Turan's theorem on lower bound of size of independent set
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
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exact sequences
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Ring theory lecture
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group theory lecture
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Category theory
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Field theory in abstract algebra
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7
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showing Longest PATH is NP Complete
showing Longest PATH is NP-Complete
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Complexity Theory:
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Group representation for finite group
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exact sequences
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Ring theory lecture
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group theory lecture
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Category theory
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Field theory in abstract algebra
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7
views
Prove golden thompson inequality (1) and holder inequality
Prove golden Thompson inequality (1) and holder inequality
Lie product formula:
https://youtu.be/LEjdQuzb5lY
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Group representation for finite group
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exact sequences
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Ring theory lecture
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group theory lecture
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Category theory
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Field theory in abstract algebra
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Mathematical analysis
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7
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prove det(e^Ae^B)=det(e^(A+B))
prove det(e^Ae^B)=det(e^(A+B))
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Group representation for finite group
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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
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Field theory in abstract algebra
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Mathematical analysis
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7
views
prove random sum principle
prove the random sum principle
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Group representation for finite group
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exact sequences
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Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u
group theory lecture
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Category theory
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Field theory in abstract algebra
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7
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construction of pairwise independent hash function
construction of pairwise independent hash function
More Complexity theory:
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7
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prove Valiant–Vazirani theorem
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
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8
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Introduce Randomized polynomial time RP
Introduce Randomized polynomial time RP
0:00 start
2:49 Introduce Randomized polynomial time RP
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8
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Arthur Merlin Protocol: What if Graph isomorphism is NP complete
Arthur Merlin Protocol: What if Graph isomorphism is NP complete
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15
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Introduce the complexity class P/poly and show that bpp is subset of P/poly
Introduce the complexity class P/poly
0:00 start
6:15 prove bpp is subset of P/poly
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9
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Arthur merlin protocol application: Prove if NP subset of BPP implies PH collapse
Prove if NP subset of BPP implies PH collapse
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7
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Complexity ma and am show that relation to PH (MA subset of sigma2)
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
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Complexity class Merlin and Arthur Protocol prove MA is subset of AM
Complexity class Merlin and Arthur Protocol prove MA is subset of AM
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9
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Prove Chernoff Bounds for Bernoulli variable
Prove Chernoff Bounds for Bernoulli variable
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exact sequences
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Complexity class Merlin and Arthur Protocol: AM MA QMA
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
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bernstein Vazirani algorithm
bernstein Vazirani algorithm
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13
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Quick explanation and detailed calculation of Quantum Forrelation
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
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6
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Separating NP from BQP relative to an oracle
Separating NP from BQP relative to an oracle
Quantum Mechanics:
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7
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prove IP=PSPACE (2) Prove TQBF is in PSPACE
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exact sequences
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Ring theory lecture
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group theory lecture
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5
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prove IP=PSPACE (1) prove sharp p subset of IP
prove IP=PSPACE (1) prove sharp p subset of IP
computational complexity theory:
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Group representation for finite group
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exact sequences
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Ring theory lecture
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group theory lecture
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Field theory in abstract algebra
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Prove and Explain Savitch's Theorem and non deterministic space
Prove and Explain Savitch's Theorem and non-deterministic space
computational complexity theory:
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Group representation for finite group
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exact sequences
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Ring theory lecture
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group theory lecture
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Field theory in abstract algebra
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5
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Prove and Explain Cook Levin Theorem
0:00 start
7:00 prove Cook Levin Theorem
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Group representation for finite group
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exact sequences
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Ring theory lecture
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group theory lecture
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5
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Prove and Explain Tsirelson's bound
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
6
views
derive and explain Bell's inequality (1)
derive and explain Bell's inequality (1)
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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
8
views