OpenLLM-France/wikimedia huggingface dataset:
# Chess Opening Theory/1. e4/1...c5/2. Nf3/2...Nc6/3. d4/3...cxd4/4. Nxd4/4...Nf6/5. Nc3/5...e5/6. Ndb5/6...d6/7. Bg5/7...a6

The primary purpose of 7...a6 is to drive the knight on b5 away from its strong position. The knight on b5 threatens to jump to c7, which would be a fork on Black's king and rook, and puts pressure on d6. By pushing the a-pawn, Black gains space on the queenside, which can support further pawn advances like ...b5, potentially leading to active counterplay on that side of the board. Forcing the knight to retreat diminishes White's immediate threats and allows Black to better organize their pieces. The knight typically moves to a3, where it is less active compared to b5.
# Portuguese Opening, Miguel Gambit

This is a dubious Gambit. Black may try to accept it.
# Bishop's Opening Classical Defence
## 3. Nf3

White position is quite sharp, an attack on the e5 pawn, a possible break on d4 would gain a tempo on the Black Bishop. Black has one one move to try for equality, that's 3...Nc6 and transpose into the Giuoco Piano.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
    1. e4 e5 2. Bc4 Bc5 3.Nf3
| | 3 | 4 |
| Giuoco Piano by transposition | Nf3 Nc6 | = |
| | ... d6 | c3 | += |
| | ... Nf6?! | Nxe5 | += |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Goeller, Michael. The Bishop's Opening.
# Portuguese Opening
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
The Portuguese Opening is a rare opening starting with the moves 1.e4 e5 2.Bb5. The bishop is ineffective on the b5 square when there is no black knight on c6. It can be easily attacked by Black's c-pawn with 2...c6. Other moves can result in a Ruy Lopez/Spanish Opening (like 2...Nc6 3.Nf3) or other situations, where Black should be fine.
After 2...c6, the bishop can move to f1 (which makes White just waste 2 tempi), c4 (which allows 3...d5 to come with tempo and gives Black a classical center), d3, e2 (which allow a classical center for Black as well) and a4 (allowing 3...b5 4.Bb3 d5 and Black has a classical center, though engines may prefer 3...Nf6).
On move 2, Black can also play Nf6, develop normally, and exploit the bishop on b5 later. The Portuguese Opening is akin to a Ruy Lopez where White does not play Nf3 and is trying to gain pressure on Black's d-pawn. White may be hoping that Black attacks the bishop too much and weakens their dark squares or overextends.
1.e4 e5 2.Bb5
| 2 | 3 |
| Bb5 c6 | Ba4 Nf6 | = |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Portuguese Opening
## 3. Ba4

White has retreated the bishop to a safe square, which is still not very effective. Black can now play 3...b5 to attack the bishop again.
1.e4 e5 2.Bb5 c6 3.Ba4
# Portuguese Opening
## 3...b5

With this move, black attacks the passive bishop again with tempo. The only move that saves the bishop is 4. Bb3.
1.e4 e5 2.Bb5 c6 3.Ba4 b5
# Bishop's Opening Classical Defence
## 2...Bc5

The position remains symmetrical. This does not work well for Black as White's move d4 can always be played first.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
    1. e4 e5 2. Bc4 Bc5
| 3 |
| d3 Nf6 | = |
| Nf3 Nc6 | = |
| Nc3 Nf6 | d3 Nc6 | = |
| Qh5 Qe7 | Nf3 Nc6 | = |
| Qh5 Nc6?? | Qxf7# N/A | 1-0 |
| c3 Nf6 | d4 exd4 | = |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Goeller, Michael. The Bishop's Opening.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Modern Defence
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. e4 d6 2. d4 g6
| | 3 | 4 | 5 |
| Modern Defence | Nc3 Bg7 | Be3 a6 | Qd2 b5 | = |
| Pirc Defence by transposition | ... Nf6 | Nf3 Bg7 | Be2 O-O | = |
| | Nf3 Bg7 | Nc3 a6 | Be2 Nf6 | = |
| King's Indian Defence by transposition | c4 Bg7 | Nc3 Nf6 | Nf3 O-O | = |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Portuguese Opening

