OpenLLM-France/wikimedia huggingface dataset:
# Instructional design/Task analysis/How HTA Works

| ID Homepage | 1. ID task analysis | 2. What is HTA? | 3. Anatomy of an HTA | 4. How HTA Works | 5. Rule of Thumb | 6. Objectives Are Not Subjective |
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## How does it work?

As mentioned in section 2 of What is HTA?, we said there is a systematic approach to completing this analysis. Let's look closer into what exactly that approach entails in terms of functions and activities.
Before the fun can begin, we have to record general information about the task. You should record:
* The date and time
* Where the task takes place
* Information about the person completing the task (name, title, age, disabilities if any, etc...)
Once you have all that good stuff recorded, it's time to get down to business! It may be helpful to use a task analysis worksheet when completing an HTA. This was developed by the Natural Resources Conservation Service. Use one of these worksheets for practice during our scenario below.

## Mmm... Peanut Butter & Jelly

Remember the PB&J example I mentioned during the introductory page? Making a PB&J sandwich is going to be our task. The first subtask would be locating the bread. This subtask would be composed of elements such as opening the fridge (if that's where this person keeps their bread), opening the bag, taking out two slices of bread, closing the bag, etc... Your goal here is to simply observe and be as least intrusive as possible. If the person completing the task stops to ask you something, this will raise inconsistancies in your analysis, especially with the timing factor. Your HTA should look similar to this:
Other factors to watch for include unnecessary interruptions or tangents the worker may find such as locating a tool when it is not in its proper place. For instance, a butter knife. Why do they all have to be dirty when I want to use one?! Record the time it takes the person you're observing to wash a knife in order to use it.
Once you have finished what you feel is a completed HTA or task decomposition, you may want to walk through the entire process again with the worker completing the task. However, this time, only use your HTA as a guide. This will reveal further inconsistancies. Take our above task of making a peanut butter and jelly sandwich. We said the first subtask was to locate the bread. Following an HTA that states this as the first subtask would clearly show one had forgotten to record the subtask of locating a paper towel or plate as to not build the sandwich directly on the counter. For all you know, there could have been some raw chicken juice on that counter last night!

## I'm done! Right?

Not so fast. You will notice toward the bottom of the worksheet it asks you to describe functional behaviors. This will aid you in developing your performance objectives, which will be discussed in the last section--Objectives Are Not Subjective.
Get another worksheet ready. You will need it for the next activity.
Click next to continue.
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| ID Homepage | 1. ID task analysis | 2. What is HTA? | 3. Anatomy of an HTA | 4. How HTA Works | 5. Rule of Thumb | 6. Objectives Are Not Subjective |
# Instructional design/Task analysis/What is HTA?

| ID Homepage | 1. ID task analysis | 2. What is HTA? | 3. Anatomy of an HTA | 4. How HTA Works | 5. Rule of Thumb | 6. Objectives Are Not Subjective |
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## What exactly is a hierarchical task analysis?

If you look up the definition of HTA, it might confuse you more when it talks about goals and subordinate goals... yadda, yadda, yadda. It always bothers me when I find a definition that uses the word I am looking up in the definition. Yes, I found the word hierarchy to be in most definitions of hierarchical task analysis.
Don't worry. Essentially, an HTA consists of starting with something to be completed (at the top) and breaking it down into smaller things to be completed (at the bottom). Therefore, it is known as a top-down process.
That sounds simple. Right? It actually is simple, but there is a systematic approach to completing an HTA. Before jumping feet first into the inner workings of it all, take a look at the simple graphic below. The flow of an HTA is easy to follow and redundant. Those two characteristics are by design and serve as the foundation of the HTA's function. Once an HTA is complete, the results should be easy to follow. The path you followed to complete one portion should be the same to complete the other portions.
* This image shows how a task can be broken into smaller components starting at the top, working your way down. Recreating the task will be done in the opposite direction--starting at the bottom, working your up to the big idea.

