OpenLLM-France/wikimedia huggingface dataset:
# Product ring/R^2/Component wise/No field/Exercise

Show that $P=\mathbb {R} ^{2}$ with componentwise addition and componentwise multiplication is not a field.
# Product set/Circle and line/Cylinder/Example

Let $S$ denote a circle (the circumference), and let $I$ be a line segment. The circle is a subset of a plane $E$, and the line segment is a subset of a line $G$, so that for the product sets, we have the relation
    $S\times I\subseteq E\times G\,.$
The product set $E\times G$ is the three-dimensional space, and the product set $S\times I$ is the surface of a cylinder.
# Psychological statistics

In professional psychology, evidence based practices are quite popular. The history of psychology predates clinical research involving deeply analyzed statistics and trials. Often, psychiatry is the dominant approach in treating psychological/emotional problems. How research is conducted and analyzed has many implications for society and human beings within society. Here you can learn about psychological statistics. You can learn what they are, how they are utilized, and how to analyze them.

## Univariate

* Data
* Variable
* Levels of measurement

## Bivariate

* Linear correlation

## Multivariate

* Multiple linear regression
* ANOVA

## Statistical software

* Comparison of statistical packages

## Readings
### Wikipedia

* Publication bias

### External

* Multiple Researchers Examining the Same Data Find Very Different Results
* Publication Bias: Does Unpublished Data Make Science Pseudo?
# Psychological research goals

There are four main goals/purposes of psychological research:
* Explore (exploratory) - scope out, get to know, and reveal more about a phenomenon (e.g., what do people think about happiness is?)
* Describe (descriptive) – describe behaviour, thoughts, emotions etc. (e.g., how happy are people?)
* Explain (explanatory) – identify causes of psychological experience (e.g., why are some people happier than others?)
* Predict (predictive) – identify factors that indicate when an event will occur (e.g., what social policy changes can improve happiness?)

## Explore/Describe

* Use observational methods, surveys, case studies.
* Give a verbal or numerical picture.
* Describe average or typical features of a group
* Present basic background information or a context.
* Describe e.g., characteristics of a group e.g., in terms of age, IQ, personality etc.
* attitudes to environment – positive or negative – but no indication of why these attitudes exist.
* Basic background information or a context.
* Find information to stimulate new explanations. e.g., criteria for classifying mental disorders (e.g., DSM)

## Explain

* Identify factors that indicate when an event will occur
* Most psychological research has explanation as its goal – how sure we can be about establishing cause & effect depends on the research design used
* Use correlational methods; correlation between two events or variables
* Do stressful life events lead to increased physical illness?
* Do stressful life events lead to increased physical illness?

## Predict

* Use experimental method to test an explanation – usually based on theory
* e.g., Environmental behaviour is predicted by intentions, attitudes, norms and pbc
* Clear test of a hypothesis derived from theory
* Extend a theory or principle in to new areas of issues
* Provide evidence to support or refute an explanation or prediction
The research goal will influence the research method.
# Psychology/Australia

This page is for organising information about teaching, learning, and research in the area of psychology in the country of Australia.
As a subject, psychology is taught at secondary and tertiary levels in Australia. At the tertiary-level, degree-granting programs may or may not be accredited by the peak professional body, the Australian Psychological Society. If you are selecting a university, then this is important to keep in mind.
# Psychology/History

In this section we will not start at the beginning of time to find the smallest trace of what we call psychology today. Instead we will start with Epistemology. Epistemology is the study of knowledge, or simply what we know.

## What do we know?

There are many forms of knowledge, such as you know your name or some fact, or that you know how to move your arm. Here we will look at two schools of thought and how for 1700 years people attempted to answer this problem. [Rationalism] and [Empiricism]

## Rationalism

   Rationalist philosophers believe that all knowledge can be understood through a process of reasoning, without any external sources. They do not believe that human beings can understand everything this way, but that it is theoretically possible.

