text:
Modern Greek/Lesson plan

The lessons shall focus on practical usage of Greek. According to the Bite-sized Language Lessons approach, not more than 15 mandatory new words shall be introduced per lesson, however there can be large sections of optional vocabulary that won't be required for the later lessons. The grammar section shall also be short and not introduce too much at once. Only use grammar terms if you have to or in such a way that the average person can understand the explanation even without having heard the term before.

Lessons and contents:
 * 1) Greetings and "How are you?" conversation. Grammar: είμαι, είσαι and/or είστε; forming questions: yes/no questions and question-word (πως) questions.
 * 2) Introducing yourself: name, nationality, profession... Grammar: the definite article (Nominative only). -ος and -α or -η (not both, to avoid confusion), possibly also -ο, as endings of names, nouns and adjectives.
 * 3) Introducing others / talking about others' situation. Maybe add sentence structure like "Είμαι απο την..." or "Είναι στο ...". the word μου to allow for a more interesting conversation. Grammar: the remaining forms of είμαι. δεν if it hasn't been introduced so far. Plural Nominative of adjectives if unavoidable.
 * 4) Talking about your hobbies or the languages you can speak. Grammar: a maximum of 3 forms of regular present tense, 1st or 2nd conjugation regular active, no Aorist.
 * 5) Talking about the weather. Grammar: the rest of regular present tense
 * 6) Asking for the way. Grammar: υπαρχει, indefinite articles
 * 7) In a cafe. Grammar: Accusative singular, maybe low numbers
 * 8) Shopping for fruit or the like. Grammar: Accusative plural, numbers
 * 9) Asking for / Telling the time. Grammar: numbers to 12 or 30.
 * 10) Regular activities. Days of the week, more about the time, κάθε
 * 11) A day in the life of ... . Grammar: regular reflexive / "mediopassive" verbs
 * 12) Asking somebody out. Grammar: Aorist
 * 13) Writing a post card or a letter home. Grammar: past tense.

This is not 100% definite yet, the order may have to be changed or new lessons inserted if there is too much of a jump in vocabulary / grammar from one lesson to the next. Particularly the later lessons are more of a rough estimate of how to use an aspect of grammar in a practical situation than. However, the content of the first few lessons is fairly confirmed and the others can only be confirmed once the previous ones have been written.

title: Modern Greek/Lesson plan


text:
User talk:84.66.7.19

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 15:47, 21 May 2007 (UTC)

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

title: User talk:84.66.7.19


text:
Lore of Learning/Patterns of Learning

Inspired by Alexander's architectural patterns and software design patterns.

These are learning/ teaching/ educating/ facilitating learning patterns.

=Template=

Name of the pattern
A concise name which communicates the scenario.

Problem statement
Describe the context and the challenge(s).

Motivation
Why this needs to be achieved, or why it is desirable.

Forces
Forces involved in meeting the challenge in context.

Solution
Instructions for this pedagogical design.

Relation to other patterns
Describe other patterns relating to this one.

Examples of Use
Real world examples of where this pattern is observed.

=Example=

Chalk and Talk
One educator at the front of the class talking to a number of learners.

Problem statement
Communicating a lot of information in broadcast style. May be useful as a prelude to other more engaging learning activities.

Motivation
It is highly criticised, and perhaps should be listed among the /Anti-patterns/. However, given the frequency of auditorium-style class-rooms, it is a good idea to specify how to do this well.

Forces
A large amount of information to be communicated in a limited amount of time to a large number of people.

Solution
Preparation. Engagement ... etc. (describe the solution - instructions)

Relation to other patterns
aka "Sage on the Stage" ....

Examples of Use
This is a common way of "teaching" around the world, ....

=See Also=

 * Pedagogical Patterns

title: Lore of Learning/Patterns of Learning


text:
Lore of Learning/Patterns of Learning/Anti-patterns

Pitfalls - see Anti-pattern and list some here.


text:
TI-Basic Programs/CStart

Program Description
CStart is a title screen start-up program which works in conjunction with prgmCHASE. A user must have both programs on their calculator in order to play Chase. When both programs are in place, the user never needs to actually run prgmCSTART, but it must be un-archived while playing Chase so that Chase can access it. The user simply runs prgmCHASE and the program will then link to CStart automatically. CStart doesn't change any part of the actual gameplay of Chase, but it displays a very cool start-up screen. As outlined in the Program Description section for prgmCHASE in this wikibook, the title screen gives the player four options: 1) New Game (to start a new game) 2) Continue (to continue a currently saved game) 3) Instructions (to bring up the instructions for Chase) 4) Quit (to leave the program and return to the main screen)

It also displays a large drawing of the word "CHASE" with the vicious ≠'s as part of the E. It displays the current High Score in the upper-right (which will show 0 if the user has not played before), and an image of a < sign with angry eyes and sharp teeth chasing a frightened X in order to eat him.

