So you want to prove things? Where do you start if you haven't ever written a proof before? In most cases, a course on discrete mathematics or mathematical structures is where someone writes their first proof and that starts with propositional calculus. In this video section, we go through the bare bones basics of propositions, truth tables, and arguments while including a few proofs and exercises to start towards thinking more about mathematical structuralism at an elementary level. It won't feel like we are doing math if you have not seen this stuff before, but this stuff is fundamental to understanding how to construct mathematical arguments and proof writing techniques.
00:00 Why are you doing this Nathan
00:44 What is a proposition in math?
02:29 What are logical operations in math?
04:04 What are some truth tables in math?
06:53 Logical Equivalence
07:53 Prop 1.1.1: A conditional is equivalent to its contrapositive
10:08 Variations of a conditional statement
11:04 What is a valid argument?
12:22 Prop 1.1.2: An argument is valid if and only if its symbolic presentation is a tautology
14:23 Why you should do math exercises
15:58 Exercises
16:12 End Card
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