This tag is for questions that are asking for online resources in mathematics (references, dictionaries, encyclopaedic collections, online tools, videos an lectures, etc), or asking about the mathematics behind tools and technology found on the internet.

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2
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3answers
70 views

How to reduce predicate logic into propositional logic?

I read that predicate logic reduces into propositional logic. However, I couldn't find anything online that explains the process. Do you know where I could find an explanation? Thank you.
3
votes
2answers
53 views

Proof that diagonally dominant matrices are regular - Reference request

I know that it is easy to proof that diagonally dominant matrices are regular (non-singular) by the gershgorin circle theorem. But the theorem that diagonally dominant matrices are regular was ...
2
votes
0answers
87 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
4
votes
3answers
100 views

What's a good resource to learn about the simply typed lambda calculus?

I've read An Introduction to Functional Programming Through Lambda Calculus by Greg Michaelson, and found it to be a very good resource to learn about the untyped lambda calculus. However, I want to ...
2
votes
0answers
36 views

Is there a source that explains or defines terms like Theorem, Proposition, Lemma and Corollary?

I will write the German names of the following English terms in brackets as it is important that I use the correct terms. This is a question about terms and I'm not completely sure if I've ...
1
vote
1answer
88 views

Good ODE Books That Explain How Solution Methods Came To Be and Their Justifications

As part of the mathematics program offered at my college, I took an introductory ODE course a few semesters back. This was the one math course in my entire college career that I was totally lost in. ...
6
votes
1answer
146 views

Animations or Pictures of Group of Rigid Motions (or Rotations) of the Cube

Consider a cube that exactly fills a certain cubical box. As in Examples 8.7 and 8.10, the ways in which the cube can be placed into the box corresponds to a certain group of permutations of the ...
18
votes
1answer
525 views

“Bad” Mathematics in Movies

There's a website and a companion book to it about bad physics in movies, called "Insultingly Stupid Movie Physics". Similar issues may exist about mathematics: What are the differences between ...
3
votes
1answer
383 views

Tool to extrapolate data

I have daily data. 6.5315 4.9240 4.3253 3.9703 3.5932 3.2923 3.0785 3.4432 2.6213 2.4083 2.2602 2.1614 2.1351 2.0412 It looks like exponential function or ...
5
votes
1answer
48 views

Detailed Visual Introduction to Complex Numbers with Problems and Solutions

I'm aware of http://tutorial.math.lamar.edu/Extras/ComplexPrimer/ComplexNumbers.aspx. It's very detailed and helpful but I'm looking for something with more pictures. It also doesn't have enough ...
5
votes
0answers
318 views

Solution manual to Larson's “Problem Solving through Problems”

I am working through Larson's "Problem Solving through Problems" (http://math.la.asu.edu/~ifulman/mat194/problem-solving.pdf) but many of the problems have neither solutions nor sources included. Does ...
1
vote
0answers
19 views

More contemporary resource for Greenberg

Is there a more modern textbook than Greenberg's forms in many variables, or a set of notes, that summarizes the developments about $C_i$ fields? Is there such a thing as $C_i$ field where $i$ is not ...
0
votes
0answers
15 views

Resources for converting a problem into a 'coefficient of $x^n$ in <exp>'

I'm getting started with generating functions, and I'm having trouble with understanding how problems get converted into 'therefore, this is is the coefficient of $x^n$ in such-and-such'. Does anyone ...
0
votes
0answers
41 views

Online testing systems with extensive question banks?

Some months ago I asked a question about online testing systems here: Online homework/testing systems? I am still searching for the best system to use with my students. When I asked that earlier ...
0
votes
1answer
34 views

Resources on Stone-Čech compactification

I'm currently studying R.C. Walker's book on the subject which seems quite extensive and detailed. I've also been skimming through Hindman and Strauss's book Algebra in the Stone-Čech ...
3
votes
1answer
106 views

Is there a 'Mathematics wiki' analogous to 'String theory wiki'?

