The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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Calculus: Differentiable Function and Tangent Line

I am not sure how to approach this question: Let $f(x)$ be a continuous and differentiable function of order 2. Let $f ''(x)>0$ for all values of $x$. The tangent line to the function at $x=1$ ...
2
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2answers
76 views

Probability: Balls in baskets

I'm self learning and I stumbled upon the following exercise but I'm not sure if I solved it correct as I'm very new to this. Problem: 7 balls fall independently into 7 baskets. Let $X_i$ = number of ...
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1answer
47 views

Probability with coins

I'm self learning and I stumbled upon the following task, but I struggle to find the solution: Two players flip coins. The first player flips 3 coins, the second player flips 2 coins. The player that ...
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1answer
37 views

Probability Question - Paper Notes in a bag

I could do with some help with this question. In a bag there are 18 paper notes. On five of them there is the digit 2, on seven the digit 3, and on six the digit 5. A man takes 3 notes by random. If ...
2
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2answers
71 views

Probability: breaking keyboard

I'm trying to self-learn theory of probability, I came across the following basic problem that I think I solved but I'm not sure as I'm very new to this. Problem: A keyboard manufacturer states that ...
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3answers
64 views

To prove $\sup B \leq \sup A$

Assume $A$ and $B$ are non empty and bounded above and satisfy $B \subseteq A$. Show that $\sup B \leq \sup A$ I am thinking of proving using contradiction, but I am getting nowhere. Someone please ...
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1answer
46 views

To show that $\sup B=\inf A$

How do i show that To show that $\sup B=\inf A$ , where $A$ is set bounded below and B ={$b \in R$ : $b$ is a lower bound for $A$} Let $x=\sup B$ and $l=\inf A$. Now All lower bounds of A are less ...
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1answer
22 views

Showing weak law of large numbers holds

My question: $\{X_n\}$ is a sequence of random variables. Var$(X_n)\le C\ \ \forall \ n$ and $\rho_{ij}=$Cov$(X_i,X_j)\to 0 $ as $|i-j|\to \infty$ . Show WLLN holds. In my book there are 3 ...
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2answers
69 views

Self Study of number theory

I have always wanted to learn about number theory. There is actually no one here who can teach me and it's also not in my regular school syllabus, but the greatness of number theory attracts me ...
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1answer
43 views

Proof for functions of matrix [closed]

Let $A \in \text{Mat} (n,n,\mathbb{C})$. Let $I$ be a subset of $\mathbb{R}$ or $\mathbb{C}$. Further, let $f:I\to\mathbb{C}$ and $g:I\to\mathbb{C}$ be two functions for which $f(A)$ and $g(A)$ are ...
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0answers
23 views

Composition of substitutions of SLD tree

I found a question on my university past paper and it asked to get the SLD tree from a computation rule using some rules and facts. However I obtained the answer and to complete the question I have to ...
1
vote
0answers
99 views

Finding total number of multi-sets

I am provided with a multi-set, let's say S with elements as [num1, num2, num3] and these elements are integers (both negative as well as non negative). As this is a multi-set, elements in the multi-...
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votes
1answer
40 views

Joint pdf of X and Y with absolute value

Question. Joint probability function of continuous probability X, Y is here : $f_{X,Y}(x,y) = k(|x|-|y|) \ \ \ \ \ \ \ \ \ \ (-1< y< x< 2)$ Then what is k? I mean how can I differentiate ...
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votes
1answer
48 views

Transformation matrix

For $x \in \mathbb{C}$ define $A,B \in M(3\times3, \mathbb{C})$ as $$ A = \begin{pmatrix} x & 0 & 0 \\ 0 & x & 1 \\ 0 & 0 & x \end{pmatrix}$$ and $$ B = \begin{pmatrix} x & ...
3
votes
1answer
54 views

I need to re-learn all highschool level mathemetics in order to attend college. (Please Help) [duplicate]

I know this isn't a research level question, but a lot of you teach, and I'm not sure where else to turn. I will just shoot straight: I am 30 years old. I have not done any type of true mathematics ...
0
votes
1answer
25 views

Understanding the definition of $UV$, where $U$ and $V$ are ideals in a ring

I have the following question at hand: I. N. Herstein Topics in Algebra: Ideals and Quotient Rings : Qn $3.4.6$ If$\ \ U,V$ are ideals of $\ R\ $,let $UV$ be the set of all elements that can be ...
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3answers
283 views

How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed]

