Questions tagged [self-learning]

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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Math Self Studying Advice

I am a sophomore math major. Because of being in a bad University I am deprived of good math instruction and peer group which has left me alone to pursue this subject. At first, I used platforms like ...
Asish Mohanty's user avatar
1 vote
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23 views

Monte Carlo Control Reinforcement Learning

I'm reading the "Reinforcement Learning" book by Sutton & Barto. It's available here http://incompleteideas.net/book/RLbook2020.pdf . I'm currently in chapter 5 on Monte Carlo methods. I ...
user278486's user avatar
1 vote
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$\|B\|_{op} \le \|A\|_{op}$ when $B_{i,j} = v_i^TAv_j$

I'm currently stuck to the following statement. Let $A\in\mathbb R^{n\times n}$ be a diagonal matrix whose diagonal elements are only 0 or 1, and let $B$ be $n\times n$ matrix such that $B_{i,j} = ...
jason 1's user avatar
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1 answer
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Gradient with respect to $LDL^\prime$ parameterization of covariance matrix

I have been working with the matrix-variate normal distribution (a.k.a., matrix normal distribution) $\mathbf{X} \sim \text{Normal}_{nm}\big(\mathbf{M},\;\mathbf{I}_n,\mathbf{V}\big)$, such that (...
ChewysCaretaker's user avatar
1 vote
0 answers
24 views

Example of convex function that does not have subgradient

Through self-study, I found out that there are some pathological functions that do not have subgradients. https://www.stat.cmu.edu/~siva/teaching/725/lec2.pdf On page 2: Except for some very ...
learning's user avatar
  • 633
3 votes
1 answer
156 views

What to do with "half-learned" material

I have somewhat often found myself in the following situation, especially when self-studying a mathematical subject: I'm reading a book on a certain topic, and at certain parts I don't immediately ...
John Doe's user avatar
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4 votes
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44 views

Asymptotic expansion via Integration by Parts

Chapter 6.3 of Bender & Orszag discusses Integration by Parts for Laplace Integrals $$ I(x) = \int_{a}^{b} f(t) e^{x \phi(t)} \mathrm{d} t \qquad \text{as} \quad x\to \infty $$ Using integration ...
123prior's user avatar
1 vote
1 answer
70 views

Inequality regarding Matrix Norm and Inverse Matrix

Currently, I'm stuck to one of a statement in a paper. Following is a brief summary of the paper regarding my question. (although the topic of the paper is mainly statistics, the question purely ...
jason 1's user avatar
  • 757
3 votes
2 answers
529 views

How can I motivate and deal with speculation?

I am a student of mathematics and have been increasingly feeling doubtful about whether or not I really understand the theory. What I mean by this is highly attributed to the style of textbooks in ...
cpt.price's user avatar
2 votes
0 answers
65 views

How to self-study a sufficient real-analysis course [closed]

I'm currently a high school freshman trying to find some resources for studying higher math. I've read through some Intro to Proof books, Stewart's Calculus (and other supplementary calculus materials)...
D P's user avatar
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1 answer
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Cylindrical Water Reservoir Model and System Behavior [closed]

System Description We're looking for the mathematical model of a cylindrical water reservoir. The reservoir is characterized by three variables: The inlet flow, $Q_e(t)$, at time t The outlet flow, ...
Knowledge Seeker's user avatar
1 vote
0 answers
84 views

Searching for textbooks that teach math differently from other textbooks about the same subject. [closed]

Famous examples would be LADR (which to an extent eschews determinants) and Aluffi's Algebra (which involves some category theory). I would like more books in this vein, that either teach differently ...
valley's user avatar
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1 vote
0 answers
40 views

Ways to learn mathematics [closed]

I will be graduating with my bachelor's degree in mechanical engineering, in a few months, but I want to pursue master's in mathematics after 2-3 years. To prepare, I am currently doing "Advanced ...
Rohan Garg's user avatar
1 vote
0 answers
66 views

Book recommendations and study aid; in need of a little help

Please excuse the placeholder header; I currently don't know what to put up there, yet I might change it in the near future! Today, I wanted to make a slightly different post and instead of asking a ...
b00nn1e's user avatar
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0 votes
1 answer
74 views

Learning effective [closed]

today I got my midterm test result of Discrete math (It can only raise the grade). I got 63, which is above the average, but still I don't feel comfortable with that. I have 7 courses in the semester, ...
miiky123's user avatar
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0 answers
61 views

How can I fix my understanding of Numerical Analysis?

