OpenLLM-France/wikimedia huggingface dataset:
# Applicable Mathematics/Odds

"Odds" is a way of expressing the likelihood of an event.
The more usual way of expressing the likelihood of an event is its "probability" (the percentage of future trials which are expected to produce the event: so in tossing a coin believed to be fair, we would assign a probability of 50% (or one half, or 0.5) to the event "heads").
The ODDS of an event, however, is the ratio of the probability of the event happening to the probability of the even not happening (i.e. the ODDS of a fair coin landing heads is 50%:50% = 1:1 = 1). It is the ODDS we are using when we use a phrase like "it is 50/50 whether I get the job" or "The chances of our team winning are 2 to 1".
Or, For example, when rolling a fair die, there is one chance that you will roll a 1 and five chances that you will not. The odds of rolling a 1 are 1:5, or 1 to 5. This can also be expressed as $1/5$ or 0.2 or 20%, but these forms are likely to be misunderstood as normal probabilities rather than odds.
To convert odds to probability, you add the two parts, and this is the denominator of the fraction of your probability. The first part becomes the numerator. Thus, 1:5 becomes 1/(1+5) or 1/6.
To convert probability to odds, you use the numerator as the first number, then subtract the numerator from the denominator and use it as the second number. Thus, 1/6 becomes 1:(6-1) or 1:5.

## See also

* Probability Distributions"Odds" is a way of expressing the likelihood of an event.
The more usual way of expressing the likelihood of an event is its "probability" (the percentage of future trials which are expected to produce the event: so in tossing a coin believed to be fair, we would assign a probability of 50% (or one half, or 0.5) to the event "heads").
The ODDS of an event, however, is the ratio of the probability of the event happening to the probability of the event not happening (i.e. the ODDS of a fair coin landing heads is 50%:50% = 1:1 = 1). It is the ODDS we are using when we use a phrase like "it is 50/50 whether I get the job" or "The chances of our team winning are 2 to 1".
Or, For example, when rolling a fair die, there is one chance that you will roll a 1 and five chances that you will not. The odds of rolling a 1 are 1:5, or 1 to 5. This can also be expressed as 1 / 5 or 0.2 or 20%, but these forms are likely to be misunderstood as normal probabilities rather than odds.
To convert odds to probability, you add the two parts, and this is the denominator of the fraction of your probability. The first part becomes the numerator. Thus, 1:5 becomes 1/(1+5) or 1/6.
To convert probability to odds, you use the numerator as the first number, then subtract the numerator from the denominator and use it as the second number. Thus, 1/6 becomes 1:(6-1) or 1:5.
* Probability
# Apples/Rootstocks

Rootstocks used to control tree size have been used in apple cultivation for over 2,000 years. Dwarfing rootstocks were probably discovered by chance in Asia. Alexander the Great sent samples of dwarf apple trees back to his teacher, Aristotle in Greece. They were maintained at the Lyceum, a center of learning in Greece.
Most modern apple rootstocks were bred in the 20th century. Much research into the existing rootstocks was begun at the East Malling Research Station in Kent, England. Following that research, Malling worked with the John Innes Institute and Long Ashton to produce a series of different rootstocks with disease resistance and a range of different sizes, which have been used all over the world.
# Applicable Mathematics
## Contents

* Systems of Equations
* Matrices
* Univariate Data
* Sets
* Transformations
* Probability
* Counting Techniques
* Bivariate Data
* Linear Programming and Graphical Solutions
* Probability Distributions
* Odds
# Arabic/Appendix B

مَن Who man مِن From min أين Where ain ما What / Negator ma ماذا What (questions with verbs i.e.: what do you study?) matha لماذا Why limatha كيف How kaifa مرحبا Hello marhaban سلام عليكم Peace be on you (hello) salaam aleikum اهلا وسهلا Welcome / You're welcome (response to thank you) ahlan wa sahlan شكرا Thank you shukran من فضلك Please min fadlik
# Arabic/Arabic alphabet step-by-step

The Arabic alphabet is a consonantal alphabet; vowels are not fully represented. It also has a very rich calligraphic history.
A word such as كتاب may seem like a scribble to the beginner, and may seem not to be composed of letters. It is, they are simply connected to each other. The first letter is kaaf it looks like this كـ . The second letter in the word is taa, it looks like this (تـ ). The third letter is alif : It looks like this: ا . The last letter is baa it looks like this بـ.
As you might have noticed, Arabic is read from right to left, down the page. The word كتاب spelled kaf ta alif ba, means book it is pronounced "kitaab".

