OpenLLM-France/wikimedia huggingface dataset:
# GCSE Computer Science/AQA GCSE Computer Science/Constants, variables and data types

* data - facts, numbers and statistics that are not in context so therefore have no meaning. eg, 75p
* information - data in context. eg, the drink costs 75p
* knowledge - the transfer of information between humans. eg, Joe Bloggs told Josh the drink was 75p
* constants - something that never changes e.g Pi
* variable - something thats changes over time eg. x +1 = Y
Data can exist in a number of different formats - typically referred to as DATA TYPES.
The range of data types within this course are: INTEGER REAL BOOLEAN CHARACTER STRING
# GCSE Computer Science/AQA GCSE Computer Science/Structures

Data structures exist to combine single items of data into groups or collections.
The simplest form of data structure is an ARRAY.
A more complex form of data structure could be a RECORD, such as that found in a database.
# GCSE Computer Science/CIE IGCSE Computer Science 0478

This section is aimed at students and teachers of the CIE IGCSE Computer Science 0478 course but it is not endorsed by CIE. It should be read together with the most recent course syllabus for this course.

## Course Structure

There are two sections to this course.
* Section 1: Theory of Computer Science
* Section 2: Practical Problem-solving and Programming
There is no coursework in this course. There are two exams of 1 hour and 45 minutes each at the end of the two year course. The section 1 exam is worth 60% of the final grade and the section 2 exam is worth the final 40%. Calculators are not permitted for either exam.

## Course Content
### Section 1: Theory of Computer Science

* 1.1 Data Representation
   * 1.1.1 Binary systems (Mar 22, 2015)
   * 1.1.2 Hexadecimal (Mar 25, 2015)
   * 1.1.3 Data storage (Mar 25, 2015)
* 1.2 Communication and Internet technologies
   * 1.2.1 Serial and parallel data transmission (Mar 25, 2015)
   * 1.2.2 Security aspects (Mar 25, 2015)
   * 1.2.3 Internet principles of operation (Mar 25, 2015)
* 1.3 Hardware and Software
   * 1.3.1 Logic gates (Mar 22, 2015)
   * 1.3.2 Computer architecture and the fetchexecute cycle (Oct 2, 2013)
   * 1.3.3 Input devices (Mar 25, 2015)
   * 1.3.4 Output devices (Mar 25, 2015)
   * 1.3.5 Memory, storage devices and media
      * Memory (Mar 25, 2015)
      * Storage (Mar 25, 2015)
   * 1.3.6 Operating systems (Mar 25, 2015)
   * 1.3.7 High- and low-level languages and their translators (Mar 25, 2015)
* 1.4 Security (Mar 25, 2015)
* 1.5 Ethics (Mar 26, 2015)

### Section 2: Practical Problem-solving and Programming

* 2.1 Algorithm design and problem-solving
   * 2.1.1 Problem-solving and design (Mar 25, 2015)
   * 2.1.2 Pseudocode (Mar 25, 2015)
* 2.2 Programming
   * 2.2.1 Programming concepts (Mar 25, 2015)
   * 2.2.2 Data structures; arrays (Mar 25, 2015)
* 2.3 Databases (Mar 25, 2015)
# GCSE Business Studies/Training
## Induction Training

Induction training is used to introduce a new employee to the company and the way it works. It can last anything from half a day to several weeks, but it is important that every company does it because:
* Most people who quit their job do it within the first weeks, because they have difficulty adapting. This reflects poorly on the image of the company and means that they have to go through the whole process of recruitment again, which is expensive and time-wasting. Induction training helps reduce this.
* Induction training is necessary so that employees know what they are expected to do.
* Given appropriate induction training, employees will become productive more quickly and adapt better to the company
* advantages? disadvantages? where are they?
* training conferences

## Training Type

Training can be divided into two main types. These are on-the-job training and off-the-job training. Most companies will use a mixture of the two methods of training.

### On-the-job Training

In this type of training, the employee learns skills from another employee (typically somebody with more experience at the job).

#### Advantages

* To the employer:
** Less expensive than sending them to a course.
** Knows where the employee is and what the employee is doing at all times.
** Training is exactly what is needed for the job.
** Skills may not be transferable to other companies, reducing the chances the employee will leave.
** The employee will continue working during the training.
* To the employee:
** Does not have to travel for training.
** Learns relevant skills which will help him in his job.

#### Disadvantages

* To the employer:
** Mistakes made by the trainee can be damaging to the company.
** The trainer will be less productive whilst they are doing the training.
* To the employee:
** Does not gain any official qualification.
** Skills learnt are often only relevant to the company, and will not help in a different job.
** Normally only a short training.
** Often, they are not trained by an expert teacher, so the quality of the training may be poor.

