OpenLLM-France/wikimedia huggingface dataset:
# Abstract Algebra/Groups/Guideline for Editors
## Motivation

    Hmm. Since I am very new to editing, when I come to this section, I would be glad to see pointers for editing.
    So I make one. Everyone is welcome to improve it. This page should be concise and organised.--Arydye001 (talk) 15:18, 18 July 2010 (UTC)

## Vision

1. Bite Size
    Not too much on a page
       ~ One page for each theorem.
       Too much on a page terrifies beginners (like me).
    Not too few on a page
       Many pages means more clicking, even if they are cross-linked
2. Color
    Proofs are long. Black and white proofs look even longer.
    Type HTML Latex Variable 1 Blue $\color {Blue}Blue$ Variable 2 Green $\color {OliveGreen}OliveGreen$ Inverse of Variable 2 FireBrick $\color {BrickRed}BrickRed$ Heading of Section in Proof Sienna $\color {RawSienna}RawSienna$

# Format

Add {{BookCat}} to end of all pages

## Issue

    1. Numbering of Equations
       Equation numbering template seems not on wikibook.
# Abstract Algebra/Lattice theory

A lattice is a poset such that each pair of elements has a unique least upper bound and a unique greatest lower bound.
# Abstract Algebra/Matroids

A matroid is an algebraic construct that is related to the notion of independence.
Matroids are an abstraction of several combinatorial objects, among them graphs and matrices. The word matroid was coined by Whitney in 1935 in his landmark paper "On the abstract properties of linear dependence". In defining a matroid Whitney tried to capture the fundamental properties of dependence that are common to graphs and matrices. Almost simultaneously, Birkhoff showed that a matroid can be interpreted as a geometric lattice. Maclane showed that matroids have a geometric representation in terms of points, lines, planes, dimension 3 spaces etc. Often the term combinatorial geometry is used instead of simple matroids. However, combinatorial geometry has another meaning in mathematical literature. Rank 3 combinatorial geometries are frequently called linear spaces. Matroids are a unifying concept in which some problems in graph theory, design theory, coding theory, and combinatorial optimization become simpler to understand.
# Afaan Oromo/Chapter 02

| ⇐ Back to Previous Chapter | Back to Contents | Continue to Next Chapter ⇒ |

## Greeting Conversation

* To play audio files, click the word, not the speaker icon. All audio files are OGG format, which are handled differently by different browsers.
* See help page for help playing these files.
Play all
Girma: Tariku, akkam bulte? play
Tariku: Akkam bulte? Fayyaa dha? play
Girma: Fayyaa, galata Waaqaa. Akkam jirta? play
Tariku: Nagaa, galata Waaqaa. Eessa deemta? play
Girma: Amma gara mana barumsaan deema. play
Tariku: Har'a galgala maal goota? play
Girma: Edana qo'achuun qaba. play
Tariku: Tole. Wal agarra. play
[For translation see here]

## Basic Sentence Structure

Afaan Oromo follows Subject-Object-Verb (SOV) format. But because it is a declined language (nouns change depending on their role in the sentence), word order can be flexible, though verbs always come after their subjects and objects. Typically, indirect objects follow direct objects. Oromo has both prepositions and postpositions, though postpositions are more common.
SOV ok, but what about
Anan namicha arga = I see the man Namicha anan arga = I see the man
Both ok?
Examples:
“I threw the ball to you” → “I ball to you threw” → “Ani kubbaa siif nan ha'e”
“She came from America” → “She America from came” → “Isheen Ameerikaa irraa dhufte”

### Modifiers

Adjectives come after the nouns they modify. Adverbs that modify adjectives go before the adjective. Adverbs that modify verbs, adverbial clauses, and relative clauses tend to go at the beginning of the sentence before the subject.
Examples:
“your blue pen is in my room” → “pen blue your room my in is” → “biirii dooqee kee kutaa koo keessa jira”
“I don't know where it is” → “Where that it is I don't know” → “Eessa akka ta'e ani hin beeku”
“How far is the post office” → “How post office is far?” → “Hagam manni postaa fagaata?”
“What are you doing tonight?” → “Tonight what will you do?” → “Edana maal gotta?”

