Questions about studying mathematics without formal instruction.

learn more… | top users | synonyms (1)

5
votes
0answers
159 views

Study group for working through Spivak/Wilson [closed]

I'm planning on working through Spivak's Calculus or Wilson's "Introduction to Graph Theory" and was wondering if anyone here might be interested in joining a study group for it. There's no ...
4
votes
1answer
110 views

Advice regarding best-practice mathematics / categorial logic.

A good heuristic is: If it doesn't cost anything, generalize. In particular, if we have a theorem, and a proof thereof, then we ought to look for a maximal generalization of this theorem, ...
0
votes
1answer
91 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) $(D^3-3D^2D'+4D'^3)u=0$ ...
6
votes
0answers
146 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, ...
0
votes
1answer
57 views

Doob's inequality application

I'm working through an example of the application of Doob's inequality in Durrett: Let $X_m$ be a submartingale, and define $\bar{X}_n = \max\limits_{0 \leq m \leq n} X_m^+$. Let $\lambda ...
1
vote
1answer
54 views

Please explain. Really I dont understand and I need to learn. Pde: : example of finding particular integral

When we look at the solution part, there is a statement The PI of the given PDE is obtained as follows After the statement, I dont really understand all of the calculation. Espacially, After the ...
1
vote
0answers
69 views

Cut-off Subtraction in Coq

I am new to the world of computer assistant proof programs in general, and Coq in particular. As a result, I have sought to prove some elementary results about integers as a way to … At the moment, I ...
0
votes
1answer
172 views

Compute the geodesic curvature of any sphere on a sphere.

Compute the geodesic curvature of any sphere on a sphere. Again there exists its answer, but not understandable for me. Please explain it explicitly. Thank you so much. (If required, i can post ...
0
votes
0answers
45 views

Mathematics Necessary for General Relativity and Quantum Physics.

I am a self-learner in Mathematics. I was wondering, given some background in calculus and a tiny bit of topology and group theory, what series of documents I would have to learn to be able to ...
3
votes
1answer
296 views

Good book for logic self-study

I know a similar question has already been asked, but can anyone suggest a good book on mathematical logic that includes answers to exercises? I am looking for something that is conducive to ...
1
vote
2answers
44 views

Matrix and eigenvectors

$\quad$The matrix $\mathbf A=\frac19\begin{bmatrix} 7 & -2 & 0 \\ -2 & 6 & 3 \\ 0 & 2 & 5 \\ \end{bmatrix}$ has eigenvalues $1$, $\frac23$ and $\frac13$n ...
0
votes
2answers
83 views

Is there any formula for summation?

$$0.01\sum_{x=1}^{30}(0.99)^{x-1} = 1-0.99^{30}$$ I wonder if there is a formula for summation and I want to know. Would anyone mind telling me? It would be better for me to solve problems, like the ...
0
votes
2answers
19 views

sum calculation

i have the follwoing values $\sum_{i=1}^{n} x_{i} = 34$ $\sum_{i=1}^{n} x_{i}^{2} = 262.22$ $a = 3.78$ $n = 9$ and i want to calculate $$ \sum_{i=1}^{n} (x_{i}-a)^2 $$ i thought this may work ...
0
votes
0answers
178 views

Orthonormal matrix and diagonal matrix.

Consider the matrix $$A=\begin{pmatrix}3&-1&1\\-1&3&-1\\1&-1&3\end{pmatrix}.$$ (a) Verify that $x=[3\,\,4\,\,1]^T$ is an eigenvector of the matrix $A$ and determine the ...
1
vote
1answer
154 views

Does De Moivre's Theorem hold for all real n?

I have seen the proof by induction for all integers, and I have also seen in a textbook that we can use Euler's formula to prove it true for all rational n, but nowhere in the book does it say its ...
1
vote
1answer
73 views

Second fundamental form question.

Honestly, I dont have any idea for that question I posted. Please can someone help me solving the question. Thank you.
2
votes
1answer
51 views

Vectors and orthonormal matrix

For 2(a)(i), are the length of a =Sqrt(14) and b = sqrt(38)? For (ii), is the angle = 4.31? For (iii), is the answer 3.73? For (iv), is the answer -i+j+k? For (b) to (e), I have no idea what I ...
0
votes
1answer
93 views

Linear Algebra: Matrix and determinant

For 1(a), is $p =12$ and $q = 6$? For b(i), is the answer $a=b$ where $a$ and $b$ do not equal to 0? for b(ii), is the answer $a\ne b$? for b(iii), is the answer $a=b=0$ and the solution is ...
2
votes
1answer
105 views

The second fundamental form and isometry.