### Off-the-job Training

In this type of training, the employee is sent to a training center to be taught skills related to his job.

#### Advantages

* To the employer:
** Any mistakes made will not affect the company.
** If courses are held outside of work hours, the employee is still working normally.
* To the employee:
** Gains an official qualification, which will help when applying for a promotion or a new job.
** Often a fun or interesting experience because it changes the normal routine of work and lets them meet new people.

#### Disadvantages

* To the employer:
** Courses are often expensive.
** The employee will be missing work time to go to the courses.
** Once the employee has gained the qualification, he may use it to find another job.
** Cannot check on the employee easily when he is away from work.
* To the employee:
** May have to travel to get to the training centre.
** Some courses may be outside of work hours.
** Some of the skills learnt may not be directly transferable to his job.
# GCSE Computer Science/AQA GCSE Computer Science 8520

This section aims to fit in with the AQA GCSE Computer Science 8520 syllabus but is not endorsed by AQA. It should be useful as a revision guide or to find alternative explanations to the ones in your textbook.
If any part of this book is unclear or even wrong then please post a comment on the discussion page or simply fix it yourself! In particular, please say if the book assumes any knowledge or skills which not all GCSE Computer Science students have.

## Syllabus Content

3.1 Fundamentals of algorithms
    3.1.1 Representing algorithms
    3.1.2 Efficiency of algorithms
    3.1.3 Searching algorithms
    3.1.4 Sorting algorithms
3.2 Programming
    3.2.1 Data types
    3.2.2 Programming concepts
    3.2.3 Arithmetic operations in a programming language
    3.2.4 Relational operations in a programming language
    3.2.5 Boolean operations in a programming language
    3.2.6 Data structures
    3.2.7 Input/output and file handling
    3.2.8 String handling operations in a programming language
    3.2.9 Random number generation in a programming language
    3.2.10 Subroutines (procedures and functions)
    3.2.11 Structured programming
    3.2.12 Robust and secure programming
    3.2.13 Classification of programming languages
3.3 Fundamentals of data representation
    3.3.1 Number bases
    3.3.2 Converting between number bases
    3.3.3 Units of information
    3.3.4 Binary arithmetic
    3.3.5 Character encoding
    3.3.6 Representing images
    3.3.7 Representing sound
    3.3.8 Data compression
3.4 Computer systems
    3.4.1 Hardware and software
    3.4.2 Boolean logic
    3.4.3 Software classification
    3.4.4 Systems architecture
3.5 Fundamentals of computer networks
3.6 Fundamentals of cyber security
    3.6.1 Cyber security threats
       3.6.1.1 Social engineering
       3.6.1.2 Malicious code
    3.6.2 Methods to detect and prevent cyber security threats
3.7 Ethical, legal and environmental impacts of digital technology on wider society, including issues of privacy
3.8 Aspects of software development
# GCSE Business Studies/What is Marketing?

Marketing is finding out what the customer wants (market research) and providing to them.

## Marketing Objectives

Firms will use marketing in order to achieve objectives. Some common objectives are:
* Introducing a new product, or increasing sales of an existing one.
* Introduce an established product to a new market segment.
* Change the image of a brand.
If a business gets its marketing right, it will be easy to sell its product.

## What is a Market?

The term market means the place where buyers and sellers meet. In other words, where goods are traded. It describes the type of product been traded, too - e.g. the global oil market.
* Mass markets sell ordinary things to very large numbers of people.
* Niche markets sell things to specialist consumers.

## Market Segmentation

A market can be divided into different groups of people (market segments). Markets can be divided in different ways based on different things, such as:
* Age
* Gender
* Social class
* Location
* Culture or religion

## Orientation

There are two marketing orientations that businesses use:
* Market orientation involves researching what people want or need, and then researching and developing it in order to provide it to them. This usually means that the product is more likely to be useful, and so it is more likely to be successful.
* Product orientation involves designing a new product and then persuading people to buy it. This is commonly used with high-tech goods, for example. Customers may not feel they need the product until after it has already been developed. There is often a risk that the business makes something that nobody wants, and so the product may not be successful.

