OpenLLM-France/wikimedia huggingface dataset:
# Problem-Solution Performance Task
## Instructions

This performance task template is based on Wiggins & McTighe's book, Understanding by Design. Create a new page in Wikiversity and copy-and-paste this template to get started. In this section include specific teaching and learning contexts that allow another educator to better understand the educational context with which this performance task was designed. Refer to this list of performance tasks for examples.

## Essential Question

Add an essential question that provides the throughline for the entire performance task.

## Goal

The goal of the performance task should be an authentic one and not an academic one. The goal of the performance task is closely related to the purpose of doing the task.

## Role

What role is the learner going to take? A good performance task allows learners to assume relevant roles that are expected from a real-world experience.

## Audience

Ideally, the performance task will involve an actual audience. When a performance task services a public good, an authentic audience becomes a key aspect of the educative experience. In less than ideal situations, an authentic audience is assumed or imagined.

## Situation/Context

A good performance task is situational or contextualized so that the performance assumes given characteristics based on the relationships between the actors involved along with other key aspects to purposeful discourse: intention, persuasion, argumentation, resolving cognitive conflict, reaching a consensus, etc.

## Purpose/Process/Product

It should be clear to learners why they are doing the performance task. Also, depending on educational context, a certain level of differentiated instruction is assumed: content, process, product, and environment.

## Standards/Criteria

The criteria for doing a successful performance should be explicit from the beginning of the learning sequence. Rubrics, checklist, etc. can either be mandated by an institution or outside body, come from the instructor, and/or can result from a negotiation between learners and the instructor.

## Learning Design Sequence

In this section, provide a sequence overview of the educative experience in way that leaves plenty of room for differentiating instruction so that learners remain a key part of the decision-making process as to what, how, and why they are learning. Learning design sequencing will depend on context: teacher profile and preference, profile of the learners, institution/school culture, objectives of the course, etc.
# Perfect gas equation

A perfect gas is one in which intermolecular forces are considered negligible.
Common forms of the equation of state of an ideal gas:
where n is the number of moles, R$_u$ is the universal gas constant, and R is the specific gas constant. The universal and specific gas constants are related as follows: R=R$_u$/M, where M is the molecular weight of the gas. Using this relation and the fact that n=m/M, the two equations above can be derived from each other. The value of the universal gas constant is:
Note: Some textbooks do a poor job of specifying whether to use the universal or specific gas constant. Remember that if the equation contains mass (or density) use the specific gas constant. If the equation contains the number of moles, use the universal gas constant. If you still aren't certain, make sure the units check out.
# Introduction to Programming/Programming Languages
### Introduction

Programming languages are the method used to instruct a computer on how to accomplish a task.
A programming language is a collection of operators and instructions, with specific rules or syntax regarding how the instructions are placed together. Various operations can be combined in an almost infinite number of ways to achieve the tasks we want the computer to perform.
Some programming languages are bound to a particular set of hardware, commonly called "low level" languages. An example of a low level language is Assembly, where the target is for a particular CPU instruction set. Other languages are more abstract from the hardware, and are known as "high level" languages. An example of a high level language is Java.
Early generations of computer languages were mostly procedural in nature. Theory taught that code should be logically divided, but left that division up to the programmer. More recently, Object Oriented languages have become more prominent. These languages encourage a more standard division of code.
Programming languages are tools, and every tool has its strengths and weaknesses. While a high level language isolates a programmer from hardware, the programmer loses the ability to directly control that hardware. Choosing the right tool for a problem is very important.
* Next Lesson
* Previous Lesson
# Introduction to Programming/Organization
## How is a program organized and used? [part 1]

A simple program is a list of statements. When the program is invoked, the computer starts at the beginning of the list and executes each statement in order until it reaches the end. Then it stops. The exact form of a program, where the "first statement" is located as well as what can be done in a statement are all determined by the programming language being used.
From here on, this learning activity will be covering all material that should be reinforced through actual programming exercises. If you have not yet selected a programming language, please do that now and do the first lesson. This lesson will usually introduce a minimalistic program known as Hello, world!. Though seemingly meaningless, this lesson is nevertheless important because it gives students three critical skills—editing a source file, compiling the source file (if it is a compiled language) and running the resulting program.
* Break to do the first programming exercise
** Java version

## Statements

Most computer programming languages have statements or something similar to them. The terms line and line of code are also used.
A statement is a more-or-less atomic piece of code that is clearly differentiated, usually by a special character or character sequence called a statement terminator.
In C (and languages like C such as C++, Java, etc.) the statement terminator is a semi-colon (;). In BASIC (and languages like BASIC such as Fortran, Ruby, Python, etc.) the statement terminator is a newline. In Prolog and Erlang the statement terminator is a period (.).
The syntax rules for statements are very rigid and ruthlessly enforced by the compiler/interpreter. Inexperienced programmers sometimes miss subtle nuances in programming language rules, causing them no end of trouble. When learning a new programming language, you should have access to an experienced programmer who can help you with these kinds of problems.
* Next Lesson
* Previous Lesson
# Introduction to Programming/Answers to the exercises
### Checking An Error Condition

