Канал: Math Geeks

prove all norms are equivalent in finite dimensional vector space

prove all norms are equivalent in finite dimensional vector space

Two random variables have the same moment but different distribution

Two random variables have the same moment but different distribution

prove jordan's inequality using calculus

prove jordan's inequality using calculus

Explain and derive Gaussian Tail bound

Explain and derive Gaussian Tail bound

Derive Einstein field equation from Einstein Hilbert action

Derive Einstein field equation from Einstein Hilbert action

可愛的鸚鵡吃紙

可愛的鸚鵡吃紙

Prove corners theorem via Triangle removal lemma

Prove corners theorem via Triangle removal lemma

prove roth's theorem about lengh3 arithmetic progression

prove roth's theorem about lengh3 arithmetic progression

Prove triangle removal lemma

Prove triangle removal lemma

prove triangle counting lemma

prove triangle counting lemma

Prove Szemeredi regularity lemma

Prove Szemeredi regularity lemma

introduction to sidon set and its lower and upper bound

introduction to sidon set and its lower and upper bound

statement of Szemerédi regularity lemma

statement of Szemerédi regularity lemma

sum product problem and its lower bound

sum product problem and its lower bound

explain and prove Szemeredi Trotter theorem

explain and prove Szemeredi Trotter theorem

Prove and Explain Crossing number inequality

Prove and Explain Crossing number inequality

explain and prove Erdos Ginzburg Ziv theorem

explain and prove Erdos Ginzburg Ziv theorem

additive combinatorics (2) SUMSET prove and explain cauchy davenport theorem

additive combinatorics (2) SUMSET prove and explain cauchy davenport theorem

additive combinatorics (1) SUMSET in real number

additive combinatorics (1) SUMSET in real number

prove Partition is NP complete

prove Partition is NP complete

prove law of large numbers

prove law of large numbers

explain and prove quadratic variation of brownian motion

explain and prove quadratic variation of brownian motion

solve 1/a plus 1/b = n/(a+b)

solve 1/a plus 1/b = n/(a+b)

definition of Martingale and show brownian motion and its variants are martingale

definition of Martingale and show brownian motion and its variants are martingale

How Newton showed the orbit is ellipse

How Newton showed the orbit is ellipse

Is there a function having a limit at every point while being nowhere continuous

Is there a function having a limit at every point while being nowhere continuous

probability interview question choose two random subsets one is another

probability interview question choose two random subsets one is another

Explain Ramsey's theory and prove Ramsey's theorem

Explain Ramsey's theory and prove Ramsey's theorem

Schrödinger–HJW theorem and purification of quantum state

Schrödinger–HJW theorem and purification of quantum state

112 分科測驗試題數學甲考科多選詳解7

112 分科測驗試題數學甲考科多選詳解7

112 分科測驗試題數學甲考科多選詳解8

112 分科測驗試題數學甲考科多選詳解8

112 分科測驗試題數學甲考科多選詳解6

112 分科測驗試題數學甲考科多選詳解6

112 分科測驗試題數學甲考科多選詳解4,5

112 分科測驗試題數學甲考科多選詳解4,5

112 分科測驗試題數學甲考科單選詳解

112 分科測驗試題數學甲考科單選詳解

extremal graph theory: prove Kovari-Sos-Turan theorem

extremal graph theory: prove Kovari-Sos-Turan theorem

Property of Permanent, Glynn's formula and permanent of unitary matrix

Property of Permanent, Glynn's formula and permanent of unitary matrix

extremal graph theory: explain Erdos Stone Simonovits theorems

extremal graph theory: explain Erdos Stone Simonovits theorems

Probabilistic Proof for Turan's Theorem

Probabilistic Proof for Turan's Theorem

Extremal graph theory: prove Turan's theorem

Extremal graph theory: prove Turan's theorem

Extremal Graph theory: Mantel's theorem proof

Extremal Graph theory: Mantel's theorem proof

prove Bhatia–Davis inequality

prove Bhatia–Davis inequality

Turan's theorem on lower bound of size of independent set

Turan's theorem on lower bound of size of independent set

showing Longest PATH is NP Complete

showing Longest PATH is NP Complete

second moment method application

second moment method application

Prove golden thompson inequality (2) by showing holder inequality

Prove golden thompson inequality (2) by showing holder inequality

Prove golden thompson inequality (1) and holder inequality

Prove golden thompson inequality (1) and holder inequality

prove det(e^Ae^B)=det(e^(A+B))

prove det(e^Ae^B)=det(e^(A+B))

