Mathematics Stack Exchange

4

votes

1

answer

167

views

How to show $n=1+\sum_{k=1}^{n}\left\lfloor{\log_2\frac{2n-1}{2k-1}}\right\rfloor$ for every natural number $n$.

elementary-number-theory summation logarithms natural-numbers

modified 2 mins ago John Omielan 29.7k

0

votes

0

answers

9

views

Ker and Img of cochain Map -subcomplex -

differential-geometry differential-topology geometric-topology

modified 3 mins ago adawi 1

0

votes

0

answers

16

views

How to solve this Differential equation(Integrating-factor)?

ordinary-differential-equations integrating-factor

modified 4 mins ago PhysicsMathsLove 2,380

0

votes

1

answer

26

views

If $\partial\Omega$ is of class $C^1$, does it need to be the boundary of a $C^1$-regular domain?

differential-geometry differential-topology smooth-manifolds manifolds-with-boundary submanifold

answered 7 mins ago Jack Lee 33.5k

3

votes

3

answers

198

views

Use class algebra to prove the following: If $A\cap B = \emptyset$ and $A\cup B = C$, then $A = C-B$

elementary-set-theory

modified 9 mins ago Khashayar Baghizadeh 1,102

2

votes

2

answers

79

views

Find the value of $\sin^{-1}(\cos 2)-\cos^{-1}(\sin 2) +\tan^{-1}(\cot 4) -\cot^{-1}(\tan 4)+\sec^{-1}(\csc 6)-\csc^{-1}(\sec 6)$

trigonometry solution-verification inverse-function

modified 9 mins ago ABCD 912

0

votes

0

answers

11

views

writing Mathematica code

harmonic-functions

asked 9 mins ago iman 1

0

votes

0

answers

11

views

Why $|P \oplus P^{'}| = |P| + |P^{'}| - |P \cap P^{'}|$ in Hopcroft & Karp's article?

graph-theory algorithms

modified 14 mins ago tchappy ha 2,964

0

votes

0

answers

9

views

Equivariant Diffeomorphism $S^2 \times S^3$ to itself with respect to the following $\mathbb{Z}_4$ action

differential-geometry algebraic-topology riemannian-geometry group-actions equivariant-maps

asked 18 mins ago TuoTuo 3,894

0

votes

0

answers

20

views

Why is the angle at the centre is twice the angle at the circumference

geometry circles

modified 19 mins ago Greg Martin 48.9k

0

votes

0

answers

3

views

Numerically Computing the eigenvector of a large sparse matrix when the eigenvalue is known

matrices numerical-methods eigenvalues-eigenvectors matlab numerical-linear-algebra

asked 21 mins ago wjmccann 1,969

3

votes

0

answers

12

views

Why are there two sets of rules for set equality in intensional intuitionistic type theory?

type-theory intuitionistic-logic

modified 22 mins ago Max Heiber 131

1

vote

1

answer

22

views

is there more than one answer to trig identities? Can the answer be both a pythagorean identity and a double angle?

calculus trigonometry

answered 24 mins ago Greg Martin 48.9k

0

votes

1

answer

18

views

Are directional derivatives a scalar or vector?

vector-spaces vectors partial-derivative

answered 24 mins ago singerng 512

0

votes

0

answers

3

views

Gauge Function of a star-shaped domain

geometry convex-analysis

asked 24 mins ago Jude 253

0

votes

0

answers

8

views

Counterexample to Frobenius reciprocity in a 1st-order classical hyperdoctrine?

first-order-logic categorical-logic

asked 27 mins ago Nate 1,903

1

vote

1

answer

27

views

Is each vector $y\in x^{\bot}$ a $r$-fold cross product of $x$ and some $x_1,…,x_{r-1}$?

linear-algebra

modified 29 mins ago user1551 99.1k

2

votes

1

answer

19

views

Solution verification : Truncation of $L^p$ functions

real-analysis functional-analysis measure-theory lp-spaces

modified 30 mins ago StarBug 986

5

votes

1

answer

265

views

+50

GCD and the cycle decomposition of a permutation

group-theory permutations finite-groups gcd-and-lcm

modified 31 mins ago Shubhrajit Bhattacharya 3,555

5

votes

1

answer

44

views

Ratio of the sum of the four circles to the area of the original right triangle

geometry

modified 31 mins ago Narasimham 28.6k

3

votes

0

answers

28

views

Finding the maximum value of $(\sin(2^n))$ where $n \in \Bbb N$

trigonometry arithmetic

asked 32 mins ago OUCHNA 158

0

votes

1

answer

15

views

Understanding the Topology in a Proof about Ergodic/Recurrent Transformations

general-topology analysis ergodic-theory

modified 33 mins ago Tsemo Aristide 75.5k

1

vote

1

answer

28

views

Maps between Peano spaces

general-topology compactness connectedness locally-connected

modified 33 mins ago Ishan Deo 2,678

0

votes

0

answers

5

views

Sufficient conditions on E to ensure equality of the Frechet derivatives in E of two functios f,g that agree in E.