In programming there is rarely one right answer, but for something this simple, your answer should look something like this:
back

### Fibonacci Numbers

A variation, in Perl:
Python 3 version :
back
# Introduction to Programming/Subprograms

It is an unfortunate fact of life that things break—and computer programs are certainly no exception. One of the things that engineers have learned is that, in general, complex things break more often than simple things. Unfortunately, even a well built program can be tremendously complicated. Something like Microsoft Windows XP is probably more complicated than the Space Shuttle. It isn't surprising then, that software has bugs.
In many disciplines, including mathematics, it is a common to solve big, complicated problems by breaking them down into a group of smaller, simpler problems. That is the basic principle behind subprograms. Rather than write one big, complicated program that solves the entire problem, we can write several small pieces of a program that each solve part of the problem and, then, combine them together, in some specific way, to solve the entire problem.
Subprograms go by different names—depending on the programming language being used.
* Subroutine – FORTRAN, Visual Basic, Perl
* Procedure – Pascal
* Function – Pascal, C, C++, Java, JavaScript, Python
* Super Expression – GML, GMPL
* Method – A generic term used when speaking of many programming languages that refers to any function, procedure, or subroutine.
Note: the difference between a procedure (or subroutine) and a function is that functions return a result, whereas procedures do not. In some languages, such as C# this distinction is implicit. In others, such as Pascal, it is explicit.
* Next Lesson
* Previous Lesson
# Research Administration
## Introduction

The intention of this site is to provide one location to house the resources that are needed by the Research Administrator.

## Contents

* History of Research Administration
* Body of Knowledge
* Certification
* Electronic Research Administration (eRA)
* Professional Organizations
# Research Mentoring Program

Welcome to the Research Mentoring Program at Wikiversity! This program is for students who would like to receive mentoring in research, and for others who wish to provide this mentoring. Its purpose is to provide a forum for independent research, as well as a place for freelance academics and others to be recognized through certification. This program is part of the larger Wikiversity:Mentors program.

## Research Certification

Research Certification is a verification that the User is able to perform research at a professional level, and make original contributions to the sum of human knowledge. It is conferred by one's research mentor.

### Levels of Research Certification

* Research Apprentice: Has performed original research.
* Master of Research: Has published at least one first-authored paper in a peer-reviewed professional journal.
* Doctor of Research: Has published at least three first-authored papers in peer-reviewed professional journals, as part of a single research program.

## Research Mentor Certification

Research Mentor Certification is a verification that the User is able to supervise others in their path toward Research Certification. It is conferred by one's mentee and by other mentors.

### Levels of Research Mentor Certification

* Mentor: Has verified at least one Master or Doctor of Research.
* Professor:
** Has reached Doctor of Research level in the Research certification program
** Has reached Mentor in the Research Mentor Certification program
** Has served as secondary supervisor for at least two Masters or Doctors of research in at least two Fields of Research within the same larger discipline
** Has brought at least one course from "partly developed" or lower, to "nearly complete" or higher
* Director of Research:
** Has reached Doctor of Research level in the Research Certification program
** Has reached Mentor in the Research Mentor Certification program
** Has served as primary supervisor for at least two Masters or Doctors of Research, in at least two Fields of Research within the same larger discipline
** Has served as secondary or later supervisor for at least three additional Masters or Doctors of Research, in at least one additional Field of Research within the same larger discipline.
** Has brought at least three courses and one School, Topic or Portal page from "partly developed" or lower, to "nearly complete" or higher.
# Research Administration/Body of Knowledge

The CRA Body of Knowledge can be found at: http://www.cra-cert.org/BodyOfKnowledge.htm

## Project development and administration
### Collection and dissemination of information

* Marketing (Internal and External)
* Resource Documents, Application Materials and Information
* Dissemination of Information/Publications
* Liason
* Public Relations
* Agency Structure and Practice

### Proposal development

* Proposal Writing
* Budget Preparation
* Documentation to Meet Sponsor Requirements
* Internal Proposal Processing
* Negotiation Techniques
* Contracting Basics

### Administration of awards

* Monitoring Activity
* Reports on Progress and Financial Status
* Continuation Funding
* Close Out
* Changes in Project Status

### Ethics and professionalism

* Conflict of Interest
* Boethics
* Human Subjects
* Animal Care
* Professional (i.e. Scientific Misconduct)

### Intellectual property

* Patents and Trademarks
* Copyrights
* Licensing
* Commercialization
* Data
* Proprietary Information
* University-Industry Research Relationships

