User Yos

11 votes

7 answers

3k views

Product of functions is $0$ but none of the functions is identically $0$?

functions roots

asked Mar 2, 2017 at 6:27

5 votes

2 answers

141 views

generating function: how many possibilities are there to throw 10 different dice so that their sum is 25

asked Aug 4, 2016 at 19:24

5 votes

3 answers

164 views

Matrix determinant as Dickson polynomial $\frac{x^{n+1}-y^{n+1}}{x-y}$

linear-algebra induction recurrence-relations determinant

asked May 2, 2017 at 16:22

5 votes

3 answers

11k views

How to solve $y''+y=\cos x$?

ordinary-differential-equations multivariable-calculus

asked Aug 4, 2017 at 13:33

4 votes

1 answer

910 views

How to prove that 3-CNF is satisfiable using Hall's marriage theorem?

logic graph-theory satisfiability

asked Jan 15, 2018 at 16:33

4 votes

1 answer

581 views

Prove that $I-T$ is an isomorphism if $T:V \to V$ and $T^3=0$ and find $(I-T)^{-1}$

linear-algebra linear-transformations

asked Jun 20, 2017 at 14:22

4 votes

3 answers

345 views

Is $T(p(x))=p(x+1)$ a linear map if $T:\mathbb{R}[x]\to\mathbb{R}[x]$?

linear-algebra proof-verification linear-transformations

asked Jun 19, 2017 at 16:52

4 votes

1 answer

536 views

How many natural solutions to $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 24$ if $x_1 + x_2 + x_3 > x_4 + x_5 + x_6$?

combinatorics diophantine-equations generating-functions

asked Sep 20, 2016 at 18:39

4 votes

2 answers

765 views

How to solve system of linear equations with negative scalars over finite field?

linear-algebra modular-arithmetic

asked Mar 23, 2017 at 16:18

4 votes

3 answers

1k views

How to find the number of solutions to a system of equations with one parameter which cannot be reduced?

linear-algebra systems-of-equations

asked Mar 24, 2017 at 14:36

3 votes

2 answers

167 views

Prove if $B^2=I+BA$ and $A^2=AB$ then $A=0$

linear-algebra matrices proof-verification

asked Apr 20, 2017 at 12:40

3 votes

2 answers

170 views

Find $\dim(\ker T_1 \cap \ker T_2)$ if $T_1,T_2:V\to F$, $T_1 \neq 0$, $T_2\neq 0$, $\dim V=n$ and $\ker T_1\neq \ker T_2$

linear-algebra linear-transformations solution-verification

asked Jun 21, 2017 at 19:05

3 votes

1 answer

338 views

How to find $\theta$ bounds when calculating the volume enclosed between sphere $x^2+y^2+z^2=4a^2$ and cylinder $x^2+(y-a)^2=a^2$?

integration multivariable-calculus polar-coordinates volume

asked Jun 1, 2017 at 16:59

3 votes

1 answer

106 views

How to solve $z^9-(\overline z)^9=9|z|^4$ over $\mathbb{C}$?

linear-algebra complex-numbers

asked May 5, 2017 at 13:53

3 votes

2 answers

2k views

Find all the points on the cone $z^2=x^2+4y^2$ that are the closest to the point $(0,0,c)$

multivariable-calculus optimization lagrange-multiplier qcqp

asked May 19, 2017 at 18:26

3 votes

1 answer

122 views

How to prove that $W=U_1 \oplus(U_2 \cap W)$ if $U_1 \subseteq W$, given that $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are subspaces of $V$?

linear-algebra vector-spaces direct-sum

asked May 30, 2017 at 8:59

3 votes

2 answers

2k views

Can the degree sequence $2,2,2,2,2,3,3$ be Hamiltonian graph, if not can it be a simple graph?

graph-theory hamiltonian-path

asked May 18, 2018 at 15:36

3 votes

2 answers

675 views

How many labeled trees are there if there're $4$ leaves that are set?

combinatorics graph-theory trees

asked May 22, 2018 at 13:27

3 votes

1 answer

3k views

How to calculate line integral over an ellipse with vector field undefined inside the ellipse?

integration multivariable-calculus vector-fields

asked Aug 15, 2017 at 15:12

3 votes

2 answers

356 views

How to calculate $\iint\ln(x^2+y^2)$ over a part of a circle?

integration multivariable-calculus

asked Aug 15, 2017 at 12:34

3 votes

1 answer

1k views

Find shortest path in graph that visits 2 nodes from a certain node set

graph-theory algorithms computer-science

asked Nov 2, 2017 at 8:58

3 votes

1 answer

383 views

How many permutations of $0123456789$ are possible if $0123$, $2345$, $4567$, $6789$ sequences are not allowed?

