Quite easy to follow this “Mr.Bean” lecturer in Computational Topology. Pre-requisite is undergraduate elementary Abstract Algebra (Linear Algebra, Surjectivity, Injectivity, Isomorphism, Quotient Vector Space, Matrices, ….). He used Python to compute rather than Lisp.
This is a series of 6 lectures on Computational Topology : Applied Math using computer in Algebraic Topology. Computer tool languages used can be Phyton (this lecture) or Common Lisp (the preferred Functional Programming like Lisp for its rich mathematical background in Lambda Calculus — new main feature in next Java 8).
As explained by this professor in Lecture 1, Computational Toplogy begins with Algebraic Topology aided by the arrival of computers in 1950s. The role of Algebraic Topology is to study Topology (Geometric Spaces “Manifolds” (流形) with continuous functions) using algebra (mainly Advanced Linear Algebra).
Just like Google Search revolutionises the world in 2000s, using only the classical Linear Algebra; Algebraic Topology will revolutionise Big Data Analytics using the Advanced Linear Algebra — the next wave in Mobile Age.
In layman’s term, it means using this tool to analyse Big Data in a geometric picture form…
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