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Portal:Social entrepreneurship/News Archives

Add new items here in full and as an abbreviated bullet on the News page to appear on the front page-->

Currently featured on the Home Page

 * (22 Sept 2014)How to Change the World and Social Entrepreneurship (Coursera) - these courses might be worthwhile, but check the licence conditions under Coursera's terms of use - they are not compatible with those of libre projects such as those of the Wikimedia Foundation (e.g. Wikiversity, Wikipedia, ...), and other libre communities. Developing libre alternatives is important. Please add links to any you know of on this page. Thanks.
 * (22 Aug 2014)Heroic Imagination Project - "Stand Up, Speak Out, Change the World".
 * (July 2014)Imagine Chicago ... Imagine your city or community, and check out their resources for inspiration on ways of engaging and helping communities to realise their aspirations.
 * (23 April 2011) Internet entrepreneur course available.
 * The Social Enterprise World Forum 2011 - Johannesburg, South Africa, 5-7 April 2011 - 'Social enterprise as a catalyst for sustainable development'.
 * EVOKE - an online course and game for aspiring social entrepreneurs. The goal of the game is to help empower people all over the world, and especially young people in Africa, to come up with creative solutions to our most urgent social problems. See also the associated wiki.

Previously Featured on the Home page

 * Mobile networks for social entrepreneurs - on-line discussion at SocialEdge (March 2010).
 * The Skoll World Forum on Social Entrepreneurship - diarise 14-16 April 2010 - Saïd Business School, University of Oxford.
 * World Challenge - winners announced (December 2009).
 * Discuss the navigation template (ongoing).
 * Social Entrepreneurs From Around the World Come to Santa Clara University to Learn How to Grow Their Business (31 July 2009)
 * Education that Pays for Itself 2008 conference at Eden Campus Knysna 18 - 20 November.
 * Dr Susan Steinman, a social entrepreneur and Ashoka fellow, won the category of 'Social Entrepreneur of the Year' in the Nedbank Business Women's Association's Regional Business Achievers' Award 2008 on 24 July for her outstanding work in raising awareness, conducting research and introducing programmes to prevent physical and emotional violence in the workplace locally and internationally. Susan received her second doctorate, dealing with the phenomenon of social entrepreneurship in an autoethnographic study, at the University of Johannesburg (UJ) in May 2008 - she is now in the process of forming the Institute for Social Entrepreneurship at UJ.
 * Book Innovation Policy: contributions sought relating to Inclusive Innovation. See News Archives for more.
 * | CAF Southern Africa 2008 Conference: Innovating for Sustainability, 17-18 September 2008, The Wanderers Club, Illovo, Johannesburg.
 * OpenSRI launches collaborative web platform on Socially Responsible Investment (SRI) and Corporate Social Responsibility (CSR)
 * Book contribution invitation: The World Bank Institute is publishing a new book on Innovation Policy and is looking for examples for a chapter on Inclusive Innovation. In one of the parts of the chapter, the WBI would like to talk about the potential role of universities and public research centers in serving the needs of the poor as well as the underserved communities and the reforms needed to strengthen that role (e.g. improving relevance of the curriculum for the country context, requiring that each student spends a certain time working on a project relevant for the community, conducting research on issues important for the country, etc). If you have any specific examples that you would like to share from your university, please send them along for potential inclusion in the book! (to RHawkins  worldbank org ).
 * | CAF Southern Africa 2008 Conference: Innovating for Sustainability, 17-18 September 2008, The Wanderers Club, Illovo, Johannesburg. The conference will explore how innovative financial models involving local investment, private equity and social enterprise can enhance the region's sustainability. Contact Mokgaetse Thoka at mokgaetse_at_cafsouthernafrica.org, or Mihloti Mgimeti at mmgimeti_at_cafsouthernafrica.org for more details.
 * OpenSRI launches collaborative web platform on Socially Responsible Investment (SRI) and Corporate Social Responsibility (CSR).

 * New University of Michigan African Scholars Exchange Program—Deadline Sep 1, 2008

 * Discussing System Framework for guiding students of social entrepreneurship.

 * Core Team Meeting Notes (15 April 2008)

 * Reflections on South Africa Workshop for Social Entrepreneurship - 2008.

 * Core Team Meeting Notes (15 April 2008)

 * Reflections on South Africa Workshop for Social Entrepreneurship - 2008.

 * Power of Unreasonable People

 * University World News Article on Conference

 * Bill Gates on Creative Capitalism -- Jan. 24, 2008 Wall Street Journal

 * Africa Regional Science, Technology and Innovation conference - 2007


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Portal:Social entrepreneurship/Profiles/more

Candidate Profiles

 *

Social Entrepreneurs Recommended for Profiling

 * Taddy Bletcher - the visionary behind CIDA. See CIDA Foundation
 * Steve Carver - Eden Campus
 * Muhammad Yunus
 * Bill Drayton
 * Joris Komen - SchoolNet Namibia
 * Richard Stallman - Free Software Foundation
 * William Kamkwamba - see video

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Portal:Social entrepreneurship/Case Studies/more

Previously Featured Case Studies

 * Holidays of Hope

Candidate Case Studies for Front Page Feature

 * Eden Campus - community university.
 * SchoolNet Namibia - FLOSS in schools while building capacity among unemployed school leavers.
 * TuxLabs
 * WirelessAfrica
 * Digital Doorway
 * Rupani Foundation (Pakistan) - social entrepreneurship is one of their strategic focus areas.
 * The Thorn Tree Project

Case Studies South Africa

 * The Lapdesk
 * e'Pap
 * Heartbeat
 * Ikamva Labantu
 * Ithemba Institute of Technology
 * Johannesburg Housing Committee
 * KiBWE KiDS
 * Micro-MBA project

Namibia

 * SchoolNet Namibia

Other

 * CasePlace -- Site for Case Studies
 * Roberts Enterprise Development Fund -- New Social Entrepreneurs
 * Community Wealth Ventures -- Powering Social Change: Lessons on Community Wealth Generation for Nonprofit Sustainability
 * The Social Enterprise Sourcebook -- Strategic Marketing for Social Entrepreneurs


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User talk:Uditk

Welcome
Hello Uditk, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 15:11, 20 October 2007 (UTC)

copy + paste from Wikipedia
Namasté, could you have a look here please: Talk:Mughal India ? Dhanyavaad, Erkan Yilmaz ( Wikiversity:Chat, wiki blog ) 16:52, 3 December 2007 (UTC)

title: User talk:Uditk


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Portal talk:Social entrepreneurship/Curriculum/General

Comments on the General section of the Curriculum:

Environment to stimulate social entrepreneurship
This appears primarily to focus on setting up individual entrepreneurs (or groups). Shouldn't there be a parallel section which looks at setting up an environment that stimulates the emergence of entrepreneurship?

 * A good point. Would it make sense to cover this under Resources for Educators? Kim 07:54, 14 August 2008 (UTC)

Business plans vs social networks
(primarily Frances O'Brien)

Ending the student process with a "business plan" misses the point. Student activities may result in a variety of outputs including collaboration agreements, partnerships (formal or informal), social networks, etc. In some cases a business plan might be one of the outputs during the process.

 * The last item under "General" on the curriculum page is now simply "Putting it all together", and the page it links to has been edited to be more generic.

Coupled with this comment was the suggestion of having a module "Developing a business plan collaboratively". This has been added under Entrepreneurship/Business Management where it can be fleshed out later.

Begin with the end in mind
See discussion on Putting it All Together - instead of ending with a "business plan" what alternatives? Ktucker 13:31, 20 August 2008 (UTC)

Appreciative Principles
Much of the work behind the scenes has been done with Appreciative Inquiry principles in mind. The approach/paradigm seems well matched to "Social Entrepreneurship" as it draws attention to what is working in a system and growing the life energy rather than "problems" which need to be solved. Requiring people to solve problems draws attention and energy towards the problems, making them bigger and sapping the energy of the people involved.

"problems" and "challenges"
The terminology may need further discussion and refinement. Some people are positively disposed towards "challenges" which are generally framed around "opportunities". Meeting the challenges requires mobilisation of the community - acknowledging the capabilities of its members. In line with the appreciative principles above, we refer to "challenges" to inspire action - rather than "problems" and other terms which draw attention to what seems to be missing or what is wrong with the community, its gaps and shortcomings (usually from an outsider's perspective).
 * How about "aspirations" instead of "needs"? Ktucker 22:14, 22 August 2008 (UTC)
 * Added to issue tracker.

Asset-based Community Development (ABCD)
Teaching the Asset Based Approach to community development (ABCD) (Kretzmann & McKnight) was suggested, and has been added to the section on Understanding Developing Communities.

Understanding Developing Communities
Is this section needed?