## Yea, so... what else is great about it?

Let's look at some advantages:
* It allows for easy comparison among multiple task analyses of the same goal
* A completed task analysis will provide a springboard for a needs assessment
* Since HTA is conducted through observation, the observer will minimally interfere with the activity and worker.
In the name of fairness, we should also consider a disadvantage:
* While interference may be minimal during observation, the before and after observation takes time from the worker which he/she could be using to complete other responsibilities.
The approach to completing an HTA will be explained in more detail during section 4--How HTA Works.
Click next to continue.
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| ID Homepage | 1. ID task analysis | 2. What is HTA? | 3. Anatomy of an HTA | 4. How HTA Works | 5. Rule of Thumb | 6. Objectives Are Not Subjective |
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Quadratic matrix/Rank/Invertible/Linearly independent/Fact/Factreferencenumber

Corollary 26.4
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Q/b^q/Well-defined/Exercise/Exercisereferencenumber

Exercise 12.16
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real closed interval/Strictly increasing/Inverse function/Continuous/Fact/Factreferencenumber

Theorem 11.7
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real exponential function/Continuity and image/Fact/Factreferencenumber

Theorem 12.12
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real exponential function/Base/Derivative/Fact/Factreferencenumber

Theorem 16.4
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real exponential function/Base/Properties/Fact/Proof/Exercise/Exercisereferencenumber

Exercise 12.9
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real exponential function/Derivative/Fact/Factreferencenumber

Theorem 16.3
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Primitive function/Inverse function/Fact/Factreferencenumber

Theorem 20.4
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real Function/Continuous/Constant/Identity/Example/Examplereferencenumber

Example 10.
# Mathematics for Applied Sciences (Osnabrück 2023-2024)/Real cosine function/One zero between 0 and 2/Fact/Factreferencenumber

Lemma 16.10
# Differential equations/Solutions/1 over y and +-ty^3/Confirm via derivatives/Exercise

Confirm by derivation that the curves we have found in the examples are the solution curves of the differential equations
    $y'={\frac {1}{y}},\,y'=ty^{3}{\text{ and }}y'=-ty^{3}.$
# Differential equations/Power series solutions
### Definition

A power series solution to a differential equation is a function with infinitely many terms, each term containing a different power of the dependent variable. The general solution has the form $y=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots$ .

### Solution

To illustrate how to use the power series method to arrive at a solution, let's take the equation $y''+x^{2}y'+xy=0$ .
* Start with the general form of the power series: $y=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots$
* Take derivatives of the general power series until an equation exists for every order of derivative in the equation. You can shift the nth term so that all the terms end with $x^{n}$ . For example,
** $y'=a_{1}+2a_{2}x+\cdots +na_{n}x^{n-1}$ or in alternative form, $y'=a_{1}+2a_{2}x+\cdots +(n+1)a_{n+1}x^{n}$
** $y''=2a_{2}+3\cdot 2a_{3}x+\cdots +(n+2)(n+1)a_{n+2}x^{n}$
* To find a "recursive" solution, compare the general nth terms of each equation and substitute them into the original differential equation. If there are dependent variables in the differential equation, you might have to alter the nth term to get all the powers of the dependent variable the same. For example:
** $y''=(n+2)(n+1)a_{n+2}x^{n}$
** $x^{2}y'=x^{2}\lbrack (n-1)a_{n-1}x^{n-2}\rbrack =(n-1)a_{n-1}x^{n}$
** $xy'=x\lbrack a_{n-1}x^{n-1}=a_{n-1}x^{n}\rbrack$
** $\lbrack (n+2)(n+1)a_{n+2}x^{n}\rbrack +\lbrack (n-1)a_{n-1}x^{n}\rbrack +\lbrack a_{n-1}x^{n}\rbrack =0$
* Divide by the $x^{n}$ term and solve for the highest subscript coefficient ($a_{n+2}={\frac {-na_{n-1}}{(n+1)(n+2)}},n=1,2,3,\cdots$ ).
* Successive iterations produce more terms in the solution. For example:
** For $n=1:a_{3}={\frac {-a_{0}}{2\cdot 3}}=-{\frac {a_{0}}{3!}},n=2:a_{4}={\frac {-2a_{1}}{3\cdot 4}}=-{\frac {(2)^{2}a_{1}}{4!}},\cdots$
** Some terms, like $a_{2}$, do not exist because $n=0$ for that case.
* Sometimes the solution can be split up into two or more functions, each dependent on a base coefficient. For example:
** $y=y_{1}(x)+y_{2}(x)$
** $y_{1}(x)=a_{0}-{\frac {a_{0}}{3!}}x^{3}+{\frac {(4)^{2}a_{0}}{4!}}x^{6}-{\frac {(4)(7)a_{0}}{7!}}x^{9}+\cdots$
** $y_{2}(x)=a_{1}x-{\frac {(2)^{2}a_{1}}{4!}}x^{4}+{\frac {(2)^{2}(5)^{2}a_{1}}{7!}}x^{7}-{\frac {(2)(5)(8)a_{1}}{10!}}x^{10}+\cdots$
# Differential equations/Separable differential equations

First Order Differential Equations
The order of a differential equation is the largest derivative involved. For example, in the equation ${\frac {d^{2}y}{dx^{2}}}+{\frac {dy}{dx}}+y=0$, the largest derivative is the second, so the order is 2.

