ericntunctu

We show that Turan's theorem on the lower bound of the size of an independent set 0:00 start 5:11 introduce the proof and first moment method 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

showing Longest PATH is NP-Complete Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ Hope you can subscribe to my channel Complexity Theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Advanced mathematics list: 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

Prove golden Thompson inequality (1) and holder inequality Lie product formula: https://youtu.be/LEjdQuzb5lY 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

prove det(e^Ae^B)=det(e^(A+B)) 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

2023 過年 刮刮樂 實況轉播

prove the random sum principle 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

construction of pairwise independent hash function More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

prove Valiant–Vazirani theorem 0:00 start and state Valiant–Vazirani theorem 5:00 lemma 1 inclusion and exclusion lemma 11:00 lemma 2 pair wise independent function 13:00 prove Valiant–Vazirani theorem More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Introduce Randomized polynomial time RP 0:00 start 2:49 Introduce Randomized polynomial time RP More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Arthur Merlin Protocol: What if Graph isomorphism is NP complete More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Introduce the complexity class P/poly 0:00 start 6:15 prove bpp is subset of P/poly More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Prove if NP subset of BPP implies PH collapse More Complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Complexity ma and shows that relation to PH (MA subset of sigma2) 0:00 start 3:50 prove MA subset of sigma 2 prove AM subset of pi 2 More complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o 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 Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Complexity class Merlin and Arthur Protocol prove MA is subset of AM 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 complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Prove Chernoff Bounds for Bernoulli variable More inequality: https://www.youtube.com/playlist?list=PLg9w7tItBlZsF8uZLHpA7R8mzk6K1b4Nc Please subscribe to my channel Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Please subscribe to my channel 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-

Complexity class Merlin and Arthur Protocol: AM MA QMA 0:00 start 0:51 definition of MA 5:22 definition of AM 9:00 definition of QMA 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 complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

bernstein Vazirani algorithm 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 complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Quick explanation and detailed calculation of Quantum Forrelation reference: Forrelation: A Problem that Optimally Separates Quantum from Classical Computing https://arxiv.org/abs/1411.5729 0:00 start and define Forrelation 4:00 quantum circuit model 1 9:00 quantum circuit model 2 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 complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Separating NP from BQP relative to an oracle 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 complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/

Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ computational complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o 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

prove IP=PSPACE (1) prove sharp p subset of IP computational complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ 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

Prove and Explain Savitch's Theorem and non-deterministic space computational complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ 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

0:00 start 7:00 prove Cook Levin Theorem computational complexity theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu5dzTT0xqtLrx-46jCfR4o Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ 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

Prove and Explain Tsirelson's bound ################################ 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

derive and explain Bell's inequality (1) ################################ 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