Questions about studying mathematics without formal instruction.

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1
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1answer
19 views

Confused about this set representation and conclusions

I'm pursuing Set Theory by Enderton and am having trouble understanding the following idea. Early in the book, the author constructs an "informal view" of sets, which he says he will refine further ...
1
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1answer
59 views

How do you self-study Functional Analysis?

It would be very handy to know about function spaces, distributions and Fourier stuff. It looks like Rudin's Functional Analysis covers these things, but I do not yet have the foundation for it. (see ...
21
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7answers
14k views

Good books for self-studying algebra?

I have a few weeks off from school soon, and I was hoping to self-study a bit of algebra. I don't think this question has been asked on here before, but does anyone have any suggestions for algebra ...
1
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0answers
56 views

How long should you study Mathematics each day if you want to get into a graduate school? [on hold]

I'm a university student (Junior now!) and I was wondering how many hours fellow undergraduates and graduate students study a day. I hear posts about how time doesn't really matter and that it's about ...
6
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2answers
103 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
0
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0answers
38 views

Self-Contained Books / Series / Lectures for Comprehensive Introduction to College-Level Math for Someone with VERY Poor Math Foundation?

I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I ...
0
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2answers
26 views

Help with constructing power set

I' trying to construct the power set of $A = \{\phi, \{a\}\}$ and would appreciate some help. Now, the definition of a power set says that it's the set of all possible subsets of a given set. ...
2
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4answers
281 views

Should I read about Manifolds or Algebraic Topology?

I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once ...
6
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3answers
128 views

Beginning of Romance

I am a 17 guy from India. The fascination of maths has struck me recently, while I am in standard 12th. But all the resources I have, is some school textbooks. M.L Agrawal's of 11th and 12th. I don't ...
23
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11answers
12k views

How to start with mathematics?

I fell in love with mathematics a bit too late when I've already taken decisions regarding my future, career-wise. Now I would like to learn math on my own but I'm a bit confused as where to start. My ...
0
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1answer
32 views

The Landau symbol $\mathcal{o}$ as in Königsberger Analysis I

I am currently working on Chapter 14 - local approximations of function and Taylor polynomials - in Königsberger Analysis 1 Background: Königsberger introduced the Taylor Polynomial of order ...
3
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1answer
40 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
2
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1answer
32 views

Tutorial on Complex Networks

Can anyone advise mea nice and short tutorial about Complex Networks? I'm reading "Networks: An Introduction" from Mark Newman, and is a bit tedious... Thanks PS: There isn't a tag "complex networks" ...
0
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0answers
24 views

Most suitable book after Bergmann Logic Book

I'd like to know what the best book would be to pick up after this one would be. Essentially, it covers basic logical concepts (validity, soundness, consistency) and goes on to sentential and ...
0
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3answers
50 views

Learning timetables

This is a basic question, but I am revisiting them due to some examinations I need to take that involves mathematics. I want to be nimble with mental arithmetic so have decided to go back and learn my ...
0
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0answers
13 views

Volume of parallelepiped gets smaller when using projection vectors

Given a Euclidean Space R and a subspace R' (of dimension $\geq$m), consider vectors $x_1,...,x_m \in$**R**, and let $V[x_1,...,x_m]$ mean the volume of an m-dimensional parallelepiped formed by those ...
2
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3answers
79 views

Trouble with inequalities

I'm a 9th grade student, going into 10th grade. Math has always been a subject I enjoyed and excelled in. I'm writing a schoolboard-wide math contest next year in mid-February I believe. To prepare ...
4
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1answer
68 views

Riemann Sums as in Königsberger Analysis 1

Intro: I must take a small detour here which is only relevant if you do not know the book itself and care about my background. I am working with Königsberger Analysis I (can be found on Springerlink). ...
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0answers
26 views

Generator Matrix

I have a C in $F_2^6$ $(x_1,x_2,x_3,x_4) \to (x_1,x_2,x_3,x_4,x_1+x_2,x_3+x_4)$ for $x = (1,0,1,1)$ i get $c = (1,0,1,1,1,0)$ we know that $$c = G . x$$ G is the Generator Matrix in the solution ...
0
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1answer
27 views

Continuity of a map to a Frechet space

Let $(A,\| \cdot \|)$ be a normed space and $B$ be a Frechet space equipped with a family $\{ p_k \}_{k \in \mathbb{N}}$ of seminorms. Let $\phi: A \to B$ be a linear transformation satisfying the ...
5
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2answers
41 views

Area preserving transformation in a higher dimensional space is unitary.