I came across this site and am wondering if there is a similar page for Mathematics or its sub-areas. Would be very nice if there is one such site which provides 'canonical' references for each sub ...
2
votes
0answers
63 views

A Proof of Bruns' Theorem

I am looking for a proof of Bruns' Theorem. Theorem: The 10 classical integrals of the three-body problem are the only algebraically independent integrals of this 18-degree-of-freedom system.
0
votes
0answers
69 views

Bertrands theorem. The principle of least curvature.

Theorem: If a given set of impulses is applied to different points of a system in motion (either holonomic or nonholonomic), then the kinetic energy of the resulting motion is greater than the ...
0
votes
1answer
22 views

Absolutely rough planes

What is an absolutely rough plane? Can you give an analytical expression of one? Why cannot a rigid body slide on a rough plane? Why does the point of contact not move in an infinitesimal movement of ...
2
votes
3answers
185 views

Learning times tables?

I have some weird gaps in my learning, I can do lambda calculus and some basic category theory, but I do not know how to do some of the most basic of arithmetic. (I am in my mid 20s) Seeing this gap ...
1
vote
1answer
116 views

Online homework/testing systems?

I have been using Pearson's MyMathLab Global with my Engineering students. I appreciate its convenience, but the students find its inflexibility annoying (if an answer is expected to be 1.5, then the ...
0
votes
1answer
249 views

Competition style mathematics

I'm currently 18 years old and only as of the part year taken a strong interest in maths. I'm working with my school curriculum (UK a-level) and receiving A grades so I am happy with this. However I ...
2
votes
2answers
815 views

MOOCs for college-level discrete math?

Specifically I am looking for short lectures (and quizzes) on specific topics. (like Khan Academy offers) Topics I am learning about include; Intro logic-theory + set-theory Notation, negation, ...
4
votes
1answer
275 views

Online classes/books in multivariable calculus?

So does anyone know of any good online courses in multivariable calculus? (Or in a possible alternative leap of curriculum, if said path has proven to be better/moar interesting.) I'm coming straight ...
-1
votes
1answer
273 views

Sketching a piecewise function online [closed]

Is there any website I can input this function into so that I can sketch it and label any asymptotes? $$f(x)=\begin{cases} \frac{1}{x+2} & \text{if }x<-2\\\\ |x^2-4| & \text{if }{-2}\leq ...
1
vote
1answer
164 views

Producing tree diagrams of formulae and expressions. (software request)

By "tree," let us mean a tree that is finite, ordered and rooted; but not necessarily binary (that is, every node can have an arbitrary number of children). Under the definition, most mathematical ...
1
vote
0answers
92 views

What is a good source of problem-solving type problems?

I am not looking for contest problems where there is a clever trick or a standard approach, I am looking for more creative and open-ended problems such as this , and I am not looking for questions ...
0
votes
1answer
105 views

A website where I can evaluate a definite integral and also get a step-by-step solution

Does anyone know of a site where I can evaluate a definite integral and also get a step-by-step solution? Help appreciated. Thanks.
10
votes
1answer
307 views

Toddler introductions to higher mathematics

I bought my youngest (now 10 months old) "Introductory Calculus For Infants" by Omi Inouye a while back. It's actually an ABC book about the letter x and how no one ever plays with him until he meets ...
0
votes
1answer
99 views

Any two Poincare’s maps for a periodic phase space are diffeomorphic

My lectures examine in detail Poincare’s map for dynamical systems with a periodic trajectory. They, however, mention only in passing the construction for a dynamical system with a periodic phase ...
1
vote
1answer
49 views

Need a source for the following result: From $v \in H^1$ and $f$ Lipschitz it follows that $f(v) \in H^1$.

I am looking for a source of the following (or a similar) result: If $v \in H^1(\Omega,\mathbb{C})$ on a bounded domain $\Omega$ and $f: R(v) \to \mathbb{C}$ is Lipschitz continuous, then $f(v) ...
1
vote
1answer
331 views

Calculator for real and complex parts of a polynomial.

Does anyone know of a nice calculator for calculating the real and complex parts of a complex polynomial. Say, for example, I want to write the polynomial $p(z)=z^3+2z^2+1$ as a function ...
3
votes
1answer
3k views

Where can I calculate the exponential of a matrix online?