 * It at least allows the Social Entrepreneurship field to develop on the foundations of Community-based learning and Services-based learning. Being able to connect with communities is key to stimulating and catalysing social/community-led innovation.

Evaluation and Valuation
For similar reasons the "Evaluation" section was re-labelled "Valuation". See Valuation and click on the discussion link.

Social Entrepreneurship vs Community Development
(by Susan Steinman)

It has been pointed out that these are not the same thing and that "defining communities may not be that important in SE context. But some community development projects can be regarded as social entrepreneurship projects and usually have a social entrepreneur leading it".

"... in understanding social entrepreneurship one could say that social entrepreneurship is NOT limited to ... [any] ... of these:

 * community development
 * social development
 * Non-profit organisations
 * Non-governmental organisations
 * businesses

BUT that you will find social entrpreneurs operating in all of these areas.

A useful resource as to what social entrepreneurship really entails is the book of David Bornstein "How to Change the World" and that of Marti & Mair: Social Entrepreneurship.

I do think that one should distinguish the concepts and although there is no clear definition of social entrepreneurship yet, the characteristics of a social entrepreneur is important in understanding it.

Going down the community development road is helpful, but the pillars of social entrepreneurship, according to Ashoka's Bill Drayton, could be missed and these are:

 * the social entrepreneur (SE) is an individual with a unique and innovative project/idea to solve a social problem
 * the SE possesses entrepreneurial skills and use these to bring about social change and is truly committed to solve the problem
 * the project must have wide social impact - beyond regional and national boundaries
 * must be replicable in other parts of the world with no or little adaptation
 * the social entrepreneur must be a person of integrity.

... [consider] ... bring[ing] in something like "Conceptual clarification - the relationship between Social Entrepreneurship and other similar phenomena."

This is actually very important and will provide better direction.

 * The Introduction to Social Entrepreneurship includes an activity to distinguish these terms, and there is a partial response to the above here.

Tools
Should each module have a section on tools? and provide links to tutorials - e.g. "Share Ideas" could refer to blogging (e.g. How to use Wordpress) and wikis (how to use WikiSpaces) ... and other [collaborative] tools (lists)


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Portal:Social entrepreneurship/networking/Universities/more

This page serves as a channel for people to contact universities and research institutions involved in student social entrepreneurship. The institutions may indicate their activities, courses, projects, etc. to attract interested students.

 * ../Meraka Institute/
 * University of Pretoria
 * University of the Witwatersrand
 * Walter Sisulu University for Technology and Science
 * World Bank Institute
 * South African Institute of Physics

=Summary= Optionally populate the table below with details of your institution for quick reference among he most prominent institutions in this field.


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Portal:Social entrepreneurship/networking/Funding

Funding opportunities

 * Project 10 to the 100th (Google TM)
 * The BiD Network Marketplace and Award Event
 * The Draper Richards Foundation for Social Entrepreneurship
 * The Skoll Awards for Social Entrepreneurship
 * The Global Social Venture Competition (GSVC)
 * The Development Marketplace
 * Ashoka - Global Association of Social Entrepreneurs

more ...


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Portal:Social entrepreneurship/networking/Funding/more

=Calls for Proposals=

 * Project 10 to the 100th

=Foundations etc.=

=Proposals=

 * Consider this approach (WikiEducator) and develop proposals at that site.


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Portal:Social entrepreneurship/Curriculum/Entrepreneurship/Human Resources Management

 * Human Resources Management on WikiEducator


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User:Rohin Agrawal

Rohin Agrawal genetically XY was born on 11th September 1985. He was born in India and lived at Delhi. He is an undergraduating student of B.Tech. Engineering in ICT.

title: User:Rohin Agrawal


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Portal:Social entrepreneurship/Community Projects/By Region

Browse Regions =Africa=

 * FLOSS4Edu

Southern Africa

 * Free Knowledge for FLOSS Literacy

South Africa

 * Community Projects in SouthAfrica

Uganda

 * East African Center for Open Source Software (EACOSS) - based in Uganda, serving East Africa (and the world)

Nigeria
=America=

South America
=Asia=

Nepal

 * ../Youth-Managed Resource Centers (YMRC)/

=Australasia=

=Europe=
 * ProjEX-E1, East London

=Oceania=


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Portal:Social entrepreneurship/Community Projects/By Theme

Browse Themes

=Health=

=Environment=

=Poverty Reduction=

=Education=

 * example url and link title

=Other=

Holidays of Hope

 * About Holidays of Hope


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User talk:Rohin Agrawal

Welcome
Hello Rohin Agrawal, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 19:45, 20 October 2007 (UTC)

title: User talk:Rohin Agrawal


text: User:KTucker/profile

title: User:KTucker/profile


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Portal:Social entrepreneurship/networking/NGOs and CBOs/more

This page serves as a channel for people to contact NGOs and CBOs in touch with communities. The NGOS and CBOs may express community needs and offerings here, and showcase their projects requiring student participation, etc.

=NGOs and CBOs=

 * ICRD Group
 * NGO Connect Africa
 * YALDA -- Youth Alliance for Leadership and Development in Africa, a networking organization that is already at 9 universities on the continent and a branch at Harvard College.
 * Holidays of Hope
 * Junior Achievement of South Africa
 * Student Sponsorship Programme
 * SchoolNet Namibia (case study)

=Summary=


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Portal:Social entrepreneurship/networking/Research

 * Researchers
 * Research Projects

more ...


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Portal:Social entrepreneurship/networking/Research/more

 * Researchers
 * Research Projects

=See Also=

 * Research under Curriculum


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File:One bit AI.pdf

Originally uploaded by A.K.Karthikeyan at Wikibooks.

title: File:One bit AI.pdf


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File:Astronomy Student Mini-Outline.pdf

Originally uploaded to Wikibooks by User:Leesonma.

Summary
A content outline written by Michael Andre' Leeson (that's me) used in my Astronomy course. I am uploading it so it can be used as a reference to help create the "Astronomy" online course.

title: File:Astronomy Student Mini-Outline.pdf


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Portal talk:Engineering and Technology/to do

Hi. I added an item to the to-do list concerning the required coursework that is common to engineering such as introductory math and science coursework. Darrin


text: File:Keith Eppers Scary Trill.ogg

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User talk:Ashutosh~enwikiversity

Welcome
Hello Ashutosh, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 06:53, 21 October 2007 (UTC)

French Mentoring
Salut, Ahutosh. You are listed at the French stream as being a beginning student of French who is interested in learning French. The French Mentoring project has recently been launched, and if you add your name to that list, I will do my best to put you in contact with an appropriate Mentor who would be glad to help you. The Jade Knight (d'viser) 09:56, 22 November 2008 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Ashutosh. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Ashutosh~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:29, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:03, 19 April 2015 (UTC)

title: User talk:Ashutosh~enwikiversity


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Making sense of quantum mechanics/Principles of Quantum Mechanics

What are the first principles of Quantum Mechanics?

All we do is draw little arrows... Richard P. Feynman, 1985

Imagine a bunch of ordinary nails thrown through the air. Each nail will have its own velocity, some will collide, some will cross space unaffected, most will gain spinning motion, each with its own angular velocity, with its own rotation axes. This is just a quantum system. In a quantum system, the elements are represented by arrows, mathematically we call them vectors. A spinning nail has observational properties attached to it (position, translational and angular velocity,...), the same for the vector representing it. The concept vector + observational properties is called a state vector. This is the core of quantum physics.

First principle: A quantum system may be represented by a vector

Quantum systems known as such are not exactly behaving like the pseudo-quantum system described above, but... there are close similarities. And these similarities give us precious insights in the quantum laws. The first similarity between a "microscopic" quantum system and a bunch of needles, of rods, of arrows or of any linear objects, is the fact that it may be represented by a state vector. This vector bears the observational properties of the system (energy E, position r, momentum p...), which specify the state of the system. Quantum physicists call it a ket, denoted by the marks | > delimiting some symbol(s) informing about the state in which the system is, for example:

$$|\psi\rangle \equiv |\psi(E, r, p,...)\rangle \equiv |E, r, p,...\rangle$$

which are strictly equivalent notations of a state vector with energy E, position r, momentum p,...

Now imagine we draw a vector on a piece of paper. On another piece of paper, we draw exactly the same vector at the same spot. Both vectors are equal, aren't they? They have same orientation, same position. In ordinary space they are equal. Now let's imagine that the vector on the first piece of paper rotates at 1 turn per second and the vector on the second piece of paper rotates twice as fast. We presently have two different state vectors, the first with angular velocity $$\omega$$ = 1, the second with angular velocity $$\omega$$ = 2. Physicists would denote them $$|\psi(\omega = 1) \rangle $$ and $$|\psi(\omega = 2) \rangle $$. So even if the vectors are equal on paper (in ordinary space for 3D drawings), the state vectors they represent are not equal in the quantum-sensical way. Each distinct value of an observational property determines a dimension of the quantum vector state space. In this case, the two values of the angular velocity double the dimensions of ordinary space. Sometimes in the analysis of a physical problem, it is sufficient to discriminate between only two values of a physical property, for example when a rapidly rotating arrow is thrown towards a wire grid. Either it passes (if its rotational plane is closely parallel to the wires) or it is stopped (if its rotational plane has an angle with the wires). In that case, the quantum space is two-dimensional. In other cases there will be 3 possible values, or 4, or more... When there is a continuous set of observational values at stake, the quantum space is infinite dimensional. For example, if different positions determine different states of the vector, ordinary 3D space becomes an infinite dimensional state space.