In $\mathbb{R}^3$, a linear operator $Q:\mathbb{R}^3 \to \mathbb{R}^3$ preserves the area of parallelograms: that is, given $x,y\in \mathbb{R}^3$, the area of a parallelogram formed by $x$ and $y$ is ...
9
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3answers
256 views

Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ...
3
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6answers
228 views

I want a good dictionary of mathematics/ geometry

I noticed I a made a mistake in some geometrical terminology and wanted to better my life by buying a new dictionary of mathematics or more specialised Geometry. (okay I am just a shopaholic for ...
0
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1answer
12 views

quick question on measurability of random variables and what becoming a deterministic function means.

we stated a theorem in class: if X r.v. is $\sigma(Y)$ measurable then X is a function of Y, where $\sigma(Y)$ signifies the sigma algebra of Y. This is fine. The Professor sometimes states that X ...
0
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1answer
25 views

Logarithm with variable base

I am trying to define a function that maps polynomials in the form of $x^{3^n}$ to the value of $n$ in the polynomial, where $n\in{Z}$.* Is is valid to define this function as $log_{x^3}(u)$, where ...
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0answers
45 views

Soft question — I need books and exercise books that will be working on my fundamental skills.

I need help, urgently. I acquired a book called: Mathematics, Its Content, Method and Meaning. Now the problems is the book doesn't provide me with any exercises. I was searching for a book that would ...
2
votes
2answers
23 views

Probability of returning to a given state after n transitions-Markov chains

Let us denote $f_j^{(n)}$ denote the probability of the first return to state $j $after n transitions. Let $p_{jj}^{(n)}$ be the probability of returning to the state $j$ after $n$ transitions when ...
1
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1answer
16 views

Confusion with Bolyai-Gerwien theorem

The Bolyai-Gerwien theorem states: Given two polygons with the same area, it is possible to cut up one polygon into a finite number of smaller polygonal pieces and from those pieces assemble into ...
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0answers
11 views

Queuing theory-Multiple server (reducing simple recurrence formulas)

The equations given in 6.3 have been reduced which really eases the computation in further studies. But I tried to find the method of reducing these but I could not find a way at all. Any hints will ...
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2answers
27 views

Prove this result about power sets [duplicate]

I have to prove this result: If $P$ be the power set, and $B$ and $C$ are two sets, then if $B \subseteq C$ prove that $P(B) \subseteq P(C)$. Now, it seems obvious to me that since all the ...
1
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1answer
68 views

Math self-study in the holidays

In the upcoming holidays, I have got 6 weeks free to learn some new math (I was thinking of calculus and linear algebra). It's useful for my high school math skills (I don't live in America, so my ...
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0answers
39 views

Can ergodic Markov chains be periodic?

I found a statement in one of my notes which said If a state is persistent, aperiodic and not null the it is said to be ergodic Is it necessary that it should be aperiodic? This statement ...
0
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1answer
64 views

What is the metric spaces needed to motivate concepts of general topology?