I am an undergraduate student taking Numerical Analysis. I’m having a hard time understanding some of the material because it feels as though my instructor is jumping all over the place. When it comes ...
Dr. J's user avatar
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-2 votes
1 answer
74 views

Is there anything currently that generates rejection from the mathematical community? [closed]

Is there anything currently that generates rejection from the mathematical community, as happened with the complex roots of algebraic equations?
FRED ANTHONY VIGORIA HUALLA's user avatar
0 votes
1 answer
101 views

Story proofs in Combinatorics/Probability [closed]

I have been recently been going through Blitzstein in an attempt to put my probability on a stronger foundation then it currently is. There is a large emphasis on the use of "story" proofs/...
Starlight's user avatar
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0 answers
30 views

Additivity + $\sigma$-subadditivity implies countably additivity for set functions on semirings?

Let $X$ be a set, $\mathcal{S}\subseteq \mathcal{P}(X)$ be a semiring on $X$, and $\mu: \mathcal{S}\rightarrow [0,\infty]$ with $\mu(\emptyset)=0$. Assume $\mu$ is finitely additive and countably ...
cliu55's user avatar
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15 votes
2 answers
1k views

When studying a book (like Rudin ) where the problems are not intended to be fully solvable by a student, what criteria show you're ready to advance?

When self studying a text where it is not expected to be able to solve all (or most) of the problems, what are the appropriate criteria to use for advancement? A word about the problems. There are a ...
SRobertJames's user avatar
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3 votes
2 answers
349 views

When to give up on a problem (for maximal learning of a specific area)? [closed]

There are many things to admire about the so-called Moore method, in which all the theorems and aspects of a course (e.g. real analysis) become problems for you to solve on your own. But sometimes, ...
Chris Sanders's user avatar
1 vote
1 answer
382 views

What is usually taught after Linear Algebra and Real analysis? [closed]

I am a self-learner who loves pure mathematics. I study mathematics alone without university and I don't have professor or advisor to help me (So I am not sure what I can learn next). I mostly study ...
pie's user avatar
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0 votes
1 answer
123 views

How do i stop the perfectionism with textbooks? [closed]

I have this problem that whenever i want to dip my toes into a new area of math that I'm either completely new to or have so little knowledge in it, I always go and google "Best books to learn [...
AmirMohammad Shakeri's user avatar
1 vote
0 answers
70 views

How to self-learn probabilities [closed]

Bit of background: I’m 27, graduated 4 years ago with a bachelors in Computer Science in which I did well. Since I graduated, I’ve been working as an algo trader for a bank. I’d like to start applying ...
IGottaLearnMath's user avatar
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0 answers
54 views

If $ f(x)dx+g(y)dy=0$ then why this doesn't imply $f(x)=g(y)=0$?

For functions $f(x)$ of $x$ and $g(y)$ of $y$, where $x,y$ are independent, why cannot we conclude from the expression $$ f(x)dx+g(y)dy=0\tag{1}$$ that $$f(x)=g(y)=0$$ If the original equation was $$ ...
GedankenExperimentalist's user avatar
0 votes
2 answers
110 views

Alright this might sound stupid. Why do we expand by 10?

