Vision for a Mathematics curriculum

Outline of ideas for a math curriculum
- centered on the ground of core ideas needed to understand
  physical laws, data analysis, information processing,
  algorithms, formal language, and philosophy.
- emphasis on the basics.
+ primary school level:
  - numbers and how they work
    - addition, subtraction, multiplication, and division
      of fractions and decimals
    - number line (signs and inequalities)
+ middle level
  - prerequisite knowledge: numbers and how they work
  - algebra, word problems
+ secondary school level:
  - logic and geometry
  - function analysis (trig/precalc/calc)
+ undergraduate:
  + math core for all students
    - preliminaries (to demonstrate mastery of)
      - review of algebra
      - geometry and algebra of complex numbers
      - basic symbolic logic
    - linear algebra
    - calculus
      - unifying theme: local linearity
      - first pass: "physicist proofs"
        - prove theorems for piecewise linear functions.
        - goals:
          - to understand why theorems are true; not rigor
          - to see the unity and the driving principles
  + math major core
    - abstract algebra (with geometrical invariants)
    - advanced calculus (with forms) and complex analysis
+ graduate level:
  - begin by satisfying a "basics" requirement
    - linear algebra
    - advanced calculus
  - demonstrate mastery of an area
    - algebra
    - geometry/topology
    - analysis

+ math education links
  - Racial Equity Requires Teaching Elementary School Teachers More Mathematics