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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21 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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0answers
14 views

calculating $E(\Pi_{i=1}^{n}\displaystyle\frac{X_i}{X_{(n)}})$. [on hold]

suppose $X_1,X_2,...,X_n$ be a random sample of $U(0,\theta)$. how can I calculate $E(\Pi_{i=1}^{n}\displaystyle\frac{X_i}{X_{(n)}})$. $X_{(n)}$ = $max_{1\leq i \leq n}X_i$
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7answers
2k views

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
29 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
12 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 ...
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3answers
168 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
19 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 ...
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1answer
47 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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3answers
22 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 ...
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1answer
32 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
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1answer
26 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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0answers
12 views

Getting Started in Bayesian Statistics [duplicate]

I want to start learning about Bayesian statistics. What resources would you recommend? If possible, I think for future readers it would be helpful if answers could be broken up into (1) overview ...
1
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2answers
49 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
18 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
33 views

Real Analysis equivalence for Differential Equations and Matrix Theory [closed]

I know that real analysis is the study for the proofs of calculus. But what's the equivalent for differential equations and matrix theory? I'd like to know for personal study. Can any good books be ...
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2answers
23 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
63 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
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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} ...
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0answers
25 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 ...
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2answers
66 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 ...
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1answer
60 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 ...
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1answer
38 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 ...
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3answers
98 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. ...
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0answers
16 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
72 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.
2
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1answer
23 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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votes
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
24 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 ...
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0answers
22 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 ...
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2answers
25 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 ...
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0answers
17 views

optimization problem from my textbook

Given the objective function of a constrained optimization problem is $f(x₁, x₂)= c $ and the constraint is $g(x₁, x₂) = b$. How can I Show with a diagram that a unique optimum solution exist; unique ...
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2answers
59 views

What are the books that I should study for college? [closed]

Baccalaureate exam approached Real Analysis (limits, differentiation and integration), Abstract Algebra, Functional Algebra, Linear Algebra, Combinatorics, Complex numbers, Vector Geometry, Analytical ...
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0answers
30 views

Annuity question from my textbook

Assuming a pensioner expects to receive an annual pension of $20,000 for the next 5 years from his former employer. What is the present worth of the pension plan? Attempt: I'm solving annuity ...
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1answer
37 views

Show that $(a) + (b)= R$ for $\gcd(a,b) = 1$

The question I am trying to solve it: Let $R$ be a principal ideal domain, $a,b\in R$. Suppose $\gcd(a,b) = 1$. Show that $(a)+(b)=R$. First I have tried to show that $(a)+(b)$ is in R: ...
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0answers
18 views

Non-Inductive formula for subdivision operator

This problem is from hatcher 2.1.25. Find an explicit, noninductive formula for the barycentric subdivision operator. I have no idea how to get that formula. The only way I see it geometrically is ...
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0answers
61 views

A very detailed book for calculus 1-3.

Is there a very good book covering the whole calculus in detail, explaining all topics in calculus 1-3 for self-learning? I'm in geometry I, so I will start calculus in two years, and finish in five ...
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5answers
23 views

Prove the continuity on an open interval

I need to show, that function $f(x) =\frac{2x +3}{x-2}$ is continuous on the interval $(2,\infty)$ My attempt: We should find the right-hand limit to prove the continuity: and this limit is equal to ...
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2answers
37 views

What exactly does f'(x)=0 imply from the definition of differentiability?

Let f be a real valued function satisfying $|f (x) −f (a)| ≤ C|x−a|^γ$, for some γ > 0 and C >0. (a) If γ = 1, show that f is continuous at a; (b) If γ > 1, show that f is ...
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1answer
32 views

What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
2
votes
3answers
74 views

Showing $\mathbb{Q} \times \mathbb{Q}$ is not a field

I am revising and have come across the question Show that $\mathbb{Q} \times \mathbb{Q}$ with element-wise addition and multiplication is not a field I don't understand how to go about this, do i ...
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1answer
40 views

How should one without any university mathematics background study mathematical logic?

How should someone who hasn't studied any math at a university level start studying mathematical logic? (There are already questions like this but they mostly focus on book recommendation for people ...
0
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1answer
35 views

Does equality of the sum of two such series imply equality of each term of that series?

Let a(1)< a(2) < ..< a(m) and b(1)< b(2)<..< b(n) be real numbers such that $$\sum_{i=1}^m |a(i)-x| = \sum_{j=1}^n |b(j)-x|$$ for all x belonging to R. Show that m=n and ...
2
votes
1answer
30 views

Find dimension of a Vector Space.

Let $E=\{1,2,\ldots,n\}$, where $n$ is odd. $V$ is the vector space of all functions mapping from $E$ to $\mathbb R^3$. Find $\dim(V)$. Consider $T:V\to V$ such that $$ Tf(k)=[f(k)+f(n+1-k)].$$ ...
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3answers
72 views

What does x equivalent to 2 mod 15 mean?

I came across the following question: Consider the following system of equivalences of integers. $$ x \equiv 2 \bmod{15} $$ $$ x \equiv 4 \bmod{21} $$ The number of solutions in $x$, where $1\le ...
3
votes
2answers
48 views

learning linear algebra [duplicate]

So I'm a college student that has taken 3 semesters of calc/diff eq/linear algebra and I think linear algebra has been by far my favorite course so far and I would love to know more in the subject, ...
5
votes
0answers
78 views

How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very ...
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votes
1answer
33 views

I'm completely blanking on a simple exponent problem [closed]

Solve for $x$: $5x^{0.7}$ $=$ $y$