Questions tagged [online-resources]

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

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What are good free Websites for equation/expression simplification?

I could easily answer some of my questions if I were able to simplify certain equations/expressions. For example in one of my questions a user simplified this: $${\sqrt{x^2+y^2}\over |2*sin(arctan(y/x)...
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Transformation of graph resources

I was looking through a question about maximum area of triangle in an ellipse, and in the answer the coordinate system was changed to make the ellipse a circle in the new system, which made the ...
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2 votes
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Connections on indefinite inner product space bundles

Let $K$ denote a finite-dimensional vector space over $\mathbb{C}$. If $K$ is paired with a map $(\cdot,\cdot):K\times K\to\mathbb{C}$ such that, for all $\varphi,\psi,\chi\in K$ and $z,w\in\mathbb{C}$...
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Testing functions for binary optimization

It is well known that it is hard to find optimum of some functions, mainly those with lot of local extremes, discontinuities etc. To assess quality of optimization algorithms (particularly heuristics),...
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7 votes
1 answer
126 views

Formalizing Natural Languages

I've been interested in the subject of metalanguages and how (if) we can formalize them. Most metalanguages I've encountered use some variation of a natural language (such as English, German or French)...
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1 answer
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Maximum of $\frac{Bx}{x^3 + Rx + P}$

I submitted this function to Wolfram Alpha and similar tools, but none can find for me the symbolic expression for maximum value, unless I give specific values to each parameter: $$\frac{Bx}{x^3 + Rx +...
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Looking for First Year Statistics Lecture Notes

I'm looking for lecture notes for a first course of statistics. When I tried looking for lecture notes myself they were either not comprehensive or too advanced for my level. Does anybody know of a ...
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Book recommendation and proofs for first course in ODE [closed]

I just enrolled for my first course in ODE ,and would like to follow a book that gives an intuition behind the formulas being taught and the derivation of those formulas Here is the course syllabus ...
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Is there a website to find groups with given properties?

I am thinking of something like $\pi$-base but for groups: you give it properties $A,B,C,D$ of groups (or their opposites) and the website returns a list of all the groups it knows with those ...
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1 answer
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Resource recommendation

Are there more books like Div, Grad, Curl and all that by HM Schey? It's hard to describe by what I mean by "books like" to someone who hasn't read above mentioned text, but roughly it means ...
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1 vote
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Is there a database/collection of ODEs that are Lipschitz?

In order to study various ODE solvers (Forward Euler, Runge-Kutta, linear multi-step methods etc.) I would need a collection of different ODEs that are Lipschitz. Is there such a thing as an online ...
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1 vote
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Need help finding G. Pick's 1917 article "Über affine Geometrie iv: Differentialinvarianten der Flächen gegenüber affinen Transformationen"

I'm studying affine geometry and I need help finding this article "Über affine Geometrie iv: Differentialinvarianten der Flächen gegenüber affinen Transformationen" written by G. Pick in ...
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1 answer
109 views

Is there a good page where mathematic papers are uploaded?

I am looking for a website where good math papers are uploaded that you can just read. I would like to read a little through the topics, but so far I have not really found a site that is clear and ...
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Resources with examples for Bayesian Data Analysis in R

I'm taking a course on Bayesian Data Analysis, and currently I need to do a project that requires the use of $R$ as a programming language. The goal of the project is to use basic Bayesian Inference ...
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The recording of Lecture Courses by Alexandre GROTHENDIECK in 1973

According to the website https://v1.archmathsci.org/catalogue/general-chronology-of-recordings-since-1973/chronology-of-recordings-1973-1980/1973-recordings/ There are Lecture Courses by Alexandre ...
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3 votes
1 answer
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Laplace transforms of products of modified Bessel Functions

I am dealing with integrals of the form $$\int_0^\infty e^{-t}I_0(xt/a)^a\ \mathrm{dt}$$ where $I_0(x)$ is the modified Bessel function of the first kind. Clearly this is just a Laplace Transform $\...
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Mechanics of Clifford Algebra valued Möbius Maps

The Möbius maps $$ (ax+b)(cx+d)^{-1} $$ Where $a,b,c,d,x \in \mathbb{C}$ are well-understood, but how do the ones where the variable and coefficients are in Clifford Algebras act? Are there any good ...
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Resources/explanations for conformal geometry with “null cones at infinity”

In the Wikipedia article on conformal geometry https://en.m.wikipedia.org/wiki/Conformal_geometry there’s a section in Mobius geometry that says it’s the study of pseudo Euclidean spaces with either a ...
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What is the tensor power series of a vector?

