
More Thoughts about Algebra in 2014
Posted:
Jul 16, 2014 11:44 PM



I've been arguing that Algebra should meet us part way and hop on the bandwagon of computer science a little more.
Themes of hexadecimal, binary, ASCII versus Unicode and nonnumeric functions lace through STEM.
I've urged we dispose of Algebra texts (in the sense of not wasting too much time with) if all their functions are numeric, as that's too narrow a concept of function to sustain best practices going forward.[1]
Here are 26 topics I would expect to find in anything calling itself a Common Core, either in Algebra itself or one course away. Lets just call it Numeracy 101 as an alternative jargon.
(a) V + F = E + 2 (Euler's Law) (b) Descartes Deficit (720 degrees = 1 tetrahedron of angle) (c) Euclid's Method for the GCD (a Python program) (d) Fibonacci Numbers (e) Figurate and Polyhedral Numbers (1, 12, 42, 92...) (f) XYZ coordinate system (in context) (g) Vectors as Objects in an OO computer language (h) Linear Equations (i) Polynomial Equations (see "NCLB Polynomial" in [2]) (j) rates of change (precalc discussions) (k) Trignonometric functions (l) Logarithmic functions (m) numbers and bases (n) permutations and combinations (o) group, ring and field properties (p) prime versus composite (Fermat's Little Theorem) (q) totatives and totient (Euler's Theorem used in RSA) (r) weights and measures (dimensional analysis) (s) Matrices (rotational especially) (t) Mutidimensional arrays (numpy) (u) concentric hierarchy of polyhedrons [2] (v) binomial theorem (Newton) (w) Pascal's Triangle / Tetrahedron (x) Turtle / Tractor Math (Tractor stuff optional)[3] (y) Fractals (z) Cellular Automata
This need not be the order of topics. I'm aware this is not in any way an exhaustive list, just stuff to be included. More statistics, more calculus, more trig (spherical) would be in order.
Descartes (b) should maybe get credit for (a) as well.[4]
Kirby
[1] http://mathforum.org/kb/message.jspa?messageID=9430209 [2] http://mybizmo.blogspot.com/2006/09/focalpoints.html [3] http://mathforum.org/kb/message.jspa?messageID=9507410 [4] http://mathforum.org/kb/message.jspa?messageID=9509000

