OpenLLM-France/wikimedia huggingface dataset:
# Objective structured clinical examination

Welcome to the content development project for the Objective structured clinical examination. This project is where Wikiversity participants create, organize and develop learning resources for the OSCE.

## OSCE

The OSCE is the objective structured clinical examination, the exam where medical students interview an actor playing the role of patient. These usually consist of scenarios typifying cases that students are likely to come across multiple times in their medical training.

## Modules

Each module corresponds to a common OSCE station.
# Object Oriented with Java

There are many ways you can design and code systems. There are two common approaches in programming:
This module aims to enable learners to write a software program from an object-oriented perspective. Object-Oriented programming paradigm is concerned with constructing software systems out of interacting units of software called objects. The way that objects do works is by sending messages to each other during the execution of the program. The most important motive behind Object-Oriented Programming trend is the resuability issue, where the produced code can be resued which saves effort, and time of prgramming and testing process.
"Programming in an object-oriented language is more than just learning new syntax rules; it requires a new way of thinking. The idea is not to concentrate primarily on the fundamenatls of procedural languages-data structures and algorithms-but instead to think in terms of the objects that will carry out the required tasks."
Learners will know Object Oriented principles such as: objects, classes, inheritance, and polymorphism using Java language. In addition the module teaches array, and Collection Framework (Set, Map, and List), and reading from/writing to files.
The module uses BlueJ Environment to present its implemented projects.
The module consists of 12 units as below:
* Unit 1: Object-oriented programming with java
* Unit 2: Object concepts
* Unit 3: Variables, objects and representations
* Unit 4: An introduction to methods
* Unit 5: Dialog boxes, selection and iteration
* Unit 6: Subclassing and inheritance
* Unit 7: Code design and class members
* Unit 8: Designing code, dealing with errors
* Unit 9: Collections: arrays, strings and StringBuilder
* Unit 10: Collection: sets and maps
* Unit 11: Ordered and sorted collections
* Unit 12: Streams, files and persistent objects
# Object astronomy/Quiz

Object astronomy is a lecture about a specific kind of astronomical entity.
You are free to take this quiz based on object 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 {{radiation astronomy 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

* Differentiating an astronomical object from an astronomical source needs good questions.
# PlanetPhysics/Snell's Law

Snell's law describes the relationship between an incident ray of light and that of the refracted ray of light at the boundary of two uniform materials. When light goes from one medium to another, Snell's law says that the ratio of the sines of the angles between the normal to the interface and the rays in the two media equals the ratio of the speeds in the two media
   ${\frac {\sin \phi _{1}}{\sin \phi _{2}}}={\frac {s_{1}}{s_{2}}}$
The ratio of the speeds of light in any 3 media is called the index of refraction of the second medium relative to the first
   $n_{2,1}={\frac {s_{1}}{s_{2}}}$
The ratio of the speeds of light in a vacuum to the speed in a given medium is called the absolute index of refraction of the medium. If $s$ is the speed of light in a vacuum and $s_{1}$ and $s_{2}$ are the speed of light in the two media, then the absolute indexes of refraction for the two media are
   $n_{1}={\frac {s}{s_{1}}}\,\,\,\,\,\,\,\,n_{2}={\frac {s}{s_{2}}}$
Combining equations (2) and (3), Snell's law can be written in terms of the absolute indexes of refraction
   $n_{1}\sin \phi _{1}=n_{2}\sin \phi _{2}$
   \includegraphics[scale=1]{SnellsLaw2.eps}
   {\mathbf Figure 1:} Snell's law
# PlanetPhysics/Simple Harmonic Oscillator

