ericntunctu

Power of randomized algorithm: Freivalds' algorithm Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ ####################### Algorithm: https://www.youtube.com/playlist?list=PLg9w7tItBlZuXLnZO0UrW-jU3euCn17EP 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

Inverting partitioned matrices formula Subscribe to my channel more video lists: 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-

Prove Woodbury matrix identity step by step Subscribe to my channel more video lists: 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-

Computational complexity interactive proof (1) deterministic interactive proof 0:00 start 9:00 prove dIP=NP More 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/

Analytic number theory: integer partition Jacobi Triple identity 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

introduce Weird complexity class, TFNP PPA, PPAD, PPP TFNP: the complexity class TFNP is the class of total function problems which can be solved in nondeterministic polynomial time. PPAD: Polynomial Parity Arguments on Directed graphs PPA: parity arguments for undirected graphs More 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/

Prove rank(A+B) less than rank A + rank B Subscribe to my channel more video lists: 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-

Why does zero correlation not imply independence: many counter example Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV

Computational complexity BQP3 Approximate counting, Sharp and GapP introduction to bounded error quantum polynomial time BQP (1): https://youtu.be/t6MkdOedbHc More 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/

Bound for the correlation of general n random variables 0:00 start 11:00 solution 1 for general n 13:00 solution 2 for general n 15:00 construct such solution Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV

𝜋^ⅇ and e^𝜋 which one is larger -quick one-line solution Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV

Proof that Subgraph Isomorphism problem 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

Simon’s problem and Oracle separation showing BPP^A ⊈ BQP^A In this video, we'll explore the computational complexity of bounded error quantum polynomial time BQP (3). This is a very important topic for theoretical computer science, and we'll be exploring the complexity of this problem in detail. We'll be discussing both the polynomial time and exponential time versions of the problem, and shedding light on why they are different. This video is a must-watch if you're interested in computational complexity theory! introduction to bounded error quantum polynomial time BQP (1): https://youtu.be/t6MkdOedbHc More 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/

The computational complexity of bounded error quantum polynomial time BQP (2) 0:00 start 5:05 prove bqp is subset of exp 7:00 prove bqp is subset of PSPACE 14:00 prove bqp is subset of PP In this video, we'll explore the computational complexity of bounded error quantum polynomial time BQP (2). This is a very important topic for theoretical computer science, and we'll be exploring the complexity of this problem in detail. We'll be discussing both the polynomial time and exponential time versions of the problem, and shedding light on why they are different. This video is a must-watch if you're interested in computational complexity theory! introduction to bounded error quantum polynomial time BQP (1): https://youtu.be/t6MkdOedbHc 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/

Berlekamp welch proof on the average hardness of Permanent Subscribe to my channel Lipton's proof on the average hardness of Permanent: https://youtu.be/AeK_x2C_pIw 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/

Lipton's proof on the average hardness of Permanent 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 Markov inequality and reverse Markov inequality In this video, we'll prove Markov inequality and reverse Markov inequality. These two laws will help you understand probabilities and conditional probabilities. If you're interested in learning more about probabilities and conditional probabilities, then this video is for you! We'll explain these concepts using examples from mathematical and physical sciences. By the end of this video, you'll be able to prove Markov inequality and reverse Markov inequality! 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-

Prove Isserlis theorem and Wick theorem In this short video, we'll prove the Isserlis theorem and the Wick theorem. These two beautiful theorems are essential for anyone studying mathematics. The Isserlis theorem is famous for its use in the theory of György László, while the Wick theorem is used in various branches of algebra. In this video, we'll prove each of these theorems using simple but elegant proofs. After watching this video, you'll be able to understand these theorems and apply them to your own mathematical problems! Donate to Channel(斗內一下): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV

introduction to bounded error quantum polynomial time BQP Logic gate: prove NAND and NOR gate is universal: https://youtu.be/XumyJh4lIBs 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/

If there is one perfect square in an arithmetic progression, then there are infinitely many. If you think about it, this is a really interesting fact! In this video, we'll explore this fascinating theorem in more depth. This theorem is a deep mathematical discovery that has implications for infinity, probability, and more. We'll explore its meaning and implications in this video, and learn why it's so important. After watching this video, you'll be a master of the mysterious perfect square! Donate to Channel(斗內一下): 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

Computational complexity proving NP is a subset of PP 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/

In this video, we'll be talking about linear algebra, specifically the topic of upper bounds of rank. If you're looking to delve deeper into linear algebra, then this video is for you! We'll be discussing the concept of rank and how to calculate upper bounds of rank for linear systems. After watching this video, you'll have a better understanding of what the term "rank" means and be able to calculate upper bounds for systems of linear equations! 0:00 start 7:50 construction such solution three proof Sylvester rank inequality rankA+rankB less than rank AB : https://youtu.be/NIlicVrPzAc Donate to Channel(斗內一下): 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

three proof Sylvester rank inequality rankA+rankB less than rank AB 0:00 start 2:00 proof 1 5:00 proof 2 8:00 proof 3: using Kernal nullity theorem Donate to Channel(斗內一下): 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

Furstenberg's proof of the infinitude of primes (topological proof) Donate to Channel(斗內一下): 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

Existence of primitive root of odd prime Donate to Channel(斗內一下): 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