Choice 3 will clear the screen and draw up page 1 of the instructions for Chase. This page gives an introduction and a background for Chase and tells the player what his goal is. The program will be paused when this screen is displayed and it will wait for the player to press ENTER, upon which the screen will be cleared again and page 2 of the instructions will be displayed. On this page, the player will see a diagram of which keys are to be used for controlling the > symbol during gameplay. It also tells of how the game will slow down, and needs to be re-booted using the ENTER key while playing in order to get it back up to speed.

Program Code
Notes:
 * 1) Many of these lines of code can be linked together in one line by just typing a ":" instead of pressing ENTER and typing the next command on the next line. Also, some of the commands displayed here are already linked in this way.
 * 2) The "¤" found in the command, " :Text(8,69,"¤ ", is actually a very small square and it can be found in the CATALOG menu on your calculator. It will be above what looks like a small plus sign (+), near the bottom of the list.

PROGRAM:CSTART
 * "CHASE STARTUP  SCREEN      <-- This line is unnecessary, but is a helpful note
 * FnOff                             for anyone who opens the editing screen for CStart
 * AxesOff
 * ZStandard
 * 84→Xmin
 * 52→Ymin
 * ZInteger
 * Line(15,58,10,56
 * Line(9,55,6,53
 * Line(3,51,5,52
 * Line(3,50,5,47
 * Line(6,46,8,43
 * Line(9,42,12,39
 * Line(16,57,11,53
 * Line(10,52,7,50
 * Line(8,49,10,44
 * Line(11,43,13,40
 * Line(20,55,16,40
 * Line(21,55,17,40
 * Line(20,48,25,48
 * Line(20,47,25,47
 * Line(28,55,24,40
 * Line(29,55,25,40
 * Line(29,40,31,44
 * Line(32,45,35,48
 * Line(36,50,36,52
 * Pt-On(33,47
 * Line(39,56,42,38
 * Line(39,55,42,38
 * Line(34,46,40,46
 * Line(34,45,40,45
 * Line(55,52,54,52
 * Line(55,53,49,53
 * Line(53,54,51,54
 * Line(50,52,47,51
 * Line(48,52,47,50
 * Line(46,50,46,47
 * Line(47,47,48,46
 * Pt-On(47,46
 * Line(48,45,52,45
 * Line(49,44,53,44
 * Line(54,43,55,42
 * Line(53,43,55,41
 * Line(55,40,52,37
 * Line(54,40,50,36
 * Line(51,38,48,36
 * Line(49,36,45,40
 * Line(47,37,45,39
 * Line(73,54,64,54
 * Line(73,53,64,53
 * Line(62,54,57,35
 * Line(63,54,58,35
 * Line(59,36,70,36
 * Line(59,35,70,35
 * Text(15,62,"≠
 * Text(14,67,"≠
 * Line(81,54,79,55
 * Line(78,54,75,37
 * Line(81,53,80,49
 * Line(78,40,79,48
 * Line(76,37,77,39
 * Line(75,35,74,35
 * Line(75,34,74,34
 * Text(0,52,"HI SCORE:
 * Text(0,87,[J](1,5
 * If 100≤[J](1,5
 * Text(0,83,[J](1,5
 * If 1000≤[J](1,5
 * Text(0,83,"!?!?!
 * Line(0,18,1,20
 * Line(1,21,3,23
 * Line(4,23,6,21
 * Line(7,21,18,26
 * Pt-On(19,26
 * Line(18,22,10,16
 * Line(19,20,17,20
 * Line(17,19,17,16
 * Line(16,16,14,16
 * Line(13,17,13,14
 * Pt-On(9,15
 * Line(12,14,18,14
 * Line(7,13,11,12
 * Line(8,12,14,3
 * Line(11,11,11,9
 * Line(12,9,13,9
 * Line(13,8,13,6
 * Line(14,6,16,6
 * Pt-On(15,2
 * Line(16,5,16,1
 * Line(15,0,13,0
 * Pt-On(12,1
 * Line(11,2,1,10
 * Pt-On(0,11
 * Pt-On(3,22
 * Line(3,21,4,21
 * Line(3,20,5,20
 * Line(3,19,6,19
 * Line(20,17,20,14
 * Line(20,7,20,4
 * Line(21,17,21,12
 * Line(21,9,21,4
 * Line(22,13,22,8
 * Line(23,11,24,11
 * Line(23,10,24,10
 * Line(25,13,25,8
 * Line(26,17,26,12
 * Line(26,9,26,4
 * Line(27,17,27,14
 * Line(27,7,27,4
 * Line(23,15,25,16
 * Line(23,18,23,19
 * Line(26,19,26,20
 * Line(22,20,23,21
 * Line(25,21,26,22
 * Text(42,39,"(PRESS ENTER)
 * Pause
 * Text(39,37,"1
 * Text(39,40,") NEW GAME
 * Text(45,37,"2
 * Text(45,75," "              <-- These end-quote marks are unnecessary but there must
 * Text(42,76,"        "       < be this many spaces before the end of the command.
 * Text(45,40,") Continue            (There must be 1 space after "Text(45,75"
 * Text(51,37,"3                      and 9 spaces after "Text(42,76", but no
 * Text(51,40,") Instructions         close-quote mark is needed in either case.)
 * Text(57,37,"4
 * Text(57,40,") Quit
 * While 1
 * getKey
 * If Ans=92
 * Return
 * If Ans=93
 * Return
 * If Ans=94
 * Goto 9
 * If Ans=82
 * Then
 * Output(8,1,"
 * Stop:End
 * End
 * Lbl 9
 * StorePic 0
 * ClrDraw
 * Text(0,24,"INSTRUCTIONS
 * Text(7,3,"Welcome to Chase! In Chase
 * Text(8,91,",
 * Text(14,5,"You are a hungry >  symbol
 * Text(21,2,"who's always on the lookout
 * Text(28,10,"for a tasty X  to eat.  But
 * Text(35,6,"watch out for the ≠  signs!
 * Text(42,4,"They are vicious and would
 * Text(49,5,"love to have you for lunch.
 * Text(56,11,"Avoid them at all costs.
 * Pause
 * ClrDraw
 * Text(6,3,"Use the number
 * Text(12,5,"keys to move:
 * Text(8,69,"¤
 * Text(18,62,"1  2   3
 * Text(9,62,"4
 * Text(9,76,"6
 * Text(0,62,"7  8   9
 * Line(70,53,70,55
 * Line(73,53,75,55
 * Line(73,50,74,50
 * Line(73,47,75,45
 * Line(70,47,70,45
 * Line(67,47,65,45
 * Line(67,50,66,50
 * Line(67,53,65,55
 * Text(27,10,"Press ENTER to pause or
 * Text(33,1,"'Save' your game. To restore
 * Text(39,3,"the speed when Chase slows
 * Text(45,3,"down   press ENTER twice:  it
 * Text(51,9,"will save your game and
 * Text(46,20,",
 * Text(57,6,"then resume at full speed.
 * Pause
 * ClrDraw
 * RecallPic 0
 * End

