text:
User talk:Mc9000

 Hello Mc9000, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Juan de Vojníkov 18:05, 25 January 2009 (UTC)

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

title: User talk:Mc9000


text:
User talk:Judojoe300

 Hello Judojoe300, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Juan de Vojníkov 18:18, 25 January 2009 (UTC)

title: User talk:Judojoe300


text:
User talk:Aaronmorris

 Hello Aaronmorris, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Juan de Vojníkov 18:28, 25 January 2009 (UTC)

have a good luck with Wikiversity.--Juan de Vojníkov 18:28, 25 January 2009 (UTC)

title: User talk:Aaronmorris


text:
User talk:Cib4

Hola, como por el usuario Cib, tambien tenemos que descargar todas sus contribuciones. He comunicado con el jefe de la escula y le he explicado todo.--Juan de Vojníkov 18:31, 25 January 2009 (UTC)

title: User talk:Cib4


text:
User talk:Egm6322.s09.xyz

User:Egm6322.s09.mafia
You edit a user account that was not created. Can you explain why ?Crochet.david 19:01, 25 January 2009 (UTC)

title: User talk:Egm6322.s09.xyz


text:
User talk:HenkvD

 Hello HenkvD, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Juan de Vojníkov 19:16, 25 January 2009 (UTC)

category gadget
Hi, I noticed that you've been doing a lot to help organize categories. Great work! I just wanted to let you know that we have a tool that helps make it easier to place pages in a better category. If you go to Special:Preferences and click on Gadgets there is an option called HotCat. Check it out, and let me know if you need any help. --mikeu talk 13:38, 7 February 2009 (UTC)
 * Thanks. I have installed it. I am not sure if I will use it often.... HenkvD 13:46, 7 February 2009 (UTC)
 * Ok. Just thought it might save you some time and help with what you are doing.  --mikeu talk 13:48, 7 February 2009 (UTC)

Hi and welcome!
Thanks for your edits to my Neuroscience page. I was wondering what you would like to get out of Wikiversity, and how you envision the site as developing. --AFriedman 02:47, 10 February 2009 (UTC)

 Hi! Our name is Vicky-Verity. We are twins and are Wikiversity mascots. We think Wikiversity is a great place to learn and make friends (when we aren't sleeping). Leave us a message!

 * I don't have a specific vision on Wikiversity. I am doing mostly maintenance jobs on wiki's: interwiki's and sisterlinks like on commons:Category:German language. On Wikiversity I started to organize categories because I found there were a lot of duplicate categories. I will then try to add interwiki links etc. HenkvD 18:34, 10 February 2009 (UTC)

 * Good work with the categories. Do you know about the Subject, completeness level, resource type and intended audience boxes?  I like to use them.  The Subject box page has the links to the others.   I don't know what your area of expertise is, but IMO it's also important to add content to Wikiversity (e.g. working on the courses other people have started).  In particular, few people seem to have thought about how Wikiversity could offer instructor feedback or automated feedback.  Another thing I've been doing is going to Wikipedia pages and adding links to Wikiversity so more people know about the project, because Wikipedia pages tend to be well viewed.  What are your thoughts about doing these things?  --AFriedman 04:12, 11 February 2009 (UTC)

 * About Subject boxes: I personally think the Categories attached to these causes a lot of unwanted articles in higher categories (like Category:Biology if the box Template:biology is added to pages.) At this moment the Category:Biology with 73 pages is OK, but if all pages in Category:Biochemistry, Category:Cell biology, Category:Genetics, Category:Microbiology etc. etc. are added it will become a complete jungle. Just an observation from an outsider. I would prefer not to use the subject boxes but navigate via categories instead. HenkvD 19:33, 11 February 2009 (UTC)

 * About instructor feedback or automated feedback:
 * Quiz extenstion requires no human interaction
 * The wiki way would be that students grade and/or comment each other
 * I have seen homework via e-mail but that will fail when the teacher is no longer involved
 * or Wikiversity has to invent its own extention...... HenkvD 19:33, 11 February 2009 (UTC)

Fair enough. Re: boxes, many categories have subcategories and perhaps this would be the most useful way to structure WV. I just think the boxes are pretty. Wikipedia certainly has some very large categories, like "Living people." Re: feedback, I just finished an online workshop on WikiEducator (a website with a purpose similar to WV) about the wiki markup language. It's at. It's incredibly well organized, with daily instructor feedback, online chat/video meetings, a Google group and several levels of certification. IMO it's worth looking at just to see what wikis can do. These workshops are offered every month or so on WikiEducator. Even though Wikiversity is so small, quizzes don't require human feedback. Very few of them have been added and more could be. In addition, even TA grading rubrics are intended to create a very specific algorithm for the TAs to use, and some aspects of this can be automated. Just a few thoughts. --AFriedman 03:30, 12 February 2009 (UTC)

Artificial Consciousness
Hi, I see you slaving away, redoing categories, and I wondered why you were removing categories like psychology from my Artificial Consciousness pages. Is it redundant in some way?--Graeme E. Smith 20:46, 10 February 2009 (UTC)
 * In my opinion categories like psychology is indeed redundand, as the articles fall into Category:Artificial consciousness, which falls under Category:Consciousness that in turn falls under Category:Psychology. So Psychology is implied already. I just looked and found that a lot of Artificial Consciousness pages are categorized in Category:Consciousness, I would suggest to use Category:Artificial consciousness instead. Some of the pages on Category:Artificial consciousness should be moved up to Category:Consciousness as well. Any objecttions? HenkvD 16:10, 11 February 2009 (UTC)

It's tricky, I don't quite understand the category system, which is why I am probably over categorizing my work, but part of the problem is that sometimes a page has a specific reference to psychology on it. I don't know if you have looked at my Portal yet, but Artificial Consciousness is a discipline that draws from Neuroscience, as well as psychology and is dependent on Computer Science for its simulations and implementation. I haven't categorized all the infrastructure in the portal yet, but if you look it over you will see that it is not as simple as Artificial Consciousness being part of Consciousness being part of psychology. Unless psychology is categorized under neuroscience but even then, it would leave the Computer Science stuff an orphan.--Graeme E. Smith 18:05, 11 February 2009 (UTC)

 * Not every reference needs to be catogorized. As for Computer Science: I added Category:Computer science to Category:Artificial consciousness.
 * {| border = 1 |

 * rowspan=2 | Category:Artificial consciousness
 * Category:Consciousness
 * Category:Psychology
 * etc.
 * Category:Computer science
 * etc.
 * etc.
 * }
 * I hope my categorization helps you and others to goce some structure to this wiki. HenkvD 18:37, 11 February 2009 (UTC)
 * I hope my categorization helps you and others to goce some structure to this wiki. HenkvD 18:37, 11 February 2009 (UTC)

So, all I need now is to note the pages that are neuroscience separately?--Graeme E. Smith 21:01, 11 February 2009 (UTC)

 * Yes and No
 * Yes, as Neuroscience is not implied directly
 * No, because in my opinion not every reference needs to be catogorized.
 * It is up to you whether or not to add the category Neuroscience. HenkvD 18:43, 12 February 2009 (UTC)
 * PS: categories should be written like and not like  . HenkvD 19:06, 12 February 2009 (UTC)

Sorry, ever since I started work on the portal, I have been putting curly brackets in too many places, It's because I had to hack the tabs, to get them to go more than one level deep I think.--Graeme E. Smith 19:47, 12 February 2009 (UTC)

Speedy Deletion
Hi HenkvD,

Thanks for your diligence and for caring about keeping the Wikiversity categories tidy.

In this case, please reverse the speedy deletions of the categories you mentioned on my user talk page.

The project with which they are associated is due to be promoted in 2009. Having the categories already available will be useful to new entrants. The categories are listed in the guidelines for editors.

There are also many pages which still need to be categorised using these categories. I have just not had time to do it of late and don't have time now to comment on all the categories you have flagged.

Thanks

Kim Ktucker 22:37, 12 February 2009 (UTC)

 * To keep discussion central: I moved this to User talk:Ktucker. HenkvD 14:25, 13 February 2009 (UTC)

Categories
Thanks HenkvD. I think the category structure is starting to breath a sign of relief thanks to your ongoing efforts. . -- Jtneill - Talk - c 01:16, 14 February 2009 (UTC)

What are the rules?
I'm glad you're working on categories. It's important work.

At Technical writing you've removed the categories of "business" and "writing" from all the pages in the course. Before I undo your work, please let me know your reasoning for excluding technical writing from these categories.

 * Technical writing is a vital part, of business. As you'll see in the course content, it's not just writing user manuals. Everything from the conception of a project to it's creation, testing and analysis involves technical writing skills.

 * Writing about technical subjects is...well, Henrik, it's writing.

Please note you also removed these categories from the page about writing requirements specifications, which is very much a business and project management topic.

As a guy who has to index and classify things, I wonder if your object is to be inclusive or exclusive. Both have their merits, and it's important to remove obviously unsuitable subjects from a category. But in an environment like Wikiversity, I'd suggest that being inclusive should be the default decision.

So if you could do me the favor of restoring these with your clever gadget, I'd really appreciate it. If you have suggestions of how I can improve my categorization, or a set of standards you're following, please contact me.

Thanks again for your work. I appreciate the time and effort you're putting into this important effort. TWFred 00:55, 24 February 2009 (UTC)
 * All articles about Technical writing are in Category:Technical Writing. This category is included in the category Bussiness, I added that on 9/2/2009. Category:Technical Writing was already in category Writing. My rule would be: As less categories as possible in the topics and articles, and as less categories as possible on Categories itself. I think you would call it Exclusive, but I don't think that is really the case. Fot suer I am not an Inclusinist. A very clear example of remove obviously unsuitable subjects would be this change at Cognition. My guideline would be Wikipedia:Help:Category: Each page is typically in at least one category. It may be in more, but it may be wise not to put a page in a category and also in a more general category. In that way the categories like Category:Business have only one entry to Technical writing, as well as one entry on any other interesting subject. As for Category project management: it could be added to the particular article. HenkvD 19:10, 24 February 2009 (UTC)

I had a look. Thanks, Henk. Your scheme is exclusionary rather than inclusionary.

Is there a specific technical reason for this? I ask because from my perspective the purpose of categories is to aid users in finding related information...not the mental convenience of XML thinking techies. What is obvious to you, with a clearly technical background, is often completely wrong for the typical user of the system.

Were these policies agreed upon, or have they just evolved in this way because the people involved happen to be technically oriented rather than user information oriented?

You're a specialist in using this tool for assigning categories, it's clear. I'm a specialist in the presentation of semantic information to users. I don't think your work is at all bad, but I think focusing on excluding subjects from multiple categories misapplies the very concept, defeating the original purpose of having categories.