## Chapter Vocabulary

| “Akkam bulte?” / “Akkam bultani?” | “Good morning” [lit. “How did you spend the night?”] |
| “Fayyaa dha?” | “Are you well?” |
| “Galata Waaqa” | “Thank God” |
| nagaa | fine |
| “Akkam jirta?” / “Akkam jirtu?” | “How are you?” |
| “Eessa deemta?” | “Where are you going?” |
| amma | now |
| godhuu | to do, make |
| “Maal goochaa jirta?” | “What are you doing?” |
| hojii | work |
| hojjachuu | to work |
| “Maal hojjatta?” | “What are you working on?” |
| gara | to, toward |
| mana barumsaa | school |
| har'a | today |
| har'a galgala, edana | tonight |
| qo'achuu | to study |
| “Qo'achuun qaba” | “I have to study” |
| hojii manaa | homework |
| “Wal agarra” | “See you” |
| ⇐ Back to Previous Chapter | Back to Contents | Continue to Next Chapter ⇒ |
# Ancient History/Indian subcontinent/Indus Valley Civilization

The Indus Valley Civilization existed from 5500 BC to about 1300 BC. The Indus Valley Civilization covered most of Pakistan and Northwestern India during it's golden age which was from 2600 BC to 1900 BC.

## Geography

The Indus Valley Civilization covered much of modern-day Pakistan and Northwestern India. It was situated around the Indus river and the Ghaggar-Hakra river. The main cities of the civilization were Harrapa, Mohanzodro, Kalibanga, Lothal. Harrapa was the largest city in terms of area and Mohanzodro had largest population. Lothal had a Dockyard which reflect that people had sea trade to the eastern countries like Egypt.
# Ancient History/Iran/Achaemenid Empire/The Medes and the Early Achaemenids

Iranian History/Contents/The Medes and the Early Achaemenids
    *Content in this section is copied from the Wikibook on Iranian History.
# Ancient History/Iran/Achaemenid Empire/The Seleucids

Iranian History/Contents/The Seleucids
    *Content in this section is copied from the Wikibook on Iranian History.
# Ancient History/Indian subcontinent

* Introduction
* Stone Age 70,000–7000 BC
* Mehgarh Culture 7000–3300 BC
* Indus Valley Civilization 3300–1700 BC
* Late Harappan Culture 1700–1300 BC
* Vedic Civilization 1500–500 BC
* Kuru 600 BC–AD 1279
* Maurya Empire 321–184 BC
* Gupta Empire
# Ancient History/Indian subcontinent/Mehrgarh Culture

The Indus Valley Civilization was not the first settled culture in the Indian subcontinent. Archaeologists have uncovered evidence of an earlier one called the Mehargarh culture. Mehargarh is in present day Pakistan. The site is in the Baluchistan province. It is about 125 miles from the Indus Valley. The site was first occupied around 7,000 or 8,000 B.C. It started out as a small village. The initial settlement practiced farming and raised crops, including wheat. As the community grew, farming continued, but the economy expanded and large scale trading began. Evidence shows that it traded with peoples far to the west. The goods included turquoise, cotton, and copper. Commerce was carried on with places as far away as Arabia.
By 5,000 B.C. the Mehargarh people were living in mud brick houses and then built large permanent dwellings. Trade was the main aspect of the economy. The Mehargarh culture continued to exist well past 4,000 B.C. Hence it must have traded with the Indus Valley Civilization, which was in existence by then.
A French archaeologist named Jean Francois Jarrige has participated in the excavations around Mehargarh. Many of his digs took place from 1974 to 1985. He also did some field work there in 1990 and later; in 2002 Jarigge gave a presentation on evidence (such as carbon dating) to show that the Mehargarh culture began at least around 7,000 B.C. He showed slides of artifacts and gave a lecture at the Islamabad Club Auditorium.
Jarrige found a burial place with 30 graves. Most of the remains were of females of ages 18–22. Jarrige also discovered clay pots, ornaments, buildings, and other items.
# Ancient History/Iran

* Chapter 1 - Prehistoric Iran 800,000 - 3000 BCE
* Ancient pre-historic Iran
* Chapter 2 - Ancient Iran 3,000 - 1500 BCE
* The Elamites
* Chapter 3 - The Achaemenid Empire 1500 - 330 BCE
* The Medes and the Early Achaemenids
* The Era of the three Dariuses
* Chapter 4 - The Selucid Empire 330 - 65 BCE
* Alexander's Campaign and the Macedonian Conquest of Persia
* The Seleucids
* Chapter 5 - The Parthian Empire 251 BCE - 226 CE
* The Early Arsacids 251 BC - 12 AD
* The Later Arsacids 12 AD - 226 AD
* Chapter 6 - The Sassanian Empire 226 - 651
* The Early Sassanians 226 - 379 AD
* The Middle Sassanian Period 379 - 488 AD
* Qobad I and the Two Khusros 488 - 629 AD
* Anarchy and Downfall of the Sassanian Empire
* Last Remnants of Sassanian Rule
<<Return to Front Page
    *Content in this section is copied from the Wikibook on Iranian History.
# Artificial Neural Networks/Learning Paradigms
## Learning Paradigms

There are three different learning paradigms that can be used to train a neural network. Supervised and unsupervised learning are the most common, with hybrid approaches between the two becoming increasingly common as well.