This is a good developing move. 3. b4!? is the dubious Miguel Gambit.
# Arithmetic/Types of Numbers/Imaginary Number
## Imaginary Number

An imaginary number is a number whose square is less than zero.
e.g.
    $i={\sqrt {-1}}$

## Conjugate Number

    $-i=-{\sqrt {-1}}$

## Rules

1) i + i = 2i
2) i - i = 0
3) i x i = i²
4) i / i = 1
5) i + (-i) = 0
6) i - (-i) = 2i
7) i x (-i) = -i$^2$ = 1
8) i / (-i) = -1
# Arithmetic/Types of Numbers/Integer Number

An integer number is any of: a positive whole number (a positive integer), a negative whole number (a negative integer), or zero.

### Positive Integer

A Positive Integer is a natural number greater than 0, i.e. a whole number. A Positive Integer can be expressed mathematically:
    I > 0 = {+1,+2,+3,+4,+5,+6,+7,+8,+9,...}
Positive numbers are often written without a + sign:
    I > 0 = {1,2,3,4,5,6,7,8,9,...}

### Negative Integer

A Negative Integer is a negative whole number. This is represented by a - sign on the left side of the value.
    I < 0 = {-1,-2,-3,-4,-5,-6,-7,-8,-9,...}

### Number Zero

The Integers include a new number, 0.

## Rules

* a + 0 = a
* a - 0 = a
* a × 0 = 0
* a / 0 is not defined.
* a + a = 2a
* a - a = 0
* a × a = a$^2$
* a / a = 1 (except for a = 0, which is not defined, see rule 4)
* a - (-a) = 2a
* a × (-a) = - a$^2$
* a / (-a) = -1 (except for a = 0, which is not defined, see rule 4)
# Arithmetic/Types of Numbers/Natural Number

The natural numbers (i.e. counting numbers) are numbers which are used for counting and ordering.
They can be expressed mathematically as:
    ℕ = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 etc. }
Some mathematicians consider 0 to be a natural number. This convention is common in logic and computer science. ℕ⁰, ℕ₀ and ℤ₀+ unambiguously denote the set of non-negative integers, while ℕ*, ℕ⁺, ℕ₁ and ℤ+ unambiguously denote the set of positive integers.
The greatest natural number does not exist: for every possible natural number n, there exists n+1 which is also a natural number.
Natural numbers can be considered the basis of most if not all common number sets. For example, the integers (ℤ) are simply the natural numbers ℕ, 0, and the negatives of the natural numbers. Rational numbers (ℚ) can be defined as the quotients of integers, that is, fractions.

## Even Number

Even numbers are natural numbers that are divisible by 2. That is to say, natural number n is even if there exists another natural number m such that n = 2m
    2ℕ = { 2, 4, 6, 8, 10, 12, 14, ... } = { 2⋅1, 2⋅2, 2⋅3, 2⋅4, ..., 2⋅n, ... }

## Odd Number

Odd numbers are natural numbers that are not divisible by 2. That is to say, natural number n is odd if there exists another natural number m such that n = 2m + 1
    2ℕ + 1 = { 1, 3, 5, 7, 9, 11, 13, 15...} = { (2⋅1) + 1, (2⋅2) + 1, (2⋅3) + 1, (2⋅4) + 1, ..., (2⋅n) + 1, ... }

## Prime and Composite Numbers
### Prime Number

Prime numbers are natural numbers that are only divisible by 1 and by itself.
    P = { 2, 3, 5, 7, 11, 13, 17, 19,...}

### Composite Number

Composite numbers are natural numbers that are the product of some prime numbers. For example:
    4 = 2 ⋅ 2
    12 = 2 ⋅ 2 ⋅ 3
    15 = 3 ⋅ 5
Every natural number, except prime numbers and 1, is composite.

