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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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 ...
6
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0answers
95 views

How to relearn undergrad and tackle grad mathematics? Want to become a better mathematician!

I am a student who has just completed their degree in pure math. Unfortunately, my undergrad was a very... Unpleasant time for me due to personal reasons. Although math is accepted as a very "poorly-...
6
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0answers
91 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 ...
6
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0answers
95 views

Concrete examples and computations in differential geometry

I've been studying differential geometry by myself for some time now. I studied a fair amount of the basic general theory and gone through a lot of the exercises from several textbooks. Lately I ...
6
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449 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?
6
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243 views

What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, etc......
6
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0answers
192 views

Advice on learning mathematics

I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics ...
6
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0answers
224 views

The high road to learn algebraic geometry

Suppose that a student has a basic knowledge in commmutative algebra at the level of the Atiyah-MacDonald. What do you think about the following steps to learn algebraic geometry? step 1: read "...
5
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256 views

Good starting point for learning noncommutative geometry?

Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical ...
5
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0answers
172 views

WKB and asymptotic behavior of second order differential equation

I want to study the large $x$ solution to a Riccati equation. After listening to the lectures on Mathematical Physics by Carl Bender, I have fallen in love with asymptotic analysis. But, by no means ...
5
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0answers
1k views

Fubini's Theorem for Infinite series

In the book what I've read, there is one point where the author suggest to begin the proof of the Fubini's Theorem for infinite sum in the case when is non-negative after this try to generalize. But ...
4
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407 views

How much algebra is necessary to understand Rudin's “Real and Complex Analysis”?

I've been reading up on the finite element method, and the text many people recommend is The Mathematical Theory of Finite Element Methods by Brenner and Scott. As part of the background, the authors ...
4
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0answers
112 views

The canonical height of a point on an elliptic curve

I am struggling with exercise 3.3 in Silverman-Tate Rational Points on Elliptic Curves. Here is the paraphrased problem with necessary background: Let $C:y^2 = x^3 + a x + b$ be a nonsingular cubic ...
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0answers
98 views

How to select good exercises?

I'm studying on Rudin "Principles of of Mathematical Analysis" which I begin to find as a good and complete reference. I wonder how many exercises shall I do at the end of each chapter ? In case of ...
4
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0answers
153 views

Compact family of Lip functions under the sup norm metric, proof verification.

Hi everyone I'd like to know if the following is correct, I'd appreciate your opinion and also any suggestion to improve my argument. Thanks in advance for your time. If $(K,d)$ is a compact ...
4
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0answers
392 views

Isolation and self-study

A little background: I am currently a sophomore (studying mathematics) at an unknown university in the Middle East. My mother is European so it does not make sense to study mathematics in the Middle ...
4
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0answers
91 views

Prove that a series is $O(t^a)$.

Consider the series $$ u(t,x) = \sum_{i \geq 1} {u_i(x) t_1^i } + \sum_{i+2j \geq k+2, j\geq 1} {\varphi_{i,j,k}(x) t_1^i t_2^j y^k} $$ where $t \in \tilde{\mathbb{C} \setminus \{ 0 \}}$, $x$ is ...
4
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0answers
142 views

Where do I go from Linear algebra past Calc III to try to learn complex physics (relativity and quantum group theory)?

I'm mainly a programmer, but I have a love for Mathematics that's been, well, insatiable. I've had my eye on learning Quantum Groups and Relativity, but I want to stay in something I can do with ...
3
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0answers
71 views

Self Learning — Number Theory

I was wondering if there were any good online courses/lecture videos (preferably courses/videos but books would work too) for self learning algebraic number theory. I have seen sites like MIT ...
3
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0answers
56 views

Is It Worth It Working Out Every Practice Problem In Math? (Without a calculator)

I'm bouncing back between trig, algebra, and calc books. I've noticed that most of the problems at some point seem to distill into very tedious arithmetic. It is nice to have the prowess of ...
3
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0answers
109 views

What's the right way to read Princeton companion to mathematics?(for non-mathematician)

I am thinking of ways,how one(who is not a mathematician, but wants to know what's going on in the field of mathematics) can properly read Princeton companion to mathematics to make sense of it. I ...
3
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0answers
51 views

Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
3
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0answers
87 views

How to think/see point-set topology abstractly?

I've started learning point-set topology this semester. I've learned basic material about: topology on a set topological space open sets closed sets clopen sets closure neighborhoods interior point ...
3
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0answers
179 views

On the importance of the Riesz–Markov–Kakutani representation theorem.

I am following big Rudin and I have arrived at the representation theorem. Before doing the full long proof I would like to know what results are based on this theorem that for completeness I state ...
3
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0answers
80 views

What minimum subset of fields of mathematics is needed to understand homomorphic encryption?

Without the luxury of full undergraduate training in mathematics, if one worked part time could the community list the smallest set of mathematical fields needed to understand homomorphic encryption? ...
3
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0answers
104 views

Geometry textbook question

I have just started the textbook Geometry: its elements and structure by Alfred Posamentier. The first set of questions refers to the following diagram: The very first question is "What is the ...
3
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0answers
61 views

Finding dominating integrable function

Hi everyone I'm not completely familiar with this kind of argument and I'd appreciate if someone can help me to see if the argument is correct and also any suggestion to improve it. Thanks in advance. ...
3
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0answers
91 views

Periodic curve on unit sphere and torsion

Define $S^2 \subset \mathbb{R^3}$ be the unit sphere. Suppose that $\alpha :\mathbb{R} \to S^2$ is a differentiable curve parametrized by arc-length. a) Show that $\kappa(s)$, the curvature of $\...
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0answers
70 views

How to approach real analaysis

I'm just starting first year in university in Europe and here there there is no Calculus, instead you jump right into Analysis. The trouble is, for some time I self-studied through US style books and ...
3
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0answers
256 views

Rotate the unit circle by a fixed angle, what does happen is $\alpha/\pi$ is rational? and irrational?