## Supervised Learning

Supervised learning is a technique where the input and expected output of the system are provided, and the ANN is used to model the relationship between the two. Given an input set x, and a corresponding output set y, an optimal rule is to be determined such that:
    $y=f(x)+e$
Here, e is an approximation error that needs to be minimized. The input values are provided to the network which produces a result. This result is compared to the desired result, and this error signal is used to update the network weight vectors. Supervised learning is useful when we want the network to reproduce the characteristics of a certain relationship

## Unsupervised Learning

In unsupervised learning, the data and a cost function are provided that is a function of the system input and output. The ANN is trained to minimize the cost function by finding a suitable input-output relationship.
Given an input set x, and a cost function g(x, y) of the input and output sets, the goal is to minimize the cost function through a proper selection of f (the relationship between x, and y). At each training iteration, the trainer provides the input to the network, and the network produces a result. This result is put into the cost function, and the total cost is used to update the weights. Weights are continually updated until the system output produces a minimal cost. Unsupervised learning is useful in situations where a cost function is known, but a data set is not know that minimizes that cost function over a particular input space.
# Artificial Neural Networks/Introduction
## Introduction

Artificial neural networks are one of the most popular and promising areas of artificial intelligence research. Artificial Neural Networks are abstract computational models, roughly based on the organizational structure of the human brain. There are a wide variety of network architectures and learning methods that can be combined to produce neural networks with different computational abilities.

## What is This Book About?

This book is going to serve as a general-purpose overview of artificial neural networks, including network construction, use, and applications.

## Who is This Book For?

This book is going to be aimed at advanced undergraduates and graduate students in the areas of computer science, mathematics, engineering, and the sciences.

## What Are The Prerequisites?

Readers of this book are going to require a solid mathematical background that includes, but may not be limited to:
* Linear Algebra
* Abstract Algebra
* Calculus
Students may also find some benefit in the following engineering texts:
* Signals and Systems
* Engineering Analysis
Students who wish to implement the lessons learned in this book should be familiar with at least one general-purpose programming language or have a background in:
* MATLAB Programming
* Programmable Logic
# Artificial Neural Networks/Licensing
## License

The text of this book is released under the following license:
# Artificial Neural Networks/MATLAB Neural Networking Toolbox
## MATLAB

MATLAB ® is an ideal tool for working with artificial neural networks for a number of reasons. First, MATLAB is highly efficient in performing vector and matrix calculations. Second, MATLAB comes with a specialized Neural Network Toolbox ® which contains a number of useful tools for working with artificial neural networks.
This book is going to utilize the MATLAB programming environment and the Neural Network Toolbox to do examples and problems throughout the book.

## Other Neural Network Software

Even though this book is going to focus on MATLAB for its problems and examples, there are a number of other tools that can be used for constructing, testing, and implementing neural networks. E.g.
* GNU Octave.
* pybrain
* NEST
# Artificial Neural Networks/Hebbian Learning
## Hebbian Learning

Hebbian learning is one of the oldest learning algorithms, and is based in large part on the dynamics of biological systems. A synapse between two neurons is strengthened when the neurons on either side of the synapse (input and output) have highly correlated outputs. In essence, when an input neuron fires, if it frequently leads to the firing of the output neuron, the synapse is strengthened. Following the analogy to an artificial system, the tap weight is increased with high correlation between two sequential neurons.

## Mathematical Formulation

Mathematically, we can describe Hebbian learning as:
    $w_{ij}[n+1]=w_{ij}[n]+\eta x_{i}[n]x_{j}[n]$
Here, η is a learning rate coefficient, and $x_{i}[n]$ and $x_{j}[n]$ are, respectively, the outputs of the ith and jth elements at time step n.

