If you were in charge, what would elementary school children (that is, grade 7 and below), be expected to learn before going to high school.
Name:
Anonymous2007-07-20 16:55 ID:GdhKSTHm
Grade 1: predicate logic and naive set theory (inc. discussions of injections, bijections, etc.).
Grade 2: Elementary algebra (inc. arithmatic and some number theory, variables, polynomials, a more concrete discussions of functions and their roots).
Grade 3: Euclidian geometry and proof, trigonometry.
Grade 4: Elementary analysis. (rigorous treatment of limits, continuity, derivatives, integrals, differential equations).
Grade 5: Linear and abstract algebra.
Grade 6: Intermediate analysis (vector calc., Stokes' theorem, etc.etc.).
Grade 7: Point-set topology, category theory, more set theory, a survey of topology and (real) geometry.
All material will be given an informally rigorous treatment.