Hi everyone I´d like if someone could say me if the following is correct. Thanks in advance Rotate the unit circle by a fixed angle $\alpha$, say $R: C \rightarrow C$; $(1,\theta)\mapsto (1,\...
3
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0answers
398 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 -...
3
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0answers
128 views

Cauchy-Euler Equation of order $n$

What I wish to prove is that for a Cauchy-Euler equation of order $n$, the substitution $x=e^{t}$ transforms it into a linear differential equation with constant coefficients. To put it as a theorem: ...
3
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0answers
55 views

Where does this series converge?

Let $ \{r_1, r_2 ,r_3,... \}$ be an enumeration of $\mathbb{Q}$. For each $r_n \in \mathbb{Q}$ define: $$u_n(x)=\begin{cases} 1/{2^n} & x>r_n \\ 0 & x \leq r_n \end{cases} $$ and let $$h (...
3
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0answers
86 views

Prime divisor of the form $2kp+1$ that divides $2^p-1$

The book that I'm reading (Elementary Number Theory by Underwood Dudley) gives a Theorem: If $p$ and $q$ are odd primes and $q|a^p-1$, then either $q|a-1$ or $q=2kp+1$, for some integer $k$. Then it ...
3
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0answers
71 views

Totient Function: if $\gcd(m,n)=2$, then $\varphi{(mn)}=2\varphi{(m)}\varphi{(n)}$

Suppose we know that $(m,n)=2$. Show that this implies that $\phi{(mn)}=2\phi{(m)}\phi{(n)}$. My attempt: So let $m=p_1^{r_1}p_2^{r_2}...p_k^{r_k}, n=p_1^{s_1}p_2^{s_2}...p_k^{s_k}$. Then $(m,n)=...
3
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0answers
131 views

Examples of Talagrand's inequality

I am trying to understand Talagrand's inequality and when it gives better results than Markov/Chebyshev/Chernoff. However I find the formal definition hard to understand. Are there any nice simple ...
3
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0answers
197 views

Interchange of finite sum with convergence sequences.

Hi everyone I'm wondering if the following proof is correct (to be honest at the beginning I have some troubles to understand what the sequences of the sums of convergent sequences has to be, but I ...
3
votes
0answers
888 views

Find a conformal map from the disc to the first quadrant.

Find a conformal mapping of the disk $x^2+(y-1)^2\lt 1$ onto the first quadrant $x, y \gt 0$ I did something, which may be false or not, I cannot exactly say anything. I used the composition of ...
3
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0answers
157 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
2
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0answers
28 views

Specific decomposition of quadratic 2x2 matrix

Consider the matrix $A = \begin{pmatrix} 1 & 1 \\ -1 & 3 \end{pmatrix}$. Prove that there is only one decomposition A = B + C with $B,C \in \mathbb{R}^{2x2}$ that fulfill the following ...
2
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0answers
38 views

Book recommendations for someone with a B.S in mathematics - Self study

I have finished my B.S degree in mathematics recently and I would like to continue to study on my own. I'm looking for books in all subjects you can recommend. I want to start each subject from its ...
2
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0answers
19 views

Help needed with partial products

I understand that 4 times 6 tens is 240. I am now being asked to add the extra tens to 240. how do I do that? are the extra tens 40. so if I add 240+40=280 is that the answer?
2
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0answers
28 views

Estimator bias and consistency

Let $x_1, x_2, \ldots,x_n$ be a simple random sample from a random variable $X$ with support $\{0,1,2,3,4\}$ and probability function $p(0)=\frac{5}{12}(1-\lambda)^2$, $p(1)=\lambda$, $p(2)=\lambda(1-\...
2
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0answers
26 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 ...
2
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0answers
41 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; \limsup{a_n}...
2
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0answers
39 views

Between Oksendal and Karatzas books

I finished Oksendal "SDE , an introduction with applications" , did most of the exercises (not all with success, but I read the solutions for those); my next project would be to read the Karatzas "...
2
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0answers
42 views

What is the link/ relationship and difference between probability measure, Bernoulli measure, Lebesgue measure, Borel measure and Hausdorff measure

I am having difficulty in understanding what is the difference between probability measure and Bernoulli measure. Is the latter used when the random variable has a Bernoulli distribution? What is its ...
2
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0answers
83 views

Rationale behind construction of measure theory from semirings

I am studying a book (Aliprantis & Burkinshaw, "Principles of Real Analysis") that, in order to introduce the concept of measure, starts from semiring. In particular the authors state that: "...
2
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0answers
35 views

Integrating product of logs

I am failing to integrate $$ \int \log {\bigg(\frac{a}{x}\frac{x-c}{a-c}\bigg)^{s-1}} \log{\bigg(\frac{b}{x}\bigg)}\bigg(\frac{c}{x}\frac{1}{x-c}\bigg) dx $$ for a positive integer $s$, and real ...
2
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0answers
26 views

What is the purpose of continuous and differentiable dependence

In learning Gronwall's inequality you also get to learn about continuous an differentiable dependence. I know the theorems but I have no idea about their application. What is the big idea of ...