Categories are for helping users find additional information, not enforcing an arbitrary tree-like hierarchy.

This is why I cannot agree with your unilateral decision on this. I appreciate your work, but it's clear that in some cases you're doing more harm than good.

Again, if there is a specific technical reason why your approach is the only possible solution, please let me know. But if it's arbitrary, it has to be much better thought out before it's applied so indiscriminately.

Best, TWFred 20:26, 26 February 2009 (UTC)

 * There is no technical reason for this. I sometimes use the HotCat tool, but that is not relevant for this actions. My approach is a bit technical, but some Wikiversity wide improvement on categorisation was ind is certainly needed.
 * My goal too is to help users to find information. The basic difference between your view and mine is that you want the categories inside the articles and that I categorize the categories.
 * Categorisation is not only for finding related information but also for finding the initial information. I am sure you will agree on that. I still find it hard to navigate through the categories, especially from the starting point Category:Categories, or find something via Browse /my sandbox for Wikiversity:Browse. Do you have suggestions for improving it? HenkvD 12:18, 27 February 2009 (UTC)

Hi again, Henk. I again thank you for your work and diligence.

Wikiversity wide improvement on categorization is a huge undertaking. Helping people find information initially, as well as showing how categories are related to each other is our mutual goal.

When I look at Category:Categories I'm immediately struck by the fact that not even native speakers of English can differentiate between the labels. What is the difference between something being a:

 * Course
 * Field
 * Occupation
 * Profession

...and so on. Those words are semantically null. They seem to be chosen for convenience rather than inherent meaning.

Clicking on a "category" doesn't help either. To use the technical writing pages as an example, it seems obvious to me that they should be found in more than one of these categories, if not all of them. Yet my pages are only listed...all of them apparently, under the very long list of courses.

I could also look for my pages through the various portals, and not find it except by accident by scrolling through very long lists.

There needs to be a logical hierarchy that allows cross-categorization.

 * Courses
 * Writing
 * Technical Writing

 * IT
 * Programming
 * Testing
 * Documentation
 * Technical Writing

 * Business
 * Project Management
 * Project Documentation
 * Technical Writing
 * Writing Requirements Specifications

 * Professions
 * Business Analyst
 * Writing Requirements Specifications
 * Project Management
 * Writing Requirements Specifications
 * Writing
 * Technical Writing

Thanks for having this discussion with me, Henk.

TWFred 16:57, 7 March 2009 (UTC)
 * I agree with the above aproach, logical hierarchy with cross categorisation as well. I am currently working on the Topics / Category:Departments. I have not started yet with Category:Categories as indeed it has no logical structure yet. I probably should have hierachies on school subjects, on eduction level, on resoucre type and maybe others as well. HenkvD 18:15, 7 March 2009 (UTC)

Nonkilling Barnstar
For your initiative improving significantly the School of Nonkilling Studies. {{subst:Barnstar 17| --Cgnk 15:37, 6 March 2009 (UTC)

 * Thanks, just added all topics in the category structure. HenkvD 15:52, 6 March 2009 (UTC)

Departments
I noticed you removed the "Departments" cat: from European History again. May I ask what your criteria for keeping some Departments in that Category and not others is? The Jade Knight (d'viser) 18:29, 30 August 2009 (UTC)
 * The Topic:European History is already in Category:History departments, which is a subcategory of Category:Departments by subject and Category:Departments. By this way it is still on the Browse screen. HenkvD 07:11, 31 August 2009 (UTC)
 * Yes, but right now there are some Departments which are not in subcategories. Generally, people visiting Browse are more likely to only look at those Departments.  I am of the opinion that either only particularly developed departments should be directly in the Departments category, or none should be.  Your opinion?  The Jade Knight (d'viser) 15:52, 31 August 2009 (UTC)
 * Putting all in the main category makes this too big. Having none in this category is a good principle, but difficult. Maybe we should create a Misceleneous department category or Other department category. Should this then be placed on Category:Departments by subject? HenkvD 07:26, 1 September 2009 (UTC)
 * Good idea. But would it maybe be better to simply move all of the groups in "Departments by Subject" right into "Departments"?  The Jade Knight (d'viser) 04:54, 2 September 2009 (UTC)
 * Fine by me, but in future we might have groups like Departments by Educational Level etc. Do you want me to move all of the groups in "Departments by Subject" right into "Departments" ? HenkvD 09:48, 2 September 2009 (UTC)
 * Well, but virtually all departments currently at Wikiversity intend to cover all education levels (at least in theory), with very few exceptions. But sure, let's move them all right into "Departments" and put all of the extras in an "Other" or "Miscellaneous" category.  The Jade Knight (d'viser) 18:50, 2 September 2009 (UTC)

✅ I created Category:Miscellaneous departments and moved all topices not categorized as subject into it. Furthermore I removed the level of Category:Departments by subject. It looks much better Browse this way. HenkvD 10:10, 3 September 2009 (UTC)
 * Yes, I agree. Much, much better.  Thanks!  The Jade Knight (d'viser) 02:00, 4 September 2009 (UTC)

title: User talk:HenkvD


text:
User:Mindytonti

bio
My name is Mindy Tonti I am currently getting my degree in Fashion Design at the art institute of Seattle. I love to travel and experience different cultures outside of seattle and outside the US. I spent the last year living in Ireland and working. After attaining my degree I want to start a fashion conscious clothing line collaborating with my sister, who is a law school student at seattle U, to make clothes that are not only economically responsible but also broaden peoples knowledge on critical issues needed to be addressed in our country for example domestic violence and drug abuse. If you have more questions on how we plan to do this please ask, it is a working process and we would appreciate any ideas other have.

assignments
I have driven by the sculpture park many times and there has always been one piece that I notice with disgust. For some reason I have always taken great offense to this piece, ‘typewriter eraser”. I decided to go take a closer look at the piece and with that my dislike intensified. Typewriter eraser was made by Claes Oldenburg, an American artist who was born in Sweden in 1929. I researched Claes Oldenburg and found that many of his other pieces of artwork reflect the same style of ‘typewriter eraser’. Very modern and realistic, something I have a hard time appreciating. I looked at pictures of all of these pieces and eventually one did catch my eye, ‘bottle o notes’. Although this is a sculpture still within his general style I found it interesting because it made me think, I didn't just see the piece as a large metal bottle constructed by an artist I already had a presumed disliking for. I went back to the sculpture park to look again at ‘typewriter eraser’. Although my feelings have not diminished towards this piece, I still strongly dislike it I am able to appreciate it more after learning about Oldenburg and starting to understand why he sculpts what he does. I don't feel I am the correct judge of someone else’s art, art is so subjective. To many people this could be a beautiful sculpture and to others it could be viewed as I see it, horrible. But even with all of my distaste for this piece I still appreciate it as a piece of art that someone put a lot of work into, that came directly out of them that is trying to be understood by the public it was made to be seen

final
Mindy Tonti

By the end of this quarter, I want to have started writing a book. I’ve always wanted to write my story. Not that I think my life has been all that special but I have lived through a lot that I feel others can relate to and also draw inspiration from. In the end I want my book to be a collection of short stories, poetry, letters, and artwork taking the form of a novel.

Research component: There are a few books I have read that have really touched me and inspired me in the way that I hope mine will do to others. I want to re read them to help me with my project. The books are more now and again, the perks of being a wallflower, and running with scissors. I will also do research on these three particular authors and look for different techniques and tools to help me write a book.

Week 2: Start reading More Now and Again. Look through the work I already have written that I can use in my project. Look up helpful hints online about writing a book.

Week 3: Finish reading More Now and Again. Start to fill a binder with the work I have and begin to make an outline of chapters and information that will fall into each one.

Week 4: Start reading Running with scissors. Finish the outline and begin to fill in the holes of what writing needs to be done.

Week 5: Finish Running with scissors and continue writing various parts of my book.

Week 6: Read the Perks of being a wallflower and begin to look through my artwork to see what pieces are significant that I want to be a part of my book. Continue writing.

Week 7: Start working on my final presentation for the project. Having the outline complete I will put all of the work I have collected together into a notebook and organize it as I want it to be in the book.

Week 8: Continue to write and finalize the outline and organization of the binder to be presented

Note: This is a very personal project. A lot of the material I am writing about may not be appropriate to be read in class. I will try and pick a few things that I think may be appropriate and go over them with you before the presentation. Although this will be my personal story I am not sure yet if I want to divulge that information to the class. If I ever do try and publish the finished book it will most likely be under another name to protect not only me but the people that are in it.

reflective assessment
4. When you're

title: User:Mindytonti


text:
User:Egm6322.s09.mafia/HW1

 See my comments below. On-going work, not finished yet.

Please don't remove this comment box; if you make any corrections, modifications, etc. you can add comments to this comment box to explain what you did.

Egm6322.s09 19:13, 27 January 2009 (UTC)

Added signature and comment in box below as requested.

--Egm6322.s09.lapetina 14:35, 28 January 2009 (UTC)

Added a section regarding contributions.

--Egm6322.s09.lapetina 22:28, 30 January 2009 (UTC)

Added signature for member XYZ of Team Mafia

--Egm6322.s09.xyz 22:01, 8 February 2009 (UTC)

 Added the list of contributing members after the deadline of 22:00 UTC. The difference between the present version (before adding this comment box) and the official version before the deadline is given here.

This page is best viewed with the "Math" settings in the "Preferences" Section of Wikipedia placed on "Always Render PNG". Otherwise, math environments may not appear as math environments.

Team coordinator signs here.--Egm6322.s09.lapetina 14:35, 28 January 2009 (UTC)

 Nice tip on the Math settings to view math environments.

Problems: (1) Looking at the history page of this report, one can see that there was too much imbalance in the contribution of different team members to the report: Essentially, one team member did all the work (about 21,000 bytes), another one contributing about 300 bytes (1.4%), and another team member about 200 bytes (1%). You want the history page to show that everyone contributed more or less equally.

(2) Another problem is that user "EGM6322S09TIAN" may not exist at all. First, the username did not correspond to the convention explained in class (see the username of your other teammates); second, this user may not have created his/her account (registered).

Egm6322.s09 15:12, 28 January 2009 (UTC)

=Preface=

--Egm6322.s09.xyz 18:29, 24 April 2009 (UTC)

Partial differential equations (PDEs) are a class of mathematical expressions that include one or more independent variables and their respective derivatives. These equations describe a host of physical occurrences in the real world. Examples of PDEs in everyday life can be as simple as tracking the change in temperature for a can of soda that is placed on a kitchen counter after being removed from the refrigerator (see Heat Conduction Equation, ). More complex examples of PDEs can be found in Schrodinger's Equation which describes the quantum state of a system, , or, the Monge Ampere equation that occurs most often in studies of differential geometry. A brief introduction to the basic tenets in the study of partial differential equations is presented here. Information given on this Wiki page are from lecture notes of EGM 6322 taught by Dr. Vu-Quoc.

