OpenLLM-France/wikimedia huggingface dataset:
# Mathematics/Applied sciences/Introduction/Section

Mathematics has a multitude of applications. E.g., it helps to find a suitable room for a given audience, by comparing the number of seats with the number of persons. Both sets are counted with the natural numbers and mathematics provides methods to compare the two numbers directly, so that one does not have to try several rooms with the people. Mathematics helps to balance monthly debits and credits into balance by computing from the monthly income how much one may spend per day.
Mathematics has applications in the technical area, in image processing, in medicine, in data transmission and data storage, in the design of search algorithms, in solving logistic problems, in data science, machine learning, artificial intelligence. Here, we are mainly interested in applications of mathematics in other sciences. Mathematics is used in many different sciences, in the natural sciences like physics, chemistry, biology, in computer sciences, it is used in the form of statistics in psychology, sociology and history, as geometric device in cartography, in economics. Mathematics provides a language to describe empirical incidents in a quantitative way, it helps modelling theories about observable phenomena. Using techniques like interpolation and extrapolation, it allows giving predictions like for the weather or the development of the population on earth.
In these different areas, a huge variety of mathematical methods is applied, which differs strongly in its complexity, in terms of the mathematical structure and in terms of the application. E.g., statistics is a complex mathematical discipline, but in many sciences it is used (for good reason) directly as a black box without deeper reflection, for example to evaluate the reliability of a psychological test. On the opposite side, in (theoretical) physics there is such a tight connection with mathematics so that the theories in physics can not even exist without the mathematics and that a large portion of mathematics originates from physics. Regarding differential equations, one might be only interested in their numerics (concrete approximating techniques of computations), or whether they are adequate for a certain problem, or for the qualitative behavior of a solution. So mathematics is used in a broad range regarding depth in the sciences.
However, for most mathematical applications, it seems fair to say that an appropriate and reasonable use of mathematics requires a profound mathematical education, which can not be acquired in the context of concrete problems alone. It is the target of this course to build a mathematical base in order to persist in several scientific contexts.
# Mathematics/Calculuses/Quiz

Calculus is a lecture, part of a mathematics series on college mathematics.
You are free to take this quiz based on calculus at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{mathematics resources}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Calculus uses the shrinking neighborhood to approximate or derive the infinitesimal effect.
# Mathematics/Logic/Exercise

Why is mathematics difficult, though anything in it is logical?
# Mathematics Assistance

This is the Wikiversity School of Mathematics General assistance area. If you have a question that is not answered in one of the course tutorial pages, or the course tutorial page doesn't exist yet, feel free to ask the question here.

## Questions

Yeah, so I ultimately want to understand Eigenvalves, but before that I need to understand linear transformations but before that vector spaces but before that ring theory but before that field theory but before that group theory (I might not need this background, I don´t really know, but I´d like to understand them nonetheless). I read the wikibook on group theory, thought I got it, tried the first problem set, and noticed I did not get it. Is there a prereq to group theory? I have a high school mathematics background up to integrals (Calc II) (I also learned modulo systems from somewhere, but it wasn´t in the high school curriculum).
I´m guessing set theory might be a good idea, but are there pre-reqs for that too?
Thanks,
Fephisto

## Reply to Above

You don't really need to know field/group/ring theory to understand eigenvalues. Generally, math curriculums teach linear algebra before those topics, and that usually includes eigenvalues and eigenvectors. If you know a little bit about matrices already, it's not a huge leap to linear transformations and then to eigenvalues. Group/Field/Ring theory is generally reserved for those majoring in mathematics and are not used or learned by most people in scientific and technical fields.

## Questions

I have never tried this before, but here goes. I am a member of the over the hill gang (60 yrs), but a long time ago in a universe far far away I studied math for awhile (never finished tho) Actually, my background is somewhat non-standard as I was involved in an experimental program that spent a good deal of time constructing the real numbers instead of doing "real" real analysis. Now I am starting to read Tom Apostol's Volume I and am having a fairly good time doing it. I plan to read both Volumes I and II. I have no idea if I will continue in this reading, but I may very well do it. How much maths I may learn probably depends on how long my brain continues to function. At my stage in life, I am really not interested in getting formal credit for anything but I thought it would be nice to talk with some person about what I am doing from time to time. If you are interested in beginning a conversation, let me know by adding to this page.
Dave
Hello Dave
Don't know when you wrote the above, but I'm in your situation. Over 60, interested in math, took calculus, statistics, a bit of this and that in college in the last millennium. I do some reading in math, am trying to learn a little tensor algebra, and took some MOOCs. I heard about Very Large Numbers, and am fascinated by that topic. Am willing to engage and see if we are on the same page.
Ed
# PowerShell/Examples/Install-Flowgorithm
## See Also

