Modern Algebra (Abstract Algebra) Made Easy

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Modern Algebra (Abstract Algebra) Made Easy

This video series is really well done ! short and sharp, yet cover the entire syllabus in the Group Theory.

Strongly recommended for those Math-inclined students from upper secondary schools (Secondary 3 to JC2). Although the Singapore school Math syllabus based on Cambridge ‘O’ and ‘A’ level do not cover modern math – which is a serious weakness for being biaised on computational applied math, an outdated pedagogy for the last 40 years with no major changes – we miss the latest Math development since 19 century, the so called ‘Modern Math’ but already 300 years old.

Group Theory is the stepping stone to open the door of interesting advanced Math, physics, chemistry, bio-science and engineering. It should not be limited only to the Math-major undergraduates in university. (Note: Why France and China make Modern Algebra compulsory for all science and engineering students )

Part 0: Binary Operations

Part 1: Group

Note: Why ‘e’ for Identity, ‘Z’ integers

Part 2: Subgroup

Part 3: Cyclic Group & its Generator

Part 4: Permutations

Part 5: Orbits & Cycles

Part 6 : Cosets & Lagrange’s Theorem

Part 7 : Direct Products / Finitely generated Abelian groups

Part 8: Group Homomorphism

Part 9: Quotient Groups

Part 10: Rings & Fields

Part 11: Integral Domains

Reference: further studies in deeper and advanced Abstract Algebra at:

Harvard Online Free Course by Prof Benedict Gross

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