=Introduction=

Before discussing PDEs, it is best to review a few basic mathematical topics, and introduce the notations which will be used throughout the article.

Variables and Vector Notation
--Egm6322.s09.lapetina 17:39, 24 April 2009 (UTC)

N independent variables can be expressed as:

$$  \left \{ {x}_{i} \right \}=   \left \{ {x}_{1},...,{x}_{n}   \right \} $$.

An example of this would be single dimensional case with a time variable.

$$ \left ( x,t \right)=  \left ( {x}_{1}, { x}_{2 } \right )  $$

where $$ {x}_{1} = {x}  $$, a spatial variable

and $$ {x}_{2} = {t}  $$, a temporal variable.

A more complex situation would be a three dimensional, time dependent problem:

$$  \left (x,y,z,t  \right )=  \left({x}_{1},...,{x}_{4}  \right )$$.

In this case, $$ {x}_{1} = {x}  $$, $$  {x}_{2} = {y}  $$, $$  {x}_{3} = {z}  $$, and $$  {x}_{4} = {t}  $$.

Functions and Partial Derivatives
--Egm6322.s09.lapetina 01:50, 17 April 2009 (UTC)

$$ n $$ unknown functions $$ {u}_{i} $$ can be expressed as:

$$ {u}_{1}, {u}_{2} ,... , {u}_{n}$$

For our present discussion, this can be restricted to one unknown function $$ u $$, containing $$ n $$ independent variables $$ {{x}_{i}} i=1,...,n $$

The mth partial derivative of this function can be expressed as:

$$ \frac{\partial^m u}{\partial x_i\ ,...,\partial x_m} $$ where

$$ {{i}_{1},...,{i}_{m}} $$ is the subset of m indices among n possible indices

$$ {i}_{i}, ..., {i}_{m}=1,...,n $$.

 Use "Image:" command, instead of "File:" command to insert images so you can include the image caption. Also improve image quality in the future.

Egm6322.s09 13:04, 4 February 2009 (UTC)

The unknown function $$ u $$ maps numbers from the domain $$ \Omega $$ to the real numbers $$ \mathbb{R} $$ In two dimensions, this means:

$$ \left( x,y \right) \in \Omega $$

$$ u \left( x,y \right) \in \mathbb{R} $$

and

$$ \Omega \rightarrow \mathbb{R}$$

$$ \left( x,y \right) \mapsto u \left( x,y \right) $$

which means that $$\Omega $$ is the domain of u, $$ \mathbb{R}$$ is the range of u, and $$u \left ( \Omega \right )$$ is the image of $$\Omega $$ under the mapping of $$ u $$.

An example of this is the Navier-Stokes Equations in 3-D:

$$ {u}_{i} ( \left \{  {x}_{j} \right \} ) $$

where $$ {u}_{i} $$ is the velocity field in x, y, z; $$ {u}_{1}, {u}_{2}, {u}_{3} $$, dependent upon variables $$ {x}_{1}, ... {x}_{4}$$, where $$ {x}_{1} = {x}  $$, $$  {x}_{2} = {y}  $$, $$  {x}_{3} = {z}  $$, and $$  {x}_{4} = {t}  $$.

More on Mapping

AFFINE MAPPING

Definition: "In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, 'connected with') between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation:" Source:Affine_transformation

LINEAR MAPPING

Definition: "In mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. The expression "linear transformation" is in particularly common use, especially for linear maps from a vector space to itself (endomorphisms). In advanced mathematics, the definition of linear function coincides with the definition of linear map." Source :Linear_transformation

 Nice contribution with proper references. You want to make the title of this collapsible box clearer by specifying that the mappings discussed in the box are affine mapping and linear mapping. Egm6322.s09 19:16, 27 January 2009 (UTC)

Tensor Notation
--Egm6322.s09.lapetina 01:51, 17 April 2009 (UTC)

--EGM6322.S09.TIAN 17:48, 24 April 2009 (UTC)

Often we will use vector operators and tensor notation when studying PDEs.

For example, the function:

$$u_xx+u_yy+f(x,y)=0$$

can be rewritten as div( $$\kappa$$ $$\cdot$$$$grad u$$$$+f(x,y)=0$$

Here, $$\kappa$$ is a continuity tensor (2nd order tensor).

$$\kappa$$ = $$\kappa$$ $$e_i$$ $$\otimes$$ $$e_j$$ 2nd-order tensor

$$v$$ = $$v_i$$ $$e_i$$ vector,1st-order tensor

A 0th order tensor is a scaler.

Vector Operators
--EGM6322.S09.TIAN 17:48, 24 April 2009 (UTC)

There are many examples of vector operators, which will be expanded upon in discussions of order and linearity

$$grad$$ $$u$$ $$=$$ $$\frac{\partial u}{\partial x_i}$$ $$e_i$$

$$div$$ $$v$$ $$=$$ $$\frac{\partial v_i}{\partial x_i}$$ $$e_i$$

$$\kappa$$ $$\cdot$$ $$grad$$ $$u$$ =( $$\kappa_{ij}$$ $$e_i$$ $$\otimes$$ $$e_j$$ ) $$\cdot$$ ($$\frac{\partial u_k}{\partial x_k}$$ $$e_k$$ )

=$$\kappa_{ij}$$ $$\frac{\partial u}{\partial x_k}$$ ( $$e_i$$ $$\otimes$$ $$e_j$$ ) $$\cdot$$ $$e_k$$

Here, $$e_i$$ $$\otimes$$ $$e_j$$ $$\cdot$$ $$e_k$$ = $$e_i$$ ( $$e_j$$ $$\cdot$$ $$e_k$$ )

Vector operators often act differently depending upon the order of tensor they act upon.

For example:

$$u(x,y)$$ is a scaler function $$\Rightarrow$$ 0th order tensor $$gradu$$ is a vector field $$\Rightarrow$$ 1st order tensor

while

$$grad$$  ($$\cdot$$) increases tensor order by 1

but

$$div$$  ($$\cdot$$) decreases tensor order by 1

We can let $$v$$ : = $$\kappa$$ $$\cdot$$ $$gradu$$

$$div$$ $$v$$ = $$\frac{\partial }{\partial x_i}$$ $$\kappa_{jk}$$ $$\frac{\partial u}{\partial x_j}$$

Kronecker delta
--EGM6322.S09.TIAN 17:48, 24 April 2009 (UTC)

Definition: If $$e_j$$ $$\otimes$$ $$e_k$$ = $$\delta_{jk}$$, $$\delta_{jk}$$ is called Kronecker delta.

$$ \delta_{jk} = \begin{cases} 1 & for \ j=k \\ 0 & for \ j \neq k \end{cases} $$ = $$\kappa_{jk} \frac{\partial u}{\partial x_i} $$ $$e_i$$

Leopold Kronecker (1823 - 1891)

--Egm6322.s09.xyz 18:31, 24 April 2009 (UTC)

Kronecker Delta was named after Leopold Kronecker, a 19th century mathematician from Prussia. Born in 1823, Kronecker studied at the University of Berlin and later went on to teach at what is now known as Humboldt University in 1883. He specialized in the areas of number theory, finitism, and continuity before dying in Berlin in 1891. source:

 Good idea and contribution to find out well-known historical figures who contributed to this classical field of PDEs and related fields.

Egm6322.s09 13:04, 4 February 2009 (UTC)

=Order=

Definition
The order of a PDE is the order of highest derivative in the PDE. This is the highest number of derivatives in any term of the equation.

 I added the section References at the end of the report, and the command to render the references.

Egm6322.s09 15:44, 28 January 2009 (UTC)

Examples of First Order PDE's
--EGM6322.S09.TIAN 17:50, 24 April 2009 (UTC)

Linear
$$5u_x-7u_y=0$$

Non-Linear
--Egm6322.s09.xyz 18:32, 24 April 2009 (UTC)

$$6(u_x)^3+2(u_y)^2+(u)^{1/2}+x^2+sin xy=0$$

Prove Non-Linearity --Egm6322.s09.xyz 18:33, 24 April 2009 (UTC)

We can assume that $$D(u)=6(u_x)^3+2(u_y)^2+(u)^{1/2}$$

Show D(u) is not linear.

(Solution)

Again, $$D \left( u \right) = 6 \left( u_x \right)^3 + 2 \left( u_y \right)^2 + \left( u \right)^{1/2}$$.

D(u) is linear if the following formula holds:

$$D \left( \alpha\cdot u + \beta\cdot v \right) = \alpha\cdot D \left( u \right) + \beta\cdot D \left( v \right) $$

OR,

$$6 \left( \alpha\cdot u + \beta\cdot v \right)^3 + 2 \left( \alpha\cdot u + \beta\cdot v  \right)^2 +  \left( \alpha\cdot u + \beta\cdot v  \right)^{1/2} = \alpha\cdot \left [ 6 \left( u_x  \right)^3 + 2 \left( u_y  \right)^2 +  \left( u  \right)^{1/2} \right ] + \beta\cdot \left [ 6 \left( v_x  \right)^3 + 2 \left( v_y  \right)^2 +  \left( v  \right)^{1/2} \right ]$$

The expressions on either side of the equality sign in the above equation are NOT identical. Therefore, D(u) is NOT linear.

More Examples of 1st Order PDEs --Egm6322.s09.xyz 18:33, 24 April 2009 (UTC)

Examples of 1st order linear and nonlinear PDEs are given below. For more information, see the Wiki page for Partial Differential Equations.

(LINEAR) $$ \frac{du}{dx}\ + \frac{du}{dy}\ + \frac{du}{dz}\ = 0 $$ (LINEAR) $$ \dot x \ + 42\dot y \ = 0 $$ (LINEAR) $$ t \frac{dy}{dt}\ + 4 \frac{dy}{dx}\ = 0 $$ (NON-LINEAR) $$ \left(\frac{du}{dx}\ \right)^2 + \left(\frac{du}{dy}\ \right)^3  = 0 $$ (NON-LINEAR) $$ u + \sqrt[3]{\left(\frac{du}{dy}\ \right)}  = 0 $$

As an addition proof, it should be noted that the linear PDEs given above are also separable (the non-linear PDEs are not separable expressions). More information about the linearity of PDEs is given in the following references:,.