[Please reditect me to a different site/sub-site/pretty-much-any-relevent-place if I've posted the question in the wrong forum, please do not downvote before attempting to redirect me to the adequate ...
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0answers
13 views

Analytic geometry - historical & applied

What would you suggest as good sources for a self-study of analytic geometry, from the elementary properties of quadratic curves to curves of higher degree, with emphasis on historical development and ...
2
votes
1answer
35 views

2-norm of matrix

How to prove that for a symmetric matrix A with eigenvalues $\lambda_1 \leq \lambda_ 2, ... \leq \lambda_n$ it holds that $$\vert\vert A \vert\vert = \text{max}(-\lambda_1, \lambda_n)$$ where $\vert\...
0
votes
1answer
21 views

Flag of invariant subspaces

How can I prove that for a nilpotent endomorphism $\xi: V \to V$ with $\xi^k(V) = 0$ and $k$ being the smallest natural number to do so: $$\{0\} = \xi^k(V) \subsetneq \xi^{k-1}(V) \subsetneq \dots \...
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0answers
63 views

Rigorous Approach to Precalculus

I've made the mistake of looking at more advanced texts that deal with precalculus-level mathematics in a more formal, rigorous way than usual. Perhaps this isn't a mistake, but now that I've glimpsed ...
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7answers
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Why is a square root not a linear transformation?

The question says: Prove that the function $f(x)=\sqrt{x}$ is not a linear transformation (particularly $\sqrt{1+x^2}≠1+x$) I think that this is because the exponent of $\sqrt{x}$ is $1/2$, ...
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2answers
30 views

Prove identity by induction

Recently I read in lecture notes that for $\alpha \in \mathbb{N}^m$ with $\vert\alpha\vert = r$ the following identity holds: $$ \sum_{} \frac{1}{\alpha!} = \frac{m^r}{r!}.$$ Appearently one can ...
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0answers
14 views

Linear Programming - Constraints

I am trying to encode this (a small part of a project that I am trying to do by self-learning) to linear programming: For each package p we know its length (xDimp) and width (yDimp). Also, we have ...
4
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3answers
185 views

Learning differential calculus through infinitesimals

In class, we've studied differential calculus and integral calculus through limits. We reconstructed the concepts from scratch beginning by the definition of limits, licit operations, derivatives and ...
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1answer
20 views

Explain the use of Dominated Convergence Theorem

In the proposition below from Measure Theory and Probability by Athreya and Lahiri, DCT was used to justify the existence of $t$ in the first line of the proof. But I can't think how this was ...
0
votes
1answer
52 views

Calculation of characteristic polynomial

I have to determine the characteristic polynomial of the matrix $$A = \begin{pmatrix} 0 & 0 &\cdots &0& -a_0 \\ 1 & 0 & \cdots & 0 & -a_1 \\ 0 & 1 & \cdots &...
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votes
3answers
24 views

To show that Z(G) = $\cap_{a \in G} C(a)$

To show that Z(G) = $\cap_{a \in G} C(a)$ (Intersection of all subgroups of form C(a)) Let $a \in Z(G)$. Then $ax=xa$ for all $x$ in G. IN particular we can say that $ax_1=x_1a$ and $ax_2=x_2a$ and $...
0
votes
1answer
62 views

Is there a list of recommended problems to do in each chapter of Spivak's Calculus anywhere?

I've recently been self-studying Spivak's Calculus, and since I don't have the time to do every problem from every chapter at a and finish at reasonable rate, I've looked for a course syllabus or ...
1
vote
1answer
27 views

Doubt in Dihedral group $D_4$ regarding reflections [duplicate]

This question is from Gallian Page 69 Q 9. Suppose a subgroup od D_4 contains H and D. I want to show that these two generated whole of $D_4$. Now rotation will generate other rotations which is ...
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2answers
57 views

Check equivalence of quadratic forms over finite fields

How to check whether the two quadratic forms \begin{equation} x_1^2 + x_2^2 \quad \text{(I)}\end{equation} and \begin{equation} 2x_1x_2 \quad \text{(II)} \end{equation} are equivalent on each of ...
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0answers
21 views

Equivalent complexity of graph algorithms

Given a directed graph G = (V,E) with edge weights c: E -> R and r $\in$ V i have to show that the following 3 problems are equivalent: 1) Find a branching with maximum weight 2) Find a spanning ...
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2answers
27 views

utility function question from my textbook

Suppose there are two goods with prices $ p₁ = 2, p₂ = 5, $ the income is $ M = 40 $ and the utility function is $ U (x₁, x₂) = (x₁)^⅓ . (x₂)^ ½, $ Find the optimum consumption plan. Attempt: I do ...
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0answers
79 views

Finding an Elliptic Curve with 103 points

I am trying to solve the following problem: Find an elliptic curve over F101 with 103 points. I know all of the equations when needing to find alpha, and beta and all that when I am given two points ...
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0answers
17 views

Is there any way to enter and review formulae on computer?