2023 過年刮刮樂刮中 100000 實況轉播

2023 過年刮刮樂刮中 100000 實況轉播

prove random sum principle

prove random sum principle

construction of pairwise independent hash function

construction of pairwise independent hash function

prove Valiant–Vazirani theorem

prove Valiant–Vazirani theorem

Introduce Randomized polynomial time RP

Introduce Randomized polynomial time RP

Arthur Merlin Protocol: What if Graph isomorphism is NP complete

Arthur Merlin Protocol: What if Graph isomorphism is NP complete

Introduce the complexity class P/poly and show that bpp is subset of P/poly

Introduce the complexity class P/poly and show that bpp is subset of P/poly

Arthur merlin protocol application: Prove if NP subset of BPP implies PH collapse

Arthur merlin protocol application: Prove if NP subset of BPP implies PH collapse

Complexity ma and am show that relation to PH (MA subset of sigma2)

Complexity ma and am show that relation to PH (MA subset of sigma2)

Complexity class Merlin and Arthur Protocol prove MA is subset of AM

Complexity class Merlin and Arthur Protocol prove MA is subset of AM

Prove Chernoff Bounds for Bernoulli variable

Prove Chernoff Bounds for Bernoulli variable

Complexity class Merlin and Arthur Protocol: AM MA QMA

Complexity class Merlin and Arthur Protocol: AM MA QMA

bernstein Vazirani algorithm

bernstein Vazirani algorithm

Quick explanation and detailed calculation of Quantum Forrelation

Quick explanation and detailed calculation of Quantum Forrelation

Separating NP from BQP relative to an oracle

Separating NP from BQP relative to an oracle

prove IP=PSPACE (2) Prove TQBF is in PSPACE

prove IP=PSPACE (2) Prove TQBF is in PSPACE

prove IP=PSPACE (1) prove sharp p subset of IP

prove IP=PSPACE (1) prove sharp p subset of IP

Prove and Explain Savitch's Theorem and non deterministic space

Prove and Explain Savitch's Theorem and non deterministic space

Prove and Explain Cook Levin Theorem

Prove and Explain Cook Levin Theorem

Prove and Explain Tsirelson's bound

Prove and Explain Tsirelson's bound

derive and explain Bell's inequality (1)

derive and explain Bell's inequality (1)

explain quantum chsh game

explain quantum chsh game

Computational complexity: Prove IP is subset of PSPACE

Computational complexity: Prove IP is subset of PSPACE

Computational complexity: Graph non isomorphism is in IP

Computational complexity: Graph non isomorphism is in IP

interview question: Urban Planning

interview question: Urban Planning

Solving Heat equation (partial differential equation) and heat kernel

Solving Heat equation (partial differential equation) and heat kernel

Leetcode 2490 Circular Sentence

Leetcode 2490 Circular Sentence

Leetcode 2492 Minimum Score of a Path Between Two Cities

Leetcode 2492 Minimum Score of a Path Between Two Cities

leetcode 1524 Number of Sub arrays With Odd Sum

leetcode 1524 Number of Sub arrays With Odd Sum

Leetcode 2481 Minimum Cuts to Divide a Circle

Leetcode 2481 Minimum Cuts to Divide a Circle

Leetcode 2491 Divide Players Into Teams of Equal Skill

Leetcode 2491 Divide Players Into Teams of Equal Skill

leetcode 2256 Minimum Average Difference

leetcode 2256 Minimum Average Difference

Stochastic Calculus Change black Scholes equation to heat equation

Stochastic Calculus Change black Scholes equation to heat equation

stochastic calculus using Ito's formula to solve Vasicek model

stochastic calculus using Ito's formula to solve Vasicek model

Stochastic Calculus: use Ito’s formula and solve geometric Brownian motion

Stochastic Calculus: use Ito’s formula and solve geometric Brownian motion

stochastic calculus: Wiener process and Brownian motion

stochastic calculus: Wiener process and Brownian motion

Prove sylvester criterion for positive definite matrix

Prove sylvester criterion for positive definite matrix

probability of Y greater than 4X when X, Y are independently drawn from 0,1 uniform of Gaussian

probability of Y greater than 4X when X, Y are independently drawn from 0,1 uniform of Gaussian

