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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19 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 ...
0
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0answers
47 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 ...
1
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1answer
1k views

Equivalent systems of Linear equation

I've just begun to re-learn linear algebra because is so important, the book that I chose is naturally the Hoffman's for a lot of reason. Well, In the first chapter I'm stuck with the following, ...
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0answers
15 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 $E(\Pi_{i=1}^{n}\displaystyle\frac{X_i}{X_{(n)}})$. $X_{(n)}$ = $max_{1\leq i \leq n}X_i$
4
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3answers
173 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 ...
0
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2answers
292 views

Complex form of Fourier Series

So, the last part of the university syllabus in the chapter of Fourier Series is: ...
3
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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} & ...
13
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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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9answers
2k views

A linear operator commuting with all such operators is a scalar multiple of the identity.

The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study. We are given a linear operator $T$ over a finite dimensional vector space $V$. We have to show that $T$ is a ...
4
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1answer
1k views

Preferable Order of Mathematics Study

I was just wondering if someone would be kind enough to tell me in what order (I know that there is no real "best order") one would most profitably study these subjects/books: (edited to conform with ...
1
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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 ...
0
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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 ...
0
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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 ...
1
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1answer
36 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
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 ...
4
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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 ...
1
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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 ...
3
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3answers
494 views

Any good introductory book/tutorial on Fourier Transform (up to FFT) with plenty of exercises and solutions?

I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I ...
1
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3answers
749 views

why does double rounding 9.46 give 10 but “regular” rounding gives 9?

What's the correct way to round, or estimate, a number to a specified precision? Starting with wikipedia: Rounding a number twice in succession to different precisions, with the latter ...
1
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2answers
51 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 ...
0
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0answers
19 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 ...
0
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1answer
455 views

How to decide whether PDE is Homogeneous or non-homogeneous.

I am studying second order PDE. And I have seen homogeneous and non-homogeneous PDE. But I cannot decide which one is homogeneous or non-homogeneous. For examples; (1) $(D^3-3D^2D'+4D'^3)u=0$ ...
37
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9answers
4k views

Is complex analysis more “real” than real analysis?

In physics, in the past, complex numbers were used only to remember or simplify formulas and computations. But after the birth of quantum physics, they found that a thing as real as "matter" itself ...
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1answer
447 views

Expected value of division

Let $X,Y$ and $Z$ be three indenependent real valued random variables. Al with finite second momennt and all with mean $0$ and variance $1$. Define $$ W= \frac{X+YZ}{\sqrt{1+Z^2}} $$ Show that ...
0
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2answers
25 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
69 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 ...
0
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1answer
74 views

Bolzano-Weirstrass

This is derived of other question where my proof of the Bolzano theorem is as follows Proof: Suppose that $(a_n)$ is a bounded sequence then we have to show that it has a convergent subsequence. ...
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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 ...
0
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1answer
39 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 ...
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
238 views

Machine learning: beginner study material.

Can anyone suggest to me some beginner study material for Machine learning applications in fields of 1) Financial forecasting and 2) Online advertisement? Thanks in advance!
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0answers
26 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
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} ...
3
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2answers
67 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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3answers
99 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. ...
1
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1answer
15 views

Functions of Mixing random variables

If $X_t$ and $Y_t$ are independent random processes that are $\alpha$-mixing, is a linear combination, $aX_t + bY_t$ also $\alpha$-mixing? What about other functions $f(X_t,Y_t)$? How does one ...
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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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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 ...
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 ...
2
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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 ...
0
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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 ...
2
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1answer
277 views

Progressively Measurable for Rigth Continuous Adapted Processes

Any adapted and right continuous process $X_t$ is progressively measurable. For the above statement, I found proof in several books. They all have similar argument as follows. For a given $t > ...
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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 ...
0
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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 ...
32
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8answers
14k views

Game theory - self study

I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
2
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2answers
822 views

Introduction into Operations Research

I am a first year graduate student who advisor wants me to learn about operations research and to use stochastic integer programming in my research. He keeps giving me papers to read but they ...
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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
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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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 ...