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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32 views

Recovering past years [on hold]

I am a senior math student studying at an average college. I was familiar with abstract algebra and number theory before I start the college. However, for the past 4 years, I have faced some ...
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0answers
22 views

Space, symmetry and undecidability. [on hold]

So I went to a lecture a few months ago on symmetry. My question is at what point does symmetry or group theory become undecidable? How come I improve my understanding on trivial symmetry and ...
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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
92 views

I want to self study systematically pure mathematics? Where do I start? [on hold]

I am an undergraduate student in Mechanical Engineering and I am highly interested in studying pure mathematics systematically.I have a fair amount of knowledge on real and complex analysis, ...
1
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1answer
38 views

Why is the map $f(x)=e^{i2\pi x}$ from $[0, 1)$ to the unit circle continuous?

This seems to be a really silly question, I just couldn't think it straight. The definition of a continuous map: $f: X \to Y$ is continuous if for any open set $U$ in $Y$ , $f^{-1}(U)$ is open in ...
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1answer
43 views

Computation of large powers

How do I check if $2^{123456789}$ is divisible by 9? I tried using modular exponentiation but it is way too tedious. Is there an easier or faster way to solve it? Thanks!
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3answers
117 views

Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
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0answers
34 views

How do I memorize mathematical proofs?

I first started wanting to know about the derivation of theorems because certain ones help you memorize the theorems better. But as I take harder math classes, it turns out better for me to use ...
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0answers
31 views

How to solve system of equilibrium probability state equations

I have started studying markov chains where i have these statistical equilibrium probability state equations.These equations are solved for a particular case $s_1=4,a_1=5,s_2=2, a_2=1$ and a 15*15 ...
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2answers
85 views

Prove that if $G$ is an Abelian group, then for all $a,b$ in $G$, $(ab)^{n} = a^{n}b^{n}$

This question have already been asked on this site, but i could not understand the details so i ask it again. Also what i have done is that first for $n=1$ its trivial, for $n=2$ we have ...
0
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1answer
371 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) $(D^3-3D^2D'+4D'^3)u=0$ ...
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4answers
571 views

To prove that every element of $G$ has finite order.

Let $G$ be a group such that the intersection of all its subgroups which are different from $e$ is a subgroup different from $e$. Prove that every element of $G$ has finite order. Can i get some ...
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1answer
55 views

To show a function is Riemann integrable.

Given a function $$v(x) =\begin{cases} 0&\text{if } x=0\\ 1&\text{if }x\in(0,1]\end{cases}$$ How do I show that $v$ is Riemann integrable in $[0,1]$? Hints on how to do this??
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3answers
248 views

If $M, N$ are finite dimensional vector spaces with same dimension, then if $M$ is subset of $N$, then $M=N$.

If $M, N$ are finite dimensional vector spaces with same dimension, then if $M$ is subset of $N$, then $M=N$. I think i need to show that both vector spaces are spanned by the same bases in order to ...
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0answers
165 views

Suppose a finite set $G$ is closed under associative product and that both cancellation laws hold in $G$. Prove $G$ must be a group.

Suppose a finite set $G$ is closed under associative product and that both cancellation laws hold in $G$. Prove $G$ must be a group. I somehow need to prove identity, inverse, that closure holds to ...
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1answer
593 views

If $G$ has no non trivial subgroups, then show that $G$ must be of prime order.

If $G$ has no non trivial subgroups, then Show that $G$ must be of prime order. This question is from Herstein Page 46 Question 3. Attempt: Let $G$ has prime order(say $p$). By Lagrange theorem, ...
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3answers
166 views

How to Catch Up?

I am finishing up my bachelor's degree in mathematics at the University of North Florida, and I plan on going to graduate school, but I feel very behind. One of my professor's gave us this problem: ...
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1answer
514 views

Prerequisites for Bredon's “Topology and Geometry”?

My background in topology is the first 6 chapters of Munkres's "topology" and in algebra Herstein's "Topics in Algebra". Both of them I self studied. A look at the table of contents of Bredon's ...
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2answers
83 views

recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
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0answers
63 views

Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read? [closed]

I've noticed that many books that are difficult to read are considered some of the best. Why does hard to read indicate that it is rigorous? For example: Rudin, Apostol, Lang, Hungerford, Ahlfors, ...
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1answer
372 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 ...
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1answer
25 views

Weak law of large numbers without figuring out the distribution.

let $X_{1},X_{2},\dots$ be i.i.d. random variables with common probability density function. $$f(x)=\begin{cases} \frac{1}{2}e^{-\left(\frac{x-1}{2}\right)},& \text{if } x>1\\0,& ...
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4answers
2k views

What is a good book to study classical projective geometry for the reader familiar with algebraic geometry?

The more I study algebraic geometry, the more I realize how I should have studied projective geometry in depth before. Not that I don't understand projective space (on the contrary, I am well versed ...
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0answers
44 views

How to learn math by self-teaching [Without books, or outside help]

I'm thinking along the lines of attempting to explore mathematics by making my own discoveries as if it's the new frontier. As if I was a mathematician from 2000 B.C. I know this sounds really ...
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1answer
683 views

video lectures on Lie algebra

Is there any video lecture on first course on Lie algebra available online? , by the first course I mean, The complete book of Introduction of Lie algebra and its representation theory by James ...
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1answer
34 views

Testing of hypothesis

Following is a question from my textbook. My approach is different from one explained in the book. I cannot understand what is wrong with my solution. I have explained both solutions below. Kindly ...
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0answers
18 views

Showing there is a cartesian coordinate system in Euclidean geometry.

