Questions about studying mathematics without formal instruction.

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1
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1answer
35 views

Optimization with both equality and inequality constraints

I need to minimize the following quantity: $$\min x_1^{-1/n}- \left(1-x_2 \right)^{-1/n}$$ subject to: $1-x_1-x_2=\gamma$ and $0<x_1+x_2<1$ $\gamma$ being a constant. Had it been two ...
26
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8answers
2k views

Complex analysis is 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 ...
1
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2answers
25 views

law of total probability and conditiona probability exercise.

Exercise: Let $X$ be an uniform discrete r.v. with four possible values: 1, 2, 3, 4. Let $Y$ be an exponential variable whose parameter is the value taken by $X$. So, if $X = 3$, $Y$ is Exp (3). ...
4
votes
3answers
171 views

Show that $\lim_{x \rightarrow 1} \frac{x^4-2x+1}{x-1} + \sqrt{x} =3$

Show that $\lim_{x \rightarrow 1} \frac{x^4-2x+1}{x-1} + \sqrt{x} =3$ from the definition (using $\epsilon-\delta$) Why can't I do something like this? We want: $|\frac{x^4-2x+1}{x-1} + ...
0
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1answer
32 views

Gauss-Jordan Method

I keep getting the wrong set of solutions can someone help me. I know that when using the Gauss-Jordan method, the rules that I must follow can be applied in a variety of different procedures then why ...
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2answers
20 views

Inverse function of borel sets when function is a constant.

Following a simple proof my professor explained in class I am having problems with a specific step: The proof is of probabilistic nature and we are trying to prove that If $X$ (random variable) is ...
0
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0answers
44 views

Difficulty parsing combinatorics exercise

I am working through the wonderful book Proofs and Confirmations by David Bressoud. In the section 2.2, I came across the following exercise, which has me scratching my head. (2.2.8) ~ Let ...
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0answers
30 views

Showing the modified Dirichlet function is discontinuous

Show, using the $\epsilon-\delta$ definition of continuity, that the modified Dirichlet function, i.e., $f(x) = x$ if $x$ is rational and $f(x) = 0$ if $x$ is irrational, is discontinuous at ...
7
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0answers
627 views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
2
votes
2answers
30 views

Prove $n(A-B)=n(A)-n(A \cap B)$

Prove that: $n(A-B)=n(A)-n(A \cap B)$ This is an example from my book in which first step is like this:$$n(A)=n(A-B)+n(A \cap B) $$ But how did they get it.
2
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1answer
63 views

Decided to finally jump in

I've finally decided to jump into teaching myself math because I am a junior (soon senior) in high school and have been interested in math for the longest time. I am not sure if this question belongs ...
1
vote
1answer
41 views

The logical consequence of an empty set of premises.

I am studying propositional logic by self-study, using a dutch book. I hope I am translating the terms to the correct English term. If my words are confusing, please please just let me know instead of ...
6
votes
0answers
91 views

Who wants to learn set theory? [closed]

So set theory is something I really want to learn. I found this document that I really like, except the fact that it doesn't prove all of it's theorems in with a lot of detail (a lot of times they say ...
0
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2answers
58 views

Find out the value of $d$

If the mean deviation of number $1,\ 1+d,\ 1+2d,\ 1+3d,\ldots,1+100d$ from their mean deviation $255$ then $d$ equals to ? This was the question asked in AIEEE 2009. MY EFFORTS: ...
1
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2answers
35 views

How to get the number of ways of getting a five card hand that is a straight flush from a standard deck of cards

I do not get the result at this page, ex. 13-7: Suppose that Aces can be either high or low; that is, that {Ace, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. The number of ...
0
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1answer
67 views

Starting Calculus with a weak foundation in Pre-Calculus

I am struggling in Pre-Calc mathematics, and I want to know is it ok if I start Calculus I with a weak foundation in Pre-calculus mathematics? I understand the general gist of limits, function ...
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0answers
25 views

Proving that the $[g,x]^n=e$ if $G$ is nilpotent of degree $n$

This is an article from wikipedia which I saw wondering as to how to prove it. The question is If $G$ is nilpotent of degree $n$ then $[g,x]^n=e$ for all $x \in G$, where $[g,x]=g^{-1}x^{-1}gx$. I ...
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0answers
53 views

Most Suitable Book after Kline's Calculus?