A set of arrows may be represented by a set of vectors, which is equivalently just another vector (a vector of vectors). If any elementary linear object is represented by a vector, this guarantees that to every system of linear objects also corresponds a vector.

If we keep in mind that state vectors represent ordinary linear objects, there is nothing mysterious about quantum physics. We may deduce some trivial quantum laws, the first of them being that the direction of linear objects varies when physical conditions change.

Second principle: The orientation of the vector representing a quantum system evolves
Quantum evolution laws determine how the orientation of the state vector changes, given some modifications or perturbations of the physical conditions. For example, the time evolution law states that the vector difference of the vectors representing a needle at two infinitesimal close instants $$t$$ and $$t+dt$$ is perpendicular to the vector at instant $$t$$ and proportional to the angular velocity $$\omega$$ of the needle multiplied by the time difference (see Figure Time evolution of a state vector).

An elegant way to represent changes of orientation of vectors is through Argand's method: multiplying by the complex factor $$e^{i \theta}$$, where $$\theta$$ is the rotation angle (also called the phase or phase angle). Perpendicularity between two equally normed vectors may therefore be seen as equality between one vector and the other vector multiplied by $$e^{i{\pi\over 2}} = i$$.

The vector equation pictured in figure "Time evolution of a state vector" therefore writes as: $${d|\psi(\omega, t) \rangle \over dt} = -i \omega |\psi(\omega, t) \rangle$$

if the time axis is set in the negative z-direction. This formula is a general deterministic law characterizing the time evolution of systems of linear objects, whether microscopic or macroscopic. For a system of fundamental particles, it usually appears with a factor $$\hbar$$ at both sides (and i at the left):

$$i \hbar {d|\psi(\omega, t) \rangle \over dt} = \hbar \omega |\psi(\omega, t) \rangle$$

The factor $$\hbar \omega$$ multiplying the ket then represents the energy content of the system. This is Schrödinger's time-dependent equation. So we have a second close similarity between quantum systems and macroscopic linear objects: they both obey Schrödinger's equation.

In Schrödinger's time dependent equation, we focus on the way the phase of the vector changes with varying time. If we had focused on another varying parameter (like position, momentum, external energy,...), the formulation of the evolution law would be different, but it would always obey the trivial principle that the orientation of the vector evolves. We will therefore always find a complex factor i in quantum differential equations with terms of odd parity.

The Schrödinger ket equation shows that a ket may be transformed into another ket by means of a differential operation. In this differentiation, a proportionality factor $$\hbar \omega$$ emerges which has some physical meaning. This leads us to our third quantum principle.

Third principle: Kets are transformed into other kets by means of operations that reveal an observational property
In the time dependent Schrödinger equation, the operator $$i \hbar {d \over dt} $$ operates on the ket $$ |\psi \rangle $$ giving the same ket multiplied by the factor $$\hbar \omega$$. For elementary particles, this factor is the measure of the energy of the particle.

The general form of the equation where a ket (just an arrow) is transformed into another ket, shows as:

$$ \hat{A} |\psi \rangle = |\chi \rangle$$

where $$ |\psi \rangle $$ and $$ |\chi \rangle $$ may be any imaginable ket and $$ \hat{A} $$ denotes the appropriate operator. In quantum physics, operators are denoted by a circumflex on the letter.

The operator $$i \hbar {d \over dt} $$ of the Schrödinger equation is called the Hamiltonian operator $$\hat{H}$$. Operating with the Hamiltonian on a ket extracts the energy from the ket.

In the preceding section, we introduced Argand's construction because it allowed us to formulate the rotation of a vector through an angle $$\phi$$ in a very powerful way: multiplying the vector by $$e^{i \phi}$$. Through the rotation operator $$\hat{R}(\phi )$$, the ket $$|\psi \rangle$$ is transformed into a rotated ket and we may write:

$$ \hat{R}(\phi ) |\psi \rangle = |\chi \rangle = e^{i \phi} |\psi \rangle$$.

Another example of an operator is the time evolution operator Û(t, t+dt) (letting time pass by from instant t to t+dt). For a freely rotating vector with constant angular speed $$\omega$$, Û(t, t+dt) operating over $$|\psi \rangle $$ yields the equation:

$$ \hat{U}(t, t+dt) |\psi (t)\rangle = e^{-i \omega dt} |\psi (t) \rangle = |\psi (t+dt)\rangle$$.

Û is a unitary operation because it leaves the length of the ket unchanged. It has physical meaning because operating with it on a ket representing the state of a linear object results in another ket representing also a physical state (its state at a subsequent instant).

In the preceding equation, Û acts on the ket $$|\psi (t) \rangle $$ and gives a resultant ket $$|\psi (t+dt)\rangle$$ at a subsequent instant. We could also see it the other way round: what is the operator that would act on the ket $$|\psi (t+dt)\rangle$$ and give $$|\psi (t) \rangle $$? That operator is the reversed operator of Û, $$\hat{U}^{-1}$$, equivalent to the conjugate operator Û* in case of unitary operators, where the phase is changed by $$\omega dt$$:

$$ \hat{U}^{-1}(t, t+dt) |\psi (t+dt)\rangle = e^{i \omega dt} |\psi (t+dt) \rangle = |\psi (t)\rangle$$.

Example: Particle in a box

The quantum principles of preceding sections may be applied to the behavior of an arrow in a one-dimensional box of length L. Let the arrow bounce back and forth with constant velocity $$v_c$$ between two parallel walls. The period between two bounces is $$L/v_c$$. The needle is plane rotating in the x-z plane with angular velocity $$\omega$$. We will assume that the arrow acquires rapidly a stationary state characterized by the fact that it is parallel to the wall at each instant of bouncing. Therefore, at equilibrium, the arrow must rotate about an angle $$n \ \pi$$ between two bounces, with n integer-valued. This condition is expressed as:
 * $$\omega = n \ \pi \ v_c / L$$.

The rotational state of the arrow is quantized due to the boudary conditions. n may take any integer value between $$-\infty$$ and $$+\infty$$.

We may characterize the state of the arrow by the ket $$|\psi_0(\omega_n) \rangle$$, say a representation of the needle with angular velocity $$\omega_n$$ at the instant of bouncing at the left wall (taken as t=0). We also set x=0 at that wall. At a later timestamp, the state of the needle is represented by the initial ket, multiplied by its phase factor:
 * $$|\psi(t, \omega_n) \rangle = exp(-i \omega_n t) |\psi_0(\omega_n) \rangle$$.

Once the in initial ket given, we may as well characterize the state of the needle by the complex scalar function $$exp(-i \omega_n t)$$. This function is called the wave-function of the needle and is generally denoted by the ket without the brackets: $$\psi(t, \omega_n)$$. We may write:

 * $$|\psi(t, \omega_n) \rangle = \psi(t, \omega_n) |\psi_0(\omega_n) \rangle$$,

or more concisely:

 * $$|\psi \rangle = \psi \ . \ |\psi_0 \rangle$$

holding in mind that we are dealing with functions of time.

We could however see it otherwise, forgetting the time parameter and concentrating on the x-coordinate of the needle. For this stationary state, the phase of the arrow is also a function of the x-coordinate. We may therefore as well write the preceding equation as:

 * $$|\psi(x) \rangle = exp(-i k x) |\psi_0 \rangle$$,

with k the wave-number $$n \pi L$$ and $$|\psi_0 \rangle$$ the ket at x=0. Or concentrating only on the direction of the needle, we could write:

 * $$|\psi(\phi) \rangle = exp(-i \phi) |\psi_0 \rangle$$.

These equations are equivalent for this particular stationary state in a 1-dimensional box. We could write them in different ways, even involving other physical properties such as the direction of the rotation axis, the energy, the momentum, the potential or any imaginable physical property of the system. They illustrate that, given an initial ket, the real issue of quantum mechanics is the complex (wave-)function that operates on the ket. That function contains all that can be known about the physics of the system. It tells us how a ket is transformed into another ket, it tells us which physical observables can be extracted from it and how they are related.