In this Wikipedia article https://en.m.wikipedia.org/wiki/Jet_(mathematics) there’s Taylor’s theorem for functions $f: \mathbb{R}^m \to \mathbb{R}^n$ where $f(x)=\sum_{n\in \mathbb{N}} D^n f(x_0) (x-...
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1 answer
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Resources/explanations of the Darboux Derivative

I recently came across the Darboux Derivative $\omega _f\equiv f^* \omega_G$, where $f:M \to G$ maps from a manifold to a Lie group, $f^*$ is its pullback, and $\omega _G$ is the Maurer-Cartan form of ...
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  • 491
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1 answer
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Proof for the Characteristic Path Length [closed]

Where is there proof on the characteristic path length I have been looking online and can't seem to find any? I find the equation a lot however, I don't seem to find any actual proof is there a ...
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25 views

Searching formula with vertical bar (absolute value) in Google

I'm wondering if it's possible to search a formula with vertical bars inside in Google. If I try to search: integral "|x^n|" Google is not able to understand that the vertical bars represent ...
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2 votes
0 answers
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On spherical distributions in abstract harmonic analysis

I need a detailed and comprehensive guidance or possibly relevant materials that can help me in my research on spherical distributions on a locally compact group. Jacques Faraut wrote on spherical ...
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1 answer
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Resources recommandation of probablity theory without measure theory which is suitable for machine learning?

When I finished a course learning elementary probability as a student majoring in computer science, I try to dive into machine learning theory. However, I find my knowledge acquring from the ...
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2 votes
0 answers
63 views

Exercise sources for an engineering freshman

I'm an engineering freshman and I want to know good sources for exercises only that have a variety of different problems on subjects with answers, Any recommendations would be appreciated for the ...
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1 vote
1 answer
137 views

"Sequence-builder" notation

I am somewhat familiar with set-builder notation, but I'm wonder what the equivalent notational conventions for sequences are. I know that one can denote a sequence as the following: $$\{a_n\}_x^y \ \ ...
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0 votes
1 answer
133 views

Resources to accompany First Course in Probability by Sheldon Ross [closed]

Probability Resources I am taking a probability course this semester and we are using (First Course in Probability by Sheldon Ross 9th edition) textbook.Unfortunately I can't understand from my ...
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1 answer
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Is there a more specific name for this PDE and how do I solve it?

I have reduced a problem I am working on down to finding a solution $u: \mathbb{R}^2 \to \mathbb{R}$ for a PDE of the form $$u_t(t, x) + (a x f(t) + b) u(t, x) + (c x + d)u_x(t, x) = 0$$ where $a, b,...
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0 votes
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Resources for group theory? [duplicate]

I have recently started studying abstract algebra (specifically group theory). So far my learning has consisted of videos giving an intuition (e.g. 3blue1brown) and various lecture notes I've found on ...
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3 votes
2 answers
55 views

An analogue to OEIS for graphs and ordered pairs?

Does anyone know if such a thing exists already? I was able to find a number of seemingly very comprehensive encyclopedia-like reference pages on many species of graphs, but it seemed that the use ...
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3 votes
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Looking for group theory exercises

I'd like to have, please, some recommendation for free sources for group theory exercises with solutions. I have looked online but couldn't find some good resources. Thank you.
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Visualizing vanishing sets, online tools for algebraic geometry

Is there an online tool which can visualize algebraic sets such as $V(x+xy^2)$ or similar vanishing sets? More generally, are there some neat programs found online, which help getting a grasp of such ...
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Looking for a discrete mathematics course by programming

Background: I am a totally blind programmer. That is, I cannot see at all. I am using a screen reading software to read texts, but not images. I am unable to get a computer science degree. Now I am a ...
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1 vote
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How is the pair of adjoint functors defined in this ncat article?

