Math Duality

Singapore still follows the outdated UK Math pedagogy, using the old term “Advanced Calculus” (高等微积分) for the huge discipline of “Analysis” (分析) — the ‘Micro’ view of Math.

Math Online Tom Circle

Mathematics is roughly divided into 2 categories:

‘Macro’ Math: Algebra

‘Micro’ Math: Analysis (or the outdated name Calculus)

Algebra has been transformed rapidly from 19th century after Galois’s invention of Group Theory, and expanded by David Hilbert and his students E. Noether, Artin, etc in Axiomatic Algebra, takes a very macro view of Mathematical structures in abstract thinking.

Analysis, also after 19th century Cauchy and Wierestrass’s invention of ‘epsilon-delta’ micro view of Calculus, transformed the Newton Calculus into rigourous Math.

The old school of division of Pure and Applied Math is no longer valid. Take for example, the Applied Math used in Google Search Algorithm uses abstract Vector Space of Matrices in Linear Algebra (Pure Math).

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About tomcircle

Math amateur
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