When we look at the figure of that arrow that bounces back and forth in a box, we may grasp it as a whole, visualizing the motion classically, knowing how to describe the configuration deterministically. However, at the quantum level, observations are discrete. For example, when we observe the position of the arrow quantum-mechanically, we in fact only notice the location of the interaction of that arrow with another quantum particle (arrow). That location is a point, while the arrow is extended. So we have an intrinsic indeterminacy in the measurement of the position. The same for the direction of the arrow. Because measurements at the quantum level are discrete, it is impossible to determine the phase of the arrow through a single observation. There is an intrinsic indeterminacy of an angle $$2 \pi$$ in the phase $$\phi$$ of the quantum particle. This leads us to our fourth quantum principle, the Heisenberg indeterminacy principle.

Fourth principle: In quantum measurements, the result is always undetermined
Physically, quantum measurements rest on the observation of interactions between two quantum particles. An interaction between two arrows is located at a point, while the arrows are extended. A measurement outcome therefore only shows us a facet of the state of the arrow.

If we try to measure the position of the arrow, there is an indeterminacy in the outcome that equals (twice) the length L of the arrow. For the same event, the arrow could as well have been observed at any place between x - L and x + L.

The phase of the arrow (its direction projected on a plane) is totally undetermined. If we denote the indeterminacy of the phase as $$\Delta \phi$$, we may write:

 * $$\Delta \phi = \Delta k \ .\ \Delta x = \Delta \omega \ . \ \Delta t = 2 \pi$$.

Because measurement outcomes are undetermined, quantum mechanics only give us statistical means to make predictions. This leads us to the next principle: the probability of an experimental outcome is deduced from the probability that the observed arrow interacts with the observing arrow.

Fifth principle: Quantum probabilities involve interaction cross sections of both observed and observing particles
Imagine we want to observe quantum-mechanically the arrow in the particle box of the figure. In order to 'detect' that arrow, we need a second arrow (that will also bounce back and forth between both walls). The probability of interaction between both arrows is therefore proportional to the projection of the first arrow multiplied by the projection of the second arrow perpendicularly to the line of interaction, which is just the wavefunction squared. This principle is known as Born's rule


text:
User talk:JimScarver

Welcome
Hello JimScarver, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 09:03, 21 October 2007 (UTC)

title: User talk:JimScarver


text:
User:JimScarver

Jim Whitescarver

http://Whitescarver.com/jim - resume

http://WikiWorld.com/JimScarver

title: User:JimScarver


text: Category:Bloom clock project templates/bcp3


text: Category:Bloom clock project templates/tracking


text: Category:Bloom clock project templates/regional tags/Southeastern Pennsylvania


text: Category:Bloom clock project templates/regional tags


text:
Template:Bcp3-log links

(add new log entry)

title: Template:Bcp3-log links


text:
Advanced Wikiediting

The mediawiki software used by Wikiversity, our sister Wikimedia Projects, and many other websites is very adaptable, and a knowledge of more "advanced techniques" for creating content can produce excellent results.

Resources

 * Templates
 * Tables
 * Using div
 * DynamicPageList
 * Cascading Style Sheets (css)

title: Advanced Wikiediting


text:
Advanced Wikiediting/Templates

Outline:

 * Transclusion: how it works
 * Transcluding templates
 * Transcluding other pages
 * inclusion and noninclusion
 * defining variables
 * using #if
 * using #switch

title: Advanced Wikiediting/Templates


text:
Advanced Wikiediting/DynamicPageList

DynamicPageList is a mediawiki feature that is enabled on some Wikimedia projects, inclucing Wikiversity and Wikibooks. The version used by Wikimedia foundation projects is an old version, which runs solely off of categories.

See mw:Extension:DynamicPageList (Wikimedia)

Example
The markup: yeilds:

 category            = MediaWiki count               = 50 order               = decending addfirstcategorydate = true

See also Help:Dynamic page list

title: Advanced Wikiediting/DynamicPageList


text:
User talk:Uniqueuponhim~enwikiversity

Welcome
Hello Uniqueuponhim, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 13:14, 21 October 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Uniqueuponhim. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Uniqueuponhim~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:09, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:24, 19 April 2015 (UTC)

title: User talk:Uniqueuponhim~enwikiversity


text:
Advanced Wikiediting/Tables

If you want to start with just a few simple examples, go to: Help:Table.

Simple Example 1
.

Simple Example 2
.

Simple Example 3
.

Simple Example 4
.

Simple Example 5
text text text

text text text

.

Simple Example 6
{| border="0" cellpadding="0" cellspacing="16"

 * }

.

Simple Example 7
{| border="0" cellpadding="0" cellspacing="16"

 * }
 * }

.

Practical Example 1
A useful location finder for all Wikiversity pages.

.

Practical Example 2
Table of contents

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 2: What is narrative music?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 3: What computer software do I need?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 4: Getting started with GarageBand
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 5: List of moods and actions for you to work on
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 6: Narrative music created by Mad Max's students
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental A: Examples of Narrative Music
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental B: A simple movie for scoring
 * }
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 2: What is narrative music?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 3: What computer software do I need?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 4: Getting started with GarageBand
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 5: List of moods and actions for you to work on
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 6: Narrative music created by Mad Max's students
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental A: Examples of Narrative Music
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental B: A simple movie for scoring
 * }
 * }

.

Practical Example 3
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Practical Example 5
This is a film strip.

{| cellpadding="0" cellspacing="5" style="width: 500px; background-color: #e0e0ff; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: white; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" |

 * }

{| cellpadding="0" cellspacing="5" style="width: 500px; background-color: #e0e0ff; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: white; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" |

 * }

Practical Example 6
This is an empty table.

---

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---

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Practical Example 8
This is tables within a table.

{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Left

 * style="width: 40%; background-color: #e0e0ff; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" |

Right

 * }

{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Left

 * style="width: 40%; background-color: #e0e0ff; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" |

Right

 * }

.

Practical Example 9
A simple framework

{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto" ! style="background-color: #ffffaa; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" | Title

 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |
 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Left

 * style="width: 40%; background-color: #EFFFEF; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" |

Right
{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * }
 * style="background-color: #e0e0ff; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" |

Full
{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * }
 * style="background-color: white; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" |

Full 2

 * }

{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto" ! style="background-color: #ffffaa; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" | Title

 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |
 * style="width: 60%; background-color: #ffffe0; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Left

 * style="width: 40%; background-color: #EFFFEF; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" |

Right
{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * }
 * style="background-color: #e0e0ff; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" |

Full
{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * }
 * style="background-color: white; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" colspan="2" |

Full 2

 * }

.

Practical Example 11

Text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text.

Text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text.

Picture is 150px rather than 50px.

Text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text.

Text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text.

Practical Example 12
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Second page of this help page for tables

title: Advanced Wikiediting/Tables


text:
Wikiversity:Wikimedia fund raising

 * Fund raising FAQ - 2007 fund raising drive starts Monday, October 22
 * Jimmy Wales Video about donating to the Wikimedia Foundation
 * Finance reports - reports available through June 2006. Report through June 2007 expected before December 2007.
 * Spending plans for 2007 to 2008, estimated spending level of USD 4,600,000.00 for 2007-2008 see also.
 * Historically, a major expense for the Wikimedia Foundation has been servers and internet bandwidth.
 * Read comments from donors

title: Wikiversity:Wikimedia fund raising


text:
Talk:Making sense of quantum mechanics/Principles of Quantum Mechanics

Quantum probabilities principle
This (fifth) principle needs to be much more worked out. I am not really satisfied with the header "Quantum probabilities involve interaction cross sections of both observed and observing particles". I intended to say that probabilities are given be square wavefunction amplitudes (Borns probability interpretation), because both observed and observing particle are subjected to the same pilot wavefunction, which gives probabilities of the kind $$|\psi^2|$$. This probability principle is therefore a corollary of a more fundamental principle, which is rarely mentioned as such: the phase of the particles are steered by the phase of a pilot wave (de Broglie's or Bohm's principle). This principle is suggested by the figure of the arrow bouncing back and forth in the box: even if the walls weren't there, the arrow-particle would rotate in phase with the wave. Arjen Dijksman 19:48, 21 October 2007 (UTC)

Generalized Schroedinger equation
I propose a generalized Schrödinger equation which is, as far as I see, the most general form of the central quantum evolution law. This equation is valid for any vector-like object (macroscopic or microscopic). It may be deduced directly from the geometrical consideration of the following figures. Starting from an arbitrary vector $$|\psi \rangle$$, we subtract it from the rotated vector $$e^{i{\Delta \phi}}.|\psi\rangle$$, giving the little vector $$\Delta |\psi \rangle$$. If we draw the vector $$i |\psi \rangle$$ and multiply it by the amount $$\Delta \phi$$, we obtain an equivalent vector $$\Delta \phi. i |\psi \rangle$$ for $$\Delta \phi$$ going to 0. This gives the equation: $$i |\psi \rangle d \phi = d |\psi \rangle$$

Considering that $$d \phi$$ = $$\omega dt + t d\omega$$ or $$k dx + x dk$$ depending on the variables you choose, specialized Schroedinger equations may be obtained. Arjen Dijksman 18:45, 20 November 2007 (UTC)


text:
User talk:Florinpopa10~enwikiversity

Welcome
Hello Florinpopa10, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 19:48, 21 October 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Florinpopa10. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Florinpopa10~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:32, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:08, 19 April 2015 (UTC)

title: User talk:Florinpopa10~enwikiversity


text:
Talk:Finite elements/Vectors

Length of a vector
This section refers a few times to the length of a vector $$|\mathbf{b}|$$. Should we explain that this is calculated by

|\mathbf{b}| = \sqrt{\sum_i b_i^2} $$ to the reader? Papna 20:29, 21 October 2007 (UTC)

title: Talk:Finite elements/Vectors


text:
User:Papna~enwikiversity

I'm a graduate student in Civil/Structural engineering who is interested in elasticity, FEA, mechanics of materials, typography, linguistics, open-source software, nerdiness in general, graphic design, and lots of other things. I've edited wikipedia and wikibooks for years, casually.