### Sample questions
## Legal requirements and sponsor interface
### Regulations and Statutes

* Overview
* Governmental Relations
* Mandated Requirements

### Compliance - Federal/Sponsors and General Management Practices

* Representation and Certification
* Federal Management Requirements
* Institutional Committees (i.e. IRB, IACUC)
* Federal Disclosure Requirements
* Institution and Sponsor Publicaiton Requirements
* Federal Labor Standards

### Sample questions
## Financial management
### Budgeting/accounting

* Accounting Systems
* Management Information Systems
* Special projects

### Costs

* Direct costs
* Indirect costs (overhead)
* Indirect cost rates
* Cost sharing and matching

### Sample questions
## General management
### Facility management

* Specialized Facilities
* Property Utility and Equipment Management
* Safety and Health Requirements and Procedures
* Hazardous and Nonhazardous Materials
* Security
* Renovation and Construction
* Biohazards

### Contracts and purchasing

* Basic Legal Concepts
* Management of Contracts and Purchasing
* Termination and Appeals
* Records Management
* Human Resource Management

### Sample questions

What are the methods adopted by large indian companies for procurrement of materials , weather thru tender or open enquiries and how do they proceed about it.
# Research Administration/Certification

* CRA
* Graduate Certificate in Research Administration
# Research Administration/History
## External links and resources

* Science and the Endless Frontier: A Report to the President by Vannevar Bush (1945)
* Allocating Federal Funds for Science and Technology - National Academy of Sciences (1995)
* The Belmont Report -- Ethical Principals and Guidelines for the Protection of Human Subjects in Research
# Research Administration/Professional Organizations

* National Council of Research Administrators (NCURA) (Wikipedia)
* Society of Research Administrators (SRA)
* Research Administration Listserv RESADM-L : Instructions on how to use the RESADM-L Mailing List, including subscription information and a web-searchable archive, are available via our web site at http://www.hrinet.org (click on "Listserv Lists")
# Research Administration/Electronic Research Administration

* History of Electronic Research Administration
* Current events
* Grants.gov
# PlanetPhysics/Categories and QAT Bibliography Algebraic Topology

This is an extensive, but not intended to be comprehensive, list of relevant, selected references for several areas of both abstract and applied mathematics. A more extensive bibliography on category theory can be found on the web at the Plato, Stanford Encyclopedia of Philosophy web site on category theory and its applications.

### Literature for the following areas of mathematics:

* algebraic topology,
* Quantum Algebraic Topology,
* N-logic algebraic categories,
* Theory of categories, functors and natural transformations, Topoi and categorical ontology
# PlanetPhysics/Categories and Supercategories in Relational Biology

This topic entry introduces one of the most general mathematical models of living organisms called `organismic supercategories' (OS) which can be axiomatically defined to include both complete self-reproduction of logically defined $\pi$-entities founded in Quine's logic and dynamic system diagrams subject to both algebraic and topological transformations.

### Organismic Supercategories (OS)

OS mathematical models were introduced as structures in higher dimensional algebra that are mathematical interpretations of the axioms in ETAS- a natural extension of Lawvere's $elementary\;theory\;of\;abstract\;categories$ (ETAC) to non-Abelian structures and heterofunctors.
When regarded as categorical models of supercomplex dynamics in living organisms OS provide a unified conceptual framework for relational biology that utilizes flexible, algebraic and topological structures which transform naturally under heteromorphisms or heterofunctors. One of the advantages of the ETAS axiomatic approach, which was inspired by the work of Lawvere (1963, 1966), is that ETAS avoids all the antimonies/paradoxes previously reported for sets (Russell and Whitehead, 1925, and Russell, 1937). ETAS also provides an axiomatic approach to recent higher dimensional algebra applications to complex systems biology (, and references cited therein.)

### Selected Examples of OS Applications to Relational and Complex Systems Biology

Whereas super-categories are usually defined as n-categories or in higher dimensional algebra, organismic supercategories have flexible, algebraic and topological structures that transform naturally under heteromorphisms or heterofunctors. Different approaches to relational biology and biodynamics, developed by Nicolas Rashevsky, Robert Rosen and by the author, are compared with the classical approach to qualitative dynamics of systems (QDS). Natural transformations of heterofunctors in organismic supercategories lead to specific modular models of a variety of specific life processes involving dynamics of genetic systems, ontogenetic development, fertilization, regeneration, neoplasia and oncogenesis. Axiomatic definitions of categories and supercategories of complex biological systems allow for dynamic computations of cell transformations, neoplasia and cancer.
# PlanetPhysics/Categories of Groupoids

