Mathematics

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  1. A sum for $\binom yz$

  2. There are n husbands and n wives to be seated at... Find var(X)
  3. If the positive integers $n$ and $n+k$ are prime, then: $(k!)^2((n-1)!+1)+n(k!-1)! \equiv 0$ (mod $n(n+k))$.
  4. find the value of (1-n) mod n with proofs

  5. A Suspected Mean Value Problem

  6. When is there an assignment that respects the natural constraints on a poset of systems?

  7. Number of different terms in a polynomial
  8. Suggestion of books of Topology and Graph Theory

  9. How to find the Maclaurin series
  10. Smallest $x+y$ for integer equation $n = 5x + 3y$ in closed form

  11. Does the set $\{\tan n, n\in\mathbb{Z}\}$ contain any integers?
  12. If $\sum_{n=1}^\infty b_n^{1/\alpha} < \infty$ for some $\alpha > 1$, then $\sum_{n=1}^\infty b_n|x-a_n|^{-\alpha}$ converges almost everywhere.
  13. If a and b are the same sign but different then prove: $\log|a+b|-\log|a-b|=\frac{1}{2}\log2 <>a^2+b^2=6ab$

  14. gradient of logdet of sum of two matrices

  15. Are triangles rigid in 4 dimensions?

  16. Is the diagonal matrix the only matrix whose square is diagonal?

  17. Quotient topology R/Z homeomorphic to [0,1]/{0,1}

  18. Which values of Lambert W function are rational?

  19. Volume of truncated prism
  20. Prove a sigma algebra contains element of a specific form

  21. Solve system:$yz(y+z-x)= a(x+y+z)\\ zx(z+x-y)= b(x+y+z)\\ xy(x+y-z)= c(x+y+z)$
  22. Showing $\{ 0, 1 \}^{\mathbb{N}} $ is totally disconnected with given metric

  23. What exactly do the sin, cos, tan buttons do on a calculator?

  24. Finding The Shortest Distance Between Two 3D Line Segments
  25. Unconditional result for the existence of primes in intervals of lenght one

  26. Can hyperbolic functions be defined in terms of trignometric functions?

  27. Can a bipartite graph have only 3 vertices?

  28. Binary string to boolean polynomial

  29. Infinite Circles

  30. Finding the equation for a parabola given two points and a vertex on a line.

  31. 1 to the power of infinity, why is it indeterminate?
  32. Calculate principal curvature of an hypersurface

  33. Determine the domain : $ y=\sqrt{\log_x 2-\log_2 x}$

  34. Transformations of Random Variables

  35. 95th percentile of average
  36. How to understand following vector fields on manifold

  37. Number of spanning trees in a graph with a vertex of degree N
  38. Eisenbud, Algebraic Geometry, Theorem 3.1 proof, pg 94
  39. function transitive. How can we prove it?
  40. Proof involving Ramsey numbers

  41. Relationship between intersection and compositum of fields

  42. Evaluation of a strange multinomial sum

  43. Finding the ratio of students who attended less than $H/2$ hours of lectures
  44. Closed-form solution to a nasty Integro-Differential equation?
  45. Poincare Inequality
  46. How to carry out an infinite-dimensional induction?

  47. Use cardinality to show the canonical embedding $c_0\rightarrow c_0^{**}$ is not surjective.
  48. Understanding Quantifier Elimination
  49. Non-pythagorean triples
  50. Eigen Values and Probability Question. Not for the faint of heart

  51. Cardinality of Vitali sets: countably or uncountably infinite?

  52. Use residues to evaluate $\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x$, where $|a|<1$
  53. Finding interval of uniform convergence for $\sin^2(tx)/x^2$

  54. Find the Vertices of an Ellipse Given Its Foci and Distance Between Vertices

  55. If A=XY, what is the standard error in A?

  56. Proof that the categorical product is associative

  57. Expanding logarithms

  58. induction with recursive elements $y_{k}=y_{k-1}+k^2$
  59. Either there exists an extended real number $A$ such that $X_n \to A$ almost surely or the sequence $X_n$ diverge almost surely.

  60. Weakly compact subset of $l ^{\infty}$
  61. Eigenvalues of elements of a Weyl group

  62. How to find vector that is in the same plane and perperndicular to a side of a triangle?
  63. Square root of a nilpotent matrix

  64. Why is the Euler phi function $\varphi(n)> 2$ for $n\ge 7$?

  65. Regarding sets with size distinct from a power set of $\mathbb{N}$

  66. A characterization of functions that preserve weak-majorization ordering

  67. Use the Cauchy Integral Formula to evaluate the following integral: $\int \frac{e^z \,dz}{z^2+1}$
  68. Multiplication of Moduli in Modular Congruences

  69. Variance estimation question and unbiasedness.

  70. weak type bound for fourier series of an L^1 function on the circle
  71. $\lim_{x \to \infty } \left (\frac{2\tan^{-1}x}{\pi}\right)^x$ =?

  72. Question about essential singularity

  73. Odds of winning 3 of next 5, given 60% odds of winning each game

  74. Prove odd degree polynomials have roots.

  75. Using Perron's formula for asymptotic behaviors

  76. Riemann-Lebesgue lemma for periodic functions
  77. Line intersect spline surface
  78. Proving that if $\lim\limits_{n\to\infty}a_n=+\infty$ and $\{b_n\}$ is a bounded sequence, then $\lim\limits_{n\to\infty}(a_n+b_n)=+\infty$

  79. Spinner numbers probability
  80. A question about topological group related to prime numbers induced by order relation
  81. Thermodynamics: Mathematical Derivation of the speed of sound
  82. Solve nonlinear equation with symmetric and diagonal matrices $\mathbf{X} = \mathbf{A}-vv'\left((k+D(\mathbf{X}v)\right)^{-2}$
  83. projective plane RP2 to be a differential manifold?

  84. Partial integration in MATLAB
  85. Finding a cochain with specific coboundary

  86. When does the defect group grow in size?
  87. Find the Generating Function from the sequence (0,1,0,3,0,5,...)

  88. Is there a symbol that denotes a finite set?
  89. A limit involving the Thue–Morse sequence

  90. Deriving properties of logarithms from the definition $\ln(x) = \int_{1}^{x} \frac{\mathrm{d}t}{t}$

  91. estimation of error in numerical methods
  92. Derivative w.r.t. matrix
  93. The set of sequences $e_j= (0,...,0,1,0,...)$ is closed in $\ell_1$.

  94. Reflection in a tube

  95. Conjecture : $\int_{0}^{\pi\over 2}\mathrm dt{\ln[2\cos(t)]\over t^2+\ln^2[2\cos(t)]}={\pi\over 4}?$
  96. What are different ways to compute $\int_{0}^{+\infty}\frac{\cos x}{a^2+x^2}dx$?

  97. When is there a solution to the generalized Pell's equation?

  98. What is $\int\frac {dx} {x!}$?
  99. Find $\lim_{(x,y)\to(0,0)}{\frac{x^2y}{y+x^2}}$

  100. Simulation of PDF of inverse random varible