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Curated by: Dr. Trefor Bazett (643 videos)
Keep exploring at ► https://brilliant.org/TreforBazett to get started for free for 30 days, and to get 20% off an annual premium subscription! 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! Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://beautifulequations.net/pages/trefor 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. COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►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 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok: http://tiktok.com/@drtrefor ►Instagram (photography based): http://instagram.com/treforphotography