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 ...
7
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536 views

Convex analysis books and self study.

I have taken some courses in Convex optimization. Now I would like to know a little bit more about the pure mathematical side. Is there any good books in convex analysis? I have read and worked with ...
6
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129 views

Finitely additive function on an infinite set, s.t., $m(A)=0$ for any finite set and $m(X)=1$ (constructive approach)

Other exercise which I found in Dudley's Analysis book: Show that there is a measure on a infinite set $X$, defined on $2^X$ s.t. is finitely additive, $m(A)=0$ for any finite set and $m(X)=1$. ...
6
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203 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, ...
6
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0answers
171 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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201 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 ...
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285 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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72 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 ...
4
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90 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 ...
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108 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
306 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 ...
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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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595 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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0answers
559 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 ...
4
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0answers
128 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
38 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
172 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 ...
3
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0answers
72 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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91 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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53 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
78 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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65 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 ...
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140 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 ...
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299 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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104 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
118 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 ...
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49 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 ...
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0answers
77 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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66 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 ...
3
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0answers
121 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
140 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
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0answers
142 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
14 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 ...
2
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0answers
37 views

Help with Definition of Limits (Finding a delta given epsilon)

The problem says: Find a $\delta$ such that $|f(x)-l| < \epsilon$ for all x satisfying $0 < |x-a| < \delta$ when $f(x) = x^4; l = a^4$. What I did so far was $|x^4-a^4| < \epsilon$ so ...
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0answers
21 views

Explanation - singling out terms

i am trying to understand the derivation of the mean field equations - and my text books shows the following formulas (as part of a larger derivation). $$L(q_j)=\sum_{x}\prod_{i}q_i(x_i)[\log ...
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0answers
50 views

equivalent form of almost sure convergence

Consider random variables $X_1, X_2, \dots$ and $X$ on $(\Omega, \mathcal F, \mathbb P)$. We say that $X_n$ converges to $X$ almost surely if $$\mathbb P\left(\lim_{n \to \infty} X_n =X\right)=1.$$ It ...
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0answers
26 views

Show that $f$ is constant on the convex set $S$

Call a set $S$ convex if whenever $x,y\in S$, then $tx+(1-t)y\in S$ for any $t\in[0,1]$. Suppose that $S$ is an open convex set in $\mathbb R^n$ and suppose that $f:\mathbb R^n\to\mathbb R$. If ...
2
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0answers
56 views

How do I make sure that I've learned and mastered a part of the Visual Complex Analysis book?

So I'm reading Visual Complex Analysis by Tristan Needham. It's a beautiful book that's not very hard to understand at all; however, I just don't know if I have sufficiently learned what I'm supposed ...
2
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0answers
18 views

Discrete-Time Stochastic Calculus and Stopping Times: Resources

In my measure-theoretic probability course we covered what the professor called "discrete-time stochastic calculus". Essentially, it was a three part method for computing certain quantities such as ...
2
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0answers
46 views

Reference request - Problem book by subject

I'm looking for good problem textbooks for self-study. I know only of two of this sort: "Introduction to Measure Theory" by Terry Tao, and "Problems in Algebraic Number Theory" by Esmonde and Murty. ...
2
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122 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 ...
2
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0answers
58 views

Double Integral of an Exponential Function with an Absolute Value in the Numerator of the Exponent

This is a question related to statistics, but my major concern relates to the setup and evaluation of integrals. So I decided this question was better suited for Mathematics Exchange than CV. I know ...
2
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0answers
101 views

Unable to understnad how a map is one-to-one in the proof for conjugacy

I need to prove that amp is a homeomorphism. I am following the basics from the book For the proof I have taken the help of the book "An introduction to dynamical system" Download link ...
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0answers
61 views

Can anyone check if this correct?

Convert to spherical coordinates and evaluate:$$\iiint_{E}z(x^2+y^2+z^2)^{-3/2}dV$$ where E is the region satisfying the following inequalities:$$x^2+y^2+z^2\le16,z\ge 2$$ This is what i have done so ...
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0answers
22 views

Uniform probability bound - checking my understanding

Let x and y be two independent random variables. What is the difference between (1) $P_x[\forall y, f(x,y) < \epsilon] >1- \delta$ (uniform bound), and (2) $\forall y, ...
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0answers
82 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 ...
2
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0answers
90 views

What is the best way to master my algebra skills without taking an algebra class?

I was in advanced math my entire life. I got through all the math I needed for my original degree. 8 years later here I am changing degrees and I need more math. I just took calculus I and I passed ...
2
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0answers
68 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? ...
2
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0answers
71 views

Open sets in the topology of weak convergence

I do have various questions regarding the topic of probability measures on polish spaces in general, thus I am trying to divide them in “small” subquestions. Hence, this is my first question on this ...
2
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0answers
66 views

Help with a Proof of exercise 7.3 Apostol on two different definitions of the Riemann integral.

This is a follow-up to this question. Here I ask to check my work and improve the final part that I feel is missing some important steps: So to prove what is asked for in the link above (I am not ...