## The Marketing Mix

There are four main factors that make a customer decide to buy a product or service, these are:
* Product
* Price
* Promotion
* Place
We call these factors the four Ps or the marketing mix.
# General Ring Theory/Integral elements and extensions

Definition (integral element):
Let $R$ be a ring, and let $S/R$ be a ring extension. An element $s\in S$ is called integral over $R$ if there exist elements $a_{0},a_{1},\ldots ,a_{n-1}\in R$ such that
    $s^{n}+a_{n-1}s^{n-1}+\cdots +a_{1}s+a_{0}=0$.
# General Ring Theory/Prime ideals

Definition (prime ideal):
Let $R$ be a ring. A prime ideal of $R$ is an ideal $p\leq R$ such that whenever $I,J\leq R$ are ideals of $R$ so that $I\cdot J\subseteq p$, then either $I\subseteq p$ or $J\subseteq p$.
Definition (prime ring):
A ring $R$ is called a prime ring iff its zero ideal is a prime ideal.
Proposition (characterisation of prime ideals):
Let $R$ be a ring, and let $P\leq R$ be an ideal. The following are equivalent:
* $P$ is a prime ideal of $R$
* $R/P$ is a prime ring
* Whenever $I,J\leq R$ are left ideals in $R$, then $I\cdot J\subseteq P\Rightarrow (I\subseteq P\vee J\subseteq P)$
* Whenever $I,J\leq R$ are right ideals in $R$, then $I\cdot J\subseteq P\Rightarrow (I\subseteq P\vee J\subseteq P)$
* Whenever $x,y\in R$ are such that $xRy\in P$, then either $x\in P$ or $y\in P$.
Proof: We'll prove $1.\Rightarrow 2.\Rightarrow 5.\Rightarrow 3.\Rightarrow 1.$, since $3.\Leftrightarrow 4.$ follows by symmetry. Suppose first that $P$ is a prime ideal. Let ${\overline {I}},{\overline {J}}\leq R/P$ so that ${\overline {I}}\cdot {\overline {J}}\subseteq \{0+P\}$, the zero ideal of $R/P$. Then if $\pi :R\to R/P$ is the projection, consider $I:=\pi ^{-1}({\overline {I}})$, $J:=\pi ^{-1}({\overline {J}})$. Then $I\cdot J\subseteq \pi ^{-1}({\overline {I}}\times {\overline {J}})\subseteq \{0+P\}$ (since $\pi$ is a ring homomorphism), so that without loss of generality $I\subseteq P$, and hence ${\overline {I}}\leq \{0+P\}$. Suppose now that $R/P$ is a prime ring. Let then $x,y\in R$ such that $xRy\in P$. We use the bar notation ${\overline {z}}:=\pi (z)$ ($\pi :R\to R/P$ being the projection) for $z\in R$. Then we get that ${\overline {xzy}}\in R/P$ is zero for all $z\in R$. Then define the ideals $K:=\langle {\overline {x}}\rangle \leq R/P$ and $L:=\langle {\overline {y}}\rangle$, so that then $K\cdot L\leq \{0+P\}$, hence without loss of generality $K=\{0+P\}$ and hence $\pi ^{-1}(K)\leq P$ and thus $x\in P$. Suppose now that 5. holds, and let $I,J\leq R$ be left ideals such that $I\cdot J\leq P$. Suppose that there existed $x,y\in R$ so that $x\in I\setminus P$ and $y\in J\setminus P$. Then still $xRy\in P$, a contradiction. Note finally that $3.\Rightarrow 1.$ is trivial. $\Box$
# General Ring Theory/Derivations

Definition (derivation):
Let $S$ be a unital $R$-algebra. Moreover, let $M$ be a module over the algebra $S$. Then a derivation on $S$ over $R$ with values in $M$ is a morphism of $R$-modules $d:S\to M$ such that
    $d(st)=sd(t)+td(s)$
for all $s,t\in S$. We denote the $S$-module of all derivations of $S$ over $R$ with values in $M$ by $\operatorname {Der} _{R}(S,M)$.
Definition (universal derivation):
Let $S$ be a unital $R$-algebra. Then the universal derivation of $S$ over $R$ is the derivation $d:S\to \Omega _{S/R}$, where $\Omega _{S/R}$ is the $S$-module that arises by taking the free $S$-module generated by the formal symbols $ds$ (one for each $s\in S$) and dividing out the ideal generated by elements of the form $d(ts)-tds-sdt$ as well as $d(rs)-rd(s)$ (where $r\in R$, $t,s\in S$), and $d$ sends $s$ to $ds$.
Proposition (universal property of the universal derivation):
Let $S$ be a unital $R$-algebra and let $M$ be a module over the algebra $S$. Then for each $\delta \in \operatorname {Der} _{R}(S,M)$, there exists a unique morphism of $S$-modules $f:\Omega _{S/R}\to M$ such that $\delta =f\circ d$. This pairing induces an isomorphism of $R$-modules
    $\operatorname {Hom} _{S}(\Omega _{S/R},M)\cong \operatorname {Der} _{R}(S,M)$.
Proof: For uniqueness, note that the universal derivation $d$ is surjective, so $f$ is determined by $\delta =f\circ d$. For existence, note that if $F$ is the free $S$-module with generators $ds$ for all $s\in S$, then there is a morphism $F\to M$ that sends $ds$ to $\delta (s)$, and it factors over the quotient in the definition of $\Omega _{S/R}$ by the properties of $\delta$. $\Box$
Proposition (universal derivation is unique):
The universal derivation of a unital $R$-algebra $S$ together with its target module is uniquely defined.
Proof: This follows immediately from the universal property that defines the corresponding object uniquely. $\Box$
# General Ring Theory/Ring extensions