combinatorics proof-verification permutations

asked Jun 12, 2018 at 16:22

2 votes

2 answers

167 views

How to prove that if a graph and its complement graph are trees then there're $4$ vertices in the vertex set of the graphs?

proof-verification graph-theory

asked Jun 15, 2018 at 14:01

2 votes

2 answers

187 views

How to prove that if a simple graph has a vertex which splits it into at least $2$ connected components does not have Hamiltonian cycle?

graph-theory

asked Jun 27, 2018 at 14:23

2 votes

1 answer

476 views

How many positive integer solutions are to a system of linear equations?

linear-algebra combinatorics systems-of-equations

asked Jun 29, 2018 at 12:26

2 votes

1 answer

839 views

How to find the equivalence classes of a formal language complement?

equivalence-relations formal-languages regular-expressions

asked Nov 23, 2018 at 18:19

2 votes

2 answers

64 views

How to define a grammar which creates a language from words of another grammar without one of the letters?

proof-explanation formal-languages

asked Dec 15, 2018 at 9:17

2 votes

2 answers

54 views

Give an example of a language $L$ where $\min(\max L)\neq \max(\min L)$

proof-verification formal-languages

asked Jan 27, 2019 at 18:57

2 votes

1 answer

244 views

How to find minimum Hamming distance of concatenated two encoded words?

coding-theory

asked Apr 11, 2020 at 19:04

2 votes

2 answers

49 views

Does the curve $c(t)=\langle \sqrt{1-t^2}\cos t,\sqrt{1-t^2}\sin t,t\rangle$ lie on unit sphere?

multivariable-calculus parametric

asked Aug 20, 2017 at 13:11

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259 Questions

Product of functions is $0$ but none of the functions is identically $0$?

generating function: how many possibilities are there to throw 10 different dice so that their sum is 25

Matrix determinant as Dickson polynomial $\frac{x^{n+1}-y^{n+1}}{x-y}$

How to solve $y''+y=\cos x$?

How to prove that 3-CNF is satisfiable using Hall's marriage theorem?

Prove that $I-T$ is an isomorphism if $T:V \to V$ and $T^3=0$ and find $(I-T)^{-1}$

Is $T(p(x))=p(x+1)$ a linear map if $T:\mathbb{R}[x]\to\mathbb{R}[x]$?

How many natural solutions to $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 24$ if $x_1 + x_2 + x_3 > x_4 + x_5 + x_6$?

How to solve system of linear equations with negative scalars over finite field?

How to find the number of solutions to a system of equations with one parameter which cannot be reduced?

Prove if $B^2=I+BA$ and $A^2=AB$ then $A=0$

Find $\dim(\ker T_1 \cap \ker T_2)$ if $T_1,T_2:V\to F$, $T_1 \neq 0$, $T_2\neq 0$, $\dim V=n$ and $\ker T_1\neq \ker T_2$

How to find $\theta$ bounds when calculating the volume enclosed between sphere $x^2+y^2+z^2=4a^2$ and cylinder $x^2+(y-a)^2=a^2$?

How to solve $z^9-(\overline z)^9=9|z|^4$ over $\mathbb{C}$?

Find all the points on the cone $z^2=x^2+4y^2$ that are the closest to the point $(0,0,c)$

How to prove that $W=U_1 \oplus(U_2 \cap W)$ if $U_1 \subseteq W$, given that $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are subspaces of $V$?

Can the degree sequence $2,2,2,2,2,3,3$ be Hamiltonian graph, if not can it be a simple graph?

How many labeled trees are there if there're $4$ leaves that are set?

How to calculate line integral over an ellipse with vector field undefined inside the ellipse?

How to calculate $\iint\ln(x^2+y^2)$ over a part of a circle?

Find shortest path in graph that visits 2 nodes from a certain node set

How many permutations of $0123456789$ are possible if $0123$, $2345$, $4567$, $6789$ sequences are not allowed?

How to prove that if a graph and its complement graph are trees then there're $4$ vertices in the vertex set of the graphs?

How to prove that if a simple graph has a vertex which splits it into at least $2$ connected components does not have Hamiltonian cycle?

How many positive integer solutions are to a system of linear equations?

How to find the equivalence classes of a formal language complement?

How to define a grammar which creates a language from words of another grammar without one of the letters?

Give an example of a language $L$ where $\min(\max L)\neq \max(\min L)$

How to find minimum Hamming distance of concatenated two encoded words?

Does the curve $c(t)=\langle \sqrt{1-t^2}\cos t,\sqrt{1-t^2}\sin t,t\rangle$ lie on unit sphere?