A simple harmonic oscillator is a mechanical system which consists of a particle under the influence of a Hooke's law force. The equation of motion of such a system is
   $m{\ddot {x}}+kx=0$
It is typical to define the quantity $\omega ={\sqrt {k/m}}$ and write this equation as
   ${\ddot {x}}+\omega ^{2}x=0$
Note that this equation is linear. Among other consequences, this means that the period of oscilltions does not depend on amplitude. It is rather simple to solve this equation in TEMs of trigonometric functions to obtain a general solution. This solution is typically written in one of two forms.
   $x=v_{0}\sin(\omega t)+x_{0}\cos(\omega t)$
   $x=A\sin(\omega t+\phi )$
Either of these solutions shows that the frequency of oscillation is $\omega$ (independent of the amplitude). The relation between the two solutions is provided by the angle addition law for the sine. One finds that the constants appearing in the two solutions are related in the following way:
   $v_{0}=A\cos \phi$
   $x_{0}=A\sin \phi$
   $A={\sqrt {v_{0}^{2}+x_{0}^{2}}}$
   $\phi =\arctan(x_{0}/v_{0})$
These constants have the following interpretation: $A$ is the amplitude of the oscillation. $\phi$ is the phase of the oscillation. $v_{0}$ is the velocity at time $t=0$. $x_{0}$ is the position at time $t=0$.
# PlanetPhysics/Sole Sufficient Operator

A sole sufficient operator or a sole sufficient connective is an operator that is sufficient by itself to define all of the operators in a specified set of operators.
In logical contexts this refers to a logical operator that suffices to define all of the boolean-valued functions, $f:X\to \mathbb {B}$, where $X$ is an arbitrary set and where $\mathbb {B}$ is a generic 2-element set, typically $\mathbb {B} =\{0,1\}=\{\mathrm {false} ,\mathrm {true} \}$, in particular, to define all of the finitary boolean functions, $f:\mathbb {B} ^{k}\to \mathbb {B}$.
# PlanetPhysics/Small Category

A (small) category ${\mathcal {C}}$ consists of a set of objects $C_{0}$ and a set of arrows $C_{1}$ together with the following structure:
* a source map $s:C_{1}\to C_{0}$ assigning an object $s(f)$ to each arrow $f\in C_{1}$ ,
* a target map: $t:C_{1}\to C_{0}$ assigning an object t(f) to each arrow $f\in C_{1}$ ,
* an identity map $1:C_{0}\to C_{1}$ assigning to each object $A$ an arrow $1_{A}$ with $s(1_{A})=t(1_{A})=A,$
* a composition map $\circ :C_{1}\times C_{1}\to C_{1}$ assigning to each pair of arrows $f,g$ , such that $s(g)=t(f)$, a third arrow $g\circ f$ with $s(g\circ f)=s(f)$ and $t(g\circ f)=t(g)$.
* The composition thus defined "$\circ$" is associative, that is, $h\circ (g\circ f)=(h\circ g)\circ f$ whenever these compositions make sense.
* the identity map satisfies $f\circ 1_{A}=f$ for any $f$ such that $s(f)=A$ and $1_{A}\circ g=g$, and any $g$ such that $t(g)=A$.
# PlanetPhysics/Soliton

A soliton is a non-linear object which moves through space without dispersion at constant speed. They occur naturally as solutions to the Korteweg - de Vries equation. They were first observed by John Scott Russell in the 19th century and then by Martin Kruskal and Norman Zabusky (who coined the term soliton) in a famous computer simulation in 1965. Insight into solitons can be obtained by noting that the Korteweg - de Vries equation satisfies D'Alembert's solution:
   $u(x,t)=f(x-ct)+g(x+ct)$
We see at once that this satisfies two important criteria: it has a constant velocity $c$, and it can also be shown that the two functions $f$ and $g$ can collide without altering shape. Solitons also occur in non-linear optics and as solutions to field equations in quantum field theory.
# Introduction to Abstract Algebra/Problem set 2