## Plausibility

The Hebbian learning algorithm is performed locally, and doesn’t take into account the overall system input-output characteristic. This makes it a plausible theory for biological learning methods, and also makes Hebbian learning processes ideal in VLSI hardware implementations where local signals are easier to obtain.
# Artificial Neural Networks/Hopfield Networks
## Hopfield Networks

Hopfield networks are one of the oldest and simplest networks. Hopfield networks utilize a network energy function. The activation function of a binary Hopfield network is given by the signum function of a biased weighted sum:
    $y_{i}=\operatorname {sgn}(\zeta _{i}-\theta _{i})$
Hopfield networks are frequently binary-valued, although continuous variants do exist. Binary networks are useful for classification and clustering purposes.

## Energy Function

The energy function for the network is given as:
    $E=-{\frac {1}{2}}\sum _{i}\sum _{j}w_{ij}y_{i}y_{j}$
Here, the y parameters are the outputs of the ith and jth units. During training the network energy should decrease until it reaches a minimum. This minimum is known as the attractor of the network. As a Hopfield network progresses, the energy minimizes itself. This means that mathematical minimization or optimization problems can be solved automatically by the Hopfield network if that problem can be formulated in terms of the network energy.

## Associative Memory

Hopfield networks can be used as an associative memory network for data storage purposes. Each attractor represents a different data value that is stored in the network, and a range of associated patterns can be used to retrieve the data pattern. The number of distinct patterns p that can be stored in such a network is given approximately as:
    $p_{max}\approx 0.15n$
Where n is the number of neurons in the network.
# Artificial Neural Networks/Optimization

Optimization ANNs are concerned with the minimization of a particular cost function with respect to certain constraints. ANN are shown to be capable of highly efficient optimization.
# Artificial Neural Networks/Feed-Forward Networks
## Feedforward Systems

Feed-forward neural networks are the simplest form of ANN. Shown below, a feed-forward neural net contains only forward paths. A Multilayer Perceptron (MLP) is an example of feed-forward neural networks. The following figure below show a feed-forward networks with two hidden layers.

## Connection Weights

In a feed-forward system PE are arranged into distinct layers with each layer receiving input from the previous layer and outputting to the next layer. There is no feedback. This means that signals from one layer are not transmitted to a previous layer. This can be stated mathematically as:
    $w_{ij}=0{\mbox{ if }}i=j$
    $w_{ij}=0{\mbox{ if }}layer(i)\leq layer(j)$
Weights of direct feedback paths, from a neuron to itself, are zero. Weights from a neuron to a neuron in a previous layer are also zero. Notice that weights for the forward paths may also be zero depending on the specific network architecture, but they do not need to be. A network without all possible forward paths is known as a sparsely connected network, or a non-fully connected network. The percentage of available connections that are utilized is known as the connectivity of the network.

## Mathematical Relationships

The weights from each neuron in layer l - 1 to the neurons in layer l are arranged into a matrix w$_l$. Each column corresponds to a neuron in l - 1, and each row corresponds to a neuron in l. The input signal from l - 1 to l is the vector x$_l$. If ρ$_l$ is a vector of activation functions [σ1 σ2 … σn] that acts on each row of input and b$_l$ is an arbitrary offset vector (for generalization) then the total output of layer l is given as:
    $\mathbf {y} _{l}=\rho _{l}(\mathbf {w} _{l}\mathbf {x} _{l}+\mathbf {b} _{l})$
Two layers of output can be calculated by substituting the output from the first layer into the input of the second layer:
    $\mathbf {y} _{l}=\rho _{l}(\mathbf {w} _{l}\rho _{l-1}(\mathbf {w} _{l-1}\mathbf {x} _{l-1}+\mathbf {b} _{l-1})+\mathbf {b} _{l})$
This method can be continued to calculate the output of a network with an arbitrary number of layers. Notice that as the number of layers increases, so does the complexity of this calculation. Sufficiently large neural networks can quickly become too complex for direct mathematical analysis.
# A-level Computing/AQA/Problem Solving, Programming, Data Representation and Practical Exercise/Skeleton code/2016 Exam