## Empiricism

   Empiricism is a theory of that believes that all knowledge comes from experience.
# Psychological well-being

This psychology resource is a "stub". Learn how you can help Wikiversity to develop it.
According to Pavot and Diener (1993), psychological well-being refers to the subjective experience of two aspects of one's psychological experience:
* Emotional or affective experience (i.e., positive and negative affect)
* Conceptual or cognitive experience (i.e., satisfaction with life, relationships, work, and leisure)
# Psychology/Articles

This psychology resource is a "stub". Learn how you can help Wikiversity to develop it.

## To be sorted

* Average salaries of PhDs in psychology by geographical area (2003)
* Sheep In Human Clothing: Scientists Reveal Our Flock Mentality (2008)
* Psychologists are beating mathematicians in the Netflix challenge (2008)
* New theories on binge eating formulated. (2007, April 8)
# Psychological needs

This psychology resource is a "stub". Learn how you can help Wikiversity to develop it.
Psychological needs, according to self-determination theory, include:
* Autonomy
* Competence
* Relatedness
These are proposed as universal needs.
# Psychological therapy

This psychology resource is a "stub". Learn how you can help Wikiversity to develop it.
Psychological therapy is the use of psychological methods to help people overcome problems.

## Discussion questions

* Is nonconsensual psychological therapy ever helpful?
* How can psychological therapy be helpful?
* What are some potential goals of psychological therapy?
# High risk research

* Please help develop and classify this resource
* Learn how you can develop this resource to teach participants about High risk research. Choose a subject, education level, and resource type to classify the resource by. You may learn more about the topic to help you develop and classify the resource from:
High risk research involves conducting research that has a large potential reward, but also has a significant potential to fail or prove not-fruitful.
High risk research can include research and technologies that may only be theoretically possible and may in fact actually be impossible to create. Part of high risk research may include simply researching whether or not something is even actually possible.

## Examples of high risk research

High risk research could include research related to some of the following.
* Faster than light travel/Faster than light technology
* Stopping human aging/Ending aging
* Teleportation technology
* Ending poverty
* Anti-gravity technology
* Artificial gravity technology
* Fusion power research
# High School German/German I

* Einleitung
* This course is an introduction to German for American students with no prior experience to foreign language. The material is divided into 10 Units and should represent 135-150 hours of coursework (A standard High School class).
* Kurseinheiten
* Learning a Language
* A1.1 Wie heißt du?
* Wortschatz
* Wohin soll es gehen?
* Once you have completed this course, you have learned enough to take this course:
* High School German/German II
* Need to certify your ability? After finishing this course you should be at the A1 level.
* Certify your ability with an A1 Fit in Deutsch test.
vteAdditional German Resources :
# High school physics
## Fundamental Concepts

* Introduction
* Basics
* Scientific Method (also Experiment, Observation and Testing Hypotheses)
* Units and dimensions/Dimensional Analysis
* Metric system
* Precision, Accuracy, Rounding, and Significant figures
* Scientific notation
* Trigonometry
* Vectors

## Mechanics

* Motion - Mechanics
* Motion - Kinematics
* Motion - Dynamics
* Energy

## Kinematics: Objects in Motion
### Translational Motion

* Motion in a straight line
* Newton's Laws of Motion
* Work, Power, and Energy
* Gravity
* Motion in two dimensions

### Rotational Motion

* Circular Motion
* Angular Velocity
* Centripetal acceleration
* Center of mass
* Torque and Angular Acceleration
* Moment of Inertia

## Fluid Mechanics

* Hydrostatics: Fluids at Rest
* Hydrodynamics: Fluids in Motion

## Thermodynamics

* Basic Definitions
* Zeroth Law of Thermodynamics
* First Law of Thermodynamics
* Second Law of Thermodynamics
* Third Law of Thermodynamics

## Electricity and Magnetism

* Electric charge
* Coulomb's Law
* Electric Fields and Forces
* Electric Circuits
* Electric flux and Gauss's law
* Magnetic Fields and Forces
* Electromagnets
* Permanent Magnets
* Magnetism
* Kirchhoff's current law, and Kirchhoff's loop law

## Oscillations and Waves

* Simple Harmonic Motion
* Pendulums
* Waves
* Sound
* Light and Optics

## Atomic, Nuclear, and Particle Physics

* The Atom
* Basic atomic physics
* Particle Physics

## Advanced Topics for Exploration

* Special Relativity
* General Relativity
* Cosmology
* Quantum Mechanics

## Physics Study Guide

Also look at the Physics Study Guide
# High intensity training

High Intensity Training (HIT) is a form of strength training popularized since 1970s by Arthur Jones. HIT focuses on performing quality weight training repetitions to the point of momentary muscular failure.
The training takes into account the number of repetitions, the amount of weight, and the amount of time the muscle is exposed to muscle tension in order to maximize the amount of muscle fiber recruitment. One of the possible examples of HIT is illustrated in the animation below.

