OpenLLM-France/wikimedia huggingface dataset:
# Eventmath/Lesson plans/Age and Voting Preferences in Cross-Tabulation

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## Activities

This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.
You can use LaTeX to render mathematical symbols, such as $\sum _{k=1}^{n}k={\frac {1}{2}}n(n+1)$. See the Help:Formula page for more details.
You may also wish to include helpful materials for an instructor, such as:
* solutions to problems posed by the lesson,
* anticipated points of confusion and suggestions,
* discussion topics that may arise when working with students, or
* any other relevant ideas or materials.

## Assignments

You're welcome to suggest exercises, activities, assignments, or projects based on the material of this lesson.

## Resources

(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)

### Background

You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.

### Explorations

You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.

## Feedback

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# Eventmath/Lesson plans/Brian Williams thinks there are only 300 people in the US

* Please help develop this lesson plan!
* This lesson plan is currently in draft status.
* Since this is a wiki page, anyone can help make it better! If you don't know how, check out the Editing FAQ.
* If you like, you can check out more Eventmath lesson plans.

## Activities

This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.
You can use LaTeX to render mathematical symbols, such as $\sum _{k=1}^{n}k={\frac {1}{2}}n(n+1)$. See the Help:Formula page for more details.
You may also wish to include helpful materials for an instructor, such as:
* solutions to problems posed by the lesson,
* anticipated points of confusion and suggestions,
* discussion topics that may arise when working with students, or
* any other relevant ideas or materials.

## Assignments

You're welcome to suggest exercises, activities, assignments, or projects based on the material of this lesson.

## Resources

(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)

### Background

You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.

### Explorations

You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.

## Feedback

Have you found this lesson plan helpful? Tell us about it!
Just click Endorse below to open up an editor and type your comments. When you're ready, they'll appear at the bottom of this section to help other educators looking for good lesson plans.
(Alternatively, if you see a way to improve this lesson plan, be bold and make an edit! You're also welcome to discuss the lesson plan or provide constructive feedback on its Discussion page.)
# Even number/Last digit/Exercise

Show that a natural number $n$ is even if and only if its last digit in the decimal system equals $0,2,4,6$ or $8$.
# Fair use/Case law/Quiz

Fair use case law is a lecture focused on case law applicable to fair use of copyrighted material such as published articles or images.
You are free to take this quiz based on fair use case law 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 {{humanities 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

* A claim of copyright infringement or copyright violation for a fair use of text, cited or unattributed but attributable, on a dot org or dot edu may libelous.
# Fairy Rings

| Main Page | Goals | Database (How to contribute) | [Fairy Rings/Contacts|Contacts (Discussion)]] |
# Fairy Rings/Database

| Main Page | Goals | Database (How to contribute) | [Fairy Rings/Contacts|Contacts (Discussion)]] |
# Fair use

Welcome to the Wikiversity learning project for Fair Use.

## Reading

* Fair use considerations and Exemption Doctrine Policy.
* m:Fair use
* w:Wikipedia:Non-free content

## Fair use at Wikiversity
### Screen shots of reviewed software

Wikiversity has many learning resources that are tutorials for software or that review the utility of software (example). When discussing copyrighted software, it is often useful to provide screenshots as visual aids. Wikiversity has Template:Software-screenshot that can be used as explained at Wikiversity:Uploading files.
In some cases, parts of copyrighted works can be used without permission in order to illustrate commentaries or for education/teaching (see Non-free content). One concern for "fair use" is that it does not disrupt the potential market for or value of the copyrighted work. In the United States, this does not mean that reviews and commentaries cannot be critical. However, at Wikiversity, extra care should be taken when using screenshots to illustrate copyrighted software features that are not viewed as useful to learners. It is not the purpose of Wikiversity to complain about software, but rather, to help learners use software to achieve their learning goals.
It is good practice to find webpages such as this before you upload screenshots of copyrighted software. Microsoft has ten specific guidelines for screen shots of works that they own. For example, the image on the right side of this page shows copyrighted Microsoft software. Microsoft allows fair use of such screen shots for educational purposes such as tutorials. Their instructions say, "You may not use portions of the screen shots". Does this mean that you are required to show the entire captured image as seen on the computer screen when the screen shot was captured? If so, then the image used here to illustrate a screen shot does not meet their requirements. This illustrates the many ambiguities that can arise when fair use is claimed and when attempts are made to follow the wishes of a copyright holder. Wikiversity is always ready to remove fair use images if the copyright holder requests that an image not be used.
Corel also explicitly allows fair use screen shots, but they also have a long list of restrictions and rules.

## Other uses

See Wikiversity:Uploading files#Fair use considerations.
# Federal Writers' Project – Life Histories/2015/Fall/Section 018/Granville Brooks
## Mary Hines

Mary Hines (March 3, 1883- March 31, 1951) of Charleston, South Carolina was an African American cook.