I want to learn and contribute here.

Facebook

title: User:Papna~enwikiversity


text:
User talk:Sebmol/Archive/2007-IV

Archive Bot
En.wikibooks is looking for an automatic archival bot. Is there anyway that we could either (a) borrow ArchiveBot for this purpose, or (b) get our own copy? I could sit down at the text editor and try to reinvent the wheel, i suppose. I would prefer to have a tested solution instead, however. Please let me know. --Whiteknight (Versity) (Books) 20:58, 1 October 2007 (UTC)
 * I would be happy to add wikibooks to the sites the bot goes over if you're interested. sebmol ? 19:36, 3 October 2007 (UTC)
 * It would be really great! What do we need to do for this? Create templates? jump through hoops? Let me know. --Whiteknight (Versity) (Books) 00:10, 5 October 2007 (UTC)
 * It would really help a lot if you could just copy over the templates that I've created here. Specifically, you will need Template:auto archive and Template:auto archive/documentation. Could you let me know once those are set up? I will register the bot's account right away. sebmol ? 21:52, 6 October 2007 (UTC)

 * w:User:Misza13 replied to an older message of mine, and appears to be setting up an archive bot of his own for en.wikibooks. To that effect, I dont think we are going to need yours (at least not immediately). I wanted to thank you for your generous offer to let us use your bot, and I'll let you know if we have need of it in the future. --Whiteknight (Versity) (Books) 00:36, 8 October 2007 (UTC)

Archives
Are new Colloquium archives being created correctly? --JWSchmidt 14:46, 16 November 2007 (UTC)
 * I made some more links at Colloquium/archives. I guess all is fine. --JWSchmidt 14:55, 16 November 2007 (UTC)

Missing page perhaps deleted or merged .... Resolved to my satisfaction.
Hi Sebmol, I am attempting to track down some content that was here. It seems to say you deleted the file after it was redirected or merged with another game learning file. These were two separate files at one time. Can you help me find this missing material? Thanks! Mirwin 00:39, 23 December 2007 (UTC)

 * An update. This file: http://en.wikiversity.org/wiki/Image:LunarRoverTestShot2.jpg was used in the page content to illustrate results of boolean modeling.  It is no longer linked to so I suspect someone has deleted the file without placing the content anywhere else.   If possible I would like the entire file back so it may be placed appropriately within School:Game Design and others, and linked to from Lunar Boom Town. Mirwin 00:45, 23 December 2007 (UTC)

 * There are a lot of red links within the game design area. Might be useful to find out who deleted this file and check the contribution page.  There has been a lot of file shuffling or perhaps even deleting of existing files and link structure that may approach vandalism ... although a lot of this material is so old that it was placed and linked before existing standard organization of content and links was in place.  Perhaps someone shuffling files does not know how to check on existing links and repair them?  Mirwin 00:50, 23 December 2007 (UTC)

 * Sebmol, this has been resolved to my satisfaction. It looks like I was moving files and materials around and lost the stub in question.  The critical material is in other files.  Sorry to bother, may all your problems resolve themselves before you see requests for assistance! Have a Merry Christmas and awesome New Year celebration!  O_O  Mirwin 01:37, 23 December 2007 (UTC)

title: User talk:Sebmol/Archive/2007-IV


text:
Secondary dominants

The dominant note in a scale is the fifth note of that scale.

The C major scale consists of the notes C D E F G A B. In C Major, G would be the dominant or fifth note. The tonic note in a scale is the first note of that scale, in C Major C would be tonic. The secondary dominant is the the dominant of the dominant or the five-of-five. If you begin in C major the secondary dominant would be D, which is the dominant of G.

However the scale that begins and ands on D in the key of C major is a minor one (actually, it is known as the 'dorian' mode WWHWWHW [W=Whole tone/Maj 2nd, H=half tone/min 2nd]).

So to strengthen the 'dominant effect', we raise the F one half step to F# (not coincidentally this is the 'leading tone' for the root of the next intended chord: G) Thus creating a major chord which has a strong harmonic tendency to resolve to the G major chord that is functioning as the dominant in the key of C major. This is one of the natural ways that accidentals can occur and is not considered in itself a full 'modulation'.

The secondary dominant can be used to prepare chords on other 'degrees' of the scale as well; the tonic, with the addition of the lowered 7th degree, is often used as the dominant of the sub-dominant etc.

title: Secondary dominants


text: File:TrussJoint.jpg

title: File:TrussJoint.jpg


text: Template:Bar

title: Template:Bar


text:
United States Law/Criminal

Unlike other subjects, you will spend a fair amount of time reading statutes as well as cases.

title: United States Law/Criminal


text:
Naegleria infection

Naegleria infections are caused by Naegleria fowleri. Infection of the central nervous system (CNS) can causes death in 4 to 21 days. This organism enters the CNS through mucus membranes of the nose. Once it enters the CNS it is very difficult to treat. Symptoms; nausea,vomiting,loss of sense of smell, irrational behavior, coma, death. PREVENTION; keep your head above water.

External resources

 * Primary amoebic meningoencephalitis - at Wikipedia
 * Naegleria Infection - at Centers for Disease Control and Prevention
 * PCR-Based Diagnosis of Naegleria sp. Infection in Formalin-Fixed and Paraffin-Embedded Brain Sections
 * Environmental contamination with protozoan parasite infective stages: biology and risk assessment
 * Animal model of human disease. Primary amebic meningoencephalitis, Naegleria meningoencephalitis, CNS protozoal infection

title: Naegleria infection


text:
Electric Circuit Analysis/Resistors in Parallel

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Lesson 3 : Review
What you need to remember from Resistors in Series. If you ever feel lost, do not be shy to go back to the previous lesson & go through it again. You can learn by repetition.

 * Total Series Resistance: ($$R_E = R_1 + R_2\!$$)
 * The total Resistance of Resistors in series is the sum of all resistors in series.

 * Voltage Divider Equation 2.3: $$V_1 = \frac{R_1 \times V_s}{R_1 + R_2}$$

 * Current through Resistors connected in Series is the same for all resistors.

Lesson 4: Preview
This Lesson is about Resistors in Parallel. The student/User is expected to understand the following at the end of the lesson.

 * two resistors connected in Parallel: $$R_{eq}=\frac{R_1 \times R_2}{R_1 + R_2}$$

 * Current Divider Principle: $$I_1 = I_s \times \frac{R_{eq}}{R1}$$
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Introduction
The best way to understand Parallel circuits is to start with the definition. A circuit is parallel to another circuit or several circuits if and only if they share common terminals; i.e. if both the branches touch each other's endpoints. Here is an example:

R1, R2, and the voltage source are all in parallel. To prove this fact consider the top and bottom parts of the circuit.

The areas in yellow are all connected together, as well as the areas in blue. So all the branches have the same terminals, which means that R1, R2, and the source are all in parallel. If we take this discussion of the water flow analogy. Electric current can be seen as water and the conductors as water pipes.

Something interesting happens as the current reaches the common node of resistors that are connected in parallel: the total current is divided into the parallel branches.

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Voltage Rule
If two or more branches are parallel then the voltage across them is equal. So based on this we can conclude that VR1=VR2=5volts. However unlike series resistors, the current across the branches is not necessarily equal.

Equivalent resistance
For series resistors to find the total resistance we simply add them together. For parallel resistors its a little more complicated. Instead we use the following equation:

 * $$R_{eq} = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}}$$

However for the case of only two resistors we can use the following simplified form:

Equation 4.2: Total Parallel Resistance

 * $$R_{eq}=\frac{R_1R_2}{R_1 + R_2}$$

It is well to note at this point that the total resistance of parallel-connected resistors will always be less than the resistance of smallest of the individual resistors.

