter 1 (after the preface which explained the history of the term functions, which touched on philosophers like Descartes and Leibniz, of course!) states: “We locate a point on the real number line by assigning it a single real number, called the coordinate of the point. For work in a two-dimensional plane, we locate points by using two numbers.” This is very basic stuff, but it has been an eternity since my eyes have passed over that postulate. And all I could think of was the feeling and thrill of reading Spinoza’s geometric method and the Kantian divide between intuitions and concepts. Glorious stuff. I am having a nerd-gasm.
Natural Causes 
Might I recommend a little discrete mathematics which seems to have come of age in an era of computing. I really love Gilbert Strang’s linear algebra course which is available for free from MIT OpenCourseWare.
Linear Algebra and Discrete Mathematics are intense courses. They will make you either love or loathe mathematics.
I will keep tabs on this and watch it when I can, but I have a feeling I won’t be able to understand any of it until my brain gets a math upgrade.
Kamran, I recommend this essay titled “A Mathematician’s Apology” you will like it:
Click to access GHHardy-AMathematiciansApology.pdf
Thank you! I read half of it this morning, and will try to fit the rest in this evening. The structure and tack reminded of Bertrand Russell’s writing, especially his short essay “The Value of Philosophy” that is the concluding chapter of his book ‘The Problems of Philosophy.” So on page 13 (essay page, not document page), when Hardy reveals that he’s had a friendship with Russell, I smiled.
It also reminded me of how little I remember of mathematics. When given the number (a/b)^2, for example, I can’t remember how to work it out (I can’t even remember the word for it), ie., the order of operations. Is it equal to (a^2)/(b^2)? Or what? I’m not asking you about this specific problem, actually; I’m just reminded that I will have to take it upon myself to do a lot of independent review of the basics.