Fundamentals of Mathematical Logic: An Introduction

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 Hang out with me while I work through some of my problems on Twitch: https://www.twitch.tv/chalknd My Kofi Page: https://ko-fi.com/chalknd _____________________ Last PhD Update: https://youtu.be/D4HKX9LaaGM Last Academic Talk/stream: https://youtu.be/odThHozSwuE Last CHALK video: https://youtu.be/-tEnL7vStXA The CHALKboard: http://www.youtube.com/c/CHALKboard _____________________ A BOOK ON MATHEMATICAL STRUCTURES: https://amzn.to/3Smku4a WHAT GEAR I USED FOR THIS VIDEO: Camera - https://amzn.to/30bJRho Lens - https://amzn.to/3fgDaPa SD card - https://amzn.to/2PbTiag Microphone - https://amzn.to/2D3KYXE Lighting Kit - https://amzn.to/3ffibMH Editing Hard Drive - https://amzn.to/2P7hSsM DISCLAIMER: Links included in this description may be affiliate links. If you purchase a product or service with the links that I include here, I may receive a small commission. There is no additional charge to you! Thank you for supporting my channel and for helping me create these free videos! Subscriber Count as of scheduling to post: 12,329 (+ 41😮) #CHALK #Logic #MathStructures #CHALKND