Expected number of cards you should turn before finding an ace

Expected number of cards you should turn before finding an ace

prove Hockey Stick Identity

prove Hockey Stick Identity

how many parts at most is a plane cut by n lines, how many parts at most is a space cut by n plane

how many parts at most is a plane cut by n lines, how many parts at most is a space cut by n plane

The expected number of picks from uniform distribution needed to first exceed 1

The expected number of picks from uniform distribution needed to first exceed 1

prove Law of total Covariance

prove Law of total Covariance

prove Law of total Variance

prove Law of total Variance

Gambler's ruin using ansatz solutions

Gambler's ruin using ansatz solutions

prove law of total expectation

prove law of total expectation

Power of randomized algorithm: Freivalds' algorithm

Power of randomized algorithm: Freivalds' algorithm

Inverting partitioned matrices formula

Inverting partitioned matrices formula

Prove Woodbury matrix identity step by step

Prove Woodbury matrix identity step by step

Computational complexity interactive proof (1) deterministic interactive proof

Computational complexity interactive proof (1) deterministic interactive proof

Analytic number theory: The divisor bound (the upper bound of divisor)

Analytic number theory: The divisor bound (the upper bound of divisor)

introduce Weird complexity class, TFNP PPA, PPAD, PPP

introduce Weird complexity class, TFNP PPA, PPAD, PPP

Prove rank(A+B) less than rank A + rank B

Prove rank(A+B) less than rank A + rank B

Why does zero correlation not imply independence: many counter example

Why does zero correlation not imply independence: many counter example

Computational complexity BQP (3) Approximate counting, Sharp and GapP

Computational complexity BQP (3) Approximate counting, Sharp and GapP

Bound for the correlation of general n random variables

Bound for the correlation of general n random variables

𝜋^ⅇ and e^𝜋 which one is larger -quick one line solution

𝜋^ⅇ and e^𝜋 which one is larger -quick one line solution

Proof that Subgraph Isomorphism problem is NP Complete

Proof that Subgraph Isomorphism problem is NP Complete

Simon’s problem and Oracle separation showing BPP^A ⊈ BQP^A

Simon’s problem and Oracle separation showing BPP^A ⊈ BQP^A

Computational complexity of bounded error quantum polynomial time BQP (2)

Computational complexity of bounded error quantum polynomial time BQP (2)

Berlekamp welch proof on the average hardness of Permanent

Berlekamp welch proof on the average hardness of Permanent

Lipton's proof on average hardness of Permanent

Lipton's proof on average hardness of Permanent

Prove Markov inequality and reverse Markov inequality

Prove Markov inequality and reverse Markov inequality

Prove Isserlis theorem and Wick theorem

Prove Isserlis theorem and Wick theorem

introduction to bounded error quantum polynomial time BQP (1)

introduction to bounded error quantum polynomial time BQP (1)

If there is one perfect square in an arithmetic progression, then there are infinitely many

If there is one perfect square in an arithmetic progression, then there are infinitely many

Computational complexity proving NP is a subset of PP

Computational complexity proving NP is a subset of PP

Upper bound of rank A if A^k=0 and find the solution

Upper bound of rank A if A^k=0 and find the solution

three proof Sylvester rank inequality rankA+rankB less than rank AB+n

three proof Sylvester rank inequality rankA+rankB less than rank AB+n

Furstenberg's proof of the infinitude of primes (topological proof)

Furstenberg's proof of the infinitude of primes (topological proof)