Current Rule
In series connection, we deduced that voltage is divided amongst resistors. For parallel-connected resistors, however, current is divided. So, as we did with the voltage division principle, here is the mathematical formula:

Equation 4.3: Current Divider Formula

$$I_1 = I_s \times \frac{R_{eq}}{R1}$$

Using this formula you can work out the currents flowing through individual resistors.

 * }

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Application
We have spent three lectures hacking on about what and why resistors and& resistive circuits in two connection schemes are used, (i.e. series and parallel connections). The question now is, where & how in real life do these connections happen?

One simple application of these connection schemes is the Shunt Application. In the electric measurement industry, most often enough, we wish to measure currents and voltages of very high magnitudes (in the range of 500kV upwards). The problem is that metering devices have delicate electronic components and usually have small voltage and current ratings.

The solution to the above problem is to have a metering device connected in parallel to a resistor,with the resistor thus called a "shunt" resistor since it is there to protect (shunt) the metering device as shown in Part 4.

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Part 4
If we know the current rating of a device and the total current in the system, we can then work out the shunt current and, thus, the shunt resistance.
 * }

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Part 5: Examples
Figure 3.4 shows a parallel resistive circuit with the following parameters. $$V_s=10Volts$$ ; $$R_1=3\Omega$$;$$ R_2=7\Omega$$; Find $$R_{eq}$$; $$I_1 and I_2.$$

Solution: from Equation 4.2 we see that.

 * $$R_{eq}=\frac{R_1R_2}{R_1 + R_2}$$

Thus it can be said that the supply current has been divided between R1 and R2.

We know that when solving these problems, we look at the data given and thus we can see how we need to manipulate our equations in order to achieve our objective.The following example highlights this point. See to it that you follow the method used and the reasoning behind it.

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Part 6: Examples
Figure 4.5 shows a parallel resistive circuit with the following parameters. $$I_s=5Amps$$ ; $$R_1=2\Omega$$; $$R_2=3\Omega$$; Find: $$I_1 ; I_2$$ and $$V_s$$.

Solution: from Equation 3.2 we see that.

 * $$R_{eq}=\frac{R_1R_2}{R_1 + R_2}$$

 * }

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Do you Remember?
Let's take some time to Reflect on Material covered thus far. We have learned a great deal about simple resistive circuits and the possible connections they afford us. Here I think you'll want to remember:

 * Voltage: (V or v - Volts)The electrical potential between two points in a circuit.
 * Current: (I or i - Amperes)The amount of charge flowing through a part of a circuit.
 * Power: (W - Watts)Simply P = IV. It is the current times the voltage.
 * Source: A voltage or current source is the supplier for the circuit.
 * Resistor: (R measured in Ω - Ohms)A circuit element that "constricts" current flow.

 * Total Series Resistance: ($$R_E = R_1 + R_2\!$$)

 * Voltage Divider : $$V_1 = \frac{R_1 \times V_s}{R_1 + R_2}$$

 * Current through resistors connected in series is the same for all resistors.

 * Two resistors connected in parallel: $$R_{eq}=\frac{R_1 \times R_2}{R_1 + R_2}$$

 * The Current Divider Principle: $$I_1 = I_s \times \frac{R_{eq}}{R1}$$

Do Exercise 4 in Part 8. After being completely satisfied with your work, you can go on to the next page - for the quiz! Good luck :-)

Related Topic(s) in Wikiversity
Please visit the following page to supplement material covered in this lesson.

 * The role of resistors in electrical circuits
 * Resistor Reduction

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Part 8: Exercise 4

 * 1) Given 2 Resistors $$R_1 = R_2 = 5\Omega$$ in parallel find the $$R_{eq}$$.
 * 2) Given 3 Resistors $$R1 = 2\Omega$$; R2 = 3$$\Omega$$ and R3 = 7$$\Omega$$ in parallel and supply current as 15A, find $$R_{eq}$$ ; $$I_1$$; $$I_2$$ & $$I_3$$ and the supply voltage across these resistors.
 * 3) Given 4 Resistors: R1 = 2$$\Omega$$ connected in series to a parallel branch of 3 resistors: R2 = 3$$\Omega$$ ; R3 = 7$$\Omega$$ and R4 = 4$$\Omega$$ Find: total resistance as seen by the voltage source.
 * 4) Is it possible to effectively connect voltage sources in parallel? If so, what conditions must be met?

 * Answers to Exercise 4

Completion list
Once you finish your Exercises you can post your score here! To post your score just e-mail your course co-ordinator your name and score *@undefined.

 * Ozzimotosan -- 100%
 * Doldham -- 75% & Corrected

 * }


text:
User talk:Tlep

Welcome
Hello Tlep, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWS 13:40, 22 October 2007 (UTC)

title: User talk:Tlep


text:
User talk:Bsheehan5013

Welcome
Hello Bsheehan5013, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWS 13:43, 22 October 2007 (UTC)

title: User talk:Bsheehan5013


text:
User talk:Basekid

Welcome
Hello Basekid, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 15:41, 22 October 2007 (UTC)

title: User talk:Basekid


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Template:Bloom clock plant top

Global data:

Regional data and additional images for

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Hold-Up Problem Part 1 Payoffs

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Hold-Up Problem Part 2 Payoffs

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Template talk:Bloom clock plant top

Protected Edit Request
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 * ✅ -- Dave Braunschweig (discuss • contribs) 13:54, 12 April 2020 (UTC)

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Category:Wikiversitians who are currently online

Materials having to do with Wikiversitans who are currently online.


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Category:Wikinode

Materials having to do with WikiNode.

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Template:Bloom clock plant bottom

This template is used for adding identification characteristics on Bloom Clock Profiles. The data collected on this template adds categories which are used to create dichotomous keys.

New version:

'''Due to heavy usage, this template is protected. To experiment, use Template:Bloom clock plant bottom-test'''

title: Template:Bloom clock plant bottom


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Hydrology

Hydrology is a science concerned with the properties of the Earth's water, especially its movement in relation to land.

The science of hydrology is also being applied to astronomical objects that contain water in various forms. For students interested in off-world water, several lectures have been included.

More appropriately, hydrology directly applied to the Earth may be called geohydrology.

Content summary
Hydrology is the study of the water cycle. Natural and man-made processes guide water in its varied forms to a variety of ends. Use as irrigation, drinking water and process water by man is very common.

Def. "hydrology as used in the processing of radioactive materials" is called radiohydrology.

Def. the "study of the ecological processes associated with hydrology" is called ecohydrology.

Def. "the science that uses dendrochronology to investigate and reconstruct hydrologic processes, such as river flow and past lake levels" is called dendrohydrology.

Theoretical hydrology
Def. the "science of the properties, distribution, and effects of water on a planet's surface, in the soil and underlying rocks, and in the atmosphere" is called hydrology.

Chemical hydrology

 * Waters
 * Chemicals/Oxidanes

Glaciology

 * Ices
 * Black ices
 * Brittle ices
 * Sea ices
 * Drift ices
 * Ice sheets
 * Glaciers
 * Glaciology
 * Classification of glaciers
 * Alpine glaciers
 * Maritime glaciers
 * Tidewater glaciers
 * Piedmont glaciers
 * Polar glaciers
 * Rock glaciers
 * Tributary glaciers
 * Valley glaciers
 * Outlet glaciers
 * Isolated glaciers
 * Crater glaciers
 * Cirque glaciers
 * Hanging glaciers
 * Surging glaciers
 * Temperate glaciers
 * Ice streams
 * Ogives
 * Dirt cones
 * Astroglaciology
 * Ice cores

Paleohydrology

 * Huronian ice age
 * Cryogenian ice age
 * Andean-Saharan ice age
 * Karoo Ice Age
 * Holarctic-Antarctic Ice Age
 * Little Ice Age

Physics

 * Liquids
 * Liquid objects
 * Salinity
 * Hydromorphology
 * Oceans
 * Oceanography
 * Gulf Stream

Meteorology

 * Atmospheres
 * Weather
 * Fair weather
 * Telluric sources
 * Hydrometeors
 * Showers
 * Rains
 * Cryometeors
 * Clouds

Ecohydrology

 * Coral reefs
 * Forests
 * Phytoplanktons
 * Ecology

Texts

 * Water Resources Directory/Education
 * Water Resources Directory/USA/Education
 * Applied Ecology/Wetland Engineering
 * Georgia Water/Best Practices/Simulation
 * Georgia Water/External Links/Education
 * Basic Geography

Diffusion
For a source contaminant concentration $$\ C_0$$ entering a flow of velocity $$ \vec U $$ at a distance $$\ x $$ upstream from a point, the downstream concentration $$\ C $$ at that point is determined by the ratio...

$$ \frac{C}{C_0} = e^{\frac{x*\vec U}{D}} $$

Where... $$\ D $$ is the local dispersion coefficient determined by $$\ D = 0.067 * depth * V_f$$

and where friction velocity is $$V_f = \sqrt{g*depth*ChannelSlope}$$

Velocity Distribution in an Open Channel (River)
Velocity distribution within a river follows a standard velocity profile for a confined space (pipe-flow)with the exception that the vertical distribution is truncated at the surface due to reduced friction with atmospheric gases versus the high friction against riverbed materials.