## Exercise 1

Give the names of each letter, start at the right. كـ ، تـ ، ا ، بـ ، تـ ، ا ، بـ ، تـ

## Exercise 2

Write the Arabic letter that best represents the first sound in the following words:
* cave
* tape
* coconut
* bill
* apple
* ant

# Answers
## Ex.1

kaf, ta, alif, ba, ta, alif, ba, ta

## Ex.2

* كـ
* تـ
* كـ
* بـ
* ا
* ا
# Arabic/Basic Sentences
## "The"-the definite article

In Arabic the word ال "el/èl" does what the English word "the" does. It is pronounced [ al ] but the "a" at the beginning is often elided (not pronounced, because the previous word ended in a vowel).
Examples: رَجُل
rajuluń = a man
Pronounced: ra-jul
الرَّجُل èl rajul= the man pronounced: ar-ra-jul.
الرجل èl rajul is pronounced ar-ra-jul instead of al-rajul, because "r" is a sun letter. Whenever el is prefixed to a sun letter the transliteration system will indicate this by writing èl instead of el. There is no need to memorize sun letters. e.g. الشمس èl shams is pronounced ash-shams (meaning: the sun).
Add ال el to the beginning of a word, is like adding "the" before a word in English.

## Writing it

Here is an example of what not to do:
Notice that the ل (laam) must connect to the next letter, which was a ر (raa') in the case above.
ال el also has a second use. When you find ال it usually has the same function as "the" in English. It is also often used to talk about a thing in general.
man إنسان mankind الإنسانThe previous example shows one word meaning "a man." The second is the same word with the prefix "ال" (al), and it means man in general (i.e. mankind). So in English where one says "owls go to sleep at night" in Arabic we would say "the owl goes to sleep at night." This would indicate owls in general and not a specific owl.
So what word holds the same functions as the word "a", you might ask? In Arabic there is no word that holds that function.
So "a man" is just one word, رجل
There is no word, or prefix, that has the same function as "a".
* Next Lesson
# Arabic/ArabicWriting

Purpose of this page: explains how the Arabic words will be displayed. Proposals:
* Use Arabetics fonts in some of sections of the book.
* Include Arabic type with fathäh, kasräh, etc. So that the Arabic text is adequate enough to figure out the pronunciation. This probably requires the next proposal to be implemented.
* Show Arabic type as a picture so it is viewable on all computers. This is necessary to show the vowelizing symbols (a.k.a. "tashkiil") (fathäh, kasräh, etc.) properly.
* Make transliteration optional to view.
* Allow the user to choose to see vowelized or unvowelized texts, when viewing a page.
These are to be discussed on the talk page.
Anything agreed upon goes below for future authors.
# Arabic/Basic Sentences/ain't

mish=ain't Note that the word "lissa" is used in exactly the same way by some speakers. Note that "mish" can be pronounced "mush".
mish is a useful Arabic slang word. We will use it to make sentences that would translate to... _________ ain't __________.
So why would we teach a slang word to say "is not" rather than the other type?
* "mish" is extremely useful
* "laisa" is a verb and therefore requires conjugations
* because "laisa" is a verb the predicate changes case

## Words

notebook (daftar) دفتر
book (kitaab) كتاب
man (rajul) رجل
woman (imra'ä) إمرأة
big (kabiir) كبير

## examples

el-kitaab mish kabiir.
The book ain't big.
èl-daftar mish kabiir.
The notebook ain't big.
In the next lesson we will learn how to make "is" sentences such as:
The book is big. The notebook is big.
This requires the removal of "mish" from the sentence.
# C Programming/stdio.h/vwprintf

vwprintf is a C standard library function as defined in wchar.h .It has function signature as
In signature of function vwprintf, format is format specialisation and args is pointer to arguments.