## Separable Equations

One of the easiest class of ODEs to solve is separable equations.

### Definition

A differential equation is called separable when it can be manipulated into an equation with the dependent variable and its differentials on one side of the equality, and the independent variable and its differentials on the other side. Thus, each side is in terms of a single variable.

### Example

The equation ${\frac {dy}{dx}}=y$ has a fairly obvious solution if you know your differentiation rules well. Recall that ${\frac {d}{dx}}e^{x}=e^{x}$ and hence $y=e^{x}$ is a solution. But how could we have found this if we did not remember that $e^{x}$ happened to be its own derivative? Additionally, is it possible to find any more solutions? Observe that the equation above is separable, and can be written as ${\frac {1}{y}}dy=dx$. Now that both sides are in terms of their own variable, we can integrate:
$\int {\frac {1}{y}}dy=\log {|y|}+C_{1}=x+C_{2}=\int dx$
And thus, $|y|=e^{x+C_{2}-C_{1}}=e^{x}e^{C_{2}-C_{1}}=Ae^{x}$. Since $C_{1}$ and $C_{2}$ are arbitrary constants of integration, $A=e^{C_{2}-C_{1}}$ is another arbitrary constant, so that the final solution is $y=Ae^{x}$ for any $A$.

### General Solution

Suppose we have some separable equation:
$f(y)dy=g(x)dx$
Then we can integrate both sides:
$F(y)+C_{1}=G(x)+C_{2}$
Since the constants are arbitrary, we really only need one. However, do not forget the constant of integration, or you will lose a large number of solutions. Additionally, do not wait until the last step to add the constant of integration. Many times when learning calculus, students add a $+C$ to the end of a problem without really thinking, but remember that the $C$ comes from the integration, so you need to add it at that step. In the above example, adding the $C$ at the last step would give $y=e^{x}+C$ as a solution. But we can see that, for example, ${\frac {d}{dx}}(e^{x}+1)=e^{x}\neq e^{x}+1$, so that $e^{x}+C$ is not a solution (whenever $C\neq 0$)!
At any rate, the equation is now of the form $F(y)=G(x)+C$, which can be solved for $y$ using any available algebra tools.
In short:
* If possible, manipulate the equation using algebra to get each variable on its own side of the equation. The form should be $f(y)dy=g(x)dx$.
* Integrate both sides of the equation. Include a constant of integration.
* Solve for the function in terms of the independent variable.
It can be misleading, however, to think that a constant of integration necessarily must appear in the solution of a differential equation. This is true for linear equations, but for nonlinear ones, all bets are off.
Consider for example the equation
    $|y'|+|y|=0$.
The only solution to this equation is $y=0$, and no arbitrary constant of integration can be imposed anywhere.
# Differential logic

☞ This page belongs to resource collections on Logic and Inquiry.
Differential logic is the component of logic whose object is the successful description of variation — for example, the aspects of change, difference, distribution, and diversity — in universes of discourse that are subject to logical description. In formal logic, differential logic treats the principles that govern the use of a differential logical calculus, that is, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
A simple example of a differential logical calculus is furnished by a differential propositional calculus. This augments ordinary propositional calculus in the same way that the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.

## Syllabus
### Focal nodes

* Inquiry Live
* Logic Live

### Peer nodes

* Differential Logic @ InterSciWiki
* Differential Logic @ Subject Wikis
* Differential Logic @ Wikiversity
* Differential Logic @ Wikiversity Beta
# Differential operator/Algebraic/Inductive and product condition/Fact/Proof/Exercise