Groupoid categories , or categories of groupoids , can be defined simply by considering a groupoid as a category {Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \mathsf{\G}_1} } with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \mathsf{\G _2} }, is defined as the $2$-category whose objects are Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G _1} } categories (groupoids), and whose morphisms are functors of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \mathsf{\G _1} } categories consistent with the definition of groupoid homomorphisms, or in the case of topological groupoids, consistent as well with topological groupoid homeomorphisms. The 2-category of groupoids Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G _2} }, plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors.
Let Failed to parse (unknown function "\G"): {\displaystyle {\mathsf{\G}}_1} and Failed to parse (unknown function "\G"): {\displaystyle {\mathsf{\G}}_2} be two groupoids considered as two distinct categories with all invertible morphisms between their objects (or `elements'), respectively, Failed to parse (unknown function "\G"): {\displaystyle x \in Ob({\mathsf{\G}}_1) = {{{\mathsf{\G}}_0}}^1} and Failed to parse (unknown function "\G"): {\displaystyle y \in Ob({\mathsf{\G}}_2) = {{{\mathsf{\G}}_0}}^2} . A groupoid homomorphism is then defined as a functor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle h: {\mathsf{\G}}_1 \longrightarrow {\mathsf{\G}}_2} .
A composition of groupoid homomorphisms is naturally a homomorphism, and natural transformations of groupoid homomorphisms (as defined above by groupoid functors) preserve groupoid structure(s), i.e., both the algebraic and the topological structure of groupoids. Thus, in the case of topological groupoids, ${\mathsf {G}}$, one also has the associated topological space homeomorphisms that naturally preserve topological structure.
Remark: Note that the morphisms in the category of groupoids, $Grpd$, are, of course, groupoid homomorphisms, and that groupoid homomorphisms also form (groupoid) functor categories defined in the standard manner for categories.
# PlanetPhysics/Categorical Physics 2

This is a contributed topic on categorical physics, presenting initially a list of subtopics and key concepts in categorical physics.

## Categorical Physics

One can describe categorical physics as the application of category theory concepts and approaches to problems in mathematical physics, such as the formulation of quantum gravity theories, or unified field theories.
# PlanetPhysics/Categories of Polish Groups and Polish Spaces
### Introduction

Let us recall that a Polish space is a separable, completely metrizable topological space, and that Polish groups $G_{P}$ are metrizable (topological) groups whose topology is Polish, and thus they admit a compatible metric $d$ which is left-invariant; (a topological group $G_{T}$ is metrizable iff $G_{T}$ is Hausdorff, and the identity $e$ of $G_{T}$ has a countable neighborhood basis).
Polish spaces can be classified up to a (Borel) isomorphism according to the following provable results:
* All uncountable Polish spaces are Borel isomorphic to Failed to parse (syntax error): {\displaystyle \mathbb{R } equipped with the standard topology;} This also implies that all uncountable Polish space have the cardinality of the continuum.
* Two Polish spaces are Borel isomorphic if and only if they have the same cardinality.
Furthermore, the subcategory of Polish spaces that are Borel isomorphic is, in fact, a Borel groupoid.

### Category of Polish groups

The \htmladdnormallink{category {http://planetphysics.us/encyclopedia/Cod.html} of Polish groups} ${\mathcal {P}}$ has, as its objects, all Polish groups $G_{P}$ and, as its morphisms the group homomorphisms $g_{P}$ between Polish groups, compatible with the Polish topology $\Pi$ on $G_{P}$.
${\mathcal {P}}$ is obviously a subcategory of ${\mathcal {T}}_{grp}$ the category of topological groups; moreover, ${\mathcal {T}}_{grp}$ is a subcategory of Failed to parse (unknown function "\grp"): {\displaystyle \mathcal{T}_{\grp}} -the category of topological groupoids and topological groupoid homomorphisms.
# PlanetPhysics/Categorical Quantum LM Algebraic Logic 2

This topic links the general framework of quantum field theories to group symmetries and other relevant mathematical concepts utilized to represent quantum fields and their fundamental properties.

### Fundamental, mathematical concepts in quantum field theory

Quantum field theory (QFT) is the general framework for describing the physics of relativistic quantum systems, such as, notably, accelerated elementary particles.
Quantum electrodynamics (QED) , and QCD or quantum chromodynamics are only two distinct theories among several quantum field theories, as their fundamental representations correspond, respectively, to very different-- $U(1)$ and $SU(3)$-- group symmetries. This obviates the need for `more fundamental' , or extended quantum symmetries, such as those afforded by either larger groups such as $SU(3)\times SU(2)\times U(1)$ or spontaneously broken, special symmetries of a less restrictive kind present in `quantum groupoids' as for example in weak Hopf algebra representations, or in locally compact groupoid, $G_{lc}$ unitary representations, and so on, to the higher dimensional (quantum) symmetries of quantum double groupoids, quantum double algebroids, quantum categories,quantum supercategories and/or quantum supersymmetry superalgebras (or graded `Lie' algebras), see, for example, their full development in a recent QFT textbook that lead to superalgebroids in quantum gravity or QCD.