## comparision with other functions

The functioning of vwprintf is same as that of swprintf. The difference between both functions is that the argument list has been replaced by a pointer to a list of argument. vwprintf performs the wide character output to the string like stdout and stdout should not be byte oriented.
The functioning of vwprintf is same as that of swprintf.The difference between both functions is that the argument list has been replaced by a pointer to a list of argument. vwprintf performs the wide character output to the string like stdout and stdout should not be byte oriented. this function return the number of characters not including the null character and any negative value if an output error occurs vwprintf is equivalent to wprintf with argument list replaced by arg and which can be initialised by vastart macro.

## return values

vwprintf returns number of characters written but excluding the NULL character on success.But on failure it returns an error and errno is set.
# C Programming/stdio.h/wprintf

wprintf is a C standard library function as defined in wchar.h. It has function signature as
The wprintf writes output to stdout, the standard output stream. It uses variable argument lists. This function and also functions like vprintf, vfprintf, vsprintf, vsnprintf, and vasprintf offer the ability for programmers to essentially create their own printf variants.

## Usage

The wprintf function is found in C, in which writes the output to the stream under control of format strings. the format string specifies how subsequent arguments are converted for output.
wprintf is a wide character version of printf format. The format is a wide character string where wprintf and printf bahave similarly as they are opened in ANSI mode.

## Example

Following is the sample code for understanding of working of the wprintf.
code:
After running the code output will be as follows:

## Limitations

limitations: 1. wprintf is not portable function. 2. wprintf cannot be mixed with printf. 3. wprintf cannot print the double values.
# C Programming/stdio.h/ungetc

Ungetc is a version of a C standard library function ungetch. It is somewhat a restricted function.

## Declaration

int ungetc (int c, FILE *stream)
Here, c is a character variable, stream is a file pointer and the overall function is expressed in integer data type.

## Description

As mentioned above, rather it is a restricted version of ungetch, the function pushes the character specified by the value of c. At the time of pushing, the character c is converted to a unsigned char and then pushed to the input stream. The pushed character can be returned back if a getc function is applied to the stream.

## Calling capacity

A single push back of the character is allowed at a call. Trying to do a push back in a succession may or may not work properly. In normal and usual practices, 4 times the function is called and hence 4 characters are pushed consecutively. It means that the process of this function is totally machine dependent. Hence if memory is large in extent in a machine then there is a possibility to have the push backs for infinitly large times.

## Return value

The characters which are pushed back are returned by any subsequent read on the stream (in reverse order) and if the input from the stream is buffered, it means that the last character pushed will be returned first. When a normal push back of the character is done, the function returns the last pushed character. If the push back operation is not done properly means if the push back of a character is unsuccessful (e.g. if the file is not open) then EOF character is returned as an error. One can not push back the EOF character to the stream using ungetc. A successful call to ungetc function clears the EOF indicator for the stream.
To erase the push back characters came from call to ungetc function, a call to fseek, fsetpos or fflush functions is made before the character is read from the stream. As all the characters are pushed back are read in, the file position indicator is same as before pushing back the characters.

## Ungetc, a restricted version of ungetch

As stated already it is a restricted version of function ungetch, it has same restrictions like when a read operation is immediately folllowed by a write operation or vice versa. That is why, there is a requirement of a intervening reposition between ungetc and the subsequent write or read function.
# C Programming/stdlib.h/atexit

atexit (at exit) is a function that is in the C Programming Language to register the given function to be executed at normal process termination, either via exit or via return from the program's main function.
The atexit function takes, as argument, the reference of the function to be registered for call back. Functions so registered are called in the reverse order of their registration; no arguments are passed.

## POSIX Usage

The atexit function is standardized by the POSIX specification.
The prototype of the function is as below:
The function returns zero (0) if it completed execution successfully. Non-zero return values signify an error.
POSIX requires that an implementation of atexit allow at least ATEXIT_MAX (32) such functions to be registered.

## Example

The following example demonstrates the use of the atexit function.

## References

ISO/IEC 9899:1999 specification (PDF). p. 315, § 7.20.4.2.