I've been working through Morris Kline's Calculus: An Intuitive and Physical Approach and it's an absolutely excellent book for self-studying applied single-variable (and some multi-variable) calculus ...
1
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1answer
65 views

Help me with a learning plan!

Now I'm a third-year software-engineering undergraduate and my university doesn't provide proper mathematical basis, so I want to learn all the basic things by myself. Here are subject I'd like to ...
1
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2answers
67 views

Find the limit of $a_n = e^ne^{-e^n}$

Consider the sequence $(a_n)$ where $a_n = e^ne^{-e^n}$, what is $\lim_{n \rightarrow \infty} (a_n)$? I have a feeling it's 0 because $\displaystyle a_n = \frac{e^n}{e^{e^n}}$ and $e^n$ grows ...
4
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0answers
62 views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
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1answer
76 views

What is purpose of these paragraph?

The following paragraphs are from my study notes on probability theory. It is a section within the independence discussion. But to me, they seem to appear here out of blue. I do not understand what ...
6
votes
1answer
78 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
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0answers
25 views

Are there online-platforms where to find people for joint learning and discussions?

After quite some time in academia I ended up in a nice company but the math to use is not really demanding. Hence I am still reading and working a bit on some university level math. It's roughly at a ...
4
votes
3answers
109 views

How is math used in computer graphics? [closed]

I'm doing a research paper on the mathematics of computer graphics and animation (3D) and I do not know where to start. What mathematical equations and concepts are used for computer graphics and ...
0
votes
1answer
10 views

Finding out number of observation

There are $n$ scores $X_1,X_2,X_3,....,X_n$ and their sum is $80$ and sum of their squares is $400$ then which among them is the probable value of $n$ A)$10$ B)$9$ C)$15$ ...
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2answers
64 views

How wrong is it? - A “proof” of the FTC that I came up with in high school by hand-waving.

In high school calculus, I was first taught that the area under a curve $f(x)$ between $x=a$ and $x=b$ is given by: $$ A = \lim_{\delta x \rightarrow 0} \sum \limits_{a}^{b} f(x) \delta x $$ Then ...
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3answers
281 views

Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ...
0
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1answer
23 views

Convergence in Probability and in Quadratic Mean for a sequence of random variables

I have been trying to determine whether a sequence of random variables, $X_1,X_2,\ldots,X_n$, such that $$P\left(X_n= \frac{1}{n}\right)=1-\frac{1}{n^2}\\ \text{and}\\ ...
2
votes
1answer
89 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering ...
3
votes
2answers
29 views

Zero divisors in ring of real valued functions.

I'm working though Pinter's A book of Abstract Algebra and would like a quick verification on a simple problem. Exercise 17.B2 asks Describe the divisors of zero in $\mathcal{F}(\mathbb{R})$. ...
7
votes
3answers
140 views

Beginning of Romance

I am a 17 guy from India. The fascination of maths has struck me recently, while I am in standard 12th. But all the resources I have, is some school textbooks. M.L Agrawal's of 11th and 12th. I don't ...
0
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2answers
38 views

A few questions on Minimal Polynomials

I have been trying to see the properties of Minimal Polynomials. So from the examples I guessed the following properties but I am not sure whether they are true. The properties are: 1) If $\alpha$ is ...
1
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0answers
30 views

Wedge product of Lie algebra valued differential forms [duplicate]