I'm pretty sure I should just show there is a bijection between the points in Euclidean Geometry and elements of $\mathbb{R^2}$. How do I do this?
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3answers
7k views

Functional analysis textbook (or course) with complete solutions to exercises

I am a Ph.D. student in economics and I plan to study functional analysis by myself either this winter or the next summer. I am currently looking for a textbook, and since I am studying it by myself, ...
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1answer
24 views

What does “modulo equivalence relationship” mean?

I am reading something on completion of metric spaces and it says: Let $\hat S$ be $\mathcal{C}$ modulo equivalence relationship of co-Cauchy sequences. Where $\mathcal{C}$ is the set is all ...
0
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1answer
59 views

Re-learning Maths for physics (particle and space) [closed]

I know there's a lot of "how do I learn maths" questions out there but I wanted to lay down my history and interest to possibly get a better approach. When I was in secondary school ( high school ) ...
0
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0answers
23 views

Is reading a textbook and doing problems the best way to self-study game theory?

In preparation for a research position, I'm supposed to self-study the first six chapters of Osborne Introduction to Game Theory over the next two weeks, and complete corresponding problem sets. Is ...
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7answers
13k 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?
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1answer
44 views

Textbook Accompanying Naive Set Theory

I'm in the process of self-studying from the very popular Halmos book "Naive Set Theory" and I must say I can say only the best about the book. However, although the book has some excercises I would ...
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0answers
8 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 ...
4
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1answer
66 views

Looking Away from the Temptations of the Solution Key [closed]

This is quite a soft question and I believe that it is a very important one and one that many self-learners can relate to. So I recently was going through a problem set in topology and I came across ...
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2answers
96 views

Should I continue trying to solve Spivak or pick up a lighter book?

Some background: I have no mathematical maturity. Last year I completed my schooling and the only time I picked up a math/science book was when exams were due, needless to say I haven't actually given ...
2
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1answer
730 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 ...
2
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0answers
21 views

Website for sharing solutions/proof verification?

Is there a website for sharing solutions to exercises in math books? I'm self-studying math and I find solution manuals like this very helpful. When I do an exercise, I usually scribble down a few ...
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1answer
30 views

$f(\alpha _I) \ne 0$

I need help in this question... Let $F$ be a field of characteristic zero and let $V$ be a finite dimensional vector space over field $F$. If $\alpha _1,\dots , \alpha_m$ are finitely many vectors in ...
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3answers
729 views

Math blogs, pros and cons for writers?

I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics. But now I am more interested in the writers' perspective, and I ...
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0answers
13 views

Exterior Robin Boundry Condition

Exterior Robin boundary is expressed as the following in the book $\partial{u}/ \partial{v}-\lambda u=f$ on the boundary and $v$ is normal. Also u satisfies Laplace Equation in exterior domain in ...
4
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1answer
171 views

Properties of Weak Convergence of Probability Measures on Product Spaces

EDIT: For the Bounty, I made a substantial edit revision concerning the structure of the question, to make it more readable (hopefully). Moreover I added a question on problem 2.7 of Billingsley’s ...
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1answer
69 views

Soft question — I need books and exercise books that will be working on my fundamental skills.

I need help, urgently. I acquired a book called: Mathematics, Its Content, Method and Meaning. Now the problems is the book doesn't provide me with any exercises. I was searching for a book that would ...
1
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1answer
23 views

infinite subset of discrete metric space is not compact

The question is Im not really sure how to go about this So far i am trying to show that for an open cover of the infinite subset X, there isn't a finite sub cover and therefore X is not compact I ...
0
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0answers
49 views

Comparing the methods of applied mathematics to computer graphics

As an applied mathematician working towards my PhD, I have some personal interest in aspects of computer graphics and procedural animation. Looking up people and reading papers in the field of ...
0
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1answer
194 views

To prove in a Group Left identity and left inverse implies right identity and right inverse

Let $G$ be a nonempty set closed under an associative product, which in addition satisfies : A. There exists an $e$ in $G$ such that $a \cdot e=a$ for all $a \in G$. B. Given $a \in G$, ...
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2answers
67 views

What are some good resources to review basic university calculus, years later?

So, I have reason to be returning to school, many years (5+) after my last attendance; and although I took (and passed, barely, after much strife) Calculus 1 and 2 at my previous university, I am very ...
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3answers
56 views

Permutations and combinations textbook recommendations

I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. ...
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2answers
382 views

To prove any two basis of Finite Dimensional Vector Space have same number of elements

To prove any two basis of Finite Dimensional Vector Space have same number of elements If i take bases as $S_!$ = {$\alpha_!$ ,$\alpha_2$ ,....$\alpha_n$ } $S_2$ = {$\beta_!$,$\beta_2$ .... ...
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2answers
346 views

Baby Rudin Chapter 4 Exercise Questions 5 and 6

4.5: If f is continuous on a closed set in $R^1$, prove there exist continuous functions $g$ on $R^1$ such that $g(x)=f(x)$ for all $x \in \mathbb{E}$. 4.6: Suppose $\mathbb{E}$ is compact, and prove ...