title: TI-Basic Programs/CStart


text:
User:Giftedproject350

ATLANTIS
Was Atlantis real or was it made up. This is a often asked question. Well heres the truth about Atlantis.

title: User:Giftedproject350


text:
Music Theory/Counterpoint

/Fugue/
Fugue is sometimes considered to be the goal of contrapuntal study. Its definition may vary, depending upon the person asked but this book will consider three definitions.

 * Fugue : (1) A formal compositional structure, consisting of a fugal exposition of a subject, a development with one or more middle entries, and a recapitulation
 * (2) A compositional device for the elaboration and development of a single (or multiple) musical idea(s)
 * (3) A texture within a larger compositional structure or form which utilizes fugal devices or parts of a formal fugue

Traditional part writing is often based on counterpoint (adjective contrapuntal), in which a second melody is written to use harmonic intervals that create primarily consonant (good sounding) relationships between notes. First, a leading melodic line must be written, then contrapuntal methods may be used to add additional melodic lines. Consonants are further divided into perfect and imperfect consonants and contrasted by dissonance (which sounds bad). Traditionally the unison, the octave and the fifth were considered perfect consonances while the third and sixth were considered imperfect consonances; the fourth was considered a dissonance if it was above the leading line but a consonance if below, though modern theorists have questioned the need for this distinction. Other notes are considered dissonant. Additional melodic lines beyond the second may be added by writing them in counterpoint to all the lines already written.

In addition, the types of movement made a difference. In early theory there were three types of movement: direct, in which both melodic line move in the same direct, oblique in which one line moves and the other does not, and contrary in which both lines move in opposite directions. Some modern theorists further divide direct motion into similar motion, in which both lines move different distances in the same direction, and parallel motion in which both lines maintain the same interval between them. Early counterpoint texts (such as Johann Joseph Fux's Gradus ad Parnasum) listed several rules for moving lines, however these can be boiled down to one: Don't move from perfect consonance to perfect consonance by direct motion. The addition of dissonance may be added on an off beat, to be resolved on the next on beat. Large jumps are discouraged, and it is recommended that they be followed by stepwise motion in the opposite direction. The octave should be used vary sparingly and the unison avoided, however, as these tend to make the melodic lines blur together.

Various rhythms could be used in the various melodic lines, and this was encouraged with the goal being "florid counterpoint" in which various rhythms are mixed in an elaborate way. If a smaller note is used in the following line then dissonance must be on the second note; if the following note starts after the leader, then it must start on the dissonance. Of course, neither have to be dissonant, and a consonance may be used in both places. A series of stepwise movements may also be used to move over several dissonances between consonances. However, two notes one semitone apart (sometimes described as "fa on mi") should always be avoided.