Proposition (commutative ring extension is a module):
Let $R$ be a commutative ring and let $S$ be a commutative extension ring of $R$. Then $S$ with its own addition and the restriction of the multiplication of $S$ to $R\times S$ is a module over $R$.
Proof: From the axioms holding for rings, we deduce the module axioms as follows as follows: Let $\lambda ,\mu \in R$ and $a,b\in S$. Then
* $\lambda (a+b)=\lambda a+\lambda b$ (distributivity)
* $(\lambda +\mu )a=\lambda a+\mu a$ (distributivity)
* $\lambda (\mu a)=(\lambda \mu )a$ (commutativity of multiplication)
* $1a=a$ (unit),
the ring axiom that's being used being indicated in the brackets. $\Box$
Proposition:
Let $S/R$ be a ring extension. Then the function
    $I\mapsto I\cap R$
defines a function from ideals of $S$ to ideals of $R$.
Proof: Indeed, $I\cap R\leq R$ because it is certainly closed under addition and multiplication by elements of $R$. $\Box$
Proposition:
Let $S/R$ be a ring extension, and suppose that $T\subseteq S$ is a multiplicative set. Then $T\cap R$ is a multiplicative set of $R$.
Proof: $T\cap R$ is closed under multiplication because both $T$ and $S$ are. $\Box$
# General Ring Theory

* Ring extensions
* Integral elements and extensions
* Ideals and multiplicatively closed sets
* Greatest common divisors
* Principal ideals
* Prime ideals
* Noetherian rings
* Kähler differentials
# General Securities Representative Exam

This book covers the information needed to pass the NASD series 7 securities license exam in the United States. It is required to pass this exam to be a "general securities representative".

## Contents

* Equity Securities
* Debt Securities
* Municipal Securities
* Options
* Customer Accounts
* Margin Accounts
* Securities Issuance and Investment Banking
* Securities Trading
* Brokerage Support Services
* Investment Company Products
* Retirement Plans
* Variable Annuities
* Direct Participation Programs
* Economics and Analysis
* Ethics
* Taxation
* Government and State Regulations
* Self Regulating Organizations Regulations

## External resources

* Study Guide for Series 7
# General Ring Theory/Ideals and multiplicatively closed sets

Proposition (ascending union of ideals is an ideal):
Let $\Lambda$ be a totally ordered set, and let $(I_{\lambda })_{\lambda \in \Lambda }$ be a chain of left, right or both-sided ideals of a ring $R$. Then
    $J:=\bigcup _{\lambda \in \Lambda }I_{\lambda }$
is a left- right- or both-sided ideal of $R$ respectively.
Proof: Indeed, let first $a,b\in J$. Then $a\in I_{\lambda }$ and $b\in I_{\mu }$ for certain $\lambda ,\mu \in \Lambda$. Set $\eta :=\max\{\lambda ,\mu \}$, then $a+b\in I_{\eta }$ since we are dealing with a chain, and consequently $a+b\in J$. The remaining property, closedness under multiplication by $R$, we prove for left ideals, since the proof for right ideals is the same, and the claim for both-sided ideals then follows by combining the other two claims (or is proved directly in the same way). Thus, suppose that the $I_{\lambda }$ are right ideals of $R$, and let $r\in R$. Then we have $ra\in I_{\lambda }$ whenever $a\in I_{\lambda }$, but for each $a\in J$ there exists some $\lambda$ such that this is the case, hence the claim. $\Box$
Proposition (existence of prime ideal not intersecting multiplicative set and containing ideal):
Let $R$ be a ring, let $I$ be a left, right, or both-sided ideal of $R$, and let $S$ be a multiplicatively closed subset of $R$ so that $I\cap S=\emptyset$. Then there exists a left, right or both-sided ideal $J$ of $R$ respectively such that $J$ contains $I$, is prime, does not intersect $S$ and is maximal (with respect to inclusion) among all ideals that do not intersect $S$.
Proof: Define $\Omega$ to be the set of all (left, right or both-sided; we'll omit this distinction for brevity in the remainder of the proof) ideals that do not intersect $S$ and contain $I$. This is a nonempty set, since $I\in \Omega$. Moreover, given any ascending chain $(I_{\lambda })_{\lambda \in \Lambda }$ in $\Omega$ with respect to inclusion, where $\Lambda$ is any totally ordered set, we obtain that
    $K:=\bigcup _{\lambda \in \Lambda }I_{\lambda }\in \Omega$;
indeed, $K$ is an ideal, it certainly contains $I$, and finally it does not intersect $S$. Thus, $\Omega$ is inductive with respect to inclusion, and we may choose a maximal element by Zorn's lemma, which we denote by $J$. Claim that $J$ in fact does have all the required properties. All that is left to show is that $J$ is a prime ideal. $\Box$
TODO: Distinguish between completely prime ideals and prime ideals in noncommutative rings
# General Ring Theory/Noetherian rings