* PowerShell
# PowerShell/Examples/Install-SQLServerExpress2019
## See Also

* PowerShell
# PowerShell/Examples/Install-GoogleChrome
## See Also

* PowerShell
# PowerShell/Examples/Install-VisualStudioCode
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* PowerShell
# PowerShell/Examples/Disable-InternetExplorerESC
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* PowerShell
# PowerShell/Examples/Install-SQLServerManagementStudio
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* PowerShell
# Meteorology

Please see Directions for use for more information.
Welcome to Introduction to Meteorology
Meteorology is a fascinating field that changes almost daily. Weather is an event that impacts our daily lives as well as our long-term future, and many mysteries still abound as we strive to become more knowledgeable about our Earth, her atmosphere, her oceans, and all of the little nuances that connect them all together. This course is being designed to help students build a solid foundation for future learning in the Atmospheric Sciences. We will cover everything from the planet's early weather to major atmospheric events and climate change.
Within this course you will find lectures, readings (from both the Meteorology Wikibook and Wikipedia), activities/projects, and assignments based on answering questions pertaining to the reading.
This course is being developed by students of an informal meteorology class, and it should be completed by May 2013.

## Course Summary

Portal:Physical Sciences
School:Meteorology
Department: Meteorology
Level: Secondary and Undergraduate
Suggested Prerequisites: It is recommended that you have the following. If you have not brushed up on your skills in awhile or you are still in the learning process, you are encouraged to participate in additional Wikiversity math and science resources before proceeding to more advanced study in meteorology.
** Basic Algebraic understanding
** Some exposure to basic Physics and Chemistry
Total Time Investment:
Assessment Suggestions:

## Student Learning Goals

Following the end of this course, students should be able to:
Describe the earth in its relationship to the sun and the sun's effect on the earth's short-term weather, explain the structure and composition of the atmosphere, atmospheric phenomena, atmospheric dynamics, causes of changes in atmospheric conditions, read basic weather maps, and explain the relationship of meteorology to other sciences.

## Learning materials

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the lesson (lessons are independent pages in the main namespace) and start writing!
You should also read about the Wikiversity:Learning model. Lessons should center on learning activities for Wikiversity participants. Learning materials and learning projects can be used by multiple projects. Cooperate with other departments that use the same learning resource.

### Texts

Wikibook's Meteorology
Wikipedia's Meteorology

### Course Resources

Intro to Meteorology Course Outline
Intro to Meteorology Study Guide

### Assignments

Reading Questions
# Methane
## Discovery

Methane was first synthesized from carbon and hydrogen in 1904 by a Russian-American chemist, Vladimir Ipatiev (1867-1952).

## Properties

Methane is the major component of natural gas, about 87% by volume. At room temperature and standard pressure, methane is a colorless, odorless gas; the smell characteristic of natural gas as used in homes is an artificial safety measure caused by the addition of an odorant, often methanethiol]] or ethanethiol. Methane has a boiling point of −161 °C (−257.8 °F) at a pressure of one Atmosphere (unit)|atmosphere. As a gas it is flammable only over a narrow range of concentrations (5–15%) in air. Liquid methane does not burn unless subjected to high pressure (normally 4–5 atmospheres).

## Quick Facts

Name: Methane
Formula: CH$_4$
Melting Point:
Boiling Point: -161.6 celsius
Appearance:
Molar Mass:
Shape: tetrahedryl
# Meteorological Piracicaba study group
### Objective

The Meteorological Piracicaba aims to translate notable study articles from the Piracicaba Meteorológica study group of Portuguese Wikiversity, which aims to analyze the weather conditions in the city of Piracicaba, São Paulo, Brazil, including severe weather events and weather patterns.