Double Counterpoint is the practice of writing a line so that both the intervals and their inversion (usually octave inversions, but tenth and twelfth inversions may sometimes be used) follow an acceptable pattern of consonance and dissonance. This is done so that a transposed version of the resulting melodic line may be used as a separate part. This is especially common in classical and baroque fugues.

Note that a modern composition that follows a chord progression may just write all parts to fit the same chord, however, use of contrapuntal principles may still be useful in order to make to melodic lines work better together.

title: Music Theory/Counterpoint


text:
User talk:75.181.53.216

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 20:59, 21 May 2007 (UTC)

title: User talk:75.181.53.216


text:
Combinatorics/What is Combinatorics

Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics. Aspects of combinatorics include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics).

Combinatorics is as much about problem solving as theory building, though it has developed powerful theoretical methods, especially since the later twentieth century (see the page List of combinatorics topics for details of the more recent development of the subject). One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas.

There are many combinatorial patterns and theorems related to the structure of combinatoric sets. These often focus on a partition or ordered partition of a set. See the List of partition topics for an expanded list of related topics or the List of combinatorics topics for a more general listing. Some of the more notable results are highlighted below.

An example of a simple combinatorial question is the following: What is the number of possible orderings of a deck of 52 distinct playing cards? The answer is 52! (52 factorial), which is equal to about $$8.0658 \cdot 10^{67}$$.

Another example of a more difficult problem: Given a certain number n of people, is it possible to assign them to sets so that each person is in at least one set, each pair of people is in exactly one set together, every two sets have exactly one person in common, and no set contains everyone, all but one person, or exactly one person? The answer depends on n.

Combinatorics is used frequently in computer science to obtain estimates on the number of elements of certain sets. A mathematician who studies combinatorics is often referred to as a combinatorialist or combinatorist.

title: Combinatorics/What is Combinatorics


text:
Cookbook:Eastern North Carolina Barbecued Pig

| Southern U.S. cuisine

Ingredients

 * 80 pound pig (butchered with head removed)
 * Salt
 * 40 pounds charcoal (for charcoal cooking option)
 * Your favorite vinegar-based Eastern NC sauce

Procedure

 * 1) Salt hams, ribs/midsection and shoulders liberally and place skin side up on either a gas or charcoal grill or a BBQ pit.
 * 2) Keep lid closed, and aim for a heat of approximately 275–350°F.
 * 3) Allow 1 hour per 10 pounds cooking time (gas or charcoal).
 * 4) 2 hours before being done, place pig with the skin side down. As soon as it is flipped, pour BBQ sauce on meat side.
 * 5) Close lid and allow skin to crisp.
 * 6) The pig will be done to perfection when the ham bone can be twisted freely.
 * 7) Lift lid and allow guests to pick/pull meat, or the chef can remove meat and chop to their liking on a chopping block.

Notes, tips, and variations

 * Any higher heat or longer cooking time will result in the hams drying out.
 * Heat source should be as indirect as possible if using a home made pit with there being less coals under the ribs/midsection and more around the perimeter.
 * Only lift the lid when required and not to let everyone take recreational looks at the pig.
 * The more consistent you can maintain the heat source, the more evenly cooked and tender the pig will turn out. Remember “If you’re looking, you’re not cooking”.
 * If picked, provide additional sauce for guests to add; if chopped add additional sauce and salt to chef’s liking.

Uses

 * Serve with hush puppies, coleslaw, potato salad, and sweet tea.


text:
User talk:24.218.91.192

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. Mattb112885 (talk) 22:15, 21 May 2007 (UTC)

title: User talk:24.218.91.192


text: Template:Goodbook/Formal Logic

title: Template:Goodbook/Formal Logic


text: Template:Goodbook/UNDP-APDIP Books

title: Template:Goodbook/UNDP-APDIP Books


text: C++ Programming/Scope/Examples/Program Average1


text: C++ Programming/Scope/Examples/Program Namespaces


text:
User talk:72.229.199.51

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 01:28, 22 May 2007 (UTC)

title: User talk:72.229.199.51


text:
User:Lwan98/About the author

 * LW is too lazy to fill out this page.
 * or maybe he doesn't want to be known (yet).
 * Oh, it says 'he' doesn't it? Guess that eliminates part of the population.

03:25, 22 May 2007 (UTC)

title: User:Lwan98/About the author


text:
User talk:Bllovely

Hello Bllovely, Welcome to wikibooks! I met you on IRC, and I wanted to be the first to say hello. If you have any questions, you can always ask me on my user talk page. Welcome, and good luck! --Whiteknight (talk) 02:11, 22 May 2007 (UTC)

title: User talk:Bllovely


text:
User talk:203.192.65.222

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 06:04, 22 May 2007 (UTC)

title: User talk:203.192.65.222


text:
User:Librarianofages

Welcome to the user page for The Librarian of Ages.