Let $R$ denote a commutative $K$-algebra and let $E\colon R\rightarrow R$ denote a $K$-linear map. Show that the following statements are equivalent.
* $E$ is a differential operator of order $\leq n$.
* For arbitrary elements $f_{0},f_{1},\ldots ,f_{n}\in R$ we have
    ${\begin{aligned}E(f_{0}\cdots f_{n})&=\sum _{s=1}^{n}(-1)^{s+1}\sum _{I\subseteq \{0,\ldots ,n\},\,{\#\left(I\right)}=s}\prod _{i\in I}f_{i}\cdot E{\left(\prod _{i\notin I}f_{i}\right)}\\&=\sum _{I\subseteq \{0,\ldots ,n\},\,I\neq \emptyset }(-1)^{{\#\left(I\right)}+1}\prod _{i\in I}f_{i}\cdot E{\left(\prod _{i\notin I}f_{i}\right)}.\end{aligned}}$
# Minerals/Quiz

Minerals is a lecture and an article from the school of geology. It is about solid, crystalline substances that occur in and compose astronomical objects. It focuses on materials that may occur on the surface of or associated with some astronomical objects.
You are free to take this quiz based on minerals at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Minerals are a generic for formation conditions.
# Minerals/Metals/Precious/Quiz

Precious metal minerals is a lecture and an article from the school of geology. It is about solid, crystalline substances containing precious metal elements of the periodic table that occur in and compose astronomical objects. It focuses on materials that may occur on the surface of or associated with some astronomical objects.
You are free to take this quiz based on precious metal minerals at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Precious metals are usually the most chemically inert metals.
# Minerals/Metals/Transitions/Quiz

Transition metal minerals is a lecture from the school of geology and the radiation astronomy department. It is about solid, crystalline substances that occur in and compose astronomical objects including the Earth. It focuses on materials containing large amounts of metals that may occur on the surface of or associated with some astronomical objects.
You are free to take this quiz based on transition metal minerals at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Metal-based minerals make up most of the surface compositions of rocky-objects.
# Minerals/Metals/Quiz

Metal minerals is a lecture from the school of geology and the radiation astronomy department. It is about solid, crystalline substances that occur in and compose astronomical objects including the Earth. It focuses on materials containing large amounts of metals that may occur on the surface of or associated with some astronomical objects.
You are free to take this quiz based on metal minerals at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Metal-based minerals make up most of the surface compositions of rocky-objects.
# Minerals/Metals/Body-centered cubics/Quiz

Body-centered cubic metal minerals is a lecture from the school of geology. It is about solid, crystalline substances containing body-centered cubic metal elements of the periodic table that occur in and compose astronomical objects. It focuses on materials that may occur on the surface of or associated with some astronomical objects.
You are free to take this quiz based on Body-centered cubic metal minerals at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Body-centered cubic metals make up many high-temperature minerals.
# Minerals/Mineralogy/Quiz

On the right is a photomicrograph of olivine in cross-section under crossed polarizers from an Archaean Kormatite in Australia.
Mineralogy is a lecture and an article about the science of minerals offered by the school of geology in conjunction with the astronomy department of the school of physics and astronomy.
You are free to take this quiz based on planets at any time.
To improve your scores, read and study the lecture, the links contained within, listed under See also and External links, and in the {{radiation astronomy resources}} and {{geology resources}} templates. 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 using more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Minerals are a generic for formation conditions.
# Ethnic group

According to Wikipedia, "An ethnic group or an ethnicity is a grouping of people who identify with each other on the basis of shared attributes that distinguish them from other groups."

## Discussion questions and essay ideas

* What is the purpose of researching studying various ethnic groups and cultural practices?
* How can ethnographies be utilized to study various ethnic groups?

## Readings
### Wikipedia

* Ethnography
* Ethnic group
* List of contemporary ethnic groups
* Ethnic groups in the United States (Category)
* Lists of ethnic groups (Category)
* List of ethnic groups of Africa
* List of ethnic groups in China
* List of ethnic groups in Nigeria
* List of ethnic groups in the United States by household income
* List of ethnic groups in Vietnam
This Sociology resource is a "stub". Learn how you can help Wikiversity to develop it.
# Ethnobotanical research projects/Cooperative project
## Ethnobotanical master project

Welcome to the master project! This can hopefully become a useful database for those interested in herbal and indigenous medicine as well as the other traditional uses of plants. We hope to index each plant by its uses and by culture. If you are looking to build your own database of plant descriptions and notes, please do that on your own personal research project. This is a database of only the uses of plants (not where to find them, etc.) Please be aware that this project is still under construction, but do feel free to contribute and build on ethnobotanical knowledge!
* By traditional use
* By culture
* Complete alphabetical index
* Plant pages under active construction check here before creating a new page!