### Adding pages

Unlike the original Piracicaba Meteorológica study group, where study articles can have separate articles, the English version requires that they follow the standard: "Meteorological Piracicaba/[Article name]"

### Translation Guidelines

Only translate articles that:
* Are nearing completion or have already been completed.
* Analyze extreme weather phenomena (such as microbursts, hailstorms and notable windstorms)
* Analyze historical weather patterns (such as the most favorable time of year for such a weather event)
# Meteor radiation astronomy/Quiz

Meteor astronomy is a lecture for the radiation astronomy department course on the principles of radiation astronomy.
You are free to take this quiz based on meteor astronomy at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{principles of radiation astronomy}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Meteors range in size from galaxy clusters to dust grains and molecular clusters.
# Physics equations/Exams for algebra&trig based second semester course (Spring 2014)
## Test 1

* A proton is accelerated (at rest) from a plate held at 349 volts to a plate at zero volts. What is the final speed?
* How fast is a 3000 eV electron moving?
* What voltage is required to stop a proton moving at a speed of 5.4 x 10$^7$ m/s?
* What voltage is required accelerate an electron at rest to a speed of 1.4 x 10$^3$ m/s?
# Physics equations/Equations/Rotational and linear motion

| Linear motion | Angular motion |
| $x-x_{0}=v_{0}t+{\frac {1}{2}}at^{2}$ | $\theta -\theta _{0}=\omega _{0}t+{\frac {1}{2}}\alpha t^{2}$ |
| $v=v_{0}+at\,$ | $\omega =\omega _{0}+\alpha t\,$ |
| $x-x_{0}={\frac {1}{2}}(v_{0}+v)t$ | $\theta -\theta _{0}={\frac {1}{2}}(\omega _{0}+\omega )t$ |
| $v^{2}=v_{0}^{2}+2a(x-x_{0})\,$ | $\omega ^{2}=\omega _{0}^{2}+2\alpha (\theta -\theta _{0})$ |
# Physics equations/Faraday law
### Electromagnetic induction

   The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
Faraday's law of induction makes use of the magnetic flux Φ$_B$ through a hypothetical surface Σ whose boundary is a wire loop. Since the wire loop may be moving, we write Σ(t) for the surface. The magnetic flux is defined by a surface integral:
       $\Phi _{B}=\iint \limits _{\Sigma (t)}\mathbf {B} (\mathbf {r} ,t)\cdot d\mathbf {A} \ ,$
where dA is an element of surface area of the moving surface Σ(t), B is the magnetic field, and B·dA is a vector dot product (the infinitesimal amount of magnetic flux). In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.
When the flux changes—because B changes, or because the wire loop is moved or deformed, or both—Faraday's law of induction says that the wire loop acquires an EMF, ${\mathcal {E}}$, defined as the energy available from a unit charge that has travelled once around the wire loop. Equivalently, it is the voltage that would be measured by cutting the wire to create an open circuit, and attaching a voltmeter to the leads. According to the Lorentz force law (in SI units),
    $\mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)$
the EMF on a wire loop is:
    ${\mathcal {E}}={\frac {1}{q}}\oint _{\mathrm {wire} }\mathbf {F} \cdot d{\boldsymbol {\ell }}=\oint _{\mathrm {wire} }\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)\cdot d{\boldsymbol {\ell }}$
where E is the electric field, B is the magnetic field (aka magnetic flux density, magnetic induction), dℓ is an infinitesimal arc length along the wire, and the line integral is evaluated along the wire (along the curve the conincident with the shape of the wire).
The EMF is also given by the rate of change of the magnetic flux:
    ${\mathcal {E}}=-{{d\Phi _{B}} \over dt}\$,
where ${\mathcal {E}}$ is the electromotive force (EMF) in volts and Φ$_B$ is the magnetic flux in webers. The direction of the electromotive force is given by Lenz's law.
For a tightly wound coil of wire, composed of N identical turns, each with the same Φ$_B$, Faraday's law of induction states that
    ${\mathcal {E}}=-N{{d\Phi _{B}} \over dt}$
where N is the number of turns of wire and Φ$_B$ is the magnetic flux in webers through a single loop.

#### Problems and Examples

Faraday law example
# Physics equations/Faraday law/Faraday law example
## Spinning coil in a magnetic field