Let $\mathfrak{g}$ be the Lie algebra of a matrix Lie group. Furthermore, let us consider the following $\mathfrak{g}$-valued $p$-form and $\mathfrak{g}$-valued $q$-form: \begin{equation} ...
3
votes
1answer
417 views

Do only certain people exceed at math well? [closed]

It's obvious if you look around that math has always been one of the toughest subjects in all areas, from federal-traditional public schools to simply people learning it as an autodidact, hobby, or as ...
0
votes
1answer
36 views

The value of to fill the gap in the proof

I have studied a paper "On Finite Groups with Given Conjugate Types I" recently. The author use many words like "obviously", "clearly", "trivial", etc. in his proof. But these "obviously" implication ...
0
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1answer
18 views

Finding out missing observation

The Standard deviation of two observation is $2$, and one of the observation is $7$, find the other observation I have no idea how to begin with this problem. If mean was given then it would be ...
3
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0answers
121 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
0
votes
1answer
24 views

$f$ is bounded $\iff$ $F/\log$ where $F(x)= \int_{[1,x]}f(t)/t \,dt$

Hi everyone I'm stuck with one exercise. This says the following: Let $F(x)= \int_{[1,x]}f(t)/t \,dt$ where $f$ is a non-decreasing function. Show that $f$ is bounded $\iff$ $F/\log$ is also ...
1
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2answers
68 views

Predicate logic, transitivity (sort of?)

I have a question. It involves 2 pictures for which I'm supposed to write a formula which is true for one, but false for the other. The pictures can be found here on page 23 (the arrows pointing in a ...
2
votes
1answer
55 views

value of the integral $\int_0^{2\pi} \log|1-ae^{i \theta}| $

This is a problem from Complex Analysis by Stein and Shakarchi. We have to find the the value of $\int_0^{2\pi} \log|1-ae^{i \theta}| $ when $|a|<1$. So I tried to solve it in this manner. I ...
2
votes
1answer
46 views

Good resource for learning braid theory?

I recently heard about braid theory and read the Wikipedia article on it, and it seems really beautiful. What is a good resource for learning more about it? I have a background in mathematics at the ...
0
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0answers
38 views

Example of fuzzy logic problem

I am trying to grasp the concept of fuzzy logic and below is a case study. I need to classify objects using fuzzy logic. Each object is characterized by 4 features - {size, shape, color, texture}. ...
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2answers
349 views

Pure mathematics curriculum for self study with interests in foundational issues

I wonder if I want to make my own pure mathematics curriculum to study along the next 4 or 5 years. What topics should I include? I want it to be like one which an undergraduate student of pure ...
9
votes
0answers
162 views

Am I reading Bott - Tu right?

Summary: I'm finding Bott - Tu to be too brief and terse. I constantly have to look elsewhere to fill in details. This is not time-efficient. Am I missing something? If not - what other books do ...
5
votes
4answers
128 views

Evaluate $\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$

I need to evaluate the integral: $$\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$$ for $0<p<1$. Unfortunately I do not know where to begin. I tried integration by parts but got nowhere ...
16
votes
6answers
1k views

Best Math books or apps for adults to learn math from the beginning

I lost a possible job because I didn't know how to multiply and subtract negative valued integers. I also don't know how fraction manipulation works. What reference books can I read that can help for ...
0
votes
4answers
40 views

Why do you add +- to only one side when you remove square root from both sides?

As the title says, why when you take a square root of both sides of the equation do you add $\pm$ only to the side which is a number, as opposed to an unknown? For example: $$x^2 = 9 \implies x = ...
1
vote
1answer
29 views

Norms of Ideals and generators.

I'm self studying some Algebraic Number Theory, looking at norms of ideals within rings of integers for some number field. I know that if we have a principal ideal $I= (a)$, then the norm of the ...
0
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0answers
30 views

Perron Frobenius Theorem and Markov chains and more

I came across few ways of calculating convergence rates of Markov chains but I am a bit confused as to how these differ from each other and what may be the best way to calculate. The second ...