## External links

* C++ reference for std::atexit
# C Programming/stdio.h/wscanf

wscanf
wscanf is a standard C library function in C programming language. It transforms wide character input. This function is supported by the header file wchar.h. wscanf is wide character version of scanf.
Syntax int wscanf(const wchar_t*input in formatted form) It returns count of inputs which are properly formatted. Count may be zero or less than the entered inputs in case of unformatted wide character input.
example
Now if the given input is like as given below: 83 56.6 k m Scanf input 54 22.3 a f Wscanf input
then output will be like this: The number of fields input is 6 The contents are: 83 56.599998 k m Scanf input The number of fields input is 6 The contents are: 54 22.300003 a f Wscanf input Thus scanf returns no of fields which are properly formatted or in another words which are successfully assigned.it does not does not returns the count for the field which is not properly formatted and such values are read but not assigned. And EOF is returned if end of the file character is encountered in first character reading of the file. Reference
# C Programming/stdlib.h/abort

C programming standard library function .It is used in programming process or environment to stop the program or process abnormally.This function is required in the program when wrong condition gets encountered in program execution then to come out of process this function is used.

### Introduction

It deletes buffers and closes all open files before ending the program. The function abort terminates the current program. Depending on the implementation, the return from the function can indicate a canceled (e.g. you used the signal function to catch SIGABRT) or failed abort. SIGABRT is sent by the process to itself when it calls the abort libc function, defined in cstdlib. The SIGABRT signal can be caught, but it cannot be blocked; if the signal handler returns then all open streams are closed and flushed and the program terminates (dumping core if appropriate) , then it returns control to host environment.This means that the abort call never returns. Because of this characteristic, it is often used to signal fatal conditions in support libraries, situations where the current operation cannot be completed but the main program can perform cleanup before exiting. It is also used if an assertion fails.

### Return Value

This function does not return any value i.e. it is of void datatype.

### Thread safety

It is one of the thread safe functions from standard c library.i.e. function can be called by different threads without any problem.

### Example

This example tests for successful opening of the file myfile. If an error occurs, an error message is printed, and the program ends with a call to the abort function.
# C Programming/stdlib.h/abs

Many programming languages have functions that calculate absolute values of numbers, either having the name abs or Abs. In languages such as C, it has variants for long integers and floating point numbers called labs and fabs. All the functions take a signed number as a parameter, and returns the absolute value of that number in the same data type.
A very possible implementation of the abs functions, written in pseudo-code, would be:

### C or C++

These functions are defined in the standard header math.h for C and cmath for C++:
# C Programming/stdio.h/tmpfile

In computing, tmpfile is an ISO C/POSIX function for creating a temporary file, a computer file which ceases to exist when the program, which opened the file, closes it or terminates.

## Usage
### Inclusion
#### C

#include <stdio.h>

#### C++

#include <cstdio>

### Declaration

FILE* tmpfile(void);

### Semantics

The function tmpfile reports a pointer to a valid file stream on success; on failure, it returns NULL.

## Error conditions

In addition to returning NULL, tmpfile sets errno on failure. The permissible values of errno, if tmpfile fails, are:
* EINTR - if a signal was caught during the execution of tmpfile.
* EMFILE - if the maximum number of file descriptors and/or the maximum number of file streams has been reached (in the process).
* ENFILE - if the maximum allowable number of files is currently open (in the system).
* ENOSPC - if there is no space in the file system for creating the temporary file.
* EOVERFLOW - if the file is a regular file and the size of the file cannot be represented correctly in an object of type off_t.
* ENOMEM - if there is insufficient memory for allocating the file stream.

## Caveats

The tmpfile function is susceptible to a number of security vulnerabilities; use the non-portable mkstemp (UNIX) or tmpfile_s (MSVCRT) functions, instead, to avoid these issues.
The implementation of this function in Microsoft C run-time library tries to create the file in the root directory of the current drive and typically fails reporting "Access denied".

## References

* 1 2 3 tmpfile by OpenGroup
* ↑ Temporary Files by GNU C Library
* ↑ tmpfile by HMUG
* ↑ TMPNAM-TMPFILE Vulnerability by Build Security In
* ↑ VOID FI039-C. Create temporary files securely by CERT

## External links

* C++ reference for std::tmpfile
# Business Analysis Guidebook/Noted Contributors