lebesgue-measure frechet-derivative

asked 35 mins ago jlewk 526

-1

votes

0

answers

8

views

Solving unknowns in sequences

sequences-and-series

asked 36 mins ago fidelehagenimana 1

2

votes

2

answers

49

views

Proving $\Bbb C P^1 \cong S^2$

algebraic-topology continuity projective-space

answered 38 mins ago Malkoun 3,490

1

vote

2

answers

42

views

Elements in $\mathbb{Q}(\sqrt{p_1},\sqrt{p_2},\dots,\sqrt{p_n})$

abstract-algebra number-theory ring-theory field-theory algebraic-number-theory

modified 40 mins ago Shubhrajit Bhattacharya 3,555

0

votes

0

answers

12

views

$\overline{D(f)} = V(\text{ann}(f))$?

algebraic-geometry commutative-algebra

asked 41 mins ago Dean Young 4,336

0

votes

0

answers

18

views

(Correct Proof Writing) Proving basic limit theorem

proof-writing

modified 42 mins ago Jan Safronov 1

1

vote

2

answers

22

views

Finding the volume of an oblique cylinder using triple integrals

multivariable-calculus

answered 42 mins ago Stan Shunpike 4,005

4

votes

1

answer

741

views

Discriminant of a cyclotomic field

abstract-algebra number-theory algebraic-number-theory

modified 42 mins ago Sana CHALLI 76

1

vote

2

answers

4k

views

Why is this statement 'There is a real number $x$ such that $x^2 < x$.' not true?

discrete-mathematics logic

answered 43 mins ago Foster Antony 19

0

votes

0

answers

10

views

Can Gaussian elimination find a zero vector when $m < n$?

gaussian-elimination

modified 43 mins ago Ilya Gazman 1,226

1

vote

0

answers

9

views

How to modify SAGE code for find(calculate) exact generator of curve?

elliptic-curves cryptography

asked 44 mins ago Donald 31

3

votes

1

answer

784

views

How to Store a Banded Matrix by Diagonal

numerical-linear-algebra

modified 45 mins ago Community♦ 1

0

votes

0

answers

13

views

Sum of Probability Density Function outputs is larger than 1

statistics probability-distributions gamma-distribution

asked 45 mins ago FaureHu 101

2

votes

1

answer

23

views

Substitution variables in Taylor series

real-analysis power-series taylor-expansion substitution euler-maclaurin

answered 45 mins ago Digitallis 722

2

votes

3

answers

296

views

+50

Prove that $S^n/$~$_1$ $\cong RP^n$, where ~$_1$ means identify antipodal points.

general-topology algebraic-topology projective-space

modified 46 mins ago Oliver G 3,474

0

votes

1

answer

27

views

What is the 'localization $X_x$' if $X$ is a scheme and $x \in X$ a point of $X$?

algebraic-geometry reference-request notation

answered 47 mins ago KReiser 28.8k

0

votes

0

answers

7

views

Noetherian Rings and Catenary Rings

commutative-algebra

asked 47 mins ago Alan 63

0

votes

0

answers

10

views

Euler Cycle in directed cycle

discrete-mathematics graph-theory eulerian-path

modified 48 mins ago rahul sharma 271

0

votes

0

answers

11

views

Madras exercise 4.24: Confusion about function $A:[0,\infty] \rightarrow [0,1]$ such that $A(z) = z A(1/z)$ for all $z \in [0,\infty]$.

stochastic-processes markov-chains monte-carlo

asked 49 mins ago Leonidas 536

1

vote

1

answer

32

views

+50

Number of Quasi reflexive and coreflexive relations on a set with $n$ elements

combinatorics solution-verification relations

modified 57 mins ago Simon Marynissen 984

1

vote

1

answer

21

views

Fundamental doubt about property of exponentials

algebra-precalculus

modified 57 mins ago Riemann'sPointyNose 3,494

0

votes

0

answers

19

views

Exercise 11.1.G Vakil FOAG

algebraic-geometry commutative-algebra affine-schemes flatness dimension-theory-algebra

asked 58 mins ago Ignorant Mathematician 2,567

0

votes

0

answers

10

views

Orthogonal decomposition in indefinite inner products

smooth-manifolds clifford-algebras

modified 58 mins ago gcc 73

0

votes

0

answers

5

views

Are partitions of unity needed in manifolds to define a measure coinciding with the Lebesgue measure under coordinate systems?