Existence of primitive root of odd prime

Existence of primitive root of odd prime

Jacobi symbol and its theorem

Jacobi symbol and its theorem

Number theory Primitive root 2 Nonexistence of primitive root of power of 2

Number theory Primitive root 2 Nonexistence of primitive root of power of 2

Number theory: theory of Primitive root 1, introduction Primitive root

Number theory: theory of Primitive root 1, introduction Primitive root

Quadratic Gauss’s sum and quadratic reciprocity

Quadratic Gauss’s sum and quadratic reciprocity

Number theory Legendre Symbol(6) Prove Quadratic reciprocity using Gauss lemma

Number theory Legendre Symbol(6) Prove Quadratic reciprocity using Gauss lemma

Prove Fermat’s little theorem and Wilson’s theorem

Prove Fermat’s little theorem and Wilson’s theorem

Number theory Legendre Symbol 5 proves quadratic reciprocity

Number theory Legendre Symbol 5 proves quadratic reciprocity

Number theory Legendre Symbol (4) Proof of Eisenstein's lemma

Number theory Legendre Symbol (4) Proof of Eisenstein's lemma

Number theory Legendre Symbol (3): computing -1|p and 2|p

Number theory Legendre Symbol (3): computing -1|p and 2|p

Number theory Legendre Symbol 2 prove Gauss’s Lemma

Number theory Legendre Symbol 2 prove Gauss’s Lemma

Number theory Legendre Symbol(1) definition and prove Euler Criterion

Number theory Legendre Symbol(1) definition and prove Euler Criterion

Comment on examples of Big O

Comment on examples of Big O

Homology and cohomology (1): chain complex

Homology and cohomology (1): chain complex

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

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

Derivation of the one dimensional Euler–Lagrange equation

Derivation of the one dimensional Euler–Lagrange equation

lower Bound of a+sqrt2b+sqrt3c

lower Bound of a+sqrt2b+sqrt3c

AB=BA find upper bound rank of A+B

AB=BA find upper bound rank of A+B

cyclotomic polynomial (5) Every finite abelian group is the Galois group of a finite extension of Q

cyclotomic polynomial (5) Every finite abelian group is the Galois group of a finite extension of Q

cyclotomic polynomial (4) prove Wedderburn theorem

cyclotomic polynomial (4) prove Wedderburn theorem

Algebraic Numbers and Algebraic Integers

Algebraic Numbers and Algebraic Integers

cyclotomic polynomial (3) Proofs of the Irreducibility of the Cyclotomic Polynomial

cyclotomic polynomial (3) Proofs of the Irreducibility of the Cyclotomic Polynomial

cyclotomic polynomial 2 There are infinite prime numbers congruent 1 mod n

cyclotomic polynomial 2 There are infinite prime numbers congruent 1 mod n

Number theory cyclotomic polynomial (1)

Number theory cyclotomic polynomial (1)

Minimum Comparisons to find Second Largest Element (also kth)

Minimum Comparisons to find Second Largest Element (also kth)

easy Prove Hurwitz theorem in Number theory( Approximation theory)

easy Prove Hurwitz theorem in Number theory( Approximation theory)

Liouville’s number, Approximation lemma and why it is transcendental number

Liouville’s number, Approximation lemma and why it is transcendental number

State and prove Liouville's Approximation Theorem and transcendental number

State and prove Liouville's Approximation Theorem and transcendental number

Tensor product of Ox modules, locally free sheaves and Picard group

Tensor product of Ox modules, locally free sheaves and Picard group

seventh roots of unity

seventh roots of unity

prove tensor is a right exact functor

prove tensor is a right exact functor

Modules over a Scheme and localization of Module (1)

Modules over a Scheme and localization of Module (1)

Prove Hom functor is left exact

Prove Hom functor is left exact

Prove Global section and pushforward are left exact functors

Prove Global section and pushforward are left exact functors

algebraic geometry noetherian is an affine local property

algebraic geometry noetherian is an affine local property

Algebraic geometry affine local (2) Finitely generated A algebra is an affine local property

Algebraic geometry affine local (2) Finitely generated A algebra is an affine local property

Algebraic geometry: affine local (1) Reduced is an affine local property

Algebraic geometry: affine local (1) Reduced is an affine local property

algebraic geometry: prove affine communication lemma

algebraic geometry: prove affine communication lemma

Intersection of open affines can be covered by open sets distinguished in both affines

Intersection of open affines can be covered by open sets distinguished in both affines

Algebraic geometry equivalent condition for reduced schemes

Algebraic geometry equivalent condition for reduced schemes

Algebraic geometry:reduced, irreducible and integral scheme and prove their relationship

Algebraic geometry:reduced, irreducible and integral scheme and prove their relationship