Faraday's law of induction|Faraday's law of electromagnetic induction states that the induced electromotive force is the negative time rate of change of magnetic flux through a conducting loop.
${\mathcal {E}}=-{{d\Phi _{B}} \over dt},$
where ${\mathcal {E}}$ is the electromotive force (emf) in volts and Φ$_B$ is the magnetic flux in Weber (Wb)|webers. For a loop of constant area, A, spinning at an angular velocity of $\omega$ in a uniform magnetic field, B, the magnetic flux is given by
$\Phi _{B}=B\cdot A\cdot \cos(\theta ),$
where θ is the angle between the normal to the current loop and the magnetic field direction. Since the loop is spinning at a constant rate, ω, the angle is increasing linearly in time, θ=ωt, and the magnetic flux can be written as
$\Phi _{B}=B\cdot A\cdot \cos(\omega t).$
Taking the negative derivative of the flux with respect to time yields the electromotive force.
| ${\mathcal {E}}=-{\frac {d}{dt}}\left[B\cdot A\cdot \cos(\omega t)\right]$ | Electromotive force in terms of derivative |
| $=-B\cdot A{\frac {d}{dt}}\cos(\omega t)$ | Bring constants (A and B) outside of derivative |
| $=-B\cdot A\cdot (-\sin(\omega t)){\frac {d}{dt}}(\omega t)$ | Apply chain rule and differentiate outside function (cosine) |
| $=B\cdot A\cdot \sin(\omega t){\frac {d}{dt}}(\omega t)$ | Cancel out two negative signs |
| $=B\cdot A\cdot \sin(\omega t)\omega$ | Evaluate remaining derivative |
| $=\omega \cdot B\cdot A\sin(\omega t).$ | Simplify. |

#### References

* ↑ https://en.wikibooks.org/w/index.php?title=Physics_with_Calculus/Electromagnetism/Electromagnetic_Induction&oldid=1979241
# Physics equations/Equations/Rotational and linear motion analogy

The following table refers to rotation of a rigid body about a fixed axis: $\mathbf {s}$ is arclength, $\mathbf {r}$ is the distance from the axis to any point, and $\mathbf {a} _{\mathbf {t} }$ is the tangential acceleration, which is the component of the acceleration that is parallel to the motion. In contrast, the centripetal acceleration, $\mathbf {a} _{\mathbf {c} }=v^{2}/r=\omega ^{2}r$, is perpendicular to the motion. The component of the force parallel to the motion, or equivalently, perpendicular, to the line connecting the point of application to the axis is $\mathbf {F} _{\perp }$. The sum is over $\mathbf {j} \ =1\ \mathbf {to} \ N$ particles or points of application.
Analogy between Linear Motion and Rotational motion :
| Linear motion | Rotational motion | Defining equation |
| Displacement = $\mathbf {x}$ | Angular displacement = $\theta$ | $\theta =\mathbf {x} /\mathbf {r}$ |
| Velocity = $\mathbf {v}$ | Angular velocity = $\omega$ | $\omega =\mathbf {d} \theta /\mathbf {dt} =\mathbf {v} /\mathbf {r}$ |
| Acceleration = $\mathbf {a}$ | Angular acceleration = $\alpha$ | $\alpha =\mathbf {d} \omega /\mathbf {dt} =\mathbf {a_{\mathbf {t} }} /\mathbf {r}$ |
| Mass = $\mathbf {m}$ | Moment of Inertia = $\mathbf {I}$ | $\mathbf {I} =\sum \mathbf {m_{j}} \mathbf {r_{j}} ^{2}$ |
| Force = $\mathbf {F} =\mathbf {m} \mathbf {a}$ | Torque = $\tau =\mathbf {I} \alpha$ | $\tau =\sum \mathbf {r_{j}} \mathbf {F} _{\perp }\mathbf {_{j}} =\sum \mathbf {r_{\perp j}} \mathbf {F} _{\mathbf {_{j}} }$ |
| Momentum= $\mathbf {p} =\mathbf {m} \mathbf {v}$ | Angular momentum= $\mathbf {L} =\mathbf {I} \omega$ | $\mathbf {L} =\sum \mathbf {r_{j}} \mathbf {p} \mathbf {_{j}}$ |
| Kinetic energy = ${\frac {1}{2}}\mathbf {m} \mathbf {v} ^{2}$ | Kinetic energy = ${\frac {1}{2}}\mathbf {I} \omega ^{2}$ | ${\frac {1}{2}}\sum \mathbf {m_{j}} \mathbf {v_{j}} ^{2}={\frac {1}{2}}\sum \mathbf {m_{j}} \mathbf {r_{j}} ^{2}\omega ^{2}$ |
# Physics equations/Equations/Moments of inertia (large table)