measure-theory smooth-manifolds

asked 1 hour ago gpr1 192

3

votes

1

answer

40

views

Continous series on $\mathbb{R}$ vs uniform convergent series

real-analysis sequences-and-series continuity uniform-convergence

modified 1 hour ago iam_agf 5,009

0

votes

1

answer

19

views

Character table of $G=\langle (12),(34),(45)\rangle$.

representation-theory characters

modified 1 hour ago iam_agf 5,009

0

votes

1

answer

24

views

Solving a specific quadratic function for $x$ and $y$

quadratics

modified 1 hour ago Shubhrajit Bhattacharya 3,555

0

votes

1

answer

38

views

Verify if the sum of two subspaces are equal to $\mathbb R^3$

linear-algebra vector-spaces

modified 1 hour ago iam_agf 5,009

0

votes

1

answer

16

views

Let $E^*=\{E⊆X \mid E=\bigcup\limits_{i=1}^{k} C_{I}$, $C_k=E_K-F_K , E_k,F_k∈\mathbb{E}$ for some $k∈\mathbb{N}\}$

measure-theory

answered 1 hour ago Danny Pak-Keung Chan 5,303

1

vote

0

answers

18

views

Modeling a spring mass damper with variable damping

ordinary-differential-equations partial-differential-equations physics control-theory

modified 1 hour ago Robert Lewis 61.5k

1

vote

0

answers

16

views

Are there any known rigid properties of the counterexample zeroes to RH assuming the failure of RH?

soft-question zeta-functions riemann-hypothesis

asked 1 hour ago Keith Millar 339

1

vote

2

answers

31

views

Find a solution for $y$ in a nonlinear second order differential equation (missing x).

ordinary-differential-equations nonlinear-system

answered 1 hour ago Lutz Lehmann 85.8k

2

votes

1

answer

22

views

Pollaczek-Khinchine formula and Little's law for finite capacity queue

probability stochastic-processes queueing-theory

modified 1 hour ago lovemath 35

0

votes

0

answers

14

views

Problems with Set Function

measure-theory average means outer-measure amenability

modified 1 hour ago Arbuja 502

2

votes

0

answers

35

views

Calculating the number of ways a set of $n$ numbers with $k$ different possible values can yield a specific average of $m$.

combinatorics entropy integer-partitions

modified 1 hour ago Swike 168

0

votes

1

answer

34

views

Equations system from a contest

contest-math systems-of-equations nonlinear-system

modified 1 hour ago Valeria Chay 3

-3

votes

2

answers

45

views

Prove that absolute value of complex conjugate is equal to complex number

complex-analysis complex-numbers

modified 1 hour ago Bernard 153k

1

vote

1

answer

29

views

Undecidability of the Halting Problem excluding the main diagonal

logic recursion computability turing-machines

answered 1 hour ago Xoff 9,679

0

votes

0

answers

11

views

Cone's lateral surface area differential

calculus integration geometry

modified 1 hour ago Luyw 684

4

votes

0

answers

32

views

What is the best approach to graphing functions from $\mathbb R^n$ to $\mathbb R^m$?

graphing-functions visualization

modified 1 hour ago Alex 41

2

votes

0

answers

45

views

Is the set of all random $n$-vectors with arbitrary expectations an inner product space?

probability-theory statistics vector-spaces random-variables inner-product-space

modified 1 hour ago Raj Panse 197

0

votes

1

answer

16

views

Difference between joint probability and mutual information on a Venn Diagram

probability information-theory entropy

answered 1 hour ago leonbloy 47.3k

0

votes

1

answer

14

views

are the past outcomes relevant in calculating future odds.

stochastic-processes dice

answered 1 hour ago Riemann'sPointyNose 3,494

0

votes

0

answers

36

views

Dictionary of the Leibniz notation?

analysis notation

modified 1 hour ago Michael Hardy 238k

0

votes

0

answers

13

views

Why are solvmanifolds of importance?

manifolds lie-groups lie-algebras smooth-manifolds solvable-groups

asked 1 hour ago Andrew Aguilar 1

0

votes

0

answers

14

views

Is there a name for a real function that changes sign across an abcissa point $x_0$?

functions

asked 1 hour ago grav.field 1

1

vote

1

answer

23

views

Probability question regarding taking seats

probability

answered 2 hours ago Math Lover 1,240

0

votes

0

answers

12

views

Reference request: what about the first eigenvalue of the $-\Delta_p$ operator?

real-analysis functional-analysis eigenvalues-eigenvectors

asked 2 hours ago C. Bishop 659

1

vote

0

answers

10

views

Is the union of stable manifolds of gradient flows an open?