Boundary Layer thickness, also known as the displacement thickness, is defined by:

$$ \delta_d = \int_0^H \frac{1}{H} \left( 1-\frac{\vec u}{\vec U} \right) dz$$

where $$ \vec U $$ is the average velocity and $$ \vec u(x) $$ is the velocity distribution in a channel of uniform depth $$\ H$$.

$$ \bar U = \frac{\int_A \left( \rho \vec V \cdot \hat n \right) dA}{\rho A} $$

So in the case of this river, where the current is always normal to the cross-sectional area of the river (idealized)...

$$ \bar U = \frac{\int_x \int_y \left( \rho \vec V \right) dydx}{\rho A} $$

Activities:

 * Agriculture quiz
 * Astroglaciology quiz
 * Atmospheres quiz
 * Atmospheric science quiz
 * Black ice quiz
 * Brittle ice quiz
 * Glacier quiz
 * Glaciology quiz
 * Hydrology quiz
 * Hydromorphology quiz
 * Ice sheet quiz
 * Liquid-object astronomy quiz
 * Liquid objects quiz
 * Liquids quiz
 * Oceanography quiz
 * Oxidanes quiz
 * Rain quiz

Study guide:

 * Physical Properties of the Oceans
 * 1) Wikipedia article:Temperature
 * 2) Wikipedia article:Density

title: Hydrology


text:
Introduction to Category Theory

Welcome to the learning project.

Learning Project Summary

 * Project code:
 * Suggested Prerequisites:
 * None
 * Time investment:
 * Assessment suggestions:
 * Portal:Mathematics
 * School:Mathematics
 * Department:
 * Stream
 * Level:Undergraduate

What is Category Theory?
Abstract nonsense is a popular term used by mathematicians to describe certain kinds of arguments and concepts in category theory. This term is believed to have been coined by the mathematician Norman Steenrod, one of the developers of the categorical point of view. This term is used by practitioners as an indication of mathematical sophistication or coolness rather than as a derogatory designation.

Certain ideas and constructions in mathematics display a uniformity throughout many domains. The unifying theme is category theory. Rather than enter an elaborate discussion on particulars of arguments, mathematicians will use the expression such and such is true by abstract nonsense. Typical instances are arguments involving diagram chasing, application of the definition of universal property, definition of natural transformations between functors, use of the Yoneda lemma and so on.

This course is an introduction to abstract nonsense.

Scope of the course
Category theory is usually considered a hard subject, and isn't typically part of an undergraduate curriculum. This doesn't need to be so. This course is primarily intended for undergraduate students in pure mathematics. It might be useful to computer theorists, linguists, physicists, and some others. We may sometimes sacrifice a little mathematical rigor in order to make the text more accessible and stay more focused on the right kind of abstract nonsense. In particular we try to avoid set theoretic nonsense.

It is still unclear how much material can be covered in a undergraduate course.

Lessons
The full list
 * Lesson 1: Sets and Functions
 * Lesson 2: Products and Coproducts of Sets
 * Lesson 3: Monoids
 * Lesson 4: Categories
 * Lesson 4.5: /Equivalence of categories/
 * Lesson 5: Products and Coproducts
 * Lesson 6: Products are Limits
 * Lesson 7: Equalizers
 * Lesson 8: Pullbacks
 * Lesson 9: Limits
 * Lesson 10: Exponentials
 * Ideas for a new lesson:
 * generalized elements?
 * Hom(C,-) functors?
 * Yoneda embedding?
 * F-algebras (and initial F-algebras)
 * catamorphisms

Create your lesson

Related resources

 * Category Theory
 * Wikipedia article:
 * Category Theory
 * List of category theory topics
 * Category:Category theory
 * Wikibooks textbook:
 * Discrete mathematics
 * Set Theory
 * Abstract Algebra
 * Category theory

How can you help?

 * If you're a mathematician and know some category theory, you can write any lessons that haven't been written yet.
 * If you're a mathematician or a wannabe-mathematician, but know little about category theory, you can fill in the gaps or fix the errors in lessons that have been written. We also need exercises (anything from trivial computations to miniprojects (say boolean algebras)).
 * If you're not a mathematician, but you think you understand what is written, you can rewrite things in better, more readable English.
 * If you don't quite understand anything, you can write comments/questions to talk pages.

Active participants
Active participants in this Learning Group

title: Introduction to Category Theory


text:
Introduction to Category Theory/Sets and Functions

Informally, a category consists of objects, arrows between objects, and some rules between arrows. Before we can give a formal definition, we introduce simpler concepts: sets, functions, and function composition. In fact, sets and functions are a category called Sets.

Definition
A set is a collection of distinct objects considered as an object in its own right.

The elements of a set, also called its members, can be anything: numbers, people, letters of the alphabet, other sets, and so on. Sets are conventionally denoted with capital letters. The statement that sets A and B are equal means that they have precisely the same members (i.e., every member of A is also a member of B, and vice versa).

Every element of a set must be unique; no two members may be identical. All set operations preserve the property that each element of the set is unique. The order in which the elements of a set are listed is irrelevant.

Describing sets
There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description. See this example:

 * A is the set whose members are the first four positive integers.
 * B is the set of colors of the French flag.

The second way is by extension, that is, listing each member of the set. An extensional definition is notated by enclosing the list of members in braces:

 * C = {4, 2, 1, 3}
 * D = {blue, white, red}

The order in which the elements of a set are listed in an extensional definition is irrelevant, as are any repetitions in the list. For example,
 * {6, 11} = {11, 6} = {11, 11, 6, 11}

are equivalent, because the extensional specification means merely that each of the elements listed is a member of the set.

For sets with many elements, the enumeration of members can be abbreviated. For instance, the set of the first thousand positive whole numbers may be specified extensionally as:

 * {1, 2, 3, ..., 1000},

where the ellipsis ("...") indicates that the list continues in the obvious way. Ellipses may also be used where sets have infinitely many members. Thus the set of positive even numbers can be written as {2, 4, 6, 8, ... }.

The notation with braces may also be used in an intensional specification of a set. In this usage, the braces have the meaning "the set of all ..." So E = {playing-card suits} is the set whose four members are ♠, ♦, ♥, and ♣. A more general form of this is set-builder notation, through which, for instance, the set F of the twenty smallest integers that are four less than perfect squares can be denoted:

 * F = {$$n^2$$ – 4 | n is an integer; and 0 ≤ n ≤ 19}

In this notation, the vertical bar ("|") means "such that", and the description can be interpreted as "F is the set of all numbers of the form $$n^2$$ – 4, such that n is a whole number in the range from 0 to 19 inclusive."

One often has the choice of specifying a set intensionally or extensionally. In the examples above, for instance, A = C and B = D.

Membership
If something is or is not an element of a particular set then this is symbolised by $$\in$$ and $$\notin$$ respectively. So, with respect to the sets defined above:
 * $$4 \in A$$ and $$285 \in F$$ (since 285 = 17² − 4); but
 * $$9 \notin F$$ and $$\mathrm{green} \notin B$$.

Special sets
There are some sets which hold great mathematical importance and are referred to with such regularity that they have acquired special names and notational conventions to identify them. One of these is the empty set. Many of these sets are represented using Blackboard bold typeface. Special sets of numbers include:
 * $$\empty$$ = {}
 * $$\mathbb{P}$$, denoting the set of all primes.
 * $$\mathbb{N}$$, denoting the set of all natural numbers. That is to say, $$\mathbb{N}$$ = {1, 2, 3, ...}, or sometimes $$\mathbb{N}$$ = {0, 1, 2, 3, ...}.
 * $$\mathbb{Z}$$, denoting the set of all integers (whether positive, negative or zero). So $$\mathbb{Z}$$ = {..., −2, −1, 0, 1, 2, ...}.
 * $$\mathbb{Q}$$, denoting the set of all rational numbers. So, $$\mathbb{Q} = \left\{ \begin{matrix}\frac{a}{b} \end{matrix}: a,b \in \mathbb{Z}, b \neq 0\right\}$$. For example, $$\begin{matrix} \frac{1}{4} \end{matrix} \in \mathbb{Q}$$ and $$\begin{matrix}\frac{11}{6} \end{matrix} \in \mathbb{Q}$$. All integers are in this set since every integer a can be expressed as the fraction $$\begin{matrix} \frac{a}{1} \end{matrix}$$.
 * $$\mathbb{R}$$, denoting the set of all real numbers. This set includes all rational numbers, together with all irrational numbers (that is, numbers which cannot be rewritten as fractions, such as $$\pi,$$ $$e,$$ and √2).
 * $$\mathbb{C}$$, denoting the set of all complex numbers. This includes real numbers and multiples of $$i$$ (where $$i^2=-1$$), and combinations of both.