## Main principles

The fundamental principles of High Intensity Training (HIT) are that exercise should be brief, infrequent, and intense. Exercises are performed with a high level of effort, or intensity, where it is thought that it will stimulate the body to produce an increase in muscular strength and size.Advocates of HIT believe that this method is superior for strength and size building to most other methods which, for example, may stress lower weights with larger volume (sets x reps). As strength increases, HIT techniques will have the weight/resistance increased progressively where it is thought that it will provide the muscles with adequate overload to stimulate further improvements. There is an inverse relationship between how intensely and how long one can exercise. As a result, high intensity workouts are generally kept brief as shown in the following animation:
After a High Intensity workout is done, as with any other workout, the body requires time to recover and produce the responses stimulated during the workout, so there should be more emphasis on rest and recovery in the HIT philosophy than in most of the other weight training methods.
# High School German/Introduction
## Introduction

Welcome to High School German. This course is designed for High School students with no prior language learning experience. The language of the course is German, and learners will build their understanding of German over a four year curriculum.
German is a West Germanic language that is mainly spoken in Central Europe. Today, German is the most spoken native language in the European Union. German is the majority language in the DACH countries of Germany, Austria, Switzerland and Liechtenstein. As of 2012 there were 90,000,000 native speakers of German worldwide
German is also the majority spoken language in South Tyrol in Italy, and the German-speaking Community of Belgium. It is one of the three official languages of Luxembourg and a co-official language in the Opole Voivodeship in Poland.
The German language is most similar to other languages within the West Germanic language branch, including Afrikaans, Dutch, English, Frisian, Low German/Low Saxon, Luxembourgish, and Yiddish.
It also contains close similarities in vocabulary to Danish, Norwegian and Swedish, although they belong to the North Germanic group.
German is the second most widely spoken Germanic language, after English.
In this course, learners will be taught Standard German otherwise known as Hochdeutsch.

### Citations

* ↑ "Special Eurobarometer 386: Europeans and their languages" (PDF) (report). European Commission. June 2012. Archived from the original (PDF) on 6 January 2016. Retrieved 24 July 2015.
# Repl.it/GitHub Integration

Repl.it supports integration with GitHub public repositories using the graphic user interface and with public and private repositories using git commands. This resource shows how to integrate with GitHub using git commands.

## Fetch an Existing GitHub Repository

To fetch an existing repository into the current folder:
* Log in to Repl.it. Create a user account if you don't have one already.
* Create a new repl if necessary.
* Review workspace shortcuts and open a new shell, such as with Ctrl+Shift+S.
* In the terminal window, run the following command: git init
* In the terminal window, type the following command, but don't run it yet: git remote add origin
* In a separate browser tab, log into GitHub and select a repository. Select Clone or download and copy the repository URL to the clipboard.
* In the Repl.it tab terminal window, finish the git remote add origin command by pasting the repository URL at the end and run the command. The command should look like the following: git remote add origin your_repository_url
* In the terminal window, run the following commands. The repository will be merged with the current folder. git fetch --all git reset --hard origin/master

## Update the Run Button

The run button action is controlled by the .replit file:
* If necessary, create a .replit file in the root folder of your repository.
* The .replit file should contain the following lines (Python3 example): language = "python3" run = "python3 main.py"
* To run a different file, change the .replit file run line. For example, to run a file named Activity 1.py in the Assignment 1 folder, use the following. Note the nesting of single quotes inside double quotes, necessary with folder or file names containing spaces: run = "python3 'Assignment 1/Activity 1.py'"

## Synchronize Changes with GitHub

To synchronize Repl.it changes with GitHub, use the following git commands in the terminal window:
When your repository is updated outside Repl.it and you want to pull those changes into your repl, use the following command:

## See Also

* Repl.it: Repl.it + Git Tutorial
* Repl.it: Using Git with Repl.it - A Short Guide
* Repl.it: A Comprehensive Guide to Replit's New Git and GitHub Features
* Repl.it: Configuring GitHub Repos to Run on Repl.it and Contributing Back
# Reproducible Science

In times of "Faked News" and "Alternative Facts" especially the reproducibility of scientific results is targeted in this learning resource.