### One

1 is neither a prime nor composite number, as the number is only divisible by itself.
# Arithmetic Course
## Number

* Number System
* Types of Number
* Number Operation

## Variable

* Variable
* Expression
* Polynomial

## Function

* Function Definition
* Linear Function
* Non Linear Function

## Equation

* Polynominal Equation
* Differential Equation
# Arithmetic Course/Differential Equation
## Differential Equation

Differential Equation is an equation that has the general form
    $f^{'}(x)=0$

## Solving Differential Equation

* First Order Differential Equation
* Second Order Equation
# Arithmetic/Types of Numbers/Mixed Fraction

Mixed fraction is the sum of a Whole number and a fraction. Mixed Fraction can be expressed mathematically
    $A+{\frac {B}{C}}$
       A is a Whole number
       ${\frac {B}{C}}$ is a Fraction
# Arithmetic/Working with Integers

There are a number of ways to compare two arithmetic expressions. The first one can either be:
* equal to the second (=)
* greater than the second (>)
* less than the second (<)
* greater than or equal to the second (≥)
* less than or equal to the second (≤)
Examples:
    5>2 (reads: "Five is greater than Two")
    2<5 (reads: "Two is less than Five")
    7=7 (reads: "Seven is equal to Seven")
    a ≥ b (reads: "A is greater than or equal to B". This means A could be equal to B or greater than B.)
    a ≤ b (reads: "A is less than or equal to B". This means A could be equal to B or less than B.)
# Arithmetic/Zero and Numbers Greater Than Nine

This page explores more numbers by getting higher and lower than the previously introduced numbers 1-9.

## Zero

What happens when you want to show with math that there is nothing? This is where we use the number zero (0). Zero can be achieved by subtracting any number by itself. For example:
    $3-3=0$

## Numbers Larger than Nine

So far we have learned about nine different numbers. But what if we want to count higher than nine? This is where we use numbers that have more than one digit. The simplest of these numbers are:
    $9+1=10$
At first, this looks like nonsense. How can nine and one make "one-zero"? But the "one-zero", called ten is actually a number in itself. Since there is more than one digit, all but the first digit represent numbers larger than nine. 10 can be rewritten as:
    $(1*10)+(0*1)$
that is to say:
    The number 10 is equal to the total of one ten and zero ones.
Let's use another number, 58 (fifty-eight), to explain more. The number 58 can be rewritten as:
    $(5*10)+(8*1)$
that is to say:
    The number 58 is equal to the total of five tens and eight ones.
Therefore, we can safely say that the position of the digits affects its value, that is, our number system (also known as decimal or base-10), is positional.
# Arithmetic/Types of Numbers/Fraction
## Fraction

Fraction is a ratio of two integer numbers. Fraction can be expressed mathematically
    ${\frac {A}{B}}$, where B is not zero.
Where
    A is called Numerator
    B is called Denominator

## Equal Fractions

Two fractions A/B and C/D are the same if the product of numerator A and denominator D is equal to the product of denominator B and numerator C.
    ${\frac {A}{B}}={\frac {C}{D}}$ if $A*D=B*C$
    and
    ${\frac {A*D}{B*C}}={\frac {E*H}{F*G}}$ if $(A*D)(G*F)=(E*H)(B*C)$

## Rules

* ${\frac {A}{B}}$ + ${\frac {C}{D}}$ = ${\frac {AD+BC}{BD}}$
* ${\frac {A}{B}}$ - ${\frac {C}{D}}$ = ${\frac {AD-BC}{BD}}$
* ${\frac {A}{B}}$ x ${\frac {C}{D}}$ = ${\frac {AC}{BD}}$
* ${\frac {A}{B}}$ / ${\frac {C}{D}}$ = ${\frac {AD}{BC}}$, if C not zero.
# Arithmetic/Types of Numbers/Real Number

The collection of all rational numbers and irrational numbers make up what is called the Real Number system.
A number that can be expressed as a ratio of integer is a rational number.
A number that is not a rational number is an irrational number.
The following are some common irrational numbers:
* π (which can be approximated to 3.14159265 and represents the length of the circumference of a circle divided by its diameter)
* √2 (which is the square root of 2 and is approximately 1.4142)
* e (which is the base of the natural logarithms and is approximately 2.71828)
    and so on.
# ETD Guide/Universities/Measurement in Related Contexts