Specifically the math problem 90.5b+21*92/21+b=91.2. The math calculator on the internet kept giving me errors when I put it in like that. So I changed it to 90.5b+1932/21+b=91.2, and it gave me an ...
Ryan Malloy's user avatar
1 vote
1 answer
32 views

Probability Integral Transform: Proof it is distributed on $U (0,1)$

I have worked out the proof for this question but wanted to check if my intuition also holds here. Please see below for the brief proof and then my proposed explanation: For a continuous random ...
InvestingScientist's user avatar
0 votes
1 answer
121 views

Self Learning - Moonshine beyond the Monster

EDIT: I tried to introduce some of the parts that I could use extra reading in the below list, and changed the final question to be more specific to the list. I am working on a individual study as an ...
Mahammad Yusifov's user avatar
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0 answers
47 views

Get PDF from Taylor series of characteristic function

This question represents some thoughts about the following question: How to get PDF from characteristic function In that question $$f(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty} e^{-itx}\phi(t)dt,$$ ...
eMathHelp's user avatar
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0 votes
1 answer
122 views

Best Linear algebra self-study content as of Jan 2024 [closed]

I am sure this question has been asked plenty of times, but I wanted to get the most up to date answer. I am a non-stem graduate looking to sharpen my math skills and want to start with Linear Algebra....
Daniel J.'s user avatar
0 votes
0 answers
22 views

Using telescoping sum to solve this identity of product integrals

I want to show that: $$\prod_{j}(1+a_{j})-\prod_{j}(1+b_{j})=\sum_{j}(\prod_{i < j}(1+a_{i})(a_{j}-b_{j})\prod_{k > j}(1+b_{k}))$$ The only hint I have is that I can replace $$ a_j - b_j = (1-...
user1916067's user avatar
0 votes
0 answers
25 views

How to show the existence of a Bellman Equation Solution?

consider the Bellman Equation \begin{equation*} V(\alpha)=\max_{\beta} f(\beta,\alpha)+A(\beta,\alpha) V(\alpha)+B(\beta,\alpha) V'(\alpha) \end{equation*} How can I show the existence of the solution?...
Isn't Adobe Acrobat the best's user avatar
2 votes
1 answer
69 views

Lilvati as a good source to learn math. [closed]

I usually like Sanskrit text and reading their literature I am wondering if I can reinforce my math skills with this ancient Lilvati text it goes over the basics, but I find it may be handy, yet I don'...
Haridasa's user avatar
  • 141
1 vote
1 answer
69 views

Circular permutation of n married couples sitting alternatively

This is the problem statement (First Course in Prob., Sheldon Ross, 8th Ed., Q 4.67): A total of $2n$ people, consisting of $n$ married couples, subject to the constraint that the men and women ...
Roy's user avatar
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0 votes
2 answers
83 views

Does the category of Boolean algebras imbed in $\operatorname{Set}$

While trying to come up with some examples of functors, I realised that any function $f:X\to Y$ induces a function $P_f: \mathbb{P}(X) \to \mathbb{P}(Y)$ in a natural way, simply define $f_p(A) = f(A) ...
Carlyle's user avatar
  • 2,807
0 votes
2 answers
81 views

Ordinary generating function for Lah's numbers $L(n,k)$

I'm studing signed Lah's numbers $L(n,k) = (-1)^n\frac{n!}{k!}\binom{n-1}{k-1}$. It's easy to show that exponential generating function for the sequence $\{L(n,k)\}_{n\geq0}$ is equal to $$ \sum\...
Orel_Algebraist's user avatar
0 votes
1 answer
73 views

$\int_{\{x:f(x)>k\}}f(x)dx=c$ [closed]

How is to find the value of $k$ for the following equation? $$\int_{\{x:f(x)>k\}}f(x)\,dx=c,$$ where $c$ is a constant. Can anyone please show me a toy example from which I can understand how is to ...
user149054's user avatar
2 votes
0 answers
54 views

Recommendations for a new study area [closed]

Edit: I am not asking about "which course to take" or "which career path to follow". I am asking which areas of mathematics were found interesting by those that share my interests. ...
Carlyle's user avatar
  • 2,807
2 votes
0 answers
29 views

Find the behaviour of the cumulative conditional function and match it to a known distribution

The given joint distribution is: $$ f_{X, Y}(x, y)=\frac{n 2 a^2 x^{n-1}}{y^{n+3}} I_{[0, y]}(x) I_{(a, \infty)}(y), n \in \mathbb{N} $$ The exercise asks us to find the cumulative distribution of the ...
Guilherme Marthe's user avatar
1 vote
0 answers
44 views

Find the distribution of $P(X=x \mid X+Y=t)$ and calculate its expected value.

