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prove law of large numbers buy me a coffee: https://www.buymeacoffee.com/mathphytcs Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

buy me a coffee: https://www.buymeacoffee.com/mathphytcs 0:00 start Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ stochastic calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZvC7Kehw7cHB2EbP2rENAyh Please subscribe to my channel stochastic calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZvC7Kehw7cHB2EbP2rENAyh Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u

buy me a coffee: https://www.buymeacoffee.com/mathphytcs Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

buy me a coffee: https://www.buymeacoffee.com/mathphytcs Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ 0:00 start 6:00 Definition of martingale for continuous one 10:00 prove brownian motion is martingale 12:00 prove brownian^2- t is martingale 15:00 prove exponential of Brownian motion is martingale stochastic calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZvC7Kehw7cHB2EbP2rENAyh Please subscribe to my channel stochastic calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZvC7Kehw7cHB2EbP2rENAyh Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

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probability interview question choose two random subsets one is another Suppose wechoose two random subsetsA, B of {1,2,...,n} independently and uniformly atrandom. What is theprobabilitythat A ⊆ B more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b

Explain Ramsey's theory and prove Ramsey's theorem 0:00 start 1:00 motivating example 6:00 state Ramsey's theorem 8:00 prove Ramsey's theorem subscribe to my channel to support me Extremal graph theory playlist https://www.youtube.com/watch?v=aL7b4aLu33k&list=PLg9w7tItBlZt50lcqEqZgqUt3C12Wdn0W&ab_channel=MathGeeks Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Schrödinger–HJW theorem and purification of quantum state ################################ Quantum Mechanics: https://www.youtube.com/playlist?list=PLg9w7tItBlZuP5Wv2jMbeTd7uc9ZXYS6m Electrodynamics: https://www.youtube.com/playlist?list=PLg9w7tItBlZu6oIdAtRaT-Wtjkg3_dJcQ Quantum Information: https://www.youtube.com/playlist?list=PLg9w7tItBlZs2JgNL6qxtPSlnWAFkqoJG Quantum Algorithms: https://www.youtube.com/playlist?list=PLg9w7tItBlZvyCUpJAskKqpeLkKhrtQio

buy me a coffee: https://www.buymeacoffee.com/mathphytcs 112 分科測驗試題數學甲考科 多選詳解7 112 分科測驗試題數學甲考科: https://www.youtube.com/watch?v=XWt4TYQ6ol0&list=PLg9w7tItBlZvylM6Ra0qBESkr71tpivcs&ab_channel=MathGeeks Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

buy me a coffee: https://www.buymeacoffee.com/mathphytcs 112 分科測驗試題數學甲考科: https://www.youtube.com/watch?v=XWt4TYQ6ol0&list=PLg9w7tItBlZvylM6Ra0qBESkr71tpivcs&ab_channel=MathGeeks Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

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buy me a coffee: https://www.buymeacoffee.com/mathphytcs 歡迎訂閱按讚 112 分科測驗試題數學甲考科: https://www.youtube.com/watch?v=XWt4TYQ6ol0&list=PLg9w7tItBlZvylM6Ra0qBESkr71tpivcs&ab_channel=MathGeeks Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

112 分科測驗試題數學甲考科 單選詳解 歡迎訂閱按讚 buy me a coffee: https://www.buymeacoffee.com/mathphytcs Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN- Please subscribe to my channel Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

extremal graph theory: prove Kovari-Sos-Turan theorem 0:00 start Extremal graph theory playlist https://www.youtube.com/watch?v=aL7b4aLu33k&list=PLg9w7tItBlZt50lcqEqZgqUt3C12Wdn0W&ab_channel=MathGeeks Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Property of Permanent, Glynn's formula, and permanent of a unitary matrix 0:00 start 0:10 Introduce the Permanent 7:44 prove Glynn's formula 15:00 Prove the permanent of a unitary matrix is bounded by 1

extremal graph theory: explain Erdos Stone Simonovits theorems 0:00 start Extremal graph theory playlist https://www.youtube.com/watch?v=aL7b4aLu33k&list=PLg9w7tItBlZt50lcqEqZgqUt3C12Wdn0W&ab_channel=MathGeeks Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Probabilistic Proof for Turan's Theorem 0:00 start 0:10 prove Turan's theorem Extremal graph theory https://www.youtube.com/watch?v=aL7b4aLu33k&list=PLg9w7tItBlZt50lcqEqZgqUt3C12Wdn0W&ab_channel=MathGeeks Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Extremal graph theory: proves Turan's theorem 0:00 start 8:00 prove Turan's theorem Extremal graph theory https://www.youtube.com/watch?v=aL7b4aLu33k&list=PLg9w7tItBlZt50lcqEqZgqUt3C12Wdn0W&ab_channel=MathGeeks Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

prove Bhatia–Davis inequality Advanced mathematics list: Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN- Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh