Abstract Alg, Lec 8A: Rational Numbers and Equivalence Classes, Product of Subgroups, Cyclic Groups

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(0:00) Exam 1 date and content coverage.
(1:27) We are like mathematical taxonomists.
(2:35) Our main goals: observe, describe, understand, define and classify, demonstrate (prove).
(4:11) Equivalence relations in geometry and in defining rational numbers. Rational numbers are equivalence classes of fractions.
(10:48) The product of subgroups in an Abelian group is a subgroup of the Abelian group (prove with two-step subgroup test).
(18:30) Some basic facts worth emphasizing.
(23:33) Questions and empirical observations about cyclic groups. Example: a cyclic group of order 6.
(31:15) Another Example: a cyclic group of order 5.

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  1. Bill Kinney
  2. modern algebra
  3. abstract algebra
  4. taxonomy
  5. understand
  6. classify
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whif a/b IS the notation for the equivalence class

dacianbonta