Definition (right-noetherian ring):
A commutative ring $R$ is called right-noetherian iff the set of all right ideals of $R$, ordered by inclusion, satisfies the ascending chain condition.
Left-noetherian rings are similarly defined.
Definition (noetherian ring):
A commutative ring $R$ is called noetherian iff the set of all ideals of $R$, ordered by inclusion, satisfies the ascending chain condition.
We will state and prove results only for right-noetherian rings, even though they are valid mutatis mutandis for left-noetherian and noetherian rings just as well.
Proposition (ideals of noetherian rings contain powers of their radicals):
Let $R$ be a noetherian ring, and let $I\leq R$ be an ideal. Then there exists $n\in \mathbb {N}$ such that
    ${\sqrt {I}}^{n}\subseteq I$.
Proof: Let $i_{1},\ldots ,i_{k}$ be a basis of $sqrt{I}$ considered as an $R$-module. Then choose $m\in \mathbb {N}$ sufficiently large so that
    $\forall j\in [k]:i_{j}^{m}\in I$.
Then define $n:=km$ and observe that whenever $a=r_{1}i_{1}+\cdots +r_{k}i_{k}\in {\sqrt {I}}$, then by the pigeonhole principle, upon expanding the expression $a^{n}$ and considering each summand, we find that for each summand there is at least one $j\in [k]$ so that the corresponding power of $i_{j}$ is bigger than or equal to $m$. $\Box$
Proposition (elements of noetherian rings are products of irreducible elements):
Let $R$ be a noetherian ring, and let $a\in R$ be a non-unit. Then there exist irreducible elements $b_{1},\ldots ,b_{n}$ so that
    $a=b_{1}\cdots b_{n}$.
Proof: Indeed, a non-unit $a$ factors as $a=c_{1}c_{2}$, where $c_{2}$ is a non-unit and either $c_{2}$ is irreducible and $c_{1}$ is a unit, or $c_{1},c_{2}$ are both irreducible, or $c_{2}$ is not irreducible and a proper divisor of $a$. The same is true for $c_{2}=c_{3}\cdot c_{4}$, and proceeding inductively we gain an ascending chain
    $\langle a\rangle \subseteq \langle c_{2}\rangle \subseteq \langle c_{4}\rangle \subseteq \langle c_{6}\rangle \subseteq \cdots$
which stabilizes by the noetherian assumption. But if $n\in \mathbb {N}$ is chosen large enough so that the sequence stabilizes after $c_{2n}$, $c_{2n}$ is irreducible. Hence, we may factor $a=d_{1}b_{1}$, where $b_{1}$ is irreducible, and continuing in the same fashion we obtain again an ascending sequence, whose stabilization implies the desired factorisation. $\Box$
# General Ring Theory/Principal ideals

Definition (left principal ideal):
Let $R$ be a ring. A left principal ideal of $R$ is an ideal of the form $aR$ with $a\in \mathbb {R}$.
Analogously, one may define a right principal ideal.
Definition (two-sided principal ideal):
Let $R$ be a ring. A two-sided principal ideal is an ideal of the form $RaR$ for some $a\in R$.
# General Ring Theory/Greatest common divisors

Definition(Greatest Common Divisor):
Let a and b be integers,not both zero.Then the greatest common divisor of a and b written as (a,b) or gcd(a,b) is the largest possible integer d such that d|a and d|b [that is d divides a and d divides b]