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Abstract Algebra: A First Course (Section 0): Sets and Induction
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I teach concepts from Section 0 (Sets and Induction) of Abstract Algebra: A First Course (Second Edition) by Dan Saracino:
0:00 Intro
2:13 Section 0 (Sets and Induction)
2:55 Defintion of set
4:34 Definition of subset
5:37 Definition of two sets being equal
6:07 Definition of proper subset
6:43 Intersection and union
8:05 Theorem 0.1 (S⊆T if and only if S∩T=S)
9:17 Well-Ordering Principle
10:21 Mathematical Induction, first form
12:05 Mathematical Induction, second form
14:00 Definition of Inductive Hypothesis
15:00 Fundamental Theorem of Arithmetic (skipped)
15:16 More thoughts about mathematical induction
16:30 Final thoughts
0:00 Intro
2:13 Section 0 (Sets and Induction)
2:55 Defintion of set
4:34 Definition of subset
5:37 Definition of two sets being equal
6:07 Definition of proper subset
6:43 Intersection and union
8:05 Theorem 0.1 (S⊆T if and only if S∩T=S)
9:17 Well-Ordering Principle
10:21 Mathematical Induction, first form
12:05 Mathematical Induction, second form
14:00 Definition of Inductive Hypothesis
15:00 Fundamental Theorem of Arithmetic (skipped)
15:16 More thoughts about mathematical induction
16:30 Final thoughts
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