Examples of Second Order PDEs
--EGM6322.S09.TIAN 17:52, 24 April 2009 (UTC)

$$div(gradu)+f(x,y)=0$$

Note: tensorial notation = coord free notation.

$$\kappa$$ $$= const$$ $$\Rightarrow$$ is a linear second order PDE

$$\kappa$$ $$= \underline{\kappa} (x,y)$$ $$\Rightarrow$$ is also a linear second order PDE

$$\kappa$$ $$= \underline{\kappa} (x,y,u)$$ $$\Rightarrow$$ is a quasilinear second order PDE

Another example of a second order PDE is the Laplace Equation in two dimension:

$$ F \left ( \left (x,y \right) ,u,\left ({u}_{x},{u}_{y} \right), \left ({u}_{xx},{u}_{xy},{u}_{yy} \right ), ...   \right )=0 $$

also expressed as:

$$ {u}_{xx}+{u}_{yy}=0$$.

Another second order PDE is the equation:

$$ {u}_{yy} +u^2=7x $$.

$$div$$ $$v$$ = $$\frac{\partial }{\partial x_i}$$ $$\kappa_{ij}$$ $$\frac{\partial u}{\partial x_j}$$

HW：Matrix Expansion --EGM6322.S09.TIAN 17:54, 24 April 2009 (UTC)

We can expand it as: $$div$$ $$v$$ = $$\frac{\partial \kappa_{ij} }{\partial x_i}$$ $$\frac{\partial u }{\partial x_j}$$ + $$\kappa_{ij}$$ $$\frac{\partial u^2 }{\partial x_i x_j}$$

 Not exactly what was asked; you want to expand the summation indices, which take values in $$\displaystyle \{1,2\}$$. See, e.g., Team Bit.

Egm6322.s09 12:44, 30 January 2009 (UTC)

Other second order PDE's are examined in the Linearity section.

=Linearity=

Definition
--Egm6322.s09.lapetina 01:52, 17 April 2009 (UTC)

If $$ u $$ is an unknown function, the operator $$ L $$ is considered a linear operator with respect to $$ u $$ if:

$$ L \left ( \alpha u + \beta v \right ) = \alpha L \left ( u \right )+ \beta L \left ( v \right ) $$

Steps for Checking for Linearity --Egm6322.s09.lapetina 01:52, 17 April 2009 (UTC)

$$ 2{u}_{xx}+3{u}_{yy}-7{x}^{2}+x=0 $$

The operator is :

$$ \mathcal{L}= 2 \frac{\partial^2 }{\partial x^2} + 3 \frac{\partial^2 }{\partial y^2} -7 x^2-x $$

where $$ -7 x^2-x:= f(x) $$

To check the linearity, we assume $$\alpha$$ and $$\beta$$ are real number constants, and evaluate: $$ \mathcal{L} (\alpha u+ \beta v)= 2 \frac{\partial^2 (\alpha u+ \beta v)}{\partial x^2} + 3 \frac{\partial^2 (\alpha u+ \beta v)}{\partial y^2} + f(x)$$

which is equivalent to:

$$ \mathcal{L}(\alpha u+ \beta v)=2 {\left (\alpha u + \beta v \right )}_{xx}+3 {\left (\alpha u +\beta v\right )}_{yy}+f(x) $$

If we distribute the integers, as well as the second derivative operators, the equation becomes:

$$ \mathcal{L}(\alpha u+ \beta v)=2 \alpha {u}_{xx}+2 \beta {v}_{xx}+3 \alpha {u}_{yy} + 3 \beta {v}_{yy}+f(x) $$.

Grouping the terms by the constants $$\alpha$$ and $$\beta$$ concludes:

$$\mathcal{L}(\alpha u+ \beta v)= \alpha \left [2 {u}_{xx}+3{u}_{yy} \right ] +\beta \left [ 2 {v}_{xx} +3 {v}_{yy} \right ] +f(x) $$.

The operator $$ \mathcal{L} $$ is nonlinear because

$$ \alpha L(u)+ \beta L(v)= \alpha \left [2 {u}_{xx} +3 {u}_{yy} +f(x) \right ] +\beta \left [2 {v}_{xx}+3 {v}_{yy} + f(x) \right ] $$

and

$$ f(x) \ne \alpha f(x) +\beta f(x) $$

Alternative Definition of Linearity

--Egm6322.s09.lapetina 01:52, 17 April 2009 (UTC)

An alternative means of defining linearity is provided by A.N. Kolmogorov & S.V. Fomin in Introductory Real Analysis, 1975. Assuming $$x,y \in \mathbb{R}$$, they define numerical functions on linear spaces as "functionals", and describe these as "additive" if:

$$f(x+y)=f(x)+f(y)$$ for all $$x$$ and $$y$$, and "homogeneous" if

$$f(\alpha x)=\alpha f(x)$$ for all $$x$$ where $$\alpha $$ is a real constant. This can be extended to complex numbers, but is out of our present scope.

This can be extended to define linearity for operators in the following fashion:

Given:

$$f(\alpha x)=\alpha f(x)$$ where $$x,y \in \mathbb{R}$$ and $$\alpha $$ and $$\beta$$ are real constants,

$$\alpha f(x)+\beta f(x)=f(\alpha x)+f(\beta x)$$

In turn, one of the $$x$$ can be replaced with a $$y$$, yielding:

$$\alpha f(x)+\beta f(y)=f(\alpha x)+f(\beta y)$$

Since $$\alpha $$ and $$\beta$$ do not alter the real nature of the domain, then

$$\alpha x = q$$

and

$$\beta y = r$$

where

$$q,r \in \mathbb{R}$$.

The function is still additive, and:

$$f(q)+f(r)= f(q+r)$$.

or

$$f(\alpha x)+f(\beta y)= f(\alpha x+ \beta y)$$.

Using the transitive property:

$$\alpha f(x)+\beta f(y)= f(\alpha x+ \beta y)$$.

Therefore, operators which are homogeneous and additive are also linear. The definitions are equivalent.

 See better proof in class.

I added the section References at the end of the report, and the command to render the references.

Rewrite the above reference in the collapsible box so it looks better in the list of references.

Egm6322.s09 15:44, 28 January 2009 (UTC)

Second Order Linear PDEs
Second order linear PDEs can be expressed in matrix form. If $$\kappa$$ is a two by two matrix, and $$u $$ is a vector of differentials, then the operator $$\mathcal{D} \left ( u\right)= \kappa u $$ is linear if $$ \kappa=\kappa \left ( x_1, x_2 \right ) $$ where $${x}_{1}$$ and $${x}_{2}$$ are independent variables.

 Error: The diffusion operator is $$ \displaystyle \mathcal D (u) :=   {\rm div} \left( \boldsymbol{\kappa} \cdot {\rm grad} \, u \right) =  \frac{\partial}{\partial x_i} \left(     \kappa_{ij}      \frac{\partial u}{\partial x_j}   \right) $$, where $$\displaystyle \mathcal D (\cdot)$$ denotes the differential operator. You want to show that this diffusion operator is 2nd-order and linear.

Egm6322.s09 12:44, 30 January 2009 (UTC)

Proof a Tensor Operator is a Linear Second Order PDE

--Egm6322.s09.lapetina 17:42, 24 April 2009 (UTC)

Let $$ u= \nabla w $$, the gradient of w and $$ v= \nabla z $$, the gradient of z.

$$\mathcal{D} \left ( u\right)= \kappa u $$

$$\mathcal{D} \left ( u\right) =$$ $$ \begin{bmatrix} u_1 c_1 f_1(x_1,x_2)+ u_2 c_2 f_2(x_1,x_2) \\ u_1 c_3 f_3(x_1,x_2)+ u_2 c_4 f_4(x_1,x_2) \end{bmatrix} $$

where $${c}_{i} $$ are constants and $${f}_{i}$$ are functions of independent variables $$x_1$$ and $$x_2$$.

Linearity is checked using its definition

$$\mathcal{D} \left ( \alpha u +\beta v \right) = \alpha \mathcal{D} \left ( u\right )+ \beta \mathcal {D} \left ( v \right ) $$

$$\mathcal{D} \left ( \alpha u +\beta v \right)= \mathcal{D}

\begin{bmatrix} \alpha u_1+\beta v_1\\ \alpha u_2+\beta v_2 \end{bmatrix}

$$

Let $$\alpha u_1+\beta v_1 =\theta$$ and $$\alpha u_2+\beta v_2 =\phi$$

$$\mathcal{D} \left ( \alpha u +\beta v \right) =

\begin{bmatrix} \theta c_1 f_1(x_1,x_2) + \phi c_2 f_2(x_1,x_2) \\ \theta c_3 f_3(x_1,x_2) + \phi c_4 f_4(x_1,x_2) \end{bmatrix} $$

while

$$ \alpha \mathcal{D} \left ( u\right )+ \beta \mathcal {D} \left ( v \right ) =

\begin{bmatrix} \alpha u_1 c_1 f_1(x_1,x_2)+ \alpha u_2 c_2 f_2(x_1,x_2) \\ \alpha u_1 c_3 f_3(x_1,x_2)+ \alpha u_2 c_4 f_4(x_1,x_2) \end{bmatrix} + \begin{bmatrix} \beta v_1 c_1 f_1(x_1,x_2)+ \beta v_2 c_2 f_2(x_1,x_2) \\ \beta v_1 c_3 f_3(x_1,x_2)+ \beta v_2 c_4 f_4(x_1,x_2) \end{bmatrix}

$$

$$ =

\begin{bmatrix} (\alpha u_1 + \beta v_1 ) c_1 f_1(x_1,x_2)+ (\alpha u_2 + \beta v_2 )c_2 f_2(x_1,x_2) \\ (\alpha u_1 + \beta v_1 ) c_3 f_3(x_1,x_2)+ (\alpha u_2 + \beta v_2 )c_4 f_4(x_1,x_2) \end{bmatrix}

$$

$$ =

\begin{bmatrix} \theta c_1 f_1(x_1,x_2)+ \phi c_2 f_2(x_1,x_2) \\ \theta c_3 f_3(x_1,x_2)+ \phi c_4 f_4(x_1,x_2) \end{bmatrix}

$$

Therefore, tensors of the type

$$ \kappa \left ( x_1, x_2 \right ) $$ where $${x}_{1}$$ and $${x}_{2}$$ are independent variables are linear operators. In this case it is a second order operator.

Infinite examples of second order linear PDEs can come from defining the functions and constants of a the two dimensional tensor $$ \kappa \left ( x_1, x_2 \right ) $$.

 Error: Not correct, confusing notation. See my comment on the error above.

