Questions about studying mathematics without formal instruction.

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69 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 ...
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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
65 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 ...
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1answer
90 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
26 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
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3answers
176 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 ...
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1answer
11 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
65 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
313 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 ...
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1answer
28 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}\\ ...
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1answer
91 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 ...
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2answers
34 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
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3answers
145 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
39 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 ...
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0answers
31 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
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1answer
422 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 ...
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1answer
38 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 ...
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1answer
20 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
131 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 ...
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1answer
26 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 ...
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2answers
70 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
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1answer
58 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
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1answer
51 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 ...
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2answers
374 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 ...
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0answers
190 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 ...
6
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4answers
138 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 ...
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6answers
2k 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
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4answers
44 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 = ...
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1answer
30 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 ...
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0answers
32 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 ...
2
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1answer
49 views

Confused About Step in Proof of Divergence of $\sum \frac{1}{p}$

I was going through the number theory text by Ireland and Rosen, and was following the proof of the divergence of the sum of reciprocal primes. But I came across a step unclear to me. The proof so ...
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2answers
51 views

Convergence time of a Markov chain

We know that a regular Markov chains converges to a unique matrix. The convergence time maybe finite or infinite. My interest is in the case where the convergence time is finite. How can we accurately ...
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0answers
36 views

Six digit permutations of 1 to 6 - divisible by 8

I am working on a problem in A Concise Introduction to Pure Mathematics 3rd Ed under the counting and choosing chapter. It is a multipart question and I am stuck on the last part: 'The digits 1 2 3 4 ...
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4answers
86 views

A basic Combinatorics Book

So, this is my problem...I have completed my boards and among all others, I have a great weakness in combinatorics. So this means I can utilize my free time now to address this problem. I think it is ...
2
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1answer
108 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
0
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1answer
58 views

Need an Algebra 2/Precalculus text to prepare for Calculus

I'm about to finish my Algebra 1 text and I could use some recommendations for a text to prepare for Calculus. I've searched through several forums and some of the books I've seen recommended are: ...
0
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1answer
25 views

Bounded Linear Transformation proof

One paragraph in my text is to prove that $\|T\|=\sup\{|\langle Tf, g\rangle|:\|f\|<1, \|g\|<1\}$, where we have a bounded linear operator between two Hilbert spaces $T:\mathcal H_1\rightarrow ...
1
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1answer
41 views

$M_R$ is finitely generated iff Every submodule of $M_R$ is finitely generated

$M_R$ is finitely generated Every submodule of $M_R$ is finitely generated. Do the sentences above have the same meaning? Thanks for any replies.
2
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1answer
37 views

Find the permutation

This is part of an exercise I did on an assignment but I am having trouble remembering how to complete the exercise (even though I got full marks on my assignment). Let $P_1=(3\,4\,1\,2\,5), ...
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2answers
64 views

How many coefficients are in the expansion $(x + y + z)^{10}$

I need to find the number of coefficients in the expansion $(x + y + z)^{10}$. I had this exercise on a recent assignment. The answer I gave is: $3^{10} = \binom {3 + 10 - 1}{10} = \binom{12}{10} = ...
1
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1answer
41 views

A question on the morphism of projective varieties

The continuation of this, my question I want to show that $X$ and $Y$ are smooth and irreducible curves then $f(X)$ is either $Y$ or a point. Note that I know the proof of this ...
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2answers
40 views

$L^1$ is complete in its metric

Theorem: The vector space $L^1$ is complete in its metric. The following proof is from Princeton Lectures in Analysis book $3$ page $70$. Some of my questions about the proof of this theorem are as ...
2
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1answer
69 views

the diagonal $\Delta (Y) =\{(y,y)\in Y \times Y\}$ is closed in $\Bbb P^m \times \Bbb P^m $

Asumme that $\Pi : \Bbb P^n \times \Bbb P^m \rightarrow \Bbb P^m $is a closed map. $X\subset \Bbb P^n$ And $Y\subset P^m$ $f: X\rightarrow Y$ be a morphism of projective varieties. ...
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81 views

Every projective algebraic set can be written as the zero set of finitely many homogeneous polynomials of the same degree.

Definition: Let $I \subset k[x_0,\ldots,x_n]$ be a homogeneous ideal (or a set of homogeneous polynomials). The set $Z(I) := \{(a_0 : \cdots : a_n)\in P^n ; f(a_0,\ldots,a_n) = 0 \ \ \forall f \in ...
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83 views

Rings having the same characters but not isomorphic.

I want to show that these two rings have the same characters but they are not isomorphic for $\nu>2$ Thank you for helping. $$H=k+kt^{4\nu}(1+t)+kt^{6\nu}(1+t)+kt^{7\nu}(1+t)+k[[t]]t^{8\nu}$$ ...
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7answers
2k views

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable? Often times I "feel" as if I can write a proof to an exercise but most ...
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3answers
295 views

Is formal logic necessary for pure/“higher” mathematics?

I'm asking this as an autodidact who wants to learn math rigorously for its own sake. And I was just wondering if understanding proofs could be achieved without a formal grounding in symbolic logic. I ...
2
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0answers
64 views

“Teach yourself” guides [closed]

I really liked Teach Yourself Logic: A Study Guide by the user Peter Smith. It is a thorough guide how to teach yourself logic and set-theory from scratch up to any level with book recommendations for ...
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2answers
100 views

Second Course in Number Theory - Self Study

I just finished a first course in number theory using Dudley's Elementary Number Theory. This was by far my favorite math course and I want to learn more number theory this summer. As far as ...