What is the effect on the second fundametal form of asurface of applying an isometry of $\Bbb R^3$ ? Or a dilation? I posted its answer. This answer is not understandable for me in general. ...
0
votes
1answer
32 views

Surface patch are taken different for sphere, but their second fund. forms are not completely different.

Shpere First of all, I take the surface patch for sphere $$\sigma(u,v)=(\sin u\cos v, \sin u\sin v, \cos u)$$ And then I calculated its second fundametal form. And I got the following result $$ ...
0
votes
1answer
120 views

Why first fundamental form and second fundamental form are the same?

Surface of Revolution $\gamma(u)=(f(u),0,g(u))$ and $\sigma(u,v)=(f(u)\cos v, f(u)\sin v, g(u))$ Fist of all, I calculated the first fundametal form for surface of revolution. And I obtained ...
0
votes
1answer
112 views

Transition map for Möbius band in differential geometry.

Calculate the transition map $\phi$ between the two surface patches for the möbius band. These two surface patches are the following $U=\{(t,\theta) \ | -1/2\lt t\lt 1/2,\ \ 0\lt \theta \lt ...
0
votes
0answers
22 views

Kaczmarz's Projection Algorithm

I am trying to understand the derivation of the following formulas given in my lecture (sadly without any further explanation). It says the key idea is that each new prediction error is of the form ...
0
votes
1answer
61 views

Torus in differential geometry.

I want to write separately parametrizations (surface patches) $\sigma$ for torus when (1) x-axis rotation in the first part of the picture and (2) y-axis rotation in the second part of the picture. ...
3
votes
1answer
200 views

Lawvere theories: an equivalence.

I'm having trouble understanding Lawvere theories (as defined below). Definition: A Lawvere Theory is a category $\mathcal{L}$ with finite products and with a distinguished object $A$ such that ...
2
votes
1answer
72 views

Primitive Recursion Functions (Programs)

The set $F_{n}$ of primitive recursive function symbols of arty $n$ can be defined inductively as \begin{array}[lr] & Z, \text{Succ} \in F_{1} & \\ \pi_{j}^{n} \in F_{n} \quad \text{for each} ...
-2
votes
4answers
140 views

Linear Algebra and Set Theory book recommendations.

I would like to studying linear algebra and set theory. Does anyone have a a good recommendation of books/resources/etc.?
0
votes
0answers
26 views

Error of the norm of solution in linear least-squares

How can we estimate the solution norm ($\Vert x \Vert$) error, separate from the solution ($x$) error in solving $Ax=y$ (linear least-squares problem)? Is the error of $\Vert x \Vert$ higher or lower ...
0
votes
0answers
51 views

Between any rational and $\sqrt{2}$ is another rational [duplicate]

I'm self-studying analysis from Rudin, and in there is this proof. I understand the proof after reading it, but how would a mathematician come up with this or approach doing a proof like this? It ...
0
votes
1answer
174 views

Machine learning: beginner study material.

Can anyone suggest to me some beginner study material for Machine learning applications in fields of 1) Financial forecasting and 2) Online advertisement? Thanks in advance!
3
votes
1answer
163 views

What are the benefits or losses of learning real analysis through a constructivist approach instead of a standard apporach?

Recently I've found some courses on real analysis that use the constructivist approach and I got curious on some aspects: What are the benefits of learning through this approach? Is it ok to learn ...
3
votes
0answers
89 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 ...
0
votes
1answer
120 views

countably compact subset of a metric space is sequentially compact?

I'm currently trying to get my head around a proof in Lipschutz [1]. Solved exercise 21 of Chapter 11 (page 164) asks for a proof of the following statement: Let $A$ be a countably compact subset of ...
1
vote
1answer
72 views

Let $f$ be Lebesgue integrable on $\mathbb{R}$. Show that $ \sum_{n=1}^{\infty} f(x+n) $ converges almost everywhere. [duplicate]

Let $f$ be Lebesgue integrable on $\mathbb{R}$. Show that $ \sum_{n=1}^{\infty} f(x+n) $ converges almost everywhere. I was thinking that maybe the finite sum could be compared to a simple function ...
0
votes
1answer
70 views

Calculus: computation of $\sum \frac{2^i}{i!}$

$$\sum_{i=0}^\infty \frac{2^i}{i!}$$ Would anyone mind telling me what is the answer? I know this may be a silly question but I would like to know.
2
votes
1answer
110 views