Egm6322.s09 12:44, 30 January 2009 (UTC)

Quasi-Linear PDEs
These were covered in Meeting 7, and will be part of HW2.

Non-Linear PDEs
--EGM6322.S09.TIAN 17:53, 24 April 2009 (UTC)

An example of a non-linear PDE is:

$$ F \left ( \left \{ {x}_{i} \right \}, \left \{ \frac{\partial u}{\partial x_i} \right \}, \left \{ \frac{\partial^2 u}{\partial x_i \partial x_j} \right \}, ... \right ) =0$$

where there are $$n $$ independent variables $$  \left \{ {x}_{i} \right \}=   \left \{ {x}_{1},...,{x}_{n}   \right \} $$ ,

and one unknown function $$ u $$.

$$ \left \{ {x}_{i} \right \}$$ contains $$ n $$ arguments,

$$ \left \{ \frac{\partial u}{\partial x_i} \right \}$$ are the components of the $$ \nabla u$$, and

$$ \left \{ \frac{\partial^2 u}{\partial x_i \partial x_j} \right \}$$ are the components of the Hessian of $$ u $$.

Examples of first order non-linear PDE is:

$$u_x u_y u_t =7 $$

and

$$4x + 6y^3 + xy{u}_{x}=10 $$

Other non-linear PDEs are discussed in the Order Section.

The Hessian
--Egm6322.s09.lapetina 01:52, 17 April 2009 (UTC)

The Hessian Matrix is a symmetric $$ n \times n $$ matrix, thus H = HT

and $${H}_{n \times n}$$ := $$ {\left [ {H}_{ij}\right ]}_{n \times n}$$.

The Hessian is defined as:

$$ {H}_{ij} := \left \{ \frac{\partial^2 u}{\partial x_i \partial x_j} \right \}$$.

 For matrices, use square brackets, instead of curly brackets; also use a boldface symbol for a matrix quatity, i.e.,

$$ \mathbf H = \left[ {H}_{ij} \right]_{n \times n} = \left[ \frac{\partial^2 u}{\partial x_i \partial x_j} \right]_{n \times n}$$.

Egm6322.s09 15:44, 28 January 2009 (UTC)

This has many interesting properties, and is often used in optimization problems,.

 I added the section References at the end of the report, and the command to render the references.

Rewrite these references so they look better in the list of references.

Egm6322.s09 15:44, 28 January 2009 (UTC)

The Hessian contains $$ \frac{n^2+n}{2} $$ independent terms. The upper diagonal, minus the main diagonal, contains $$ \frac{n^2-n}{2} $$, while the main diagonal contains $$ n$$ terms, and

$$ \frac{n^2-n}{2} + n= \frac{n^2+n}{2}$$.

=List of Contributing Members=

--Egm6322.s09.lapetina 22:17, 26 January 2009 (UTC) Andrew Lapetina

--EGM6322S09TIAN 22:22, 26 January 2009 (UTC)Miao Tian

--EGM6322S09TIAN 22:22, 26 January 2009 (UTC)Sydni Credle, signed by Miao and Andy in her absence.

--Egm6322.s09.xyz 22:00, 8 February 2009 (UTC)

Contributions
Collaboration on this page was more substantial than indicated on the history page. Contributions were as follows:

Preface-S

Introduction- A--- and M---, with M--- doing the box on mapping and S doing the box on Mr. Kronecker.

Order- S did the proof box and the example box, and M--- did the second order examples. M--- also did the expansion box.

Linearity-A--- did the steps for checking linearity and the alternative definition box, as well as the proof of a tensor operator as a linear PDE. A--- also did the section on non-linear PDEs and the Hessian.

= References =

 Redo the references so they look better. For example, Ref.[2] should read as follows:

Kolmogorov & Fomin, Introductory Real Analysis, Dover, 1975. p.124

Egm6322.s09 17:24, 28 January 2009 (UTC)

title: User:Egm6322.s09.mafia/HW1


text:
User:Egm6322.s09.Three.ge/Report1

Test =General nonlinear PDEs=

Variables
If $$  \left \{ {x}_{i} \right \}=   \left \{ {x}_{1},...,{x}_{n}   \right \} $$,

then $$\left \{ {x}_{i} \right \}$$has n independent variables.

Example 1: 1-D Case With Time Variable (i.e. 1-D time dependent problem)

If $$(x, t)=({x}_{1},{x}_{2})$$,then

 * $${x}_{1}=x$$
 * $$ {x}_{2}=t$$

$${x}_{1}$$ is the spatial variable; $${x}_{2}$$ is the temporal variable.

Example 2: 3-D Time Dependent Problems

$$ (x,y,z,t)=({x}_{1},{x}_{2},{x}_{3},{x}_{4})$$

 * $$ x=x_{1}$$
 * $$ y=x_{2}$$
 * $$ z=x_{3}$$
 * $$ t=x_{4}$$

Components of PDE
The unknown functions are expressed as $${u}_{1}$$,$${u}_{2}$$,...

e.g.

Navier-Stokes Equation in 3D is a typical PDE where (u1,u2,u3) represents the velocity field along (x,y,z) coordinates and (x1,x2,x3,x4) represent the independent variables (x,y,z,t).

$${u}_{i}(\left \{ {x}_{j} \right \});$$ $$i=1,2,3$$ $$j=1,2,3,4$$

In this case, the PDE has one unknown function u ;

n independent variable $$\left \{ {x}_{i} \right \}$$, i=1,2,...,n;

m th partial derivative: $$\frac{\partial^m u}{\partial x_{i_1}\,...,\partial x_{i_m}}$$

i1,...,im=1,...,n

=Order= The order of a PDE is given by the order of the highest derivative. For example,

$$ 5u_{x}-7u_{y}=0$$

is a first order PDE because highest derivatives are the first derivatives of u with respect to x and y.

$$u_{x}=\frac{\partial u} {\partial x}; u_{y}=\frac{\partial u} {\partial y}$$

By that definition, the following PDE's

$$ 6\left( u_{x}\right)^{3}+2\left(u_{y}\right)^2+u^\frac{1}{2}+x^2+\sin xy=0 $$

$$ 6\left( u_{x}\right)^{3}+2\left(u_{y}\right)^2+u^\frac{1}{2}=0 $$

are also first order.

The operator D(u) is given by D(u)=... and D(.)=

A PDE can also be of higher order. For instance, the equation $$div\left(grad \cdot u \right)$$ given in cartesian form as $$u_{xx}+u_{yy}=0$$ is clearly of second order.

More generally, the form of a second order PDE is $$ div\left(\kappa\cdot grad\right)+ f\left(x,y\right)=0 $$ where $$\kappa$$ is a second order tensor

The values of $$\kappa$$ may be put into a matrix.

$$\kappa_{ij}=\begin{bmatrix} \kappa_{11} &\kappa_{22} \\ \kappa_{21} & \kappa_{22} \end{bmatrix} $$

It is important to note that while the values of $$\kappa$$ may be a matrix, this does not mean that $$\kappa$$ is the matrix. In a different coordinate system the values in the matrix would be different, but they would still represent the same second order tensor $$\kappa$$.

If $$\kappa$$ is constant, the equation is a linear 2nd order PDE.

If $$\kappa=\kappa(x,y)$$, the equation is a linear 2nd order PDE.

If $$\kappa=\kappa(x,y,u)$$, the equation is a quasi-linear 2nd order PDE.

=Linearity= A simple definition of linearity of a PDE is if it's variables and partial derivatives are of first degree. (Selvadurai 2000,p.74) A more thorough definition is that a linear PDE is both additive and homogeneous.(Kolmogorov & Fomin, p.123).

Definition
 u  is an unknown function; and  L  is an operator.

 L(u)  is linear with respect to  u  if

$$L(\alpha\,\!u+\beta\,\!u)=\alpha\,\!L(u)+\beta\,\!L(v)$$

$$F((x,y),u,({u}_{x},{u}_{y}),({u}_{xx}{u}_{xy}{u}_{yy}))=0$$

$$2{u}_{xx}+3{u}_{yy}=ax^2+bx$$

$${u}_{xx}+{u}_{yy}=0$$

If  L  is a operator, and $$L(u)=2{u}_{xx}+3{u}_{yy}-7x^2-x$$

$$ L(\alpha u+ \beta v)= \alpha \left (2 {u}_{xx}+3{u}_{yy} \right ) +\beta \left ( 2 {v}_{xx} +3 {v}_{yy} \right ) +f(x) $$.

$$ \alpha L(u)+ \beta L(v)= \alpha \left [2 {u}_{xx} +3 {u}_{yy} +f(x) \right ] +\beta \left [2 {v}_{xx}+3 {v}_{yy} + f(x) \right ] $$

$$ L(\alpha u+ \beta v) \ne \alpha L(u) +\beta L(v) $$

and then, the operator  L  is nonlinear.

Nonlinear PDEs
$$F( \left \{ {x}_{i} \right \}, \left \{ \frac{\partial u}{\partial x_i} \right \},\frac{\partial^2 u}{\partial x_i\,\partial x_j},...)=0$$, i=1,2,...,n

This general form of PDE has n independent variables: $$\left \{ {x}_{i} \right \}$$ and 1 unknown function u.

$$\left \{ {x}_{i} \right \}$$ has n arguments

$$\left \{ \frac{\partial u}{\partial x_i} \right \}$$ is computation of gradient of u, and has n arguments

$$\frac{\partial^2 u}{\partial x_i\,\partial x_j}$$ is the Hessian derivative, and has $$\frac{n(n+1)}{2}$$ arguments

$${H}_{ij}$$ is the Hessian Matrix, and $${H}_{ij}:=\frac{\partial^2 u}{\partial x_i\,\partial x_j}$$, (":=" means "equal by definition")

$$H^T=H$$

The PDE F[(x,y),u,(ux,uy),(uxx,uxy,uyy)]=0 has 2 independent variables (x,y), and 1 unknown function u.

e.g. $$2{u}_{xx}+3{u}_{yy}=ax^2+bx$$

Laplace Equation: $${u}_{xx}+{u}_{yy}=0$$

$$5({u}_{xx})^2+7({u}_{yy})^2=0$$ is a nonlinear PDE since the second derivatives uxx and uyy are squared.

title: User:Egm6322.s09.Three.ge/Report1


text:
User talk:Egm6322.s09.Three.ge/Report1

I'm trying to figure out how this discussion page works so that we don't clog up our e-mail. I think you sign your comments with 4 tildes (~). Egm6322.s09.Three.ge 21:24, 25 January 2009 (UTC)

Ok, I think I got it. Just click on edit this page to type what you want to say and remember to sign with the 4 ~'s. Egm6322.s09.Three.ge 21:28, 25 January 2009 (UTC)

title: User talk:Egm6322.s09.Three.ge/Report1


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User:Archolman

Hello!
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title: User:Archolman


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User:Vader's Middle Finger

Hey everyone,

I'm a Duke University Class of 2012 Mathematics and Physics double major. I firmly believe that books are meant to be read and knowledge is meant to be shared. Its a light that we have to keep alive- because historically it has been knowledge that has freed man from the horrors of bigotry and hatred.

