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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How to effectively learn from and use Ramanujan's notebooks? [duplicate]

I will come back and elaborate on the question if necessary (I must be off for a while...). But I'll try being specific. I have all four of Ramanujan's notebooks, with their respective Errata ...
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2answers
32 views

Find the density of their average

If $f_{X,Y,Z}(x,y,z)=e^{-(x+y+z)}I_{[0,\infty]}(x)I_{[0,\infty]}(y)I_{[0,\infty]}(z)$ find the density of their average $\frac{X+Y+Z}{3}$ I'm a little lost on how to solve this exercise, ...
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2answers
54 views

Disjoint events

Let $A$ and $B$ two disjoint events such that $P(A)=0.3$ and $P(B)=0.5$. Find the probability that i)$A$ or $B$ ocurrs ii)$A$ occur but not $B$ iii)repeat $i)$ and $ii)$ with $A$ ...
4
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1answer
113 views

Is Alfred Tarski's Introduction to Logic still helpful for self study?

I am trying to setup a self study path to enhance my knowledge of mathematical logic. I haven't taken a logic course for a few years and my confidence on mathematical proofs is unnerving. I am ...
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1answer
43 views

Principle of well ordering

Every non-empty set $A\subset\mathbb{N}$ have a smallest element, i.e. an element $n_0\in A$ such that $n_0\leq n$ $\forall n\in\mathbb{A}$ Proof: Let $I_n=\{p\in\mathbb{N};p\leq n\}$ the set ...
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2answers
92 views

Reference request for this topics

I'm a second year undergraduate statistic student, I need a good reference to learn these topics Markov Chains in discrete time.    1.1. Classification of states, recurrence notions of transience. ...
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4answers
52 views

Logic, writing proof

i)Suppose that $x$ and $y$ are real numbers. Prove that if $x\neq 0$, then if $y=\frac{3x^2+2y}{x^2+2}$ then $y=3$ ii)Suppose that $x$ and $y$ are real numbers. Prove that if $x^2y=2x+y$, ...
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42 views

Integral gaussian hypergeometric function

How can we define integral with interval $[b,\infty)$ $$ \begin{align} C(b,\alpha) & = \int_b^\infty \frac{1}{1+w^{\alpha/2}}\,\mathrm{d}w \\[8pt] & = 2\pi/\alpha \csc(2\pi/\alpha)-b_2 F_1 ...
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0answers
66 views

How to prove it and how to solve it

Tomorrow I will begin my studies, real analysis, however I have some difficulties in making statements so I thought before starting the study in real analysis, learn how to do demonstrations properly. ...
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0answers
51 views

How to obtain the genus of the Riemann surface corresponding to an algebraic curve

I am trying to read about the genus of an algebraic curve. I have been told that there is a connection between topological genus and genus defined for an algebraic curve. Since an algebraic curve ...
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0answers
25 views

non-linearity and non-convexity

I am taking a course on linear regression online and it talks about the sum of square difference cost function and one of the points it makes is that the cost function is always convex i.e. it has ...
4
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1answer
86 views

Finiteness of the sum of the product of an i.i.d. sequence

Before I go to the statement of my question I just want to say a few words about the personal background of this question. I have recently taken a course on stochastic differential equations without ...
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2answers
65 views

What kind of geometry is useful to study for mathematical competitions?

I'm bad in geometry but I would like to be better. What kind of geometry is useful to learn olympiad level geometry? I mean, can projective geometry solve more problems than geometry with complex ...
1
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1answer
59 views

Learning Galois theory - required subtopics that are prerequisite?

This is not a reference request, that is, I have access to many textbooks I am happy with. What I don't know is, what are the things I need to know to get started? My idea on the path of knowledge ...
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4answers
125 views

Why memorize trig identities?

I want to be a mathematician or computer scientist. I'm going to be a junior in high school, and I skipped precalc/trig to go straight to AP Calc since I've studied a lot of analysis and stuff on my ...
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1answer
111 views

Conditional Expected Value of Product of Normal and Log Normal Distribution

Could someone please provide the answer and steps to solve this expression? \begin{eqnarray*} E\left[\left.\left(e^{X}Y+k\right)\right|\left.\left(e^{X}Y+k\right)>0\right]\right. \end{eqnarray*} ...
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1answer
81 views

Seeking your recommendation on Abstract Algebra textbooks

S.E advisers, I am a college sophomore with major in mathematics. I wrote this email to seek your recommendation on the good, starting textbook for the abstract algebra. I want to start studying ...
2
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1answer
95 views

Looking for Advice Self Study Analysis [closed]

$\space$ This summer I have some spare time and I was wanting to dedicate some time to self studying some more math. The reasons are many, but mostly because I am wanting to be best prepared for my ...
9
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1answer
216 views

How to begin self study of Mathematics?

I'm aware that this question has been asked several times, but I have specific questions hence why I'm asking again. I began to appreciate the beauty of mathematics when I glossed over the ...
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0answers
56 views

Kline, Lang, Silverman…which author provides thorough and rigorous Calculus up Multivariate & Advanced Calculus?