I'm trying to read the article about spaces and quantities on ncat. I find it very interesting, but I'm afraid I can't follow how technically they are defining the functors – either because it's ...
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1 vote
1 answer
87 views

What are the important things to study in infinity categories?

I am reading about infinity categories. My source is http://www.mathematik.uni-regensburg.de/cisinski/CatLR.pdf My aim is to think categorically so that all the constructions I deal with are natural (...
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3 votes
1 answer
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Modules of quotients of enveloping algebras

I'd like to ask for any resource recommendations whether research literature or pedagogic, on working out the representation theory (i.e. finding all simple modules) for quotients of universal ...
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1 vote
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How to get solutions of this book?

I am reading the book, "Lemmas in Olympiad Geometry".This book has a nice collection of problems at the end of almost every chapter but unfortunately, there is no solution given to it. Now I ...
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3 votes
0 answers
48 views

Resources for operator algebraists interested in understanding category theory?

Just wondering if there are any resources for learning category theory that might be particularly interesting or helpful for someone mainly studying things under the umbrella of operator algebras. I'...
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4 votes
0 answers
134 views

Software to explore abstract algebra and/or category theory [closed]

Is there any software that lets one explore group theory, ring theory, and category theory visually and theoretically that is tailored for education purposes? I'm not talking about using software like ...
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Resources for learning Mathematics for new devotee

After a random encounter with Mathematics, I was astounded to discover that it finally began to click. With this new finding, I decided to get myself a beginner's book to brush up on my math skills. I ...
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1 vote
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Online Math Colloquia

One of the formative experiences of my undergraduate education in math was attending department math talks. These were usually aimed at general faculty members, so they went well over my head at the ...
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References for Euclidean geometry of quadrilateral

I'm quite familiar with the results in Euclidean geometry of triangles. However, it's not the case with quadrilateral. Is there any sources to learn and to check the complicated, advanced results in ...
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0 votes
0 answers
117 views

Source for learning etale cohomology

I want to understand the concepts of etale cohomology and I have absolutely no background on homological algebra. I have a basic understanding about algebraic geometry. Can anyone suggest me a source ...
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5 votes
0 answers
73 views

What would be an alternative to Robogebra to animate mathematical writing? [closed]

Yesterday, I came across a website called Robogebra. It does exactly what I wanted: It creates animations simulating the handwriting of mathematical equations, it supports LaTeX syntax and does many ...
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Good online course recomendation for Topology

I want to learn the field of topology from scratch. I am working on a self-project for classifying using neural networks based on topology statistics features. I am looking for recommendations for ...
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Is there a "structured catalog" of mathematical structures?

There are nice small overviews of classes of mathematical structures like this overview of group-like structures that organize different classes of mathematical structures by the data and axioms that ...
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2 votes
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Linear Algebra equivalent of Paul's Online Math Notes (Lamar)

I'm not sure if this is question is a better fit for the main site or the meta site, but I was wondering if there are any beginner-friendly websites to learn linear algebra, similar to Paul's online ...
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4 votes
0 answers
79 views

How to define the shapes and orientations of orbitals mathematically in a cartesian coordinate system?

I am not able to match the $d$ and $f$ orbitals in atomic structure worksheet given as homework (see the attached image). I was able to match the $p_{x}$ , $p_{y}$ , and $p_{z}$ orbitals. But I am ...
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Searching for the absorption coefficient of 6 gases

I am currenly working on heat transfer by radiation, which includes working with the absorption coefficient $\kappa$: $\frac{dI}{ds}=\kappa I_b + (\kappa + \sigma_s) + $ scattering term. However, I ...
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General approach to numerical analysis

(disclaimer: this question was posted on Physics.SE but a comment suggested posting here, so here I go) I'm choosing an advisor for my master's thesis, and in my university, there are a couple of ...
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