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Jacobi symbol and its 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

Number theory Primitive root 2 Nonexistence of primitive root of power of 2 Number theory: theory of Primitive root 1, introduction Primitive root: https://youtu.be/PbB3C7xudJ0 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

Number theory: theory of Primitive root 1, introduction Primitive root 0:00 start 9:40 classification of theory of Primitive root 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

Quadratic Gauss’s sum and quadratic reciprocity 0:00 start 7:03 definition of Quadratic Gauss’s sum 12:00 prove quadratic reciprocity geometric proof: Number theory Legendre Symbol 5 proves quadratic reciprocity: https://youtu.be/vqLLwK5SrpA Number theory Legendre Symbol(1) definition and prove Euler Criterion: https://youtu.be/QVWS8DHdhqM Number theory Legendre Symbol 2 proves Gauss’s Lemma: https://youtu.be/QmYEDJinxBw 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

Number theory Legendre Symbol(6) Prove Quadratic reciprocity using Gauss lemma 0:00 start 21:00 prove Quadratic reciprocity using Gauss lemma geometric proof: Number theory Legendre Symbol 5 proves quadratic reciprocity: https://youtu.be/vqLLwK5SrpA Number theory Legendre Symbol(1) definition and prove Euler Criterion: https://youtu.be/QVWS8DHdhqM Number theory Legendre Symbol 2 proves Gauss’s Lemma: https://youtu.be/QmYEDJinxBw 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

Prove Fermat’s little theorem and Wilson’s 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

Number theory Legendre Symbol 5 proves quadratic reciprocity 0:00 start 4:00 Proof of Eisenstein's lemma 13:30 proves quadratic reciprocity Number theory Legendre Symbol(1) definition and prove Euler Criterion: https://youtu.be/QVWS8DHdhqM Number theory Legendre Symbol 2 proves Gauss’s Lemma: https://youtu.be/QmYEDJinxBw 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

Number theory Legendre Symbol Proof of Eisenstein's lemma Number theory Legendre Symbol(1) definition and prove Euler Criterion: https://youtu.be/QVWS8DHdhqM Number theory Legendre Symbol 2 proves Gauss’s Lemma: https://youtu.be/QmYEDJinxBw 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

Number theory Legendre Symbol (3): computing -1|p and 2|p Number theory Legendre Symbol(1) definition and prove Euler Criterion: https://youtu.be/QVWS8DHdhqM Number theory Legendre Symbol 2 proves Gauss’s Lemma: https://youtu.be/QmYEDJinxBw 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

Number theory Legendre Symbol 2 proves Gauss’s Lemma 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

Number theory Legendre Symbol1 definition and prove Euler Criterion 0:00 start 7:00 prove Euler Criterion 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

Comment on examples of Big O I prove polynomial is big O of exponential 0:00 start 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

Homology and cohomology (1): chain complex homological algebra: https://www.youtube.com/watch?v=-c2W4Pcu9wU&list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 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

Euler–Lagrange equation Dido’s problem (isometry problem) ################################ 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

Derivation of the one dimensional Euler–Lagrange equation ################################ 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

lower Bound of a+sqrt2b+sqrt3c 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

AB=BA find the upper bound rank of A+B 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

cyclotomic polynomial (5) Every finite abelian group is the Galois group of a finite extension of Q More videos: Number theory cyclotomic polynomial (1): https://youtu.be/yLjolGl0DxY cyclotomic polynomial 2 There are infinite prime numbers congruent 1 mod n https://youtu.be/-lc9fnwx4Bc 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

cyclotomic polynomial (4) prove Wedderburn theorem More videos: Number theory cyclotomic polynomial (1): https://youtu.be/yLjolGl0DxY cyclotomic polynomial 2 There are infinite prime numbers congruent 1 mod n https://youtu.be/-lc9fnwx4Bc 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

Algebraic Numbers and Algebraic Integers 0:00 start 1:00 definition 12:00 show Algebraic Integers forms a ring 19:00 prove Q times Algebraic Integers = Algebraic Numbers 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

cyclotomic polynomial (3) Proofs of the Irreducibility of the Cyclotomic Polynomial Number theory cyclotomic polynomial (1): https://youtu.be/yLjolGl0DxY cyclotomic polynomial (2) There are infinite prime numbers congruent 1 mod n https://youtu.be/-lc9fnwx4Bc 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

cyclotomic polynomial 2 There are infinite prime numbers congruent 1 mod n Number theory cyclotomic polynomial (1): https://youtu.be/yLjolGl0DxY 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

Number theory cyclotomic polynomial (1) 0:00 start 7:53 prove the reciprocal formula 12:00 prove cyclotomic polynomial has integer coefficient 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

Minimum Comparisons to find Second Largest Element (also kth) 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

easy Prove Hurwitz theorem in Number theory( Approximation theory) Dirichlet approximation theorem: https://youtu.be/EgKvb7aEuHk 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