You can find me on EN.wikipedia as "Librarianofages".

or

You can find me on SCO.wikipedia as "Jin".

If you wish to discuss or take issue with any of my edits pls do so on my talkpage.

Thank you! Jin.

title: User:Librarianofages


text:
User:Xthinker

Hi,

I'm working in Semantic Web and Services. ...

title: User:Xthinker


text:
Talk:Engineering Analysis/Matrix Exponentials

Shouldn't $$e^{A}$$ expand to $$e^{A} = 1 + A + \frac{1}{2}A^2 + \frac{1}{6}A^3 + ... $$ instead of $$e^{A} = A + \frac{1}{2}A^2 + \frac{1}{6}A^3 + ... $$ where $$1$$ is the identity matrix of adequate dimension?

 * Yes, that seems correct to me. I would have to look it up though, to make sure i'm not missing some detail. --Whiteknight (talk) 13:30, 22 May 2007 (UTC)

 * fixed. You're right -- see matrix exponential. --DavidCary (talk) 16:46, 9 October 2008 (UTC)

It says in the article that sums of matrices in the exponent can't be separated. This isn't true if the matrices commute. See http://en.wikipedia.org/wiki/Matrix_exponential#The_exponential_of_sums Is this deliberately left out? --213.100.169.83 (discuss) 00:15, 15 October 2013 (UTC)


text:
Talk:Korean/Verbs

Lesson plan
See Korean/Grammar course plan. Rodasmith 22:25, 13 June 2007 (UTC)

Removal of examples
I'm removing the following examples for now in order to introduce topics slowly. They may be reincorporated after the lesson matures to a point where there student can understand the examples. Rodasmith 01:25, 23 May 2007 (UTC)

Special honorific verb forms:

Advanced
Perhaps the following should be in an advanced verbs lesson: (Rodasmith 22:25, 13 June 2007 (UTC))

A few verbs have special humble forms, used when the speaker is referring to him/herself in polite situations. These include 드리다 (deurida) and 올리다 (ollida) for 주다 (juda, "give"). 드리다 (deurida) is substituted for 주다 (juda) when the latter is used as an auxiliary verb, while 올리다 (ollida, literally "raise up") is used for 주다 (juda) in the sense of "offer".

There are several speech levels in Korean, and each level has its own unique set of verb endings which are used to indicate the level of formality of a situation. Unlike "honorifics"—which are used to show respect towards a subject—speech levels are used to show respect towards a speaker's or writer's audience. The names of the 7 levels are derived from the non-honorific imperative form of the verb 하다 (hada, "to do") in each level, plus the suffix 체, which means "style."

E.g.:
 * 합니다: (formal, polite, indicative) "does"
 * 하십시오: (formal, polite, imperative) "please do"

The highest 5 levels use final verb endings and are generally grouped together as jondaemal (존대말), while the lowest 2 levels (해요체 haeyoche and 해체 haeche) use non-final endings and are called 반말 (banmal, "half-words") in Korean. (The haeyoche in turn is formed by simply adding the non-final ending -요 (-yo) to the haeche form of the verb.)

Taken together, honorifics and speech levels form a cartesian product of 14 basic verb stems. Here is a table giving the 7 levels, the present indicative form of the verb 하다 (hada, "do" in English) in each level in both its honorific and non-honorific forms, and the situations in which each level is used.

These days, some of these speech levels are disappearing and people don't use them much in everyday life. Hasoseoche, which is only used in movies or dramas describing old times, is barely used by Koreans, and Hageche exists almost only in novels. But interestingly, Haoche is becoming more and more popular among people in their teens and 20's, and this phenomenon is considered to be one of the influences by internet users. Usually Haoche is used in only movies and dramas (similar with Hasoseoche) but it is now popular (in some internet websites, e.g. dcinside.com) among internet users but not in everyday life. Haoche is usually considered as a male-tongue, but interestingly today's internet-based Haoche is very popular in Ewhaian.com which is for students of Ewha Womans University.