The exam questions are very hard to predict and this site is by no means going to give you everything you need for the questions you'll sit. The most important thing you should do is learn how to program, and learn how to program well!
This is for the new specification A-Level Computer Science with the skeleton code being a version of the Battleships game. There is a change in the exam layout this year as the standard comp1 and comp2 some of us are used to are being changed. The main changes are that some of the questions from the comp1 (now called paper 1) have moved to the comp 2(now called paper 2) with some smaller differences in the specifications. it is advised you go through these specification to check if you have missed anything and to check for changes.
I think that that is the format for the paper 1 and it is very similar to the comp1 in the last few years, just without the section A as it is being moved onto the paper 2.(If I Say anything wrong please edit this page, I have no intention of misleading people.)
As I don't know the full layout of the paper the pages may not be in the right order or labelled right so please edit them as you see fit.
Skeleton code June 2016 Problems (Section D in Comp1 and most likely Section C in Paper 1 on new spec this year)
Sample Question Papers/
# A-level Computing/AQA/Problem Solving, Programming, Data Representation and Practical Exercise/Skeleton code/2014 Exam

The exam questions are very hard to predict and this site is by no means going to give you everything you need for the questions you'll sit. The most important thing you should do is learn how to program, and learn how to program well!
The exam is split into 4 sections that must be completed on a computer:

## Section A

<35 minutes> Theory Questions based on the material you have covered for Unit 1. For an overview of what this might include see the AQA specification and this wikibook.
* Section A

## Section B

<20 minutes> Programming solutions to short problems, not based on the preliminary material or skeleton code.
* Section B

## Section C

<10 minutes> Theory questions about the preliminary material and skeleton code.
* Section C

## Section D

<55 minutes> Program solutions based around the preliminary code. The guidance below doesn't pretend to offer the actual questions that will be set in the exam, but by doing them you should hopefully get a better grasp of the code and be able to answer any questions thrown at you during the exam.
* Section D
# A-level Computing/AQA/Problem Solving, Programming, Data Representation and Practical Exercise/Skeleton code/2015 Exam/Section C
## Validation

* Error Checking
* Example Question
* Answer:
* Example Answer
* Ways to crash game
* In VB, if you type 18 then 08. The game crashes - fix this.
* Answer:
* Function CheckMoveIsLegal(ByVal Board(,) As String, ByVal StartRank As Integer, ByVal StartFile As Integer, ByVal FinishRank As Integer, ByVal FinishFile As Integer, ByVal WhoseTurn As Char) As Boolean
* Dim PieceType As Char
* Dim PieceColour As Char
* If FinishFile = StartFile And FinishRank = StartRank Then
* Return False
* End If
* PieceType = Board(StartRank, StartFile)(1)
* PieceColour = Board(StartRank, StartFile)(0)
* If FinishRank = 0 Or FinishFile = 0 Then 'This is the required if statement
* Return False
* End If

## Variables

* Variables
* What is this function for? (code in answer)
* Answer:
* If Asc(SampleGame) >= 97 And Asc(SampleGame) <= 122 Then
* SampleGame = Chr(Asc(SampleGame) - 32)
* End If
* This converts lowercase to uppercase by using ASCII values.
* 1-What simple function can replace this code with? If Asc(SampleGame) >= 97 And Asc(SampleGame) <= 122 Then
* SampleGame = Chr(Asc(SampleGame) - 32) End If
* (Answer in Code)
* Answer:
* SampleGame = Ucase(SampleGame)
* Give the name of the identifier of a Constant
* Answer:
* BoardDimension
* Give the name of the identifier of a Fixed Value Variable
* Answer:
* SampleGame
* Give the name of a Most Wanted Holder Variable
* Answer:
* GetMove
* Give the name of the identifier of a Stepper Variable
* Answer:
* fileNo
* Give the name of the identifier of a Temporary Variable
* Answer:
* Board
* Give the name of the identifier of a Transformation Variable
* Answer:
* StartRank

## Loops

* Loops
* What is the difference between a repeat until loop and a for loop
* Answer:
* The 'for' loop will run a set number of times and finish when the count is complete. A repeat until loop will run until a condition has been met, the condition is checked at the end of the loop so it is possible for the loop to run once
* Example Question
* Answer:
* Example Answer
* Example Question
* Answer:
* Example Answer

## Sub Routines

* Sub Routine
* Give an example of a SubRoutine whose only role is to output
* Answer:
* DisplayWinner, displayWhoseTurnItIs

## Extra Stuff

* Extra Stuff
* Why is System.Math imported?
* Answer:
* To allow the use of Abs in the process of checking whether moves are legal.
* Why is Abs used?
* Answer:
* To return the absolute value. This is needed because the result of
* (FinishFile - StartFile) or (FinishRank - StartRank) may be a negative number, whilst the move is still legal.
* The Abs function returns the positive alternative, which prevents the program from crashing