## Biography

Granville Brooks was born on March 3, 1883 in Charleston, South Carolina. His parents were slaves on a plantation and he grew up on this plantation as an only child. His first wife deceased in 1905. She left him with two sons whom he never contacted after they both moved away. He married again in 1922.

##### Work Life

Brooks had a strong desire to travel. After working for eleven years as a butler for Dr. Eugene Foster in South Carolina, he resigned to move to Pensaeola, Florida where he found employment as a fireman. Soon after, he traveled to Augusta, Georgia and opened a restaurant. After a few years, he sold the place and moved to New Orleans, Louisiana. In New Orleans, he was employed as a cook at a hospital from 1915 to 1935. He was dismissed from his job, despite his satisfactory record, when the hospital began switch African American chefs for Caucasian chefs. The movement was in line with the racial segregation that was prevalent during the 1900s. His unemployment put him in distress as it led him to be unable to play for the insurance for his family.

##### Family

He met his second wife, Harriett, a maid, at the hospital. Harriett was partly crippled as a result of several paralytic strokes. Brooks did not have any children when Harriett. However, they took care of Harriett’s orphan nephew, Laden. Brooks never allowed either of his wives to work outside of the house. He supported that women should hold the traditional homemaker role because he believed that allowing them to work would cause him to lose more money than he would make. There is no more known information about him.
# Discrete mathematics

Welcome to the Main Page of Discrete Mathematics!
These are the main topics we are going over in the course:
* Logic
* Set theory
Welcome to the Topic of Discrete Mathematics, a department of the School of Mathematics and School of Computer Science. Discrete mathematics is very important for studying computer science.

## Why Learn Discrete Mathematics?

While many of the topics within Discrete Mathematics have been around for a long time, traditional education typically focused on Continuous Mathematics, such as calculus. With the widespread adoption of computers, the usefulness of discrete mathematics has dramatically increased. From basic logic in circuits, to number theory and cryptography, computer science inevitably relies upon discrete mathematics.
Learning discrete mathematics will...
* Develop your critical thinking and formal reasoning skills.
* Provide a foundation for learning computer science.
* Develop your programming abilities (regardless of whether you have programmed before).
* Familiarize you with the many different branches of mathematics.
* Help you to "read mathematics."

## Homework

To come.

## Complete List of Subjects

Discrete Mathematics is a broad subject encompassing several formal systems for dealing with discrete quantities. If you are studying Discrete Mathematics as part of a related field, you may wish to follow a streamlined set of core topics that you need. A complete list of Discrete Mathematics topics is given below.
* Algorithmics
* Collections
* Combinatorics
* Complexity
* Computability
* Counting
* Digital geometry
* Digital topology
* Functions
* Graph theory
* Information theory
* Linear algebra
* Markov chains
* Number theory
* Partially Ordered Sets
* Probability
* Proofs
* Relations

## Notable Textbooks

* Discrete Mathematics With Applications by Susanna S. Epp
* w: Concrete Mathematics: A Foundation for Computer Science by Donald Knuth.
* Discrete Mathematics. An Open Introduction 3rd Edition by Oscar Levin

## Off-site courses

* Discrete Math (Update 10/07/2024: Link doesn't work anymore), Michael Damron, New York University, Fall 2008. (Earlier versions: Spring 2007)
* Introduction to Contemporary Mathematics, Larry Bowen, University of Alabama.
* Discrete Structures, Margaret Fleck and Eric Shaffer, Spring 2009
* Discrete Mathematics, Ben Maloney, University of Wollongong, Summer 2010-2011.
* Discrete Mathematics I, Peter G. Binev, University of South Carolina, Fall 2006.
# Discrete helpers/set part

This class implements set partitions, which are essentially the same as equivalence classes. The partitioned set (called domain) is usually that of non-negative integers.

## Cayley tables

SetPart can be used to model the Cayley table of a group. It makes sense to use a set of simple IDs for the elements of the group. (Typically that should be integers or pairs of integers.) Then the domain argument is the Cartesian square of the set of IDs. The entries of the Cayley table are IDs added as labels to the blocks. The method add_label_to_element will take care of creating the blocks.
Let id_to_perm be a bidict from IDs to permutations.
What are the products of permutations 3 and 5?
Which (other) products create the permutations 1 and 2?

