In this video, we prove Banach Fixed point theorem step by step Instagram account: https://www.instagram.com/mathphyen/ Subscribe to my channel 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 Complex analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B Combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K additive combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB 微積分 高等微積分 代數 Calculus and advanced mathematics (abstract algebra): ###################################################################### Real analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63 Reduction formula in Calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke Integrals of trigonometric functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh (algebraic geometry)代數幾何筆記 https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B ... https://www.youtube.com/watch?v=ZgYbJehI36w

2148 Count Elements With Strictly Smaller and Greater Elements #################################### Please subscribe to my channel Leetcode solving videos (easy) https://www.youtube.com/playlist?list=PLg9w7tItBlZt4oUpNyWU_0rOItlScu1_d Leetcode solving videos (Medium): https://www.youtube.com/playlist?list=PLg9w7tItBlZvMGxy-y1eXURPD6Ao6kkzA Leetcode solving videos (Hard): https://www.youtube.com/playlist?list=PLg9w7tItBlZt4JQmlkGD3M5idZn14NyL6 ######################################## ... https://www.youtube.com/watch?v=HFTNdSUH1FA

Prove Van der Corput inequality Subscribe to my channel 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 Combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K additive combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB 微積分 高等微積分 代數 Calculus and advanced mathematics (abstract algebra): ###################################################################### Real analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63 Reduction formula in Calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke Integrals of trigonometric functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh (algebraic geometry)代數幾何筆記 https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B Linear algebra Proof: https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo 環論(ring theory): https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP Abstract Algebra: https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0 Group theory (群論): https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0 Galois theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG 數論跟其他: number theory and others: ########### Riemann Zeta functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM Math related to pi: https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe Number theory: Prove Van der Corput inequality https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws Set Theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J High school math & AP calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo Solving polynomial equation: https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7 工程數學 Engineering Mathematics: ########### Laplace transformation: https://www.youtube.com/playlist?list=PLg9w7tItBlZty21VgNOrLTKg3BM1sFmFE differential equation: https://www.youtube.com/playlist?list=PLg9w7tItBlZukQ1yQXKXPo4ZN2yMHwvf1 Legendre polynomial: https://www.youtube.com/playlist?list=PLg9w7tItBlZvG3Ju8YUxEct1tawePe_ZA Complex analysis: https://www.youtube.com/playlist?list=PLg9w7tIt ... https://www.youtube.com/watch?v=7ZnxSjLxc8o

algebraic geometry Scheme theory: affine scheme(3) show that it is really a ringed space show that structure sheaf on affine scheme is really a ringed space 0:00 start Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ algebraic geometry https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B 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 ... https://www.youtube.com/watch?v=JGiCh5R7NhU