Where can I exponentiate a $3\times 3$ matrix like $\left[\begin{array}{ccc} 0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 0 \end{array}\right]$ online? Is there some website where this ...
13
votes
1answer
1k views

Overview of basic facts about Cauchy functional equation

The Cauchy functional equation asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of ...
1
vote
2answers
231 views

Study regimen for discrete mathematics? - Lack high-school maths…

I have just gotten into college, and will be studying mathematics from next semester. (this course) Unfortunately I did not study mathematics for the last 2-3 years of high-school mathematics. What ...
3
votes
0answers
92 views

Online Model Theory Classes

Since "model theory" is kind of too general naming, I have encountered with lots of irrelevant results (like mathematical modelling etc.) when I searched for some videos on the special mathematical ...
0
votes
2answers
408 views

Missing Exercises in Elementary Number Theory by Underwood Dudley.

I'm a beginner in math and I just started studying Elementary Number Theory by Dudley. So far I'm impressed, but I've noticed that the book does not include all the solutions to the exercises they ...
5
votes
4answers
190 views

Math school online?

As a hobbyist programmer with little to no math skills (no science skills either, thank you religious schools) I am finding math encroaching on my life more and more often. I have always laughed and ...
4
votes
2answers
95 views

Looking for a source of an infinite trigonometric summation and other such examples.

Question: If $x \neq 0$, then prove that $\displaystyle \sum_{n=1}^{\infty}\dfrac1{2^n} \tan\left(\dfrac{x}{2^n}\right) = \dfrac1{x} - \cot x.$ My answer: I proved this result by using the ...
3
votes
1answer
952 views

Differential Geometry Video Lectures

I know there's a similar question here, however since what I found there wasn't what I was looking for I thought on creating a new question. I'm studying Differential Geometry through Spivak's book "A ...
8
votes
2answers
285 views

What kind of math topics exist?

What kind of math topics exist? The question says everything I want to know, but for more details: I enjoy studying mathematics but the problem is that I can't find any information with a summary ...
0
votes
1answer
133 views

A matrix has a real logarithm if it has a positive spectrum.

The title is a proposition I read in my notes that's left with no proof. Where can I read one?
0
votes
1answer
191 views

Dynamical Systems. Bendixson's and Dulac-Bendixson's theorems.

I am looking for a place to read the proofs of Bendixsons and Dulac-Bendixsons theorems. Namely let D be a simply connected set and the following system be defined in D. $$\dot x=P(x,y)$$ $$\dot ...
1
vote
1answer
85 views

Finding equations of lines

I'm sitting an exam soon and have been revising for a while but I sometimes get stuck with questions that I know are simple but still have no idea about how to do them at all! Please explain to me how ...
1
vote
0answers
40 views

Order of operations

Looking for a source that lists every possible proper order of operations. The reason for this is that I made a mistake with fractional exponents, I don't want to make this mistake again.
0
votes
1answer
131 views

Probability Distribution Of A Linear Combination

I have scoured my textbook for the concept alluded to in the title of this thread; however, my textbook has failed, in that it provides no such information. Does anyone know of some resources for ...
3
votes
2answers
131 views

What are good resources to learn Mathematics for a working professional?

I have been out of school and working for 17 years now. I cannot remember anything I learned about trigonometry, algebra or geometry (which I think is as far as it went in those days) but I do find ...
11
votes
4answers
2k views

Overview of basic results about images and preimages

Are there some good overviews of basic facts about images and inverse images of sets under functions?
2
votes
1answer
146 views

Steiner symmetrization preserves area?

I just finished reading (and understanding) Steiner's proof of the isoperimetric inequality. His proof (which is sadly incomplete) seems to rely much on the fact Steiner symmetrization preserves area ...
1
vote
0answers
93 views

Resources to learn more about universality?

I'm fascinated by what I think is called Universality in mathematics. What I mean by this is systems with simple rules displaying very complex behaviours in aggregate. Conway's game of life, Wolfram's ...