AI – DeepLearning – Machine Learning

3 Waves of AI Evolution:

1st Wave (1950s) : Alan Turing “The Father of AI” and his Princeton Prof Alonzo Church (Lambda Calculus). MIT Prof Malvin Minksy’s “Lisp” Functional Programming (a.k.a. Symbolic or Declarative) Language.

2nd Wave (1980s – 1990s) : Knowledge-Based Rule Engine Expert Systems.
Failed because knowledge acquisition process is too difficult with limited rigid rules.

3rd Wave (2010s -): DeepLearning is the latest AI tool for Machine Learning, famous after 2016 “AlphaGo” game by a former Funan-center UK Kid Demis Hassabis (UK/Greek father & Singapore Chinese mom teacher) beat 2 “Go” World Champions (Korean Lee Sedol 李世乭 and China 柯洁).

Great Books Recommended

1. Learn Everything in 《Deep Learning》:

  • Math (eg. Gradient Descent – by French GrandMaster Cauchy 1847),
  • Linear Algebra (eg. Matrix, Eigen-decomposition),
  • Probability (eg. Bayesian, etc),
  • Key Deep Learning techniques.

Note: Available at Singapore National Library (LKC Reference #006.31).

Order at Amazon: https://www.amazon.com/gp/aw/d/0262035618/ref=mp_s_a_1_3?ie=UTF8&qid=1516412628&sr=8-3&pi=AC_SX236_SY340_FMwebp_QL65&keywords=deep+learning

2. 《The Master Algorithm》 (Book or Audio)

http://catalogue.nlb.gov.sg/cgi-bin/spydus.exe/FULL/EXPNOS/BIBENQ/7400075/198909068,1

Notes:

1. Bill Gates recommends this excellent book for 2018 reading, also found it on Chinese President’s Xi JingPing’s Office Bookshelf in 1 Jan 2018 New Year Speech.

http://www.chinadaily.com.cn/a/201801/15/WS5a5bf75aa3102c394518f26b.html

2. All available book copies in Singapore National Library Board have been loaned out !! (Unusual in low-readership Singapore). Please reserve it in online queue.

3. Audio version (10 CDs) is excellent for in-car listening while driving, or travelling on plane/train/bus for busy persons.

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Pre-requisites For Abstract Algebra

The 2 important pre-requisites for Abstract Algebra are “abstract thinking”, namely :

  1. You must not think of “concrete” math objects (geometrical shapes, Integer, Real, complex numbers, polynomials, matrices…), but rather their “generalised” math objects (Group, Ring, Field, Vector Space…).
  2. Rigourous Proof-oriented rather than computation-oriented.

The foundation of Abstract Algebra is “Set Theory”, make effort to master the basic concepts : eg.

  • Sub-Set,
  • Equivalence Relation (reflexive, symmetric, transitive),
  • Partitioning, Quotient Set, Co-Set
  • Necessary condition (“=>”), Sufficient condition (“<=”). Both conditions (“<=>”, aka “if and only if”)
  • Proof : “A = B” if and only if a A, a B => A B, and, b B, b A =>B A [我中有你, 你中有我 <=>你我合一]
  • Check if a function is “well-defined”. (定义良好)
  • These concepts / techniques repeat in every branch of Abstract Algebra which deals with all kinds of “Algebraic Structures”, from Group Theory to Ring Theory to Field Theory … to (Advanced PhD Math) Category Theory – aka “The Abstract Nonsense”.

Mathematicians Find Wrinkle in Famed Fluid Equations | Quanta Magazine

Navier-Stokes Equation – $1 million Clay Prize and one of the 7 Millenium Problems.

This N.S. Equation predicts the movement of fluids (air current, water flow) as vector field (with value and direction), matches the physical experiment outcome, but not proven mathematically.

https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/

French Math : Introduction à la diagonalisation

This is the 1st / 2nd Year Commerce University Math (Cours Prépa).

You shall see the French lecture on Matrix diagonalisation is quite different from the MIT lecture. The French approach is abstract theoretical and more general, the American approach is more practical less theory.

[French translation]

  • Eigen Value = Valeur Propre
  • Eigen Vector = Vecteur Propre
  • Note: Eigen (german) = characteristic 真正的

The same lecture covers more in depth (below) is for Engineering students (Prépa):

https://tomcircle.wordpress.com/2016/12/19/cours-diagonalisation-12-cours-maths-spe/