Needed example:
If the result ends in a vowel followed by 르, insert an extra ㄹ, making the end ㄹ르. - one problem I've always had with instructional text which introduces a bunch of rules together is if they miss giving an example of one. I'm trying to think of a verb which meets this criteria and I can't, it would be nice if someone who knew of one could add it, as well if any others are missing.--Crossmr (talk) 01:26, 22 January 2008 (UTC)

모르다 17 August 2009

Imperative forms
For example, juseyo, and irregulars forms and polite forms...--66.214.143.64 (talk) 17:34, 12 April 2009 (UTC)

title: Talk:Korean/Verbs


text:
User talk:Librarianofages

Hello, welcome to Wikibooks!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 07:41, 22 May 2007 (UTC)

title: User talk:Librarianofages


text:
User talk:Xthinker

Hello, welcome to Wikibooks!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 07:42, 22 May 2007 (UTC)

title: User talk:Xthinker


text:
Becoming a Linguistic Mastermind/The results

This book is explicitly not a collection of one teacher’s instructions. It represents the combined wisdom of many learners. Therefore, I would like to ask everyone who is beginning a course to announce it here. Please report on your progress and share your opinions.

Everyone should insert a section beginning with the code  =Username=.  To help develop a review of the method, they should state how far they have advanced and how many weeks it has taken so far.

In this way we will be able to solve common problems and evaluate the project’s future prospects. (Is this book going in a right direction?)

If everyone shares their thoughts, soon there will be many language courses in various mother-tongues.


text:
Becoming a Linguistic Mastermind/The courses

All courses:


text:
Becoming a Linguistic Mastermind/The courses/Workshop

On this page the lesson texts for the English target language are prepared. Other languages are worked out on the partner projects of Wikibooks. The next steps are not taken until the English texts can be regarded to as discussed fully and ready for press: After that the word-by-word translation must be written and the spoken version must be recorded. These tasks are managed on the respective course page.

=Welcome, learners!= Olivia:
 * Welcome ! I am Olivia and this is Jack. We are from England.

Jack:
 * Our language is one of the easiest languages in the world.

Olivia:
 * In a few months you will be able to understand the English we speak from day to day...

Jack:
 * ...and you will be able to understand the Simple English Wikipedia.

Olivia:
 * Are you ready ? We will now start learning English the easy way.

70 spoken words

=About the English language= Jack:
 * Hello, Olivia!

Olivia:
 * Hello, Jack! You said that English is one of the easiest languages in the world.

Jack:
 * That's right.

Olivia:
 * Why do you think so?

Jack:
 * Well, more than half of our words come from Latin. If you speak Italian or French, then you already know many English words.

Olivia:
 * I suppose that it's not so easy for Japanese and Finnish people to learn English. They don't know many Latin words.

Jack:
 * Learning English is simple for them, too. I think that our language is more regular than others. There are only few irregular forms.

Olivia:
 * What do you mean? Can you give an example?

Jack:
 * Well, almost everything can be made plural by adding the letter S to the end of the word. One page has many letters, one book has many pages and I have many books. That's just one example.

141 spoken words


text:
A-level Physics/Wave properties/Superposition

When two waves are superimposed the displacement of the resultant wave is equal to the algebraic sum of the individual displacements.

Diffraction and interference
Diffraction is the spreading out of waves as they pass through a narrow gap or obstacle. When light diffracts through two slits, the relationship connecting the separation of the light sources (i.e., the separation of the slits), a, the separation of the fringes of the interference pattern, x, the wavelength of the light and the distance of the screen from the sources, D is as follows:

$$\lambda = \frac{ax}{D}$$

Superposition
At a point where two or more waves meet, the instantaneous displacement is the vector sum of the individual displacement due to each wave at that point.

Coherence
Two waves are said to be coherent with each other if the path difference between them stays constant from the source up to the detection.they may or may not have same wavelength, frequencies and amplitudes.

Monochromatic
Waves of a single wavelength or frequency are monochromatic.

Path Difference
Path difference = $$n\, \lambda$$ for constructive waves.

Path difference = $$(n\ + \frac {1}{2}) \lambda$$ for destructive waves.

(where n is an integer).

Formation of a stationary wave
It forms due to the superposition of wave travelling in 1 direction with a wave of equal amplitude and wavelength travelling in the opposite direction.

Stationary waves on a string occur when $$ 1\ = n\,\frac {\lambda}{2}$$


text:
User talk:66.220.242.162

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 12:38, 22 May 2007 (UTC)

title: User talk:66.220.242.162


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User talk:Arthomas

Testing to see how this works.

title: User talk:Arthomas


text:
User talk:82.208.184.91

Welcome to Wikibooks. We invite everyone to contribute constructively to our collection. Take a look at the welcome page if you would like to learn more about contributing. However, unconstructive edits are considered vandalism, and if you continue in this manner you may be blocked from editing without further warning. Please stop, and consider improving rather than damaging the hard work of others. Thanks. -- Herby talk thyme 12:52, 22 May 2007 (UTC)

title: User talk:82.208.184.91


text:
Stress-related Disorders/Clinical Stress

Stress as in Clinical Medicine

Acute stress disorder

 * Occurs in individuals without any other apparent psychiatric disorder, in response to exceptional physical/or psychological stress.
 * While severe, such reactions usually subside within hours or days.
 * The stress may be an overwhelming traumatic experience (e.g accident, battle, physical assault, rape) or unusually sudden change in social circumstances of the individual, such as multiple bereavement.
 * Individual vulnerability and coping capacity play a role in the occurrence and severity of acute stress reactions, as evidenced by the fact that not all people exposed to exceptional stress develop symptoms.
 * 1) Symptoms show considerable variation but usually include:
 * 2) *an initial state of DAZE with some constriction of the field of consciousness and narrowing of attention
 * 3) *inability to comprehend stimuli
 * 4) *disorientation.
 * 5) Followed either by further withdrawal from the surrounding situation to the extent of a dissociative stupor or by agitating and over activity.