Wikiversity is a great idea, but the sections I visit (math mainly) seem to be pretty empty. That's really frustrating for me. I know enough to understand and be curious, but not enough to contribute.

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User talk:Vader's Middle Finger

Hi there, and Welcome to Wikiversity.

First, let me say that you should BE BOLD and don't worry about knowing everything. Put in what you know something about, and let others fill in more. Second, if you need some help with getting the word out, either leave me a note or leave a message at the Colloquium (see link at left) -- and we'll get you what you need. Welcome aboard! Historybuff 07:23, 26 January 2009 (UTC)

title: User talk:Vader's Middle Finger


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Artificial Consciousness/Psychology

 Psychology   And How it Relates to Consciousness

Since William James wrote the seminal book on Psychology in the 1800's Consciousness has been considered part of what psychology should explain. However, over the history of psychology the main stream of science has seldom welcomed consciousness studies. The Functionalists found it nearly impossible to define functions for consciousness in their earlier approaches, and later the behaviorists concentrated on behavior and ignored consciousness. This was partly because there was a serious attempt to make psychology a hard science like physics. One notable theory of Brain Function is the Production System Theory on which computer architectures were based. This theory was that the brain was essentially a data processing unit and must therefore follow certain rules of data processing including holdovers from the Age of Reason, like logic. Later Researchers decided that the computer model did not suit. So the Cognitivist school saw consciousness as an emergent property of cognitive functions of the brain, and this view of Consciousness has persevered to this day.

Of interest recently is the shift to the Neuropsychologist school where attempts are being made to find neural correlates for the cognitive functions

--Graeme E. Smith 02:33, 27 January 2009 (UTC)

title: Artificial Consciousness/Psychology


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Artificial Consciousness/Neuroscience

 Neuroscience

Neuroscience is the catchall phrase for the various neural sciences. A Neural Science is a science that studies The Nervous System. There are a lot of Neuro-Sciences, including Neuropsychology, Neurobiology,Neurochemistry, Molecular Neuroscience, CellularNeuroscience, etc. The Neuro Sciences are all fairly young in the terms of science, if only because the Nerve was only discovered in the 1900's. What has made this field interesting in the last 20 years is the growth of technology capable of looking into the nature of the neuron, and how it connects together to form larger units like the brain.

When evaluating theories in Neuroscience we must accept that much of what we know will change over time, and that the nature of the images we get about the brain are not yet good enough to capture the whole operation of the brain at the neural level.

Phenomenal Consciousness, and especially the work of Dr. Edelman are partly supported by the Neuro Sciences Institute (NSI) which was started by Dr. Edelman as a technolgical monastery to support research into Neuroscience. As a result, the Phenomenal Consciousness School is closer to Neuroscientific thought.

For a more detailed overview, see the Fundamentals of Neuroscience course.

title: Artificial Consciousness/Neuroscience


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Artificial Consciousness/Neural Correlates

 Neural Correlates

There is a move in Neuropsychology to associate cognitive functions with mechanisms in the neurons of the brain. These neural mechanisms are called Neural Correlates because they represent locations where Neuroscience and Psychology can be correlated. In other words a definition in psychology can be associated with a neural mechanism. Ideally we want to build up theories that can be checked and correlated with other theories, Physics is the ultimate expression of this, where the theory of the atom, correlates with the theory of the elements in the periodic table, which correlate with the components of molecules, which make up everything physical.

Much of Cognitive Psychology still does not have Neural Correlates, so we are not sure that there is always a connection between what psychology says the brain does, and what the neurons in the brain actually do. However over time we have built up models of neural systems that we think have some relationship to neural function. These models explain how the neural mechanisms can achieve the psychological functions, when there is reason to question the assumptions about the nature of the psychological functions. Sometimes we find models that result in a paradigm shift, and our whole set of concepts about psychology are skewed as a result.

The following Models are transitory expressions of the current thought on how the brain works according to the current understanding. As we do more science these models might shift and new principles might emerge that change the way we look at neural correlates.

 * Synaptic Models
 * Neural Models
 * Neural Network Models
 * Neural Groups
 * Neural Maps
 * Brain Organ Models
 * Inter-Organ Connection Models
 * Functional Models
 * Hybrid Models


text: File:Assessment of academic proficiency, motivation and goals.png


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User:Farrin~enwikiversity

This is the main page for Farrin on wiki.

title: User:Farrin~enwikiversity


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Template:TemplateName

fair use

title: Template:TemplateName


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User talk:Graulys

wollen Sie Viagra billig bestellen? Dann testen Sie doch diesen Onlineshop mal aus, da gibt es preiswert und billig Viagra!

title: User talk:Graulys


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User talk:Farrin~enwikiversity

 Hello Farrin, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 15:17, 26 January 2009 (UTC)

 Hello , we are the Baah and Bahh twins and we'd both like to welcome you to Wikiversity. While you sit back and explore Wikiversity, enjoy some of our fresh goat milk. You can help us learn by creating new learning resources or help us by improving the guided tours and other exploration tools. We look forward to seeing you around. Baaaahbye for now.

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 Farrin. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Farrin~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 23:36, 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:Farrin~enwikiversity


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User talk:Jackie

 Hello Jackie, 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; 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.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. Jtneill - Talk - c 09:08, 17 July 2010 (UTC)

Account rename
As per your request, Jackie-ru-ru-new has been renamed to Jackie. Sincerely, James. -- Jtneill - Talk - c 09:09, 17 July 2010 (UTC)

title: User talk:Jackie


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User:Egm6322.s09/Lecture plan/Additional references

$$\displaystyle \clubsuit$$ Garabedian, P.R., Partial Differential Equations, Wiley, 1964. Google books: 1964 edition 1998 edition Amazon.com UF library QA377 .G26; one copy in the library (which I borrowed as of 4 Feb 09), one in storage.

$$\displaystyle \clubsuit$$ Chester, C.R., Techniques in Partial Differential Equations, McGraw-Hill, 1971. Google books Amazon.com UF does not have this book; I borrowed it through interlibrary loan; returned.

$$\displaystyle \clubsuit$$ Farlow, S.J., Partial Differential Equations for Scientists and Engineers, Wiley, 1982. Dover, 1993. Google books Amazon.com. UF does not have this book; I borrowed it through interlibrary loan; returned.


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User talk:Josevaldillez

Hi, man!
 * 161.38.223.221 16:42, 26 January 2009 (UTC)

title: User talk:Josevaldillez


text: Category:User hr-N

title: Category:User hr-N


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User:Odonnell

=Michael J. O'Donnell=

 * Professor in Computer Science and the Physical Sciences Collegiate Division, The University of Chicago
 * More information from my U Chicago Web stuff
 * My course Wikis at U Chicago
 * My course Wikis at U Chicago

title: User:Odonnell


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Portal:Microsoft/Selected picture

The .NET technology provides a new approach to the software development.

This has required Internet software developers to understand a host of technologies and integration issues. .NET is designed and intended for highly distributed software, making Internet functionality and interoperability easier and more transparent to include in systems than ever before.

title: Portal:Microsoft/Selected picture


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User:Coolpolitealex

HI" anybody ,as this is my very first time here i just want to say i think all-Wiki-ideas are great and if possible i would like to contribute ,but as my education is very limited i feel as yet i am not really qualified to say much . Wht i will say it'sthe 25th jan and i am very much looking to use this with interest as i love gaining knowledge of one sort or another,and if i can i will add a fact (just one that i know ).

WELL MY FACT IS -THAT TO-DAY FOR THE FIRST TIME EVER THE BBC AND SKY NETWORK AGREED TO NOT USE THEIR AIRTIME TO ADVERTISE FOR HUMANITARIAN HELP for GAZA and it's people. This fact is unbelievable, and rather than prove it's independent stance, I say on the contrary" it show's that the ISRAELI lot got at them, all other news outlet's broadcast the appeal on their airway's for the people in Gaza. All it proved was that the Director General of the BBC is a football and he stick's to his gun's even when he is rather stupidly put in his place by the brouhaha that he brought down on himself

title: User:Coolpolitealex


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User:DesireeMBrinson

=Bio=

My name is Desiree Brinson. I am currently a freshman at the Art Institute of Seattle majoring in Graphic Design. I hope one day to be a creative/art director providing my services to multiple industries. Soon after, I would love to own my own company envolving everything that pertains to design (i.e., interior, architectural, graphic and web).

=Assignments=

midterm
I have never visited the Sculpture Park; just driven by. As I walked up I had really no idea what to expect and when I got there that was only confirmed... It is a beautiful park with some very interesting pieces in it, but as I was walking down the walkway I was stopped by a piece by Mark Di Suvero entitled “Bunyon’s Chess.” To me it looked like three logs that wash up from the ocean sustained by chains and wire – what? I really had no idea what I was looking at. I didn’t understand where this piece of art was supposed to take me, much like all of the other pieces I saw in the park that day. I took some pictures and tried to take myself to a different place, trying to figure out exactly what he was thinking when he created this.

I spent a few days going back to look at the piece and read the quote from the artist, “unity and joy, that’s why I like to suspend elements from the beams of my works, so they can interact with the wind and other forces.” After I finished I began to take it in again and saw something completely different than what I’d seen before; I started to see how it was very kinetic; not able to stay stagnant – moving with life’s forces. When I read this it prompted me to think about life in general. Nothing in life stays the same, we are constantly changing as human beings; even from childhood to adulthood. This was very helpful in my decision about the piece, I think for the first time I understand how art is not so black and white and we don’t need to see the color to know that it exists. To me this piece describes life and its ever-changing movement. Even though this piece moves because of wind, wind is also a life force that we can’t control… We can always try to plan and move forward, but can we really guarantee this to be our end? Things happen, people change and grow, much like the wind.

final
I have chosen to move out of my parents house into an apartment downtown. I have no job, so that needs to be accomplished as well as establishing a budget. I will track the progress of my otaining a job that can pay for me to live on my own, purchase the appliances I need, search for an apartment and finally be able to walk to school!