S scheme, Category of Scheme, fiber Product of schemes

S scheme, Category of Scheme, fiber Product of schemes

Gluing sheaves and Gluing schemes

Gluing sheaves and Gluing schemes

Algebraic geometry: Non-affine scheme example3 affine plane minus the origin

Algebraic geometry: Non-affine scheme example3 affine plane minus the origin

Algebraic geometry Non-affine scheme example2 projective line

Algebraic geometry Non-affine scheme example2 projective line

Non affine schemes example 1 affine line with double origin is not affine

Non affine schemes example 1 affine line with double origin is not affine

Algebraic geometry: open immersion of scheme is a scheme

Algebraic geometry: open immersion of scheme is a scheme

Algebraic geometry definition of schemes and morphism between schemes

Algebraic geometry definition of schemes and morphism between schemes

Sheafification and what the hell it is: Construction and universal property

Sheafification and what the hell it is: Construction and universal property

A morphism of sheaves of sets is an isomorphism if it induces an isomorphism of all stalks

A morphism of sheaves of sets is an isomorphism if it induces an isomorphism of all stalks

sheaf theory: The induced map on stalks is well defined (Vakil 2.C exercise)

sheaf theory: The induced map on stalks is well defined (Vakil 2.C exercise)

More on Stalks of sheaves and morphism between sheaves

More on Stalks of sheaves and morphism between sheaves

The stalks of the affine scheme

The stalks of the affine scheme

algebraic geometry Scheme theory: affine scheme(3) show that it is really a locally ringed space

algebraic geometry Scheme theory: affine scheme(3) show that it is really a locally ringed space

scheme and affine scheme is a T0 space

scheme and affine scheme is a T0 space

Algebraic geometry Quotient Ring and its spectrum

Algebraic geometry Quotient Ring and its spectrum

Algebraic geometry: Affine scheme Is irreducible if and only if A/N Is integral domain

Algebraic geometry: Affine scheme Is irreducible if and only if A/N Is integral domain

The Induced Map on the Spectrum is continuous and contravariant functor

The Induced Map on the Spectrum is continuous and contravariant functor

Algebraic geometry Localization of ring and its ideal

Algebraic geometry Localization of ring and its ideal

algebraic geometry: affine scheme (2) example of Spectrum of ring

algebraic geometry: affine scheme (2) example of Spectrum of ring

Cauchy theorem in number theory

Cauchy theorem in number theory

The localization at a prime ideal is a local ring

The localization at a prime ideal is a local ring

Properties of nilradical of a ring and show its intersection of prime ideals

Properties of nilradical of a ring and show its intersection of prime ideals

affine scheme properties: distinguished open set forms a basis and quasi compact

affine scheme properties: distinguished open set forms a basis and quasi compact

algebraic geometry Scheme theory affine scheme (1) zariski topology and vanishing set

algebraic geometry Scheme theory affine scheme (1) zariski topology and vanishing set

state and prove Cauchy Binet Formula

state and prove Cauchy Binet Formula

state and prove Bennett's inequality

state and prove Bennett's inequality

state and prove Bernstein inequalities in probability theory

state and prove Bernstein inequalities in probability theory

hard probability question x i+x i+1 less than 1 in higher dimension

hard probability question x i+x i+1 less than 1 in higher dimension

probability question sum of two numbers is a perfect square

probability question sum of two numbers is a perfect square

probability interview x/y is closest to even

probability interview x/y is closest to even

two versions of Azuma's inequality state and its proof

two versions of Azuma's inequality state and its proof

Simple identity involving q Pochhammer symbol

Simple identity involving q Pochhammer symbol

Manahey's theorem and its proof

Manahey's theorem and its proof

Simple proof of Pinsker's inequality

Simple proof of Pinsker's inequality

Ladner's theorem proof by assuming exponential time hypothesis

Ladner's theorem proof by assuming exponential time hypothesis

Probability interview NCAA basketball pool

Probability interview NCAA basketball pool

Prove 3 by 3 determinant Krattenthaler's Identity

Prove 3 by 3 determinant Krattenthaler's Identity

Cauchy Goursat theorem and its proof

Cauchy Goursat theorem and its proof

Relativizing the P vs NP P^B not equal NP^B: baker gill solovay theorem

Relativizing the P vs NP P^B not equal NP^B: baker gill solovay theorem

Relativizing the P vs NP Question (1) P^A=NP^A

Relativizing the P vs NP Question (1) P^A=NP^A

Find Average number of updates needed to find maximum number in an array

Find Average number of updates needed to find maximum number in an array

Sipser–Lautemann theorem and its proof

Sipser–Lautemann theorem and its proof