Problem Set #2: Introduction to Abstract Algebra.
As you work through these problems, think about the logical steps you are using. You should know if your proof is correct or not if you have a reason for every step.
1: Determine if the follow maps are onto and/or 1:1:
* $f:\mathbb {R} \rightarrow \mathbb {R} ^{+}$ such that $f(x)=x^{2}$.
* $f:\mathbb {R} ^{+}\rightarrow \mathbb {R} ^{+}$ such that $f(x)=x^{2}$.
* $f:\mathbb {Z} \rightarrow \mathbb {Z}$ such that $f(x)=x^{2}$.
* $f:\mathbb {Z} \rightarrow \mathbb {Z}$ such that $f(x)=2x$.
2: Prove that if $A$ and $B$ are nonempty sets, then the function $f:A\times B\rightarrow B\times A$ given by the relation $f((a,b))=(b,a)$ is a bijection.
3: Suppose the set $A$ is finite.
* Prove that if $f:A\rightarrow A$ is an onto map, then $f$ is a one-to-one map.
* Prove that if $f:A\rightarrow A$ is a one-to-one map, then $f$ is an onto map.
4: Suppose that the set $A$ is not finite.
* Provide a counter example to the proposition that if $f:A\rightarrow A$ is an onto map, then $f$ is a one-to-one map.
* Provide a counter example to the proposition that if $f:A\rightarrow A$ is a one-to-one map, then $f$ is an onto map.
# Introduction to Abstract Algebra/Problem set 1

< School:Mathematics/Undergraduate/Pure Mathematics Problem Set #1: Introduction to Abstract Algebra.
As you work through these problems, think about the logical steps you are using. You should know if your proof is correct or not if you have a reason for every step.
1: If$B\subset A$, prove $A\cup B=A$ and conversely
2: Prove $(A\cap B)\cap C=A\cap (B\cap C)$
3: Prove $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$
4: Define the set C' to be the complement of the set C relative to a defined universal set U for which $C\subset U$ such that $\forall c\in C,c\notin C'$. Prove that $(A\cap B)'=A'\cup B'$ and $(A\cup B)'=A'\cap B'$.
# Introduction to Abstract Algebra/Problem set 3
## Derivations of Properties

In the following exercises, you are prompted to give proofs which support the statements. Let $e$ denote the identity element of some group.
* Prove that if $ca=cb$ or $ac=bc$, then $a=b$.
* Prove that if $abc=e$, then $abc=bca=cab=c^{-1}b^{-1}a^{-1}=b^{-1}a^{-1}c^{-1}=a^{-1}c^{-1}b^{-1}=(abc)^{-1}$.
In the following exercises, you are prompted for proofs supporting the statements regarding various subsets of the real numbers, $\mathbb {R}$. For reference, $\mathbb {R} ^{+}=\left\{x\in \mathbb {R} |x>0\right\}$ and $\mathbb {R} ^{-}=\left\{x\in \mathbb {R} |x<0\right\}$.
* Prove that $(\mathbb {R} ^{-},\diamond )$ is a group where $a\diamond b=-ab$ for $a,b\in \mathbb {R} ^{-}$.
* Prove that $(\mathbb {R} ^{+},+)$ does not form a group.
* Prove that a homomorphism from $(\mathbb {R} ^{+},\cdot )$ to $(\mathbb {R} ^{-},\diamond )$ exists.
* Prove that a homomorphism from $(\mathbb {R} ^{-},\diamond )$ to $(\mathbb {R} ^{+},\cdot )$ exists.
* Prove that there is a bijection, $h:\mathbb {R} ^{+}\rightarrow \mathbb {R} ^{-}$ for which it is true that $h(a\cdot b)=h(a)\diamond h(a)$ and $h^{-1}(c\diamond d)=h^{-1}(c)\cdot h^{-1}(d)$. We say that $h$ is an isomorphism between the two groups.
# Introduction to Algorithms

This course is a part of The School of Computer engineering.
* Introduction
* Sorting is an example of an algorithm, though the sort shown above is not the most efficient.
* The understanding of algorithms is one of the key differences between a good programmer and a bad one. The use of proper algorithms, and the knowledge on how to build one, leads to efficient and sturdy programs. In this course, students will become familiar with these ideas and develop good programming techniques.
* Due to the open nature of Wikiversity you are free to browse through these courses at whatever pace you desire. However, before you begin this course you should consider reviewing the material covered in the prerequisite courses (listed below) to ensure that you are prepared to learn this content.
* In each lesson there is an objective at the top of the page, review these points and keep them in mind as you go through the lesson. At the end there is an assignment to test your understanding and further explain the material. Once you have finished the entire course you may move on to another course in the unofficial degree.
* (Note: Many of these lessons are stubs, and they need a lot of help. Please excuse the mess - and help out if you can!).
* Prerequisites
* Prerequisites are courses it is suggested you understand before you attempt this course. If you're having a hard time understanding the material in this course, make sure you understand these prerequisites first.
* Introduction to Programming
* Lessons
* What is an algorithm?
* Subalgorithms
* Variables
* Efficiency
* Flow Control
* Common Algorithms
* Active Participants
* Students
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# Introduction to Algorithms/Common Algorithms