## Introduction

Reproducibility is the ability to get
* (Result) the same research results or inferences,
* (Data)
** based on the same raw data or
** with data collected with the same or very similar sampling and research procedures (replicability)
    and finally
* (Algorithms)the same computer programs (e.g. Open Source R or KnitR) provided by researchers.
* (Capacity Building) optional access to capacity building material allows other scientist re-use the provide approach for their experimental design (see Open Educational Resources)
A related concept to reproducibility is replicability, meaning the ability to independently achieve non identical conclusions that are at least similar, when differences in sampling, research procedures and data analysis methods may exist. Reproducibility and replicability together are among the main beliefs of ‘the scientific method’ - with the concrete expressions of the ideal/idea of such a method varying considerably across research disciplines and fields of study.

## Learning Tasks

* Explore the KnitR concept of integration of content, data and algorithms for data processing.
* Compare the following two different scenarios:
** A researcher collects data and applies a several methodologies of data analysis (statistical and/or numerical approaches) to the data until a significat publishable result was found.
** A researcher has to publish a KnitR document (R-Markdown) prior to sampling the data. After sampling is finished the data was processed with the KnitR document and results will be published as significant or not significant.
* Analyse the WHO Document about clinical trial. Explain, why is it important to publish negative results (e.g. statistical bias)! Why does the publication of negative results contribute to concept Reproducibility?
# Jazz improvisation

< School of Music and Dance | Jazz

## Introduction

This is my first time on the wikipedia web site. I was poking around and saw this page. I thought my contribution could be sharing an observation as a jazz educator.
Over the years I have tried many different approaches to teaching kids to improvise. Blues scales, modes pentatonic scales etc. I have found that the most beneficial bit of information is basic chord structure. By teaching students that chords are built in thirds and by practicing a universal triad (13th chord) in different key signatures, they understand note choices better. Then they plug in the formulas for Major 7th, Dominant 7th, minor 7th etc. This then leaves choosing rhythms and styles.
As usual, music and teaching are always a work in progress. What works with one group of kids may need to be modified for the next group.
Please share your thoughts.
The most complicated part of improvising is moving outside of the chord and/or key. Students must poke around and learn what works and what doesn't. You cannot simply tell someone what they should play.
If the musician is doing improv as a solo during a song, they should examine the melody and notice what notes of the melody are outside the chord, and try and incorporate those notes into the solo also.
# Jazz

< School of Music and Dance

## Introduction

Welcome to the Wikiversity School of Music Jazz Department, founded on the January 20, 2007.
Here, we will focus on developing resources, courses, lessons, and learning projects for Jazz students and practitioners. Like Jazz itself, we hope to remain informal, casual, relaxed and most-of-all creative.
The "topic" namespace contains pages that are for management and organization of small academic units at Wikiversity such as departments (see: Wikiversity:Topics).

## Learning Projects

See: Learning Projects and the Wikiversity:Learning model.

## Suggested Prerequisites

* Basic Blues & Rock
** Blues basics constitute an important part of the basics of jazz.
* Knowledge of chords is critical to understanding the building blocks of jazz music.

## Lessons

See also: Courses on the French Wikiversity's Jazz course
* Jazz harmony
* Jazz improvisation
* Jazz Piano
* Jazz Vocals

### Related topics

* Getting started with sound recording
* Jamming Online

## About the learning materials

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the learning project (learning projects are independent pages in the main namespace) and start writing! We suggest the use of the learning project template (use "subst:Learning project boilerplate" on the new page, inside the double curved brackets {}).
See code for more information.