| Description | Moment(s) of inertia |
| Point mass m at a distance r from the axis of rotation. | $I=mr^{2}$ |
| Two point masses, M and m, with reduced mass $\mu$ and separated by a distance, x. | $I={\frac {Mm}{M\!+\!m}}x^{2}=\mu x^{2}$ |
| Rod of length L and mass m (Axis of rotation at the end of the rod) | $I_{\mathrm {end} }={\frac {mL^{2}}{3}}\,\!$ |
| Rod of length L and mass m | $I_{\mathrm {center} }={\frac {mL^{2}}{12}}\,\!$ |
| Thin circular hoop of radius r and mass m | $I_{z}=mr^{2}\!$ $I_{x}=I_{y}={\frac {mr^{2}}{2}}\,\!$ |
| Thin cylindrical shell with open ends, of radius r and mass m | $I=mr^{2}\,\!$ |
| Solid cylinder of radius r, height h and mass m | $I_{z}={\frac {mr^{2}}{2}}\,\!$ $I_{x}=I_{y}={\frac {1}{12}}m\left(3r^{2}+h^{2}\right)$ |
| Sphere (hollow) of radius r and mass m | $I={\frac {2mr^{2}}{3}}\,\!$ |
| Ball (solid) of radius r and mass m | $I={\frac {2mr^{2}}{5}}\,\!$ |
| Thin rectangular plate of height h and of width w and mass m (Axis of rotation at the end of the plate) | $I_{e}={\frac {mh^{2}}{3}}+{\frac {mw^{2}}{12}}\,\!$ |
| Solid cuboid of height h, width w, and depth d, and mass m | $I_{h}={\frac {1}{12}}m\left(w^{2}+d^{2}\right)$ $I_{w}={\frac {1}{12}}m\left(h^{2}+d^{2}\right)$ $I_{d}={\frac {1}{12}}m\left(h^{2}+w^{2}\right)$ |
# Physics equations/Equations/Moments of inertia (small table)

| Description | Moment(s) of inertia |
| Rod of length L and mass m (Axis of rotation at the end of the rod) | $I_{\mathrm {end} }={\frac {mL^{2}}{3}}\,\!$ |
| Solid cylinder of radius r, height h and mass m | $I_{z}={\frac {mr^{2}}{2}}\,\!$ $I_{x}=I_{y}={\frac {1}{12}}m\left(3r^{2}+h^{2}\right)$ |
| Sphere (hollow) of radius r and mass m | $I={\frac {2mr^{2}}{3}}\,\!$ |
| Ball (solid) of radius r and mass m | $I={\frac {2mr^{2}}{5}}\,\!$ |
# Motivation and emotion/Book/2011/Dealing with conflict/Conflict styles survey
## Creation

This survey was created by user Courtney.reis 05:24, 2 November 2011 (UTC) for the purposes of the Motivation and Emotion Unit Semester 2011 textbook chapter (see "See Also" section for link to chapter with this quiz) . It was created with the information based on Calhoun, Cann, Norman and Welbourne's (2008) conflict styles model. This purports that 4 styles of conflict exist (Calhoun, Cann, Norman & Welbourne, 2008). These four styles are dominating, obliging, integrative and avoidant (Calhoun et al., 2008). For the quiz, 2 questions based on each style and the information provided on it were created. For example, for the dominating style, the characteristics are high concern for self and low concern for others (Calhoun et al., 2008). THe question created was therefore "I think about my aims and goals over others when in conflict". The same process was followed for each conflict style.
The survey was then created in Wikiversity. For each question, a yes answer gives a certain number of points. A "yes" response to a question depicting Avoidant Style of conflict will gain you 1 point, a yes to Obliging Style will gain you 2 points, a yes to Integrative Style will gain you 3 points and a yes to Dominating Style will gain you 4 points. Any scores which equal more than 8 (the maximum points you can get if you answer yes to only the 2 questions depicting one style of conflict) are said to indicate a style of conflict which utilises more than one kind of conflict style. (I.E if somebody answered yes to both dominating questions and both avoidant questions, they would get a score of 10, indicating they answered yes to alot of questions).
As it is self created and untested, the validity and reliability of this survey is in question. It would need rigorous testing and more evidence before taken as a truly informative quiz.

## See Also

Dealing With Conflict - How To Manage Emotion for Effective Conflict Resolution
# Programming Fundamentals/Introduction/VB.NET
## Try It

Copy and paste the code above into one of the following free online development environments or use your own VB.NET compiler / interpreter / IDE.
* paiza.IO
* TutorialsPoint

## See Also

* Microsoft: Hello World in Visual Basic
# Programming Fundamentals/Loops/COBOL
## Try It

Copy and paste the code above into one of the following free online development environments or use your own COBOL compiler / interpreter / IDE.
* JDoodle
* paiza.IO
* TutorialsPoint

## See Also

* TutorialsPoint: COBOL
* GnuCOBOL Manual