My Favorite Math Invariants // Big Themes in Math Episode 1

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Mathematical Invariants are properties of class of mathematical objects that don't change under various transformations. Studying invariants are one of the big themes of mathematics. In this video we will see three examples of invariants, one from graph theory called the chromatic number, one from geometry called the Euler Characteristic, and one from Linear Algebra called the Determinant (geometrically and algebraically). Enjoy!

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0:00 Graph Theory: Chromatic Number
4:52 Big Idea of Invariants
5:19 Geometry: Euler Characteristic
9:34 Linear Algebra: Determinant
13:24 brilliant.org/TreforBazett

Image Credit: The Four Color Theorem Map of the USA was found here: https://en.wikipedia.org/wiki/Four_color_theorem#/media/File:Map_of_United_States_accessible_colors_shown.svg and is shared via CC BY-SA 3.0.

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►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
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