The material included in this wikibook was authored by members of the Capital District Business Analysis Community of Practice (BACOP) Guidebook Committee, led by Barbara Ash (retired from the NYS Office of the State Comptroller) and Kelly Smith-Lawless (currently PPM Director of the General Gov't Cluster within NYS Office for Information Technology). This material was organized and drafted over a period of a couple years and care was taken to ensure representation from across various agencies within NYS Government. The goal was to establish a common framework from which all IT projects could leverage in order to develop a consistent approach across different agencies. BACOP Representatives (past and present) that contributed to this wikibook as authors and editors include:
* Jim Alderdice (ITS)
* Barbara Ash (OSC)
* Marina Brereton (PubSafety)
* Todd Britton (OSC)
* Karen Conners (PubSafety)
* Michelle Cuchelo (GGC)
* Susan Davis (NYSIF)
* Marcia Eaton (Health)
* Belinda Jackson (Health)
* Deena Jones (WCB)
* Erlene Kent (TED)
* Tina Koberger (TED)
* Nathan Kroop (Health)
* Kimberly Manion (Health)
* Prachi Mondaiyka (Health)
* Beth Ostwald (Tax)
* Kelly Smith-Lawless (GGC)
* Susan Travis (GGC)
* Elaine Wing (Health)
* Elaine Zuk (ENV)
* Elizabeth Thackeray (DOH/HRI)
# Calculus Course/Integration/Indefinite Integral
## Indefinite Integral

Indefinite Integral is a mathematic operation on a non linear function over an indefinite a boundary
    $\int f(x)dx=Lim_{\Delta x\to 0}\Sigma \Delta x[f(x)+{\frac {f(x+\Delta x)}{2}}]$

## Indefinite Integral Rules

Because antidifferentiation is the inverse operation of the differentiation, antidifferentiation theorems and rules are obtained from those on differentiation. Thus, the following theorems can be proven from the corresponding differentiation theorems:
* General antidifferentiation rule:
       $\int dx=x+C$
* The general antiderivative of a constant times a function is the constant multiplied by the general antiderivative of the function:
       $\int af(x)\,dx=a\int f(x)\,dx+C$
* If ƒ and g are defined on the same interval, then the general antiderivative of the sum of ƒ and g equals the sum of the general antiderivatives of ƒ and g:
       $\int [f(x)+g(x)]\,dx=\int f(x)\,dx+\int g(x)\,dx+C$
* If n is a real number,
       $\int x^{n}\,dx={\begin{cases}{\frac {x^{n+1}}{n+1}}+C,&{\text{if }}n\neq -1\\[6pt]\ln |x|+C,&{\text{if }}n=-1\end{cases}}$
    $\int f(x)dx=f^{'}(x)+C$
    $\int {\frac {f^{'}(x)}{f(x)}}{\rm {d}}x=\ln |f(x)|+c$
    $\int {UV}=U\int {V}-\int {\left(U^{'}\int {V}\right)}$
       $e^{x}$ also generates itself and is susceptible to the same treatment.
       $\int {e^{-x}\sin x}~dx=(-e^{-x})\sin x-\int {(-e^{-x})\cos x}~dx$
       $=-e^{-x}\sin x+\int {e^{-x}\cos x}~dx$
       $=-e^{-x}(\sin x+\cos x)-\int {e^{-x}\sin x}~dx+c$
       We now have our required integral on both sides of the equation so
       $=-{\frac {1}{2}}e^{-x}(\sin x+\cos x)+c$
* $f(x)=m$
    $\int mdx=mx+C$
* $f(x)=x^{n}$
    $\int {f(x)}dx={\frac {1}{n+1}}x^{n+1}+c$
* $f(x)={\frac {1}{x}}$
    $\int {\frac {1}{x}}dx=\ln x$

## List of Derived Integral

* List of integrals of rational functions
* List of integrals of irrational functions
* List of integrals of trigonometric functions
* List of integrals of inverse trigonometric functions
* List of integrals of hyperbolic functions
* List of integrals of inverse hyperbolic functions
* List of integrals of exponential functions
* List of integrals of logarithmic functions
* List of integrals of Gaussian functions
# Calculus Course/Sequence
## Sequence

In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.
For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

## Examples

* 1, 2, 3, ... , n
* 1, 3, 5, ... , 2n + 1
* 2, 4, 6, ... , 2n
# Calculus Course/Integration
## Integration

Integration is a mathematical operation performed on a non linear function to find the area under the graph of the function.

## Types of Integration

* Indefinite Integral
* Definitive Integral