I was wondering if there was any website or software which would allow to enter all the formulae I'd like to study and then to review them by randomly picking some of them. A bit like chrome ...
2
votes
1answer
18 views

Complex variable: studying convergence of series in terms of radius of a different series

Trying to solve this problem: If the radius of convergence of the power series $$\sum_{n=0}^\infty a_n z^n$$ is R, with $0 < R < \infty$, then the radius of convergence $R_1$ of the ...
0
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2answers
27 views

Complex variable: Study the convergence of ${f_n(z) = \frac{z^n}{n + z^n}}$

I'm trying to do this problem for complex variable: Study the convergence of this sequence of analytic functions in $D(0, 1)$. \begin{equation} i) \left\{ f_n (x) = \frac{z^n}{n + z^n} \right\}_{...
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0answers
30 views

Weil conjectures - If two varieties have the same of Fq^d - valued points for all d >> 0, then they have the same Hasse - Weil function

I was working on the following exercise for fun, and I haven't really gotten anywhere with it. Let Z( X; t) be defined as exp ( $\sum_{r= 1}^{\infty} N_r t^r/r$), where $N_r$ is the size of X($\...
3
votes
2answers
96 views

Self-study mathematics subject sequence and recommended books

I am a Physics student but I finally found that I've entered the wrong department that I am in fact much more interested in mathematics. I want to self-learn mathematics. I am now reading Artin (...
1
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1answer
66 views

Learning Abel-Ruffini

I took an introductory abstract algebra course at my university and was fascinated by the content. I would love to learn more and go into greater depth with groups, rings, and fields, but ...
0
votes
1answer
45 views

Proof regarding size and dimension of linear codes

The problem is stated as follows: Let C be a binary linear code of length n, dimension k and distance d and assume that C contains at least one element of odd weight. Let C' be the subset of C ...
0
votes
3answers
110 views

Learn mathematics

At school, I was very good at mathematics, but now I'm 40 years old and I think I have forgotten almost everything I have learnt. I want to study again mathematics because I'm very interested on it. ...
0
votes
0answers
18 views

Non linear model, logistic regression exercise

Let $y_i$ follows $Bin(n_i,p_i)$ and for $p_i$ we consider the logit quadratic model: $\log\frac{p_i}{1-p_i}=\beta_0+\beta_1A_i+\beta_2(A_i-meanA)^2$ where $A_i$ is AGE_i during ith time. As you can ...
3
votes
2answers
76 views

Absolute value and quadratic programming

I would like to solve the following optimization problem using a quadratic programming solver $$\begin{array}{ll} \text{minimize} & \dfrac{1}{2} x^T Q x + f^T x\\ \text{subject to} & \...
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0answers
16 views

How to compare two tests according to the power of the test?

enter image description here Can the rejection region calculated from the problem? I'm a little bit confused by all this staff.
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1answer
24 views

How many people did the test at most?

There are 3 questions in a test and the full mark of each question is 7. Each question can only be marked with integers: $1, 2, 3, \cdots, 7$. We know that the product of everyone's marks of the 3 ...
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1answer
27 views

Derivative notation question

$d = \frac{(u+au)^2}{\frac{u^2}{r} + \frac{(au)^2}{s}}$ I have a basic question concerning derivatives. If I need to find the max of $d(a)$, I know I need to take derivatives... but with respect to ...
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0answers
25 views

What should I be studying if I want to calculate correlation between data sets?

I'm building an app that brings in data from multiple API's (Stripe, Google Analytics, Github). I'd want to be able to analyze the different sets of data against each other if at all possible and draw ...
0
votes
0answers
24 views

Is there a broad map, guide or list of all or most of math's fields? [duplicate]

Has someone ever garthered all the different fields in maths (single variable function analisis, multivariable analisis, complex number analisis, number theory, graphs, succesions, etc) and made a (...
2
votes
2answers
28 views

Finding limit of the function by power series estimation

I want to prove that the limit of function $\displaystyle \lim_{x \to \infty}\frac{\ln(x)}{x} = 0$ Of course it is easy to find it by l'hopital's rule, but i want to find it using the power series ...