Autonomic signs of "Panic Anxiety"
The symptoms usually appear within minutes of the impact of the stressful stimulus and disappear within 2-3 days.
 * Tachycardia
 * Sweating
 * Hyperventilation

Post-traumatic disorders (PTSD)
This arises as a delayed and/or protracted response to a stressful event or situation of an exceptionally threatening nature and likely to cause pervasive distress in almost anyone.

Causes of PTSD

 * 1) Natural or human disasters
 * war
 * 1) serious accident
 * 2) witness of violent death of others
 * 3) being the victim of sexual abuse
 * 4) rape
 * 5) torture
 * 6) terrorism or hostage taking

Predisposing factors

 * 1) Personality traits
 * 2) Previous history of Psychiatric illness

Typical symptoms

 * 1) "Flashbacks" - the repeated reliving of the trauma in the form of intrusive memories or dreams.
 * 2) intense distress at exposure to events that symbolize or resemble an aspect of the traumatic event, including anniversaries of the trauma
 * 3) avoidance of activities and situations reminiscent of the trauma
 * 4) emotional blunting or "numbness"
 * 5) a sense of detachment from other people
 * 6) autonomic hyper-arousal with hyper-vigilance, an enhanced startle reaction and insomnia
 * 7) marked anxiety and depression and, occasionally, suicidal ideation

Treatment

 * Psychiatric consultation
 * Exploration of memories of the traumatic event
 * relief of associated symptoms
 * counseling

Prognosis

 * The course is fluctuating but recovery can be expected in the majority of cases.
 * Few people may show chronic course over many years and a transition to an enduring personality change

Source
Kumar and Clark Clinical Medicine 4th Edition ISBN 0 7020 2458 9 page 1134


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Stress-related Disorders/Surgical Stress

Introduction
Psychological stress may cause ordinary peptic disease but stress ulcer is different.

Q. What is Stress ulcer?
A single or multiple fundic mucosal ulcers which often gives upper gastrointestinal bleeding developed during the severe physiologic stress of serious illness.

see also psychological stress (medicine)  for more details.

Q.Ordinary peptic ulcers and Stress ulcers?

Ordinary peptic ulcers are found commonly in the “gastric antrum and the duodenum” whereas Stress ulcers are found commonly in “fundic mucosa and can be located anywhere within the stomach and proximal duodenum”.

''see also peptic ulcer for more details. ''

''see also Timeline of peptic ulcer disease and Helicobacter pylori for more details. ''

Q. Who can get Stress ulcers?

 * Those patients who are on respirators (artificial ventilator) and who have multi-system disorders (i.e. many organs malfunction).

 * Those patients with a past history of peptic ulcer or upper gastrointestinal bleeding.
 * Stress ulceration occurs in patients with major injury or illness, who have undergone major co-morbidity.
 * These are some types of acute ulcers, which develop in critically ill patients under intensive lifesaving management or after burns.
 * Focal acutely developing gastritis mucosal defects are a well-known complication of therapy with NSAIDs. Alternatively, they may appear after severe physiologic stress, whatever its nature – hence the term stress ulcers.

Example:
 * Elderly patients in a surgical intensive care unit (ICU) with heart and lung disease have a high postoperative prevalence of stress ulcers.
 * Patients in a medical ICU, particularly those who require respirators, are at high risk of development of stress ulcers.

It is possible that poor mucosal oxygenation, differences in acid-base balance, and elevated circulating corticosteroids may contribute to the formation of these ulcers.

Diagnosis
Q. When is stress ulcer suspected?

 * Stress ulcer is suspected when there is upper gastrointestinal bleeding in appropriate clinical setting.

Example:
 * When there is upper gastrointestinal bleeding in elderly patients in a surgical intensive care unit (ICU) with heart and lung disease.
 * When there is upper gastrointestinal bleeding in patients in a medical ICU who require respirators.

Q. How stress ulcer can be diagnosed?

 * After the initial management of gastrointestinal bleeding, the diagnosis can be confirmed by upper GI endoscopy.

The site of ulcerations
The ulcerations may be superficial and confined to the mucosa, in which case they are more appropriately called erosions, or they may penetrate deeper into the submucosa. The former may cause diffuse mucosal oozing of blood, whereas the latter may erode into a submucosal vessel and produce frank hemorrhage.

