Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.
The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:
Note: Lewis Carroll: the author of “Alice in wonderland”
Does it ring a bell to biologists that viruses are mathematically structured objects ? such as the deadly SARS virus with a beautiful icosahedral symmetry.
Icosahedron corresponds to the “Unsolvable Quintic equation (degree 5 and above) with no radical root”, which led the 19 CE young French math genius Evariste Galois to invent “Group Theory” – a revolutionary foundation of the Modern Math.
The problem is few biologists or doctors are good in math, and rare are mathematicians knowledgeable in Biology and Medicine.
Monads ~ “Design Pattern” in Functional Programming
Examples: “Option”, “Some”,…
Revision: Modular Arithmetics
(1/2) Fermat Little Theorem
(1/2) Chinese Theorem
(Note: This is the “RING” foundation of “The Chinese Remainder Theorem” which deals with remainders )
Cours math speciale = 2nd Year of Classe Préparatoire
L’anneau Z/nZ, niveau introduction,
[Partie 2/2]: Z/nZ
C = Chinese 中文 = Primary school Arithematics sans “Algebra” (= Singapore Modeling Math). Abacus-Algorithmic thinking.
E = English = Secondary School Math
=> Applied, Tricky, Math Olympiad-style
=> Engineering, Business, Applied Science.
F = Français (French) = High-school / Baccalaureate & University Math = Theoretical, Abstract
=> Rigorous Math Philosophy for Advanced Concepts
=> New frontier Scientific Research.
Why (C+E) ?
C + E = Basic Math Foundation.
Why * F ?
If multiply by Theoretical F, like flying with added wings (如虎添翅)。
if (C+E) -> 0 (less applied), or
if F -> 0 (lack theories),
then Total Math Education -> 0.