Mathematical induction middle level exercise
0:00 Exercise: 1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2
2:17 Exercise: 1*1!+2*2!+...n*n!=(n+1)!-1
3:07 1+1/2^2+1/3^2....less than 2-1/n
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機率
Probability and discrete mathematics:
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Probability interview questions:
https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znfyDEaqQtUx5b
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):
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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:
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Riemann Zeta functions:
https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM
Math related to pi:
https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe
Number theory:
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:
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Laplace transformation:
https://www.youtube.com/playlist?list=PLg9w7tItBlZty21VgNOrLTKg3BM1sFmFE
differential equation:
https://www.youtube.com/playlist?list=PLg9w7tItBlZukQ1yQXKXPo4ZN2yMHwvf1
0xab3acdec0919be9d429baf2190de2e2a4a384c7e
Legendre polynomial:
https://www.youtube.com/playlist?list=PLg9w7tItBlZvG3Ju8YUxEct1tawePe_ZA
Complex analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B
Gamma Function:
https://www.youtube.com/playlist?list=PLg9w7tItBlZvKhQHLzaULPNtZH7mYNIf9
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