Another important type of post-processing is the extraction of statistical information from metadata sets. For administrative purposes, institutions may be interested in the number of ETDs supervised by each professor, the keywords most used, the month(s) in which more ETDs are submitted, etc. Usually, relevant metadata are extracted from the ETD database and processed using specialized tools like Microsoft Excel. The access to the database can be done using either ODBC drivers or specialized middleware utilities.
For a broad view of counting information, two projects are widely regarded as providing interesting models and data.
* Peter Lyman and Hal R. Varian’s How Much Information project at the University of California, Berkeley is an attempt to measure how much information is produced in the world each year.
* The OCLC Web Characterization Project conducts an annual web sample of publicly available web sites to analyze trends in the size and content of the web.
Some programs that provide guidance or models for collecting institutional data in higher education are also available. These projects can provide definitions for data, survey questions, and descriptions of data collection that can be adapted for one’s own institution.
* K. C. Green has been conducting the Campus Computing Project since 1990. His work charts the increasing use of technology on campuses.
* The TLT Group’s Flashlight Program, under the direction of Steve Ehrmann, has developed a subscription-based tool kit that provides a large, structured set of assessment techniques and data collection models that can be adapted by individual campuses that want to study and improve the educational uses of technology. The Flashlight Program web site also includes valuable overviews of assessment issues and provides advice on deciding what to assess and how to develop questions.
* The Coalition for Networked Information’s Assessing the Academic Networked Environment project provides case studies of campuses that implemented assessment projects.
* One of the participants in the CNI project, the University of Washington, has a rich set of assessment instruments and reports on its web site, UW Libraries Assessment.
Next Section: Guidelines for Implementing an Assessment Program for ETDs
# ETD Guide/Universities/Intellectual Property Rights

Whether an author is creating an electronic or paper thesis or dissertation, it does not change their rights and obligations under the law. While university policies vary, it is the custom that the person who creates a work is the owner of the copyright. Therefore, the author of an electronic thesis or dissertation is the copyright holder and owns the intellectual property, their ETD. Within the United States, authors have rights protected by law particularly US Code, Title 17, especially section 106. Authors get to decide how their works will be reproduced, modified, distributed, performed in public and displayed in public. An author may use another’s work with certain restrictions known as “fair use” (US Code, Title 17, sect. 107). The four factors of fair use that must be considered equally are: (1) purpose and character of use; (2) nature of the copyrighted work; amount and substantiality; and (4) effect. In the United States, libraries are also considered in the same copyright law under section 108. [For further explanations, see http://www4.law.cornell.edu/uscode/17/ch1.html]
The owner of an ETD, as explained above usually the student, must take direct action if an ETD service is to be provided. The wording that is agreed to in writing, by student authors as well as the faculty working with them, must make clear how ETDs are handled. The wording used at Virginia Tech is one model. In the approval form used for this purpose, the following is agreed:
The student certifies that the work submitted is the one approved by the faculty they work with. The university is given authority, directly or through third party agents, to archive the work and to make it accessible, in accord with any access restrictions also specified on the form. This right is in perpetuity, and in all forms and technologies that may apply.
Next section: Publishers
# ETD Guide/Universities/Processing charges

Many universities that have paper submissions of theses and dissertations collect funds for processing these works. Usually the funds are collected from students. In some cases they might be collected from grants, or from a sponsor (e.g., from the National Library, with regard to works in Canada).
These funds commonly are called "binding fees" or are given other names designating their use for processing. A typical fee might be $20 or $30 per work.
In the case of transition to ETDs at Virginia Tech, there were changes to these fees. First, in 1996, when submission of ETDs was encouraged but voluntary, the processing fee was waived for those students submitting an ETD instead of a paper document. This provided a monetary incentive to move toward ETDs.
However, in 1997, with a requirement in place, the processing fee was re-instituted. However, it was renamed "archiving fee". Thus, funds were collected from students:
* to help defray the costs of the ETD program;
* to provide a pool of funds to archive and preserve works throughout their lifetime, allowing for migration to new media types (e.g., automatic copying to newer types of storage media, such as from one online disk to a more modern disk), as well as conversion to new formats (e.g., moving from SGML to XML, or from one version of PDF to a newer version).
Next section: Budgets
# ETD Guide/Universities/Human resources and expertise needed for an ETD program