## meet and join

The meet and join methods can be used to combine two partitions into one.
* The meet $\land$ (greatest lower bound) is the coarsest partition finer than both.
* The join $\lor$ (least upper bound) is the finest partition coarser than both.
The meet is easy to calculate. The join is currently expensive, and will hopefully be improved.
example :
| from discretehelpers.set_part import SetPart red = SetPart([[0, 1, 2, 4], [5, 6, 9], [7, 8]]) green = SetPart([[0, 1], [2, 3, 4], [6, 8, 9]]) assert red.join(green) == SetPart([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) assert red.meet(green) == SetPart([[0, 1], [2, 4], [6, 9]]) | red and green with brown intersection |

### meet

The default partition is the finest, and it can be made coarser. But one can not start with the coarsest, and make it finer. (Although theoretically there would be nothing wrong with that.) This method is a way to make blocks smaller instead of bigger.
find intersections :
show intersections :
| A Venn diagram of three sets has seven cells, not counting the one outside. The following code shows the names assigned to their cells. (The one only in set A is empty.) def block_to_cell(block): s = '' s += 'A' if set(block).issubset(a) else '' s += 'B' if set(block).issubset(b) else '' s += 'C' if set(block).issubset(c) else '' return s for block in combined_part.blocks_with_singletons: print(block_to_cell(block), '-->', block) AB --> ['Daisy', 'Donald'] B --> ['Della', 'Scrooge'] AC --> ['Dewey', 'Huey', 'Louie'] BC --> ['Gladstone', 'Gyro'] C --> ['Mickey', 'Minnie'] ABC --> ['Pluto'] | Venn diagram |
# Discrete helpers/walsh perm

A Walsh permutation is a periodic permutation (Perm) that is derived from an invertible binary matrix.
# Discrete helpers/binv

This is a simple helper class for binary vectors.
The property pretty can be used when the length is a power of two up to 64:

## integer values

* The smallest bit is on the left!
An important use is conversion to and from decimal. The interpretation is little-endian, i.e. the least-significant bit is on the left.
# Discrete helpers/perm

This class implements permutations of the non-negative integers.

## finite permutations

| $P\cdot Q=S$ | $Q\cdot P=R$ | $P^{-1}\cdot Q^{-1}=R^{-1}$ |
A permutation is only determined by the moved elements. Fixed points make no difference.
The main attribute of this class is mapping. Attributes with derived information are moved and length.

### properties
#### inversions

See Inversion (discrete mathematics). The inversion_set is the set of places on which the values are out of order. The left_rank is the reverse colexicographic rank. Its factoradic expression is the left inversion count. The right_rank is the lexicographic rank. Its factoradic expression is the right inversion count.

#### inverse

The product of a permutation and its inverse is the neutral permutation. (Same as exponentiation with −1.)

#### cycles

The usual cycle notation of a permutation as a list of lists.

#### order

Smallest positive exponent that produces the identity. (LCM of cycle lengths.)

#### parity

Parity of the number of inversions. (parity of a permutation)

#### Schoute permutation

Periodic permutation derived from a finite one. See Schoute permutation.

### methods
#### sequence

The permutation can be represented by a sequence of the required length or longer. The example perm requires length 6 or more, because the biggest moved element is 5.

#### apply on vector

The result of applying a permutation on a sequence in natural order looks like the inverse of the permutation.

## periodic permutations

A periodic permutation moves an infinite number of elements, but with a repeating pattern. Most attributes are those of the smallest corresponding finite permutation. The new attribute perilen is the period length.
For both permutations order is 2, cycles is [[3, 4]] and mapping is {3: 4, 4: 3}. These are the results of p5.sequence(20) and p10.sequence(20):
[0, 1, 2, 4, 3, 5, 6, 7, 9, 8, 10, 11, 12, 14, 13, 15, 16, 17, 19, 18] [0, 1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 13, 15, 16, 17, 18, 19]
cycles_dynamic is a method only for periodic permutations, and shows the cycles for a given length:
Schoute permutations and Walsh permutations (see WalshPerm) are periodic.
# Discrete helpers/set part comp

This class extends set partitions (SetPart) with a complement relationship between the blocks of equivalent elements.
This can be used to save equality and complement relationships between arguments of Boolean functions (Boolf).
The initial object in the following example has three blocks. The first two of them are complements.

## domain

The domain is the set of integers, including the negative ones. (This is different from SetPart, where the domain can be changed, and is N by default.) This class was developed to deal with the blight of a Boolean function. That includes blotted Boolean functions, where the arguments can be equal or complementary to the universe, which is represented by −1.

## methods
### related set partition

related_part is a derived SetPart, where complementary blocks are merged. There are related methods like number_of_related_blocks.

### set equal and complement

set_equal(a, b) merges the blocks containing the elements a and b. set_comp(a, b) makes them complementary.

### Boolean function

The method boolf returns a Boolean function (Boolf), which contains the same information. It is only blight. (Its blightless_boolf is the tautology.) If there are no gaps between the affected elements x.boolf.blight is equal to x.