Definition
A function, $$f$$, is a special type of relation between two sets, say $$X$$ and $$Y$$. Relation, here, means any subset of the Cartesian product $$X \times Y$$. Formally, $$f\,$$ is a subset of $$X \times Y$$ such that every element $$x \in X$$ is paired with a unique element $$y \in Y$$, which we denote as $$y = f(x)$$. Note that the notation is unambiguous because we require our pairing to be unique. Also, note that the uniqueness is relative to every element of $$X$$; we can still have two different elements of $$X$$ mapping to the same element in $$Y$$. We write $$f: X \to Y$$ and say that $$f$$ maps $$X$$ to $$Y$$. Also, $$X$$ is called the domain of $$f$$ while $$Y$$ is called the codomain of $$f$$. For every subset $$S \subseteq X$$, we call the set $$f(S) = \{f(x) \in Y : x \in S\}$$ as the image of $$S$$ by $$f$$. Similarly, for every subset $$S' \subseteq Y$$, we call the set $$f^{-1}(S') = \{x \in X : f(x) \in S'\}$$ as the pre-image of $$S'$$ due to $$f$$. In particular, the image of $$X$$, itself, is called the range of $$f$$.

Now, we can notice something intriguing here. It is, intuitively, the case that every function is paired with a unique domain and a unique codomain; hence, we can unambiguously write $$dom(f) = X$$ and $$cod(f) = Y$$. Here $$dom$$ and $$cod$$ are functions from the set of all functions to the set of all sets.

Function $$f: \mathbb{R} \to \mathbb{R}$$ defined by formula $$f(x)=x^2$$, takes each real number $$x$$ to its square.

In the image shown, the range of function $$f$$ is $$\{a,b\}$$. What is the range of real valued function $$f$$ with $$f(x)=x^2$$?

Composition of Functions
A composite function, formed by the composition of one function on another, represents the application of the former to the result of the application of the latter to the argument of the composite. The functions $$f:X \to Y$$ and $$g:Y \to Z$$ can be composed by first applying f to an argument x and then applying g to the result. Thus one obtains a function $$g \circ f:X \to Z$$ defined by $$(g \circ f)(x) = g(f(x))$$ for all x in X. The notation $$g \circ f$$ is read as "g circle f" or "g composed with f".

The composition of functions is always associative. That is, if f, g, and h are three functions with suitably chosen domains and codomains, then $$h \circ (g \circ f) = (h \circ g) \circ f$$. Since there is no distinction between the choices of placement of parentheses, they may be safely left off.

If function f has same domain and codomain, in other words if $$f: X\rightarrow X$$ is function from X to itself, we may compose f with itself; this is sometimes denoted $$f^2\,$$. Thus:

 * $$f^2(x) = (f\circ f)(x) = f(f(x))$$

 * $$f^3(x) = (f\circ f\circ f)(x) = f(f(f(x)))$$

Identity function
The identity function on a set $$X$$, often denoted $$\text{id}_X$$, e, or $$\varepsilon_X$$, is the function $$\text{id}_X : X \rightarrow X$$ by $$x \mapsto x$$ for all $$x \in X$$.

Injection
An injective function is a function which associates distinct arguments to distinct values. More precisely, a function $$f:X \to Y$$ is said to be injective if it maps a distinct x in X to a distinct y in Y. Put another way, f is injective if $$f(a)=f(b)$$ implies a = b (or a ≠ b implies $$f(a) \ne f(b)$$), for any a, b in the domain.

Injective functions with non-empty domain have left-inverse. That is to say, for injection $$f:X \to Y$$, there exists a function $$g:Y \to X$$ such that, for every x in X
 * $$g(f(x)) = x\ $$.

The composition $$g \circ f$$ is the identity function $$\text{id}_X$$ on the set X.

Proposition. Let g be a function from Y to Z. The following statements are equivalent:
 * 1) Function g is injective.
 * 2) For every set X and every two functions $$f_1, f_2: X \to Y$$ the following holds: $$g \circ f_1 = g \circ f_2$$ if and only if $$f_1 = f_2$$. In this case, the function g is called monic.

Proof.

$$(1) \Rightarrow (2)$$: If the set Y is the empty set (2) is trivially true. Otherwise g has left-inverse $$h:Z \to Y$$. If $$g \circ f_1 = g \circ f_2$$, then $$f_1 = \text{id}_Y \circ f_1 = h \circ g \circ f_1 = h \circ g \circ f_2 = \text{id}_Y \circ f_2 = f_2$$. Other direction is trivial.

$$(2) \Rightarrow (1)$$: Let X be a set with one element, X = {1}. For any two elements a and b in Y, let $$f_1(1) = a$$ and $$f_2(1) = b$$. If $$g(a)=g(b)$$, then $$g \circ f_1 = g \circ f_2$$. By assumption (2) this implies $$f_1 = f_2$$. Thus $$a = f_1(1) = f_2(1) = b$$ and g is injective.

Remark. As per the above proposition, monic functions are equivalent to injective functions. However, in the more general setting of category theory, monic morphisms are a more general concept than injective functions. In general, an injective function is a monic morphism; however, a monic morphism is not necessarily an injective function. In fact, in many situations, a morphism is hardly a function at all!

Surjection

A function f is said to be surjective if its values span its whole codomain; that is, for every y in the codomain, there is at least one x in the domain such that $$f(x) = y$$. Said another way, a function $$f:X \to Y$$ is surjective if and only if its range f(X) is equal to its codomain Y. A surjective function is called a surjection, and also said to be onto.

By the axiom of choice every surjective function $$f:X \to Y$$ has right-inverse. In other words there exists a function $$g:Y \to X$$ such that $$f(g(y)) = y$$ for every y in Y. That is the composition $$f \circ g$$ is the identity function on Y.

Proposition. Let f be a function from X to Y. The following statements are equivalent:
 * 1) Function f is surjective.
 * 2) For every set Z and every two functions $$g_1, g_2: Y \to Z$$ the following holds: $$g_1 \circ f = g_2 \circ f$$ if and only if $$g_1 = g_2$$. In this case, the function f is called (in all seriousness!) epic.

Proof. Exercise!

Remark. Just like the earlier remark, epic functions are equivalent to surjective functions, in set theory. However, in the more general setting of category theory, epic morphisms are a more general concept than surjective functions.

Bijection
A bijective function is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that $$f(x) = y$$. Alternatively, f is bijective if it is both injective and surjective.

Bijective function $$f:X \to Y$$ has an inverse function $$f^{-1}:Y \to X$$ such that
 * $$f^{-1} \circ f = \text{Id}_X$$ and $$f \circ f^{-1} = \text{Id}_Y$$.

Exercises

 * 1) Give feedback on this page, click discussion button at the top of this page.
 * 2) Got an idea how to improve this page? Be bold and change it!
 * 3) Injections
 * 4) * If f and g are both injective, prove that the composition g o f is injective.
 * 5) * If g o f is injective, prove that f is injective.
 * 6) * If g o f is injective, give an example showing that g need not be injective.
 * 7) Surjections
 * 8) * If f and g are both surjective, prove that the composition g o f is surjective.
 * 9) * If g o f is surjective, prove that g is surjective.
 * 10) * If g o f is surjective, give an example showing that f need not be surjective.
 * 11) Prove that the inverse of a bijection is well defined. I.e. prove that the left inverse of the injection and right inverse of the surjection are always equal.
 * 12) Create new exercises.

Related resources

 * Set
 * Function (mathematics)
 * Function composition
 * Identity function
 * Injective function
 * Surjective function
 * Bijective function


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User:Guðsþegn

See my Wikipedia page here.

title: User:Guðsþegn


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User:Georgeworks54

Hi fellow Wiki freaks. As I am just starting I don't even qualify. But I am doing this so I am one step closer.

I am a carpenter and all around craftsman. I solve alot of problems for people and that's it for now. G.

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Welcome
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --Remi 02:15, 23 October 2007 (UTC)

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User talk:Guðsþegn

Welcome
Hello Guðsþegn, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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 * Read and help develop our community policies；or
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWS 02:34, 23 October 2007 (UTC)

Greetings God's Messenger, and welcome to Wikiversity and the Wikiversity School of Theology! Your servant looks forward to your active participation. -- Dionysios  (talk), Founder of the Wikiversity School of Theology, Department of Orthodox Christian Studies, Date: 2007-10-23 (October 23, 2007) Time:  1240 UTC

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