I intend to start learning some topology on my own. I wonder How much metric spaces I should know in order to motivate the concepts of topology? I know it's possible to learn topology without any ...
2
votes
2answers
55 views

How to calculate Frenet-Serret equations

How to calculate Frenet-Serret equations of the helix $$\gamma : \Bbb R \to \ \Bbb R^3$$ $$\gamma (s) =\left(\cos \left(\frac{s}{\sqrt 2}\right), \sin \left(\frac{s}{\sqrt 2}\right), ...
10
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1answer
335 views

Looking for an easy lightning introduction to Hilbert spaces and Banach spaces

I'm co-organizing a reading seminar on Higson and Roe's Analytic K-homology. Most participants are graduate students and faculty, but there are a number of undergraduates who might like to ...
4
votes
1answer
4k views

How can I learn math of 1st to 10th Standard? [closed]

I am 30+ graduate in Arts from India. I'm very poor in math. I can do basic math calculations, i.e. addition, subtraction, multiplication, and division of simple numbers in writing (on paper only) - I ...
37
votes
3answers
2k views

Why learning modern algebraic geometry is so complicated?

Many students - myself included - have a lot of problems in learning scheme theory. I don't think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the ...
5
votes
4answers
110 views

Evaluate $\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$

I need to evaluate the integral: $$\int_0^{\infty} x p^xe^{\Large-\frac{x}{a}}\ dx$$ for $0<p<1$. Unfortunately I do not know where to begin. I tried integration by parts but got nowhere ...
0
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0answers
38 views

Describe the language generated by the grammar $G = \{\Sigma, \Delta\ S, I \} $

I need to describe the language generated by the grammar $G = \{\Sigma, \Delta\ S, I \} $, where $$\Sigma=\{0,1\epsilon \}, \Delta = \{S,X,Y,Z\}$$ and $$I = \{S \to0X|1Y, x \to1Y|1Z, Y \to0X|0Z, Z ...
1
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1answer
21 views

Markov chains: An issue in classification of states

I recently came across a lemma which goes as follows. Suppose a Markov chain has N states. Let i and j be pair of states. Then j can be reached from i iff there is an integer $ 0 ≤n< N$ such ...
153
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27answers
14k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
15
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0answers
850 views

Efficient ways to read and learn a new topic

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
0
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2answers
50 views

Find the galois group of the polynomial when a root is given

If $\alpha$ is a root of a polynomial $f(x)=x^3 +x^2-4x+1$ then show that $2 - 2\alpha - \alpha^2$ is also a root of $f(x)$. Use this fact to compute the Galois group of the splitting field of $f(x)$ ...
2
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2answers
56 views

Intersection of ideals $I=(2x)$ and $J=(2x^2)$ of $\mathbb{Z}[2x,2x^2,2x^3,\dots]$ is not finitely generated.

Consider the subring $\mathbb{Z}[2x,2x^2,2x^3,\dots]\subset \mathbb{Z}[x]$. Then show that the intersection of ideals $I=(2x)$ and $J=(2x^2)$ of $\mathbb{Z}[2x,2x^2,2x^3,\dots]$ i.e., $I\cap ...
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3answers
575 views

Do free online collaborative solution manuals exist?

I'm not a mathematician by training and a rarely come in contact with mathematicians. For this reason I find solution manuals to be incredibly useful - reading them allows me to see how experienced ...
2
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8answers
705 views

What are the most important functions every mathematician should know? [closed]

I am an undergrad in math and was wondering, what are for you the most important functions every mathematician should know? At the moment I think ...
24
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8answers
2k views

Complex analysis is more “real” than real analysis

In physics, in the past, complex numbers were used only to remember or simplify formulas and computations. But after the birth of quantum physics, they found that a thing as real as "matter" itself ...
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4answers
45 views

A simple conditional probability problem

Assume that two fair dice are rolled one at a time. Given that the sum of the two numbers that occured was at least $7$, compute the probability that it was equal to $7$. I tried computing the ...
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2answers
30 views

Proof that the subset relation is reflexive and transitive

I'm teaching myself set theory, and I'm not sure how detailed I should be when asked to prove things. Here is my proof that $A\subseteq A$ (the subset relation is reflexive): $A \subseteq B$ iff ...
1
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1answer
31 views

Optimization with both equality and inequality constraints

I need to minimize the following quantity: $$\min x_1^{-1/n}- \left(1-x_2 \right)^{-1/n}$$ subject to: $1-x_1-x_2=\gamma$ and $0<x_1+x_2<1$ $\gamma$ being a constant. Had it been two ...