### integer matches

x.int_matches(n) checks if the binary digits of n are equal or different in the way described by x. (This is used for the method bloatless_spotint of Boolf.)
# Discrete helpers/sig perm

This is an extension of the class Perm with added negators. Signed permutations of length $n$ are the $2^{n}\cdot n!$ elements of the hyperoctahedral group of dimension $n$. (See e.g. the full octahedral group for the 48 permutations of the cube.)
This class has been created to model transformations between Boolean functions in the same clan. (See Studies of Euler diagrams/transformations.)
keyneg and valneg :
This is a subclass of Perm, making the instances comparable.

## Schoute permutation

The property schoute_perm is inherited from Perm. (See there.) These are signed Schoute permutations.
| name | a | b |
| pair | (6, 3) | (5, 4) |
| sequence | [~2, 0, ~1] | [1, ~2, ~0] |
| cube permutation | | |

## parity

Like for normal permutations, the parity corresponds to the determinant of the matrix. (But the metribute inherited from Perm is wrong.)
# Discrete helpers/sig perm/parity

Like for normal permutations, the parity corresponds to the determinant of the matrix. It is the XOR of the weight parity of the negator pattern and parity of the permutation. (See Full octahedral group#8×6 matrix.)
The class inherits the metribute parity from Perm. But that result is currently wrong. (2024-05)
While this is not the parity, it is something, and deserves a name. In the following images this property is shown as the shade of the background color. It changes with every arrow. So this is the parity of the rank in the Hasse diagram.
| matrix | Hasse diagram |
# Discrete helpers/boolf

This class for Boolean functions (BF) is the biggest part of this software. It contains some unfinished and experimental features.
This project is related to many pages in Studies of Boolean functions.
There are two main goals, both not yet reached:
* find the Euler diagram of any BF, see Studies of Euler diagrams (The main problem is to find the necessary gapspots.)
* find an easy to calculate clan representative of any BF, e.g. the Smallest Zhegalkin index (The current calculation of the smallest Ж is not yet easy.)

## periodic truth tables

Within this project Boolean functions are used without specifying the arity. Their arity is implicitly infinite, and their truth tables are implicitly periodic. (But the term truth table is usually used for finite ones.) They are repeating binary fractions (just like repeating decimals) with values between 0 and 1.  (This may be the only occurence of big-endian binary in this project.)
The truth tables 0001 and 0001 0001 denote the same thing, namely the Boolean function $A\land B$. The corresponding fraction is ${\frac {1}{15}}$. (That can be expanded to ${\frac {17}{255}}$, corresponding to the longer truth table.)
The letters from the beginning of the alphabet are not meaningless variable names, but denote specific atoms.
atom fractions :

### valency ≤ adicity ≤ arity

Valency is the number of arguments actually used. Adicity follows from the biggest atom, and corresponds to the required length of the truth table. For a root BF valency and adicity are equal. E.g. Boolf('0001') ($A\land B$) has valency and adicity 2. But Boolf('0000 0011') ($B\land C$) has valency 2 and adicity 3. The term arity is only used for arguments of methods, e.g. to calculate the consul.
# English-Chinese/Since 1960, world production of wheat and other grain crops has tripled and is expected to grow further through the middle of the 21st century

Since 1960, world production of wheat and other grain crops has tripled and is expected to grow further through the middle of the 21st century.
自1960年以来，世界小麦和其他粮食作物产量增加了两倍，预计到21世纪中叶将进一步增长。
# English-Chinese/Since less blood is supplied to the heart muscle, the muscle cannot work at normal capacity

Since less blood is supplied to the heart muscle, the muscle cannot work at normal capacity. The heart muscle can become sick and weak.
由于向心肌供应的血液较少，因此肌肉无法正常工作。 心肌可能会生病和虚弱。
# English-Chinese/Singapore

Singapore is a country in the southern end of Indochina. It has a population of about 5.6 million, most of them are Chinese. Its capital is also Singapore because it is a city-state.
新加坡是印度支那南端的一个国家。 它的人口约560万，其中大部分是华人。 它的首都也是新加坡，因为它是一个城市国家。
# English-Chinese/Side effects of olanzapine

Common side effects of olanzapine include weight gain, movement disorders, dizziness, feeling tired, constipation, and dry mouth.
奥氮平的 常见 副作用 包括 体重增加，运动障碍，头晕，感觉 疲倦，便秘，和 口干。
# English-Chinese/Significant efforts in plant breeding are being made to develop lysine-rich wheat varieties, but not yet successful by 2017

Significant efforts in plant breeding are being made to develop lysine-rich wheat varieties, but not yet successful by 2017.
正在进行植物育种方面的重大努力，以开发富含赖氨酸的小麦品种，但到2017年尚未成功。
# English-Chinese/Signal (electrical engineering)

In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying quantity.
在 通信，信号处理 和 电气工程 领域中，更一般地，信号 是 任何 随时间变化的 量。