An eigen-decomposition/diagonalization question

I'm data analyst without any good math background. I'm struggling to understand and to code myself eigen-decompositions. So far, I know QR algorithm of eigen-decomposition. My problem. Let $\bf A$ be ...
2
votes
1answer
83 views

Help understanding a counting and probability exercise

I need help in trying to understand the answer to this exercise. [Question] A club is considering changing its bylaws. In an initial straw vote on the issue, 24 of the 40 members of the club favored ...
1
vote
0answers
51 views

Finding an unbiased estimator for function of Poisson

Let $X_1,...,X_n \sim Poi(\lambda)$ then unbiased estimator for $\lambda$ is obviously $\bar{X}$. What about $\tau(\lambda)=\sqrt{\lambda}$? Also how would one derive UMVUE for this lambda?
3
votes
1answer
387 views

Prerequisites for studying Homological Algebra

I have read the answers here and here and need to ask something more. I wish to study the book on Homological Algebra by Weibel but am not sure of the prerequisites. In particular how much ...
1
vote
1answer
50 views

counting and probability question - help needed

I am stuck on how to start this exercise. Any help is welcome. An instructor gives an exam with 14 questions. Students are allowed to choose any 10 to answer. Suppose the exam instructions specify ...
4
votes
3answers
76 views

Recursion, multiplication and exponential

The set $F_{n}$ of primitive recursive function symbols of arty $n$ can be defined inductively as \begin{array}[lr] & Z, \text{Succ} \in F_{1} & \\ \pi_{j}^{n} \in F_{n} \quad \text{for each} ...
0
votes
1answer
29 views

Field extension $F\subseteq L_1$ and $F\subseteq L_2$ and $[L_1L_2:F]<[L_1:F][L_2:F]$.

I'm searching for an example of field extensions $L1$, $L2$ of $F$ for which $[L_1L_2:F]<[L_1:F][L_2:F]$. Infact I'm trying prove the problem below. So any hint can be helpful. Let $K$ be a ...
1
vote
1answer
67 views

How to show that the triangle is equilateral triangle?

If $\cot A+\cot B+\cot C=\sqrt3$ then prove that the triangle is equilateral triangle. Trial: I can counter check that this is true as $\cot 60+\cot 60+\cot 60=3 \frac{1}{\sqrt3}=\sqrt3$.Here I ...
6
votes
1answer
337 views

Learning Complex Geometry - Textbook Recommendation Request

I wish to learn Complex Geometry and am aware of the following books : Huybretchs, Voisin, Griffths-Harris, R O Wells, Demailly. But I am not sure which one or two to choose. I am interested in ...
8
votes
2answers
284 views

How much Category theory one must learn?

I have learnt very basic category theory (up to Yoneda lemma from Hungerford's Algebra text). My question is how much category theory should every Mathematics student who is not planning to specialize ...
1
vote
0answers
89 views

Gamma distribution and generalized gamma distribution

The generalized gamma distribution is described as follows $$f(x)=\frac{\gamma \cdot \left(\frac{x-\mu}{\beta} \right)^{\alpha\cdot \gamma-1}}{\beta\cdot\Gamma(\alpha)}\cdot e^{- ...
2
votes
0answers
40 views

Why can the group of isomorphism classes of line bundles be identified with $H^1(C,\mathbb O_C^*)$?

This is a reference request to the fact in the title. Is there a book at most as advanced as Hartshorn's which explains this result?
2
votes
1answer
152 views

Elementary/Intermediate Algebra book with proofs

I am looking for an elementary or Intermediate Algebra book which has proofs. I would like book to present proofs for statements like If $P(x)$ is a polynomial of degree n then will have exactly ...
1
vote
1answer
92 views

Bernoulli Related Probability Distribution

Find the probability of having 4 or more girls in a family of 6 children. Find also the probability that among 5 families, each with 6 children, at least 3 of the families have 4 or more girls. An ...
0
votes
0answers
50 views

$f(x)=\sum^\infty_{n=1}\frac{1}{n(1+nx^2)}$ for $x\in\mathbb{R}$ for what interval (a,b) does it CV - I can make it con uni for |a|>0

$f(x)=\sum^\infty_{n=1}\frac{1}{n(1+nx^2)}$ for $x\in\mathbb{R}$ for what interval (a,b) does it converge uniformly - I can make it converge uniformly for a given |a|>0 For a non-zero x the denom ...