=Reflective=

title: User:DesireeMBrinson


text: File:Trail sign.png

title: File:Trail sign.png


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User:Danielhernandez

bio
Hispanic Male Age 21 Height: 5-10 Hair: Brown Eyes: Brown Birth date: 8/16/87 Driving Impairments: N/A

assignments
"Ive always wanted to" Well technically I've always wanted to go skydiving but I think it might prove to be much more of a challenge considering expenses and past efforts mentioned in class failing due to poor weather. Bungee jumping will then have to suffice my need of wanting to jump to my death (knock on wood). Don't get me wrong I also want to bungee jump but for some off reason I'd prefer the former. Of course both have their similarities as I just mentioned, chance of jumping to ones death (knock on wood) and the chance piss myself silly for the first time since I was 2.

midterm
Maybe getting to class an hour early only to find out that the door was locked was a blessing. A blessing? Unlikely. With an hour to spare, I walked a lap around the North Campus and to my demise only managed to shed about two minutes off the clock. Then I remembered about the Olympic Sculpture Park, where Steven, had told us his friend was stopped by what might of seemed like the “thought police.” I walked a few blocks North and right out of the woodwork the first sculpture I saw was “Typewriter Eraser” by Claes Oldenburg. I am not trying to say my choice was any more pure or unbiased than anyone else’s because I got an early start but it definitely helped make this feel like less of an assignment.

Now I do not really understand modern art at all or art in general. That sounded bad, what I mean is the meaning behind it all. I kind of have an understanding about art during the French revolution. I am sure to be wrong in some aspects but from what I get all art was biblical, having to do with or about anything religious. Along comes a man that paints a bowl of fruit and all of a sudden its mind blowing. That is probably oversimplified, but wait! It took me quite some years but I was able to appreciate that. I was able to understand the break in conformity, which in turn led my mind to be blown as well but that is not to say that I understand the piece itself. It need not take me a cheesy haircut, black turtleneck and glass of wine while uttering “Oh, yes… the humanity” to understand it. But sometimes it does, unluckily for me I just do not seem to follow.

The aesthetic pleasure usually followed by “what the hell were they thinking” seems to be the process in my case. Again that is not to say I mean it in a bad way at all but in this case I did. “Typewriter Eraser” although did strike the wrong chord. Most of the larger sculptures seemed to follow a certain idea from what my eye saw and contrasted some of the smaller ones. “Eagle” and “Wake” which turned out to be my favorite were large and flowing contrasted to some of the smaller ones that were painted all black with angles and identifiable shapes. Then there was the pizza cutter with dreads, which almost seemed to be careening down the hill into the traffic below, upon noticing that I chuckled a bit.

As it turns out Mr. Oldenburg’s other works seem to draw my interest. His wife Coosje Van Bruggen is actually his partner as well. She has helped him create such works as “Soft Bathtub” which is a bathtub made of cloth. Mrs. Van Bruggen normally does the sewing on the soft sculptures. Other soft sculptures include “Soft Toilet, Soft Typewriter, Soft Drums” and various other “Soft” foods. It seems Claes Oldenburg likes to take any everyday object and make a huge version of it. I wondered why then it was that I could not find “Typewriter Eraser” appealing? I realized then that it was just a lot easier to hate something than it was to like it because it is new. That is not to say that now I have come to enjoy “Typewriter Eraser”. I am very sure that there are plenty more people out there like me that just do not get it.

I this case of “bigger is better” the saying seems to be true. The same reason I came to like “Wake”; its enormous size yet smooth flowing curves of steel led me to understand and appreciate the works of Mr. Oldenburg. My science teacher told me a long time ago that humans don’t seem to understand large proportions and numbers until they grow older. Lucky for me it seems I have reached an age where I’m able to understand how mind boggling and how hard it is to create a work of are such as Claes Oldenburg’s. Who the hell makes a giant ice cream cone and sticks on the roof a building in downtown or a giant lipstick on tank tracks? Claes Oldenburg does.

title: User:Danielhernandez


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Talk:Evolutionary Synthesis

Non Genetic Darwinism
Although everything you say in this article is true, and correct, a new branch of Evolution-like effects has been noted, resulting often in self-organization in non-genetic instances. An example is Dr. Edelman's Nobel Prize for determining that the human immune system seems to operate in a way that has little to do with genetics, and evolves at a much faster rate.

More Recently he has been working on a theory of Neural Group Selection in Neurons, that takes self-organization in neural groups to the point of developing self-organizing maps. You might be interested in the many books he has written on the subject.--Graeme E. Smith 23:43, 26 January 2009 (UTC)

 * Thanks and very interesting. I just started this article and I've got plenty of things to add.  I'm interested in not only what the evolutionary synthesis of the mid-twentieth century was, but what its incarnation might be in modern times.  Would you like to join me in this project?  --AFriedman 15:33, 27 January 2009 (UTC)

The Entropy Perspective
I'd be glad to help, this next item might not be exactly mainstream science but I hope it helps you understand where I am coming from

As you may know, recently there has been an attempt to rediscover the second law of thermodynamics, because we now know that the old version of the law is not applicable because it assumes equilibrium which is a much rarer state than originally thought. Since the second law is the basis of the Entropic principle this must mean that we also take a second look at entropy, which opens it up for discussion.

Chemists have long known that it was entropy within the chemical solution that determined whether or not a chemical combination would react. This suggests that instead of just breaking down systems as they become more entropic, entropy is also involved in self-organization at the molecular level.

What does all this have to do with Evolution you ask? Simply put, I see evolution as the natural result of energy/entropy balance. If so, the viewpoint of evolution as a purely genetic process, ignores the fact that there might be millions of different evolution like systems that make up the universe as a whole.

Have you ever heard of the Evolution Algorythm? it is a simple three part algorythm requiring:
 * A general gradient
 * Something to perturb that gradient
 * A test that determines that a portion of the population will be pruned

Of course this only works if you are in population thinking mode, and thus assume that there is a population generally drifting according to the gradient. What happens is that individuals are lifted out of the gradient temporarily, and then the whole population tested, As a result of the test, a portion of the population mostly those too far down the gradient, will be pruned, making the rest of the population move in a direction away from the test, and therefore counter to the gradient.

The result is Evolution, a change in the nature of the population that seems to climb the gradient instead of drifting in its direction.

Whether you believe me or not, This means that we can build an evolutionary algorythm out of The interface between Entropy and Energy, Entropy is the natural gradient, energy perturbs that gradient, and survival of energy pockets becomes the test, that determines how nature is formed. Everything in the Universe could be seen to be made up of energy stranded in pockets away from the general cooling effect of Entropy. All we need is something that captures some of the energy and keeps it from falling back down the gradient. My personal belief is that the factor that captures the energy is the dimensional complexity of space.

--Graeme E. Smith 19:06, 27 January 2009 (UTC)

 * Interesting. I don't know what is happening in thermodynamics (or in physics), and I have not heard of the evolution algorithm.  Where did you find out about these things?  Evolutionary biologists really are interested in the thermodynamical aspect of living systems, including at the macroevolutionary time scale.  There are two professors at Duke University who just wrote a book (not yet published) about the possibility that biological complexity might show a trend toward increasing in the absence of natural selection, developmental constraints or other forces.  This has been interpreted by others as a possible ramification of the second law of thermodynamics.  Their webpages are here and here, although they don't seem to mention this work on their sites.  In general, any measurements of evolutionary trends are extremely difficult, particularly if you're trying to tease out the causes of the trends.  By the way, feel free to contribute to the main page about this and not just the talk page.  I'd especially appreciate some good references on the subject.  --AFriedman 16:45, 28 January 2009 (UTC)

The Evolution Algorythm
The Evolution Algorythm is one of a number of algorythms called Heuristic Algorythms or heuristics for short. I first read about it in some EEE literature, in the 1990's along with a similar algorythm called simulated annealing. Sorry I am not sure which EEE journal it was in. I believe they were using the algorythm at the time for placing circuits on silicon chips, essentially it was used as a MetaHeuristic to search for the best placement of the circuits, and reduced the time for doing the search, while arriving at a near optimum placement. I have heard of it used, in Genetic Programming, and in Metaheuristics associated with searches in other disciplines since then.

Thermodynamics
There was an article on thermodynamics in one of the science magazines I read when I can afford them. I think it was either Scientific American, or Discover magazine in the last four months. Sorry I can't be more helpful, I really don't do attribution well.

Another topic you might want to look into is complexity theory, this seems to be built on the precepts of A New Kind of Science sorry I can't remember the authors name, but there is a website I tripped over about it. Essentially what the author found was that class 4 cellular automata tend to oscillate between order and chaotic states when driven by an incremental input. This suggests that the big bang should be replaced with an oscillation which is the background behind the "Big Bounce" theory also suggested in one of the magazines I mentioned. What this has to do with Evolution, is that the natural energy/entropy balance probably oscillates due to the natural incremantal nature of the Universe causing changes in the speed of evolution over long periods of time. The difference in speed of evolution would probably be due to the change in the gradient of Entropy on one side, or a change to available energy levels on the other.

An interesting aspect of this characterization of the Energy/Entropy balance, is that we get almost the same effect in a decremental system, since it too would result in an oscillation between order and chaos in a class 4 cellular automata. It is probably because of experiments like these that physicists are rethinking thermodynamics.

My problem is how to present this information, previous to it being accepted as scientific fact. I could be wrong about parts of it, and don't want to come off as being religious about it. Perhaps we should present it as a possible tenative future synthesis?
 * Thanks. I've read some of the literature on complexity theory, and to me, one problem is that complexity doesn't seem like a single unified concept.  I would also guess that evolution is so localized, stochastic and context dependant, there are many other factors that influence the rate of evolution besides the energy level in the universe.  But I don't understand what your thesis is.  Re: presenting your argument, my advice to you is to try to gain access to the library of a major university (e.g. by contacting the librarian, or even enrolling in a course), look at the professional publications in the database and write a thoroughly referenced essay with a clearly defined thesis.  Have you seen the page on WV about Freelance academics?  --AFriedman 03:20, 29 January 2009 (UTC)

Uh, thanks for the reference, I am indeed a freelance scientist, although whether or not you can call me an academic, is well, academic.... Franky I hesitate to take the time to publish on evolution, when my studies right now are in Artificial Consciousness. My work with evolution is all part of a hobby I used to have called Unit Field Theory. I joke whenever I am asked about my religion that I am a Unit Field Fanatic, because I have an irrational belief that the Universe is made up of Unit Fields. Of course, all this quantum gravity stuff hides the real nature of the universe behind words like Quantum and Gravity, but I know, that really what they are describing is a Unit Field. (sic)

Of course you wouldn't find a thesis in this talk, I am only trying to widen your perspective on evolution. There are just a group of smaller topics that are linked in my mind somehow. Maybe someday I will take the time to fit them together and figure out how they work together. The main problem is that if you want me to help you synthesize a more comprehensive evolution article, we need to figure out how to get past the requirement that articles on WikiVersity not be original research or this stuff doesn't fly.

