“Algebraic Topology” can detect the Multi-dimensional neural network in our brain – by studying the Homology (同调) and co-Homology (上同调) with the help of Linear Algebra (multi-dim Matrix) & Computers.
Homology = compute the number of “holes” in multi-dim space.
Neurons formed in the brain can be modeled in Math (Topology) by Simplex 单纯 (plural : Simplices), billions of them interconnected into a complex – “Simplicial Complex” (单纯复体)。
What is Math ? Interesting article below:
- Mathematics = “that which is learned“ –(Pythagoras)
Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…
What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.
Difference between Riemann Integral & Lebesgue Integral ?
Everything in Haskell is PURE (function), including side effects (print, I/O such as open files, update data, …)
“Pure”: f (x) = a, regardless of ‘x’ value may change, always returns the result ‘a’
Parallel and Concurrent Haskell: http://www.youtube.com/playlist?list=PLbgaMIhjbmEm_51-HWv9BQUXcmHYtl4sw
3) Higher–Order Function, Closure
View story at Medium.com
Singapore scores the 2016 PISA Test World’s First in Math.
Below is the “Singapore Math” shown by a USA School adopting the pedagogy.
I had the opportunity to meet the inventor of the “Singapore Math” Prof Lee PengYee (李秉彝) in a Math seminar at NUS few years ago, who took the inspiration of the 1960s ~ 1970s Chinese School (P.S.L.E. / Secondary 1) Math 算术 (literary means “Counting Technique” sans Algebra), combined with the Polya 4-Step Problem Solving Methodology [Video by Polya], with a visual tool called “The Model Diagram”.
See here a tougher “Singapore Math” example for the 11-year-old kids at P.S.L.E. Exams.
Note: This pedagogy is based on Concrete Visualisation, while good for majority of young students (7 to 13 years old) to learn computation and problem solving, it doesn’t train the opposite skill from young in “abstractness” (eg. Basic Set Theory) which is the foundation required in university Advanced Math, where the French, Russian and USA university students excel more than the Asian cohorts.
The Ideal Math Education for the next 22nd Century:
1) Singapore Math (Computation for Primary schools ) +
2) English Math (Applied Math for High Schools) +
3) French Math (Abstract Math for Universities)
Current Math education is biased towards any one &/or two (out of the three):