This is a lesson in in the course, Introduction to Algorithms, which is a part of The School of Computer Science
* Objective
* Algorithms commonly studied
* Many algorithms are currently under intense study for various reasons. They include:
* Sorting algorithms. A sorting algorithm will take a set of objects and arrange the objects in ascending (or descending) order. While this is a simple problem and there are many existing algorithms to tackle this problem efficiently, new algorithms (and problems with older ones) are published all the time.
* Examples of sorting algorithms:
* Bubble sort
* RadixSort
* ExtraDix
* Artificial Intelligence. AI algorithms typically accept an input representing its environment (eg. a chess board) and try to find some legal move to respond favourably to the environment or an opponent (eg. calculating a good chess move). Today modern chess AIs can beat even professionals and regularly challenge world grandmasters to intense, decisive matches. Still, some simple board games remain impervious to attack. AI has also been recently employed in anti-fraud software and email spam filters.
* Numerical Computation. More and more mathematicians and computer scientists are using computers to do research, eg. to collect data, test new theories or process experimental results. Some researchers have even tried to use computers to prove theorems! (A proof to the four-color theorem was, controversially, completely produced by computer.) Ever faster algorithms need to be invented to cope with this massive increase in demand.
* Assignments
Completion status: this resource is a stub, which means that pretty much nothing has been done yet.
Previous Lesson
Course Home Page :
# Introduction to Abstract Algebra/PS1

Associated problem set for exercises:
asante appiah
# Motivation and emotion/Book/2017/Play motivation

* [Replace this text with the URL Multimedia presentation (3 min)]

## Overview

* What is Play?
* What Motivates us to Play?
* How does Self-Determination theory and research help explain why we play?
* How can this help to enhance our lives?

## What is play?

* Evolutionary
* Biological
* Behavioural
* Cognitive
* Humanist
* Psychoanalyical

## What motivates Play?

* What is Self Determination Theory.Self-Determination Theory (SDT; Deci & Ryan, 1985)
** Autonomy
** Comptetence
** Relatedness
** Extrinsic Motivation
*** Reward
*** Punishment
*** Consequence
*** Gamification
*** Addiction

## How can we use play to enhance our lives?

* Therapy
* Education and Learning
* Creativity and Performance
* Well Being

## Conclusion

Play is a fundamental element of development and learning that we can use to enhance our everyday lives!
# PlanetPhysics/Concurrent Forces in Equilibrium in Three Dimensions