--Graeme E. Smith 06:12, 29 January 2009 (UTC)

 * In the article about What is Wikiversity?, there's a section about how we're encouraged to use Wikiversity as a space for original research. In the Department of Life Sciences there are some very active research projects, such as the Bloom Clock Project and the Phage Project.  Banning original research seems to be a policy restricted to Wikipedia, that does not apply to Wikiversity.  Just to let you know.  --AFriedman 14:11, 29 January 2009 (UTC)

Color me confused... I thought the whole idea of the research areas was to segregate "original research" from normal research... Or is this in a research area? I mean it seems to have a normal header...The way I read it, you can do original research, just not on the Topic pages --Graeme E. Smith 18:38, 29 January 2009 (UTC)
 * My advice would be to place original research on pages that are clearly described as research projects and put such pages into a category such as Category:Research projects. --JWSchmidt 19:06, 29 January 2009 (UTC)

 * This isn't quite research per se, as I see it (although it isn't only mine)...I envision it as becoming a review type resource with what ultimately becomes an original angle and thesis. Graeme, thanks for your edit.  Do you think you might want to write more?  --AFriedman 19:14, 29 January 2009 (UTC)

I just created the "Future Evolutionary Synthesis sub-page I will populate it with links and add a few references to flesh it out later, take a look and tell me what you think.

--Graeme E. Smith 19:34, 29 January 2009 (UTC)

 * See the discussion for that page. --AFriedman 18:04, 30 January 2009 (UTC)

title: Talk:Evolutionary Synthesis


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Artificial Consciousness/Artificial Intelligence

 Artificial Intelligence   And How it Relates to Consciousness

Artificial Intelligence (AI) is the study of how to make an Intelligent Machine. Originally Artificial Consciousness was an offshoot of AI, but the studies diverged when it became obvious that Consciousness was something different from Intelligence although both were associated in the Human mind. Essentially what was discovered was that intelligence is necessary but not sufficient to explain consciousness.

Up until this principle was discovered it was thought that consciousness might be an emergent property of intelligence and if we developed a device that was intelligent enough it would also be conscious. For me the dividing line was written in Consciousness Explained by Daniel C. Dennett a book that apologized for even thinking of Consciousness as a separate topic. After reading that, I could no longer think of myself as an artificial intelligence researcher.

Students will probably find the work that is the closest to Artificial Consciousness is the relatively current work done on Agents, and Multiagent systems. One current Functional theory of consciousness is the Global Workspace theory which depends on a T.V. station like central network, and multiple agents competing for the right to work. Since the Functional School is partially supported by MIT's A.I. laboratories, The functional school of consciousness is also the one most closely related to A.I.

--Graeme E. Smith 00:42, 29 January 2009 (UTC)

See Also:

 * Artificial intelligence
 * Software Agent
 * Intelligent Agent
 * Multi-Agent System
 * Global Workspace Theory


text:
Artificial Consciousness/Computer Science

 Computing Science   And How it relates to Consciousness

Computer Science is the study of how to design Algorythms that facilitate the implementation of functions on a Computer System. Many computer programs simulate or emulate other systems. Computing Science is most important to Artificial Consciousness because of the lessons learned in designing synthetic languages for the computer.

One of the early thinkers in Computer Science was Alan Turing, who is best known for his Turing Test. His main contribution was the idea of tape based automata that could do "Truth preserving functions", and an early theory of Mind called the Computational Theory of Mind (CTM) It was based on this theory that he suggested the Turing Test which we can blame for the preponderance of Chatbots on the Internet.

It is partly because of Turings work, that up until recently it was assumed that any sufficiently intelligent machine would also be conscious. The reason for this is simple, Turing made no distinction in his test, between intelligence and consciousness. If we accept Turings test for Intelligence then we have to accept the precept that Intelligence is necessary and sufficient to explain consciousness. There would thereafter be no reason to study consciousness separately from intelligence.

An Early but obscure Theory of Psychology was the Production System Theory, on which all modern computer architectures are baaed. In this theory Short Term and Long Term memory serve a central processing Unit, and Short term memory consists of registers called clumps that reference Lists of Long Term Memory contents. Scientists in Psychology and Neuroscience have long held that this is a poor model for brain design, and that computers and brains do not work the same way. In short Production System Theory has been replaced with Cognitive Science, and there is no longer a direct link between the psychological theory of cognition and the architecture of the computer.

Despite the fact that scientists do not accept the computer as a model of the brain, they do tend to accept it as a research tool, and many simulations of parts of the nervous system are done every day, in an attempt to prove theories about how the nervous system might work. Once we understand the nature of consciousness we will, hopefully, be able to simulate or emulate it on a computer system, or we will be able to design a new system perhaps based on computer technology that works in a completely new way following the successful model. We will probably not however call the device a computer.

Topics of use to the Learner from Computer Science include:
 * Heuristic Algorythms
 * MetaHeuristic Techniques
 * Advanced Languages and their Design
 * Virtual Machines
 * Neural Simulation Techniques
 * Cognitive Architectures


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User talk:68.162.247.116

Thank you for experimenting with Wikiversity. Your test was recorded, and it has been reverted or removed. Please use the sandbox for further testing. You may wish to learn more about what Wikiversity is to help you contribute. Consider registering if you are keen on our project. --Juan de Vojníkov 01:18, 27 January 2009 (UTC)

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dear Moulton. I dont think so you are welcome here to disrupt the community. You are not assuming a good faight and not behaving well. Try not to continue this action and thing more about what you are doing.--Juan de Vojníkov 01:18, 27 January 2009 (UTC)

 * Think again, Juan. I am not here to disrupt.  I am here to educate and inform.  You are, of course, free to not learn.  But please don't interfere with those who wish to learn, in the tradition of Socrates.  —Moulton 01:54, 27 January 2009 (UTC)

I dont think so everybody likes your research activity here on Wikiversity "learning with emotions". So I repeat myself, "try not to offend people in here, disrupt community and go around your block here on wv using different IP adressess.--Juan de Vojníkov 07:34, 27 January 2009 (UTC)

 * Think again, Juan. Not only did half a dozen people (now driven off the site by the likes of Jimbo Wales and his mindlessly sycophantic cronies) have an interest in the research we were doing here, but thousands of people liked that very same research when I ported it over to Google Knol.  Of the 21 articles I have crafted on Google Knol, six of them have already been featured on the Google Knol Front Page. I don't know the precise algorithm for making it onto the Google Knol Front Page, but I imagine it's a combination of public interest in the subject, the quality of writing, and editorial judgment by the Google Knol staff. Authentic learning communities operate very differently from the profoundly dysfunctional way you are operating here. As you know, Jimbo failed to demonstrate just cause for his unwarranted, unscholarly, unprofessional and unethical intervention here, and his fascistic practices are null and void in the 21st Century.  —Moulton  11:41, 27 January 2009 (UTC)

title: User talk:68.162.247.116


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Artificial Consciousness/Natural Language

 Natural Language   And How it relates to Consciousness

It was partly the work of Noam Chomsky that broke the death-grip that behaviorists had on psychology. His work in discovering the nature of Natural Language, (Actual live languages) could not be explained adequately by the behaviorist model. As a result he opened the way for the later ascendence of the Cognitive model. It is partly because of his work, that Chatbots became practical and some chatbot designers claim their chatbots pass the Turing Test.

It is partly because of this claimed success that scientists have determined that language ability is neither necessary nor sufficient for either intelligence or Consciousness, since a Chat bot need not be either conscious nor intelligent to be able to pass the Turing Test, if the designers are correct. Most Chat bots take advantage of the willingness of humans to attribute intelligence to a discussion as long as it makes linguistic sense. Turing's test is therefore not especially interesting to science, and amounts to a license to trick rather than a serious test of either intelligence or consciousness.

In his book Wider than the Sky, The Phenomenal Gift of Consciousness Dr. Edelman suggests that we separate consciousness into two phases, the first phase called Primary Consciousness may be equivalent to the consciousness found in many mammals. The second phase called Higher Order Consciousness includes Natural Language capabilities and the ability to "Think". There is reason to believe that the natural language capabilities are merely extensions of capacities found in most mammals, we have taught a number of animals to understand a limited vocabulary and a limited grammar, but only humans understand the richness of human language. However, there is some discussion about this, since there is no known difference between human conscious mechanisms and mammalian consciousness mechanisms that can explain this difference in sophistication. (reference Dr. Bernard J. Baars' book on the subject.)

--Graeme E. Smith 02:46, 27 January 2009 (UTC)


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Artificial Consciousness/Linguistics

 Linguistics   And how it Impacts on Consciousness

Linguistics is the study of Language and how it is used. Although it is not considered necessary for primary consciousness to have the ability to implement language, the study of Linguistics has opened up a number of issues based on the development of language that are important enough to indicate a natural order to the development of language that implies a natural order to the processing within the brain.

In her book Beyond Modularity Annette Karmiloff-Smith, explored the nature of development as a force in the growth of so called innate knowledge as suggested by Jerry A. Fodor's Modularity of Mind. As a result of her work, scientists today routinely look for three types of knowledge when analyzing neural structures, Innate, or DNA defined knowledge, Knowledge developed as a result of Development, and Learned knowledge.

Another interesting element in Annette's book, was the mentioning of a theory called Representational Redescription (RR), Although Representation has been considered controversial up until now, recent work based on Neural Group Mapping in the individual has allowed scientists to prove that while the actual neuron in a Neural Group often changes over time, the activation of a Neural Group, can be consistently associated with a specific piece of data. Using this theory monkeys have consistently been able to activate robotic arms simply by thinking of moving their own arms. A special module that is trained on the individual monkeys nervous system, translates the unique representation of the movement into a command for the robotic arm to move in the same direction as the monkeys arm moved. This strongly suggests that representation at the Neural Group level is consistent. Annette's research was into the developmental aspects of language development which she abstracted and found in other developmental situations involving the growth of knowledge. Her theory is that the representation flows through a number of phases, and each phase corresponds to a redescription of the data, into another form.

It is important to realize that this pattern of learning might have an impact on the nature of consciousness, by impacting on the structure of the brain needed to achieve specific functions.

title: Artificial Consciousness/Linguistics


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User:Thomson~enwikiversity

Prof. Murray Thomson in charge of MIE315 course: Design for the Environment http://www.mie.utoronto.ca/staff/profiles/thomson/

title: User:Thomson~enwikiversity