So, the given distribution is a discrete $(X,Y)$ vector with the following probability mass function. $$ \mathbb{P}(X=x, Y=y)=\frac{1}{2 n+1} \frac{\left(\begin{array}{c} n \\ x \end{array}\right)\...
Guilherme Marthe's user avatar
0 votes
0 answers
42 views

Density of sum of two random variables

Let$(X,Y)$ be an RV of the continous type with PDF $f(x,y)$.Let $Z=X+Y$,then the Convolution of probability distributions told us the PDF of $Z$ is $f_{Z}(z)=\int_{-\infty}^{\infty}f(x,z-x)dx$. If we ...
user553010's user avatar
0 votes
1 answer
29 views

Find the distribution of $X|Y=y$ where X and Y look like a a bivariate poisson.

It isn't a bivariate Poisson precisely, but has a pmf of: $$ \mathbb{P}(X=x, Y=y)=\frac{\lambda^y e^{-2 \lambda}}{x !(y-x) !} I_{\{0, \ldots, y\}}(x) I_{\mathbb{N}}(y), \lambda>0$$ When I tried to ...
Guilherme Marthe's user avatar
0 votes
0 answers
27 views

Matrix operation: simplifying a simple expression

Let $X$ and $\mu$ are $p$ dimensional vector and $\Sigma$ $p\times p$ dimensional matrix. I have to simplify the following expression. $-\frac{1}{2}(X-\mu)^T\Sigma^{-1}(X-\mu)$ $=-\frac{1}{2}(X^T-\mu^...
user232597's user avatar
0 votes
2 answers
111 views

Simple question regarding the Poisson distribution

I'm just trying to wrap my head around the Poisson distribution to make it more intuitive and I'm struggling with one (seemingly) paradoxical example. Say we have a rate of 4 events in a given time ...
Daniel Podobinski's user avatar
0 votes
0 answers
36 views

Is it possible to study Measure Theory from the definition of Measure?

I would like to start studying Measure Theory in the summer of 2024. Let me tell you a bit about myself: I'm a graduate student in Mathematics from Brazil. I suspect that, by luck, I ended up being ...
Gleberson Antunes's user avatar
2 votes
0 answers
58 views

References for Exercises on Abstract Simplicial Complexes

I am currently reading Combinatorial Algebraic Topology by Kozlov. I'm enjoying it a lot, however, it regretfully does not contain any exercises (it is more along the lines of lecture notes). In the ...
pyridoxal_trigeminus's user avatar
0 votes
1 answer
53 views

Intuitive online resources/books for statistics?

(Sorry for any spelling/grammatical mistake. I am from South America.) This semester I took my first Statistics course in college, and I feel that ever since the concept of the $T$ distribution was ...
gnzlama's user avatar
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0 votes
0 answers
13 views

Please Explain why we take the product of two variables in a rate model (or any model)?

I'm trying to understand this equation: v = k[A][B] where v is the rate of a chemical reaction, k is the rate constant, and A and B are reactant concentrations. I think this equation relates reaction ...
Zak's user avatar
  • 1
1 vote
0 answers
116 views

Problem on convergence in distribution of a random vector

The issue is that I have to prove the following with limited resources. Problem: Let $X_n$ and $Y_n$ be p-dimensional random vectors. Show that if $X_n − Y_n \xrightarrow{P} 0$ and $X_n \xrightarrow{D}...
TryingHardToBecomeAGoodPrSlvr's user avatar
5 votes
1 answer
136 views

Can an exact vector field have loops as solutions?

I was asking myself this question. We define for an exact vector field $\mathbf{v}(\mathbf x) \in \mathbb{R}^n$, s.t. $\mathbf{v}(\mathbf x)=\nabla u(\mathbf x)$ for a potential $u$, a solution as a ...
Thomas's user avatar
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