Any set of concurrent forces (happening at the same time) whose vector sum or resultant vanishes is said to be in equilibrium because any particle subjected to the action of such a set of forces at their point of concurrence would not have its velocity altered and would therfore remain static. If $n$ forces are in equilibrium, we may write the vector equation
   ${\vec {F}}_{1}+{\vec {F}}_{2}+\cdots +{\vec {F}}_{n}=\sum _{s=1}^{s=n}{\vec {F}}_{s}=\sum {\vec {F}}=0$
Note that this vector equation does not imply the scalar equation $\sum F=0$ except in the very special case of collinear forces. Using double subscripts to represent the $x$, $y$, and $z$ components as well as to identify the forces, we note, however , that this vector equation is equivalent to the following set of three scalar equation:
   $F_{x1}+F_{x2}+\cdots +F_{xn}=\sum F_{x}=0;\,\,\,\sum F_{y}=0;\,\,\,\sum F_{z}=0$
Here $F_{x1}$ represents the $x$ component (scalar) of ${\vec {F}}_{1}$, etc. Any one of a set of forces in equilibrium is the equilibrant ( the negative of the resultant) of all the others.
In terms of the direction cosines of the direction angles of the individual forces designated we may also write the three scalar Eqs. (2) in the form:
$F_{1}\cos \theta _{x1}+F_{2}\cos \theta _{x2}+\cdots +F_{n}\cos \theta _{xn}=l_{1}F_{1}+l_{2}F_{2}+\cdots +l_{n}F_{n}=\sum lF=0$
   $\sum mF=0;\,\,\,\,\,\,\sum nF=0$
Here $\theta _{x1}$ is the angle between ${\vec {F}}_{1}$ and the positive $x$ direction, while $l_{1}=\cos \theta _{x1}$, etc.
With regard to the amount of information required in order to solve a problem on concurrent forces, or statics of a particle, it is important to note that the single vector of Eq. (1) or the equivalent three scalar algebraic Eqs. (2) provide the necessary and sufficient conditions for equilibrium. In the study of algebra we learned that three independent, simultaneous, linear equations such as those constituting Eqs. (2) are just sufficient to determine three unknown quantities. For a general system of concurrent forces, then, we could use Eqs. (2) to solve for as many as three unkown components, provided all the others were given. Instead of being required specifically to solve for components, we might be given everything but the magnitude and direction of one of the forces. This would be a problem with three unknowns.
The three conditions of Eqs. (2) for the equilibrium of a particle or a system of concurrent forces may be associated with the fact that three coordinates are required to specif the position of a particle in three dimensional space. Because each of these may be varied independently of the others, and three equations are required to describe its motion fully, we say that a particle whose motion is not constrained in any way has three degrees of freedom of motion. We shall find in general for any body that the number of conditions of equilibrium is equal to the number of degrees of freedom of its motion which could result from lack of equilibrium.
# PlanetPhysics/Complex Systems Biophysics
## Complex Systems Biophysics
### Introduction

Complex Systems Biophysics ($CSB$) or Complex systems biology ($CSB$) is generally described as a non-reductionist, mathematical theory of emergent living organisms or biosystems in terms of a network, graph or category of integrated interactions between their structural and functional components or subsystems. This is often abbreviated to systems biology in entries that should be described in fact as complex systems biology .

### Categorical ontology: theories of existence levels

A \htmladdnormallink{categorical ontology {http://planetphysics.us/encyclopedia/CategoricalOntology.html} theory of levels} is often defined as the classification of ontology, or theory of existence of items (objects--in the mathematical sense) by means of the mathematical theory of categories into three levels of dynamic systems pertaining to: the physical/chemical level, the biological level, and the psychological level (or human mind). Connections between the three levels of reality and their transformations are represented, respectively, by morphisms/ and natural transformations defined for categories of molecular sets, categories of $(M,R)$-systems and organismic supercategories.
From a categorical ontology theory of levels viewpoint, however, the term complex is misplaced because \htmladdnormallink{systems {http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} with chaos}, or chaotic dynamics, are currently defined by physicists as `complex systems' , which may have placed a role in the emergence of living systems that are, in fact, super-complex . Therefore, the more appropriate classification of this relatively new area in mathematical or theoretical biology and Biophysics is super-complex systems biology, $s$-complex systems biology, or simply "systems biology"--as a more general approach where the focus may be not on the super-complexity aspects of living systems but on computer modeling of physiological, or functional genomics, integration of physiological flows, signaling pathways or interactomics. However, unlike the case of purely functional $(M,R)$-systems theory in abstract relational biology (ARB), complex systems biology (or systems biology) proponents are primarily concerned with the integration of data from a multitude of bioinformatics and genomic/proteomic/post-genomic (primarily structural) data; $CSB$ scientists also aim to study interactomics or metabolomics primarily through computer-based data analysis, and often Bayesian-based attempts at integration. branches of mathematics that find applications in $CSB$ are, for example: computer modeling, colored graphs, graph-theoretical based approaches, biotopology, genetic, metabolic and signaling network theories, Bayesian models, biostatistics, correlation techniques, and less frequently: abstract algebra, group theory, groupoid and category theory modeling of cell-cell interactions and biodynamics.