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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28 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
25 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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3answers
97 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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3answers
159 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: ...
4
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2answers
81 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
61 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
23 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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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
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 ...
1
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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 ...
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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 ) ...
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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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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
65 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
95 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 ...
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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 ...
1
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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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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 ...
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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 ...
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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 ...
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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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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1answer
58 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
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1answer
32 views

$W$ intersection of $(n-1)$ dimensional subspaces

I have got a good (I think so) intuition of this problem but I am not being able to write down the crucial steps correctly. Let $V$ be a $n$ dimensional vector space over field $F$ . Let $W$ be a ...
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0answers
79 views

Next Step for Self-Learning

I am an undergraduate mathematics major and recently completed a course in real analysis. While I enjoyed this course it left out many topics that I would have liked to learn because of time ...
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2answers
29 views

Existence of maximum and minimum

Let $f:\mathbb{R}_+\rightarrow \mathbb{R}$ be continuous and such that $f(0)=1$ and $lim_{x\rightarrow+\infty}f(x) = 0$. Prove that $f$ must have a maximum in $\mathbb{R}_+$. What about the ...
0
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3answers
61 views

Express $2\cos (n\theta)$ in terms of $z$ [closed]

How can I show that $$2\cos(n\theta)=z^n + \frac{1}{z^n}$$ if $z=\cos\theta+i\sin \theta$ Can some one help me? thx!
2
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1answer
36 views

Study materials to help understanding the generalized Stokes' theorem both intuitively and rigorously?

Dear MSE: My goal is to understand the generalized Stokes' theorem both intuitively and rigorously. Could someone give advices or recommend study materials to help understanding the generalized ...
2
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0answers
23 views

where to find good review resources? [closed]

I am taking my certification test for secondary mathematics next month and I am extremely overwhelmed by the amount of stuff i need to brush up on. http://www.mttc.nesinc.com/PDFs/MI_field022_SG.pdf ...
3
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4answers
215 views

Proven Studying Habits for a Limited Memory? [closed]

I learned Calculus many years ago and at the time I thought that I knew it well. (i.e. got good grades, was employed as a tutor, etc) I am now going back and studying Calculus again with the hopes of ...
5
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3answers
212 views

How to determine if I'm talented enough to study math? [closed]

After getting Bachelor's degree from Computer Science I changed my field to Applied Mathematics. The previous degree was mostly programming-oriented, so I know quite a lot about software engineering, ...
2
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2answers
61 views

What is tangent to a curve or function?

When I read my textbooks or even type "what is a tangent?" on google, I have always got an answer similar to these lines: "A straight line or plane that touches a curve or curved surface at a point, ...
3
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4answers
205 views

Measure theory for self study. [duplicate]

I am having good knowledge of Elementary Real analysis. Now I like to study measure theory by myself (self-study). So please give me direction from where to starting? Which book is good for starting? ...
3
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0answers
44 views

Self-studying Information Geometry

I was recently exposed to the topic of Information Geometry by a friend of mine, and was looking for a good book to begin self-studying this topic. Any suggestions? Also, what subject matter would ...
3
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1answer
55 views

How to interpret the notation of a formula?

I was reading a paper where the property of light known as Illuminance, for a specific setup (as in the figure) is given with the following formula: The description below the formula says: ...
3
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4answers
127 views

Help Self-Studying Calculus

I wanted to learn calculus but I have been told that you can't learn it without first learning elementary algebra. Can someone help me devise a plan for self-study because I don't know were to begin.
2
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2answers
64 views

Algebra review for Spivak Calculus

I got a bit bored with High School maths so I picked up a copy of Calculus by Spivak. I am really enjoying the book and have found that the proofs and theorems aren't as hard as others have made them ...
2
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0answers
29 views

Cesaro summation and convergence

I am trying to makes sense of the proof to following problem: Given: $A_n = \displaystyle \frac{\sum_{k=1}^n a_k}{n}$. Can $\{A_n\}$ converge if $\{a_n\}$ diverges; $\forall n,a_n>0; ...
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13 views

Checking if estimators are sufficient

For an i.i.d. sample of random variables Xi distributed according to a normal distribution, known variance. I found a sufficient statistic—the sample mean. How do I check if other statistic like ...
5
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1answer
70 views

Important topics to know in Algebra [closed]

I'm trying to prepare for graduate algebra but after looking at Dummit and Foote I realized that there's a lot of material (1000 pages). Which topics do you think a student should study in D&F to ...
3
votes
1answer
65 views

self-teach: In what order should I structure my studies?

I'm a 19 year old, who will be 20 in may. I didn't go to the greatest high school, and I didn't get the proper education to prepare me for college. I need to make a study plan for myself to truly ...
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0answers
61 views

Proof that Poisson process interarrival time $T(N+1)-T(N)$ with $T(N)<t<T(N+1)$ is Gamma$(2,\lambda)$

Suppose a Poisson process $N(t)\sim\text{Poisson}(\lambda t)$. Let $T(N)$ be the time of the last arrival before time $t$ and $T(N+1)$ be the time of the first arrival after time $t$. From ...
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1answer
90 views

Given undergraduate Algebra background, which introductory Homological Algebra textbook?

I have read the answer for graduate-level Algebra background and all answers in stackexchange and mathoverflow discussing Homological Algebra textbooks. But none of them directly answers my question, ...
0
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0answers
18 views

Let W = X1/(X1+X2), how to prove **W** has a beta distribution?

I am confused when I come across this question, could anyone help? Thanks! Let X1 and X2 have independent gamma distributions with parameters α, θ and β and θ respectively. Now we let W = X1/(X1+X2), ...
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2answers
114 views

How do mathematicians come up with beautiful equations [closed]

In Linear regression for example, we can find weights as following: $\hat{\beta}=(X^{T}X)^{-1}X^{T}y$ how someone invented this? I mean how do they transform a problem to such an equation. And ...
3
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3answers
105 views

Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
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0answers
58 views

Proving a degree sequence satisfy Chvatal’s criterion

How can I prove that a degree sequence satisfy Chvatal’s criterion? I know that i must prove that sequence A is Hamiltonian if and only if A' is hamiltonian but i am lost on where i should start. for ...
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0answers
21 views

how to construct non-Hamiltonian graphs

I have been asked to construct a hamiltonian graph and a non-hamiltonian graph using the same degree sequence. I have had no problem constructing the hamiltonian graph however I am finding it ...