dynamical-systems gradient-flows set-invariance

asked 2 hours ago Olivier Massicot 324

0

votes

0

answers

14

views

Uniformly bounded matrix

linear-algebra partial-differential-equations

modified 2 hours ago Michael Hardy 238k

0

votes

1

answer

16

views

Generalized Cauchy–Bunyakovsky–Schwarz inequality proof by induction (Spivak calculus chapter 2 problem 21)

induction cauchy-schwarz-inequality

modified 2 hours ago Siong Thye Goh 122k

0

votes

0

answers

6

views

Define continuous Power Function for Dual Numbers (Complex or Quaternion)

logarithms exponential-function quaternions

asked 2 hours ago Spoc 101

0

votes

1

answer

23

views

Can Gaussian elimination fail finding null space?

gaussian-elimination

modified 2 hours ago Gae. S. 13.1k

0

votes

0

answers

8

views

Formula to approximate a sin wave to a Bezier curve

bezier-curve

asked 2 hours ago vila 15

0

votes

0

answers

20

views

Construction of any angle below 60°

geometry trigonometry geometric-construction

asked 2 hours ago Advaith Narayanan 1

0

votes

0

answers

14

views

Change of Variables Theorem with Inverted transformation

calculus

modified 2 hours ago Snowball 513

1

vote

1

answer

21

views

How to calculate $Card(Stab(\mathbb{N}^*_k) $?

group-theory group-actions

modified 2 hours ago user750041 163

0

votes

0

answers

38

views

Solving a $3\times 3$ magic square with exponentiated entries.

elementary-number-theory recreational-mathematics magic-square

modified 2 hours ago Khashayar Baghizadeh 1,102

0

votes

0

answers

6

views

Construct smooth function in a compact planar domain with given boundary conditions

functional-analysis multivariable-calculus

asked 2 hours ago DuFong 890

0

votes

0

answers

17

views

Search of the roots of a polynomial of grade $n$: news

algebra-precalculus polynomials numerical-methods roots

modified 2 hours ago Sebastiano 2,162

1

vote

0

answers

6

views

Can we apply Reidemeister moves to self crossings of one component only of a “trivial” link and keep the others unchanged?

knot-theory knot-invariants

asked 2 hours ago user113715 1,031

0

votes

0

answers

27

views

On the definition of an algebra

abstract-algebra

asked 3 hours ago HaKuNa MaTaTa 4,677

0

votes

0

answers

11

views

Relationship between the SVD and correlation matrices

linear-algebra correlation svd

modified 3 hours ago An Ignorant Wanderer 125

0

votes

1

answer

25

views

How many candies they have?

linear-algebra solution-verification

modified 3 hours ago Soheil 988

0

votes

0

answers

20

views

$ {{\int} f(\textbf {xt})\ d\lambda_{\Bbb R^2} (\textbf {t}) = |xy| {\int} f(\textbf {t})\ d\lambda_{\Bbb R^2} (\textbf {t})}.$

measure-theory proof-writing lebesgue-integral lebesgue-measure borel-sets

modified 3 hours ago StubbornAtom 11.7k

0

votes

3

answers

50

views

Determine whether $x^x$ function is injective or surjective $?$

functions exponential-function

answered 3 hours ago jjagmath 480

0

votes

0

answers

19

views

Linear optimization: Is the shadow price of a constraint a monotone function of the RHS?

linear-algebra linear-programming

modified 3 hours ago Ayam 37

0

votes

0

answers

6

views

Writing $(a)_k*(a)_k$ as one Pochhammer Symbol or in terms of one Gamma ($\Gamma$) function?

special-functions gamma-function pochhammer-symbol

modified 3 hours ago Shaun 23.9k

1

vote

1

answer

14

views

Best way to describe the angle from another ray on a circle

geometry angle

modified 3 hours ago ABCD 912

1

vote

0

answers

18

views

How to Have and Modify and “Local Variable” in a Sum

summation

modified 3 hours ago DUO 61

3

votes

3

answers

109

views

Prove that $-\sqrt{c}<ab<0$ if $a^4-2019a=b^4-2019b=c$.

calculus polynomials contest-math systems-of-equations real-numbers

modified 4 hours ago Aqua 73.9k

2

votes

0

answers

24

views

Applications of the Infinitesimal Lifting Property

algebraic-geometry deformation-theory

modified 4 hours ago user10354138 23.5k

0

votes

1

answer

47

views

Doubt in proof of existence of tensor product

commutative-algebra tensor-products

modified 4 hours ago Kenta S 4,033

Jul	AUG	Sep
	08
2019	2020	2021

Explore our Questions