For years now, educators, business leaders, and even politicians have begun to realize that today’s students aren’t learning enough higher mathematics. The need for civil engineers, for instance, is expected to… 436 more words

## Tags » Mathematics

#### Clarification on the proof of Carathéodory's lemma

Carathéodory’s lemma, as it appears in p. 197 (appendix A1) of the book “Probability with martingales” by David Williams, is stated as follows:

*Let* *be an outer measure on the measurable space…* 626 more words

#### Coding Information While Operators Fail to Commute. Drunken Risibility.

Suppose ∇ is a derivative operator on the manifold M. Then there is a (unique) smooth tensor field Rabcd on M such that for all smooth fields ξb, 296 more words

#### Peano's Axioms and Propositional Logic

Scientists are curious folk. They are overjoyed when they are right, and they are happy even when they are wrong – for they see it as an opportunity to learn from their mistakes. 1,262 more words

#### Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts

Can never go past Jo Boaler’s work. It just makes sense to me.