I know this question may appear subjective, but it is not, let me explain; note to mods --> please don't close this if it is considered too subjective, please alert me and I'll try to reword it. I ...
4
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1answer
130 views

Can Somebody Please Outline a Reading Course For Me in Algebraic Topology

I want to start self studying algebraic topology and I am looking for guidance regarding the same. In the past I have made the mistake of trying to learn a mathematical subject by reading fat books ...
4
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1answer
38 views

What book offers strategies and heuristics for theorem proving in the same spirit as Polya's How to Solve It?

Polya's How to Solve It is all about heuristics and strategies for problem solving, but it's mainly written for problems which require students to find values, not to prove theorems. While Polya's ...
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0answers
17 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 ...
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1answer
59 views

Website for Mathematics enigmas?

I seek some website just for the pleasure of solving mathematics enigmas. I know this website : Brilliant.org I just want to know if you know some others good sites ! Thank you
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81 views

Linear Algebra Book like Calculus Made Easy

Now, I know that there are a tons of reference requests for Linear Algebra books but mine is very specific: what is a nice, short, concise, simple, to the point book that gets at the heart of Linear ...
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1answer
25 views

Book recomendation for function sequences.

I wanted to study about sequences of functions defined in metric spaces. What book/books do you recommend? Thanks!
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0answers
44 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. ...
0
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1answer
59 views

Learning math by analyzing/proving theorems?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
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1answer
83 views

Is it useful to learn math by proving a formula/theorem?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
4
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2answers
165 views

Self Teaching Theory for Olympiad. Need advice for books.

(Cross-posted in MESE 8173.) I want to start to do mathematical Olympiad type questions but have absolutely no knowledge on how to solve these apart from my school curriculum. I'm $16$ but know ...
0
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1answer
74 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
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0answers
134 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 ...
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1answer
71 views

How should I learn the Mathematical Proofs? [closed]

S.E advisers, What is the most efficient way to learn the basic proof methodologies, which are essential for studying the mathematical analysis and number theory? I am very interested in studying ...
2
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1answer
52 views

How to practice basic probabilistic modeling?

I'm heavily struggling in learning simple and basic probabilistic modeling. So I'm learning probability from this probability book Introduction to Probability by Dimitri P. Bertsekas. Although I ...
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1answer
97 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
2
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1answer
80 views

Learning Combinatorics Further

I have completed most of the basic parts in Combinatorics like Generalised Permutation & Combination, Recurrence relations, Pigeonhole Principle, Formal power series, Stirling no, Catalan no, ...
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3answers
52 views

Let $x_n$ be a sequence. Prove that $x_n \rightarrow 0 $ iff $(x_n)^{2} \rightarrow 0 $

Let $x_n$ be a sequence. Prove that $x_n \rightarrow 0 $ iff $ (x_n)^{2} \rightarrow 0 $ Attempt Assume that $(x_n)^{2}$ converges to zero. So $| x_n|| x_n| \lt \epsilon'$ after some stage. Thus $| ...
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0answers
16 views

Good introductory texts on modular forms/L-functions

I am relatively new to these areas but would like to gain some understanding through an introductory text. I am an undergraduate math major so ideally these books should be accessible to someone with ...
3
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0answers
138 views

How to study multiple books per math subject? [closed]

S.E advisers, I am a college sophomore in US with double majors in mathematics and microbiology. I apologize for this sudden interruption but I wrote this email to seek your advice regarding to ...
3
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2answers
294 views

A path to more advanced math topics.

I am from Hong Kong and have just finished all the public exams. In my high school life, I've learned some topics on mathematics which are fundamental, yet I think are not in-depth enough. The topics ...
2
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1answer
114 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
3
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2answers
120 views

What is a good book for reviewing high school math, and preparing for university?

I'm signing up for University soon (Compsci program) as a mature student. It's been a long time since I've done any math, and I went as far as grade 11 in high school. So, I'm looking for a book that ...
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1answer
26 views

Topology of weak convergence, linear functionals and probabilistic intuition

One very basic question regarding the topology of weak convergence. We know that given the following: $X$ metrizable topological space, $\mathcal{B} (X)$ Borel $\sigma$-algebra, $\Delta (X)$ ...
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3answers
93 views

Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R?

Let $R$ be a finite ring (with unity) and $S$, $T$ be subrings of $R$. Is $S \cup T$ a subring of R? (Counterexamples are easy to find to me when $R$ is an infinite ring or a finite rng.) P.S. I am ...
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1answer
261 views

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
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70 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 ...
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3answers
142 views

Please help collecting examples of finite/infinite rings satisfying different conditions about units/zero divisors (Added question 4)

0) Every nonzero element of a finite ring is either a zero divisor or a unit. This is proved in Every nonzero element in a finite ring is either a unit or a zero divisor 1) If a ring R satisfies the ...
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1answer
15 views

Complete separable metric space X represented represented as union of closed sets

I have a problem concerning a statement I found in volume 2 of the classic reference book on measure theory by Bogachev. More precisely, I have a problem concerning theorem 6.1.13. I the proof the ...
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1answer
71 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
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1answer
24 views

Solving the equations .

Say , I have two equations : $$y_1=a+bx_{1}+e_1$$ $$y_2=a+bx_{2}+e_2$$ Say , $a=.5$ , $b=2.1$ , $x_1=2$ , $x_2=2.2$ . Now if $e_1=e_2$ , I have to find the relationship between $y_1$ and $y_2$ . ...