## Degree plans

See: Degree plan

## Streams

See: Stream plan

## Active participants

* CQ (talk • email • contribs • stats • logs • global account)
* Thierry613 (talk • email • contribs • stats • logs • global account)
* SelfieCity (talk • email • contribs • stats • logs • global account)
# Real exponential function/Base/Properties/Fact

Let $b$ denote a positive real number. Then the exponential function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto b^{x},$
fulfills the following properties.
* We have $b^{x+x'}=b^{x}\cdot b^{x'}$ for all $x,x'\in \mathbb {R}$.
* We have $b^{-x}={\frac {1}{b^{x}}}$.
* For $b>1$ and $x>0$, we have $b^{x}>1$.
* For $b<1$ and $x>0$, we have $b^{x}<1$.
* For $b>1$, the function $f$ is strictly increasing.
* For $b<1$, the function $f$ is strictly decreasing.
* We have $(b^{x})^{x'}=b^{x\cdot x'}$ for all $x,x'\in \mathbb {R}$.
* For $a\in \mathbb {R} _{+}$, we have $(ab)^{x}=a^{x}\cdot b^{x}$.
# Real exponential function/Base/Via logarithm/Definition

For a positive real number $b>0$, the exponential function for the base $b$ is defined as
    $b^{x}:=\exp(x\ln b)\,.$
# Real exponential function/Characterization with derivative/Exercise

Let
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x),$
be a differentiable function with the property
    $f'=f{\text{ and }}f(0)=1.$
Prove that $f(x)=\exp x$ for all $a\in \mathbb {R}$.
# Real exponential function/Continuity and image/Fact

The real exponential function
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto \exp x,$
continuous
$\mathbb {R}$
$\mathbb {R} _{+}$
# Real exponential function/Base/Properties/Fact/Proof/Exercise

Let $b$ denote a positive real number. Prove that the exponential function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto b^{x},$
fulfills the following properties.
* We have $b^{x+x'}=b^{x}\cdot b^{x'}$ for all $x,x'\in \mathbb {R}$.
* We have $b^{-x}={\frac {1}{b^{x}}}$.
* For $b>1$ and $x>0$, we have $b^{x}>1$.
* For $b<1$ and $x>0$, we have $b^{x}<1$.
* For $b>1$, the function $f$ is strictly increasing.
* For $b<1$, the function $f$ is strictly decreasing.
* We have $(b^{x})^{x'}=b^{x\cdot x'}$ for all $x,x'\in \mathbb {R}$.
* For $a\in \mathbb {R} _{+}$, we have $(ab)^{x}=a^{x}\cdot b^{x}$.
# Real exponential function/Base/Rules/Fact/Proof/Exercise

Prove that for the exponential function
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto a^{x},$
the following calculation rules hold (where $a,b\in \mathbb {R} _{+}$ and $x,y\in \mathbb {R}$).
    $a^{x+y}=a^{x}\cdot a^{y}\,.$
    $a^{-x}={\frac {1}{a^{x}}}\,.$
    $(a^{x})^{y}=a^{xy}\,.$
    $(ab)^{x}=a^{x}b^{x}\,.$
# Real exponential function/Derivative/Fact

The exponential function
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto \exp x,$
differentiable with
    $\exp \!'(x)=\exp x\,.$
# Real exponential function/Derivative/Fact/Proof

Due to fact, we have
    ${\begin{aligned}\exp \!'(x)&={\left(\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}\right)}'\\&=\sum _{n=1}^{\infty }{\left({\frac {x^{n}}{n!}}\right)}'\\&=\sum _{n=1}^{\infty }{\frac {n}{n!}}x^{n-1}\\&=\sum _{n=1}^{\infty }{\frac {1}{(n-1)!}}x^{n-1}\\&=\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}\\&=\exp x.\end{aligned}}$
# Real exponential function/Continuity and image/Fact/Proof

The continuity follows from fact, since the exponential function is defined with the help of a power series. Due to fact, the image lies in $\mathbb {R} _{+}$, and the image is, because of the intermediate value theorem, an interval. The unboundedness of the image follows from fact. This implies, because of fact, that also arbitrary small positive real numbers are obtained. Thus the image is $\mathbb {R} _{+}$.
Injectivity follows from fact, in connection with exercise.