While each university’s situation with regard to personnel will vary, it has been shown that ETD programs do not require a large contingency of expert professionals to initiate the program or to maintain it. With a portion of the time of one librarian and one programmer, the Virginia Tech library established the ETD Web site and documented the sequence of events that lead to the computer programs for each stage of acceptance, storage, and access, and implemented the procedures for the university.
One step that should not be overlooked is to involve every person that had a role in traditional theses and dissertation handling. This includes, but is not necessarily limited to.
* Graduate School personnel who, for example, receive the TDs as well as the various forms and payments, and who may be responsible for approving the final document
* Library personnel such as the University Archivist, reference librarian, cataloging librarian, binding clerk, and business services personnel who, for example, are responsible for the long term preservation and access as well as those responsible for processing the microfilming invoices
LIBRARY STAFFING: programmer, student assistant, faculty liaison
A programmer may spend one-half to one hour per day during non-peak periods on maintenance and development. During peak periods this person may spend eight hours per day on problems, development, and system improvements.
One or two student assistants are helpful. One student who knows programming may spend a maximum of two hours per week during non-peak times, and up to ten hours per during the periodic submission/approval peaks. Another student assistant would work face-to-face with graduate student authors to train them and to provide assistance with word processing and PDF software. This assistant might also maintain the training materials, handouts, and Web pages, including instructions for preparing and submitting ETDs.
A faculty member from the library would supervise staff; draft policies; prepare budgets; collaborate with system maintenance and developers; and monitor workflow. This person would also be a liaison to faculty, staff, students, departments, and colleges to help them to become familiar with the processing, accessing, and archiving of ETDs. The faculty liaison from the library would also conduct workshops, write articles, participate in graduate student seminars, prepare handouts and Web pages, as well as collaborate with other universities and libraries.
Next section: Sources for funding
# ETD Guide/Universities/Publishers

A continuing topic of discussion in the ETD community, including Graduate School administrators, research faculty, and librarians, is the question of “prior publication.” That is, whether publishers and editors of scholarly journals view electronic theses and dissertations that are available on the Internet and through convenient Web browsers as being published because they are so readily and widely available.
John Eaton, Dean at Virginia Tech’s Graduate School, surveyed graduate student alumni in 1998 and 1999 and he asked about publishing articles derived from their ETDs. One hundred percent of those who had successfully published had not had any problems getting published because their theses or dissertations were online and readily available on the Internet. By looking at the results Joan Dalton’s 1999 survey of publishers and Nan Seaman’s 2000 survey as well as at Eaton’s surveys of graduate student alumni, the ready availability of ETDs on the Internet does not deter the vast majority of publishers from publishing articles derived from graduate research already available on the Internet. [See "Do ETDs Deter Publishers? Coverage from the 4th International Symposium on ETDs," Gail McMillan. College and Research Libraries News, v. 62, no. 6 (June 2001): 620-621. http://scholar.lib.vt.edu/staff/gailmac/publications/pubrsETD2001.html]
Several publishers have also attested to this and these statements are available in a variety of sources such as http://www.ndltd.org/publshrs/index.html. (others?) At the Cal Tech ETD 2001 conference, Keith Jones from Elsevier stated emphatically that his company encourages its authors to link their articles in Elsevier journals to their personal Web sites and also authorizes faculty members’ departments to provide such links. Jones reported that Elsevier understands the importance of getting new authors such as graduate students to publish in his journals early in their careers because they are then likely to continue to publish with the same journal. He also pointed out the publishing in an Elsevier Science journal is an important source of validation for academics so that the subsequent availability of those articles from other non-profit and educational sources is not a threat.
Next section: Human resources and expertise needed for an ETD program