Lesion of stress ulcers
The characteristic lesions may be multiple, superficial mucosal erosions similar to erosive gastroduodenitis. Occasionally, there may be a large acute ulcer in the duodenum (Curling’s ulcer).

Generally, there are multiple lesions located mainly in the stomach and occasionally in the duodenum. They range in depth from mere shedding of the superficial epithelium (erosion) to deeper lesions that involve the entire mucosal thickness (ulceration).

Stress Ulcer formation
The pathogenic mechanisms are similar to those of erosive gastritis.”

Q. How and why Stress ulcer is developed?

The pathogenesis of stress ulcer is unclear but probably is related to a reduction in mucosal blood flow or a breakdown in other normal mucosal defense mechanisms in conjunction with the injurious effects of acid and pepsin on the gastroduodenal mucosa.

Prophylaxis
Prevention of this condition is far better than trying to treat it once it occurs.

'''Q. How to prevent its development? ''' In recent years by using Ranitidine (H2-receptor antagonist)[] and nasogastric administration of sucralfate has reduced the incidence of stress ulceration.

Management
The principles of management are the same as for the chronic ulcer.

The steps of management are similar as in erosive gastritis.

Treatment
Endoscopic means of treating stress ulceration may be ineffective and operation required. It is believed that shunting of blood away from the mucosa makes the mucous membrane ischaemic and more susceptible to injury.

Treatment of stress ulceration usually begins with prevention. Careful attention to respiratory status, acid-base balance, and treatment of other illnesses helps prevent the conditions under which stress ulcers occur. Patients who develop stress ulcers typically do not secrete large quantities of gastric acid; however, acid does appear to be involved in the pathogenesis of the lesions. Thus it is reasonable either to neutralize acid or to inhibit its secretion in patients at high risk.

In case of severe hemorrhagic or erosive gastritis and stress ulcers, a combination of antacids and H2-blockers may stop active bleeding and prevent re bleeding. In selected patients, either endoscopic therapy or selective infusion of vasopressin into the left gastric artery may help control the hemorrhage.

Selected Readings

 * Cheung, L. Y. Pathogenesis, prophylaxis and treatment of stress gastritis. Am. J. Surg. 156:437, 1988.
 * Craven, D. E., et al. Risk factors for pneumonia and fatality in patients receiving continuous mechanical ventilation. Am. Rev. Respir. Dis. 133:792, 1986.
 * Driks, M. R., et al. Nosocomial pneumonia in intubated patients given sucralfate as compared with antacids or histamine type 2 blockers. N. Engl. J. Med. 317:1376, 1987.
 * DuMoulin, G. C., et al. Aspiration of gastric bacteria in antacid-treated patients: A frequent cause of postoperative colonisation of the airway. Lancet 1:242, 1982.
 * Lamothe, P. H., et al. Comparative efficacy of cimetidine, famotidine, ranitidine, and Mylanta in postoperative stress ulcers: Gastric pH control and ulcer prevention in patients undergoing coronary artery bypass graft surgery. Gastroenterology 100:1515, 1991.
 * Priebe, H. J., et al. Antacid versus cimetidine in preventing acute gastrointestinal bleeding: A randomized trial in 75 ill patients. N. Engl. J. Med. 302:426, 1980.
 * Shuman, R. B., Schuster, D. P., and Zuckerman, G. R. Prophylactic therapy for stress ulcer bleeding: A reappraisal. Ann Intern. Med. 106:562, 1987.
 * Tryba, M. Stress bleeding prophylaxis with sucralfate: Pathophysiologic basis and clinical use. Scand. J. Gastroenterol. [Suppl. 173] 25:22, 1990.


text:
User talk:139.67.41.48

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 14:38, 22 May 2007 (UTC)

title: User talk:139.67.41.48


text:
Linear Algebra/Column and Row Spaces

The column space is an important vector space used in studying an m x n matrix. If we consider multiplication by a matrix as a sort of transformation that the vectors undergo, then the null space and the column space are the two natural collections of vectors which need to be studied to understand how this transformation works. While the null space focussed on those vectors which vanished under action of the matrix (i.e. the solutions of Ax = 0) the column space corresponds to the transformed vectors themselves (i.e. all Ax). It is the totality of all the vectors after the transformation. Those readers who have studied abstract algebra can relate the null space to the kernel of a homomorphism and the column space to the range.

Another important space associated with the matrix is the row space. Like its name suggests it is built entirely out of the rows of the matrix. We shall later see that the row space can be identified with the column space in a particular sense. In the special case of an invertible matrix, the row space and the column space are exactly equal.

The Column Space
Given an m x n matrix A the column space of A, denoted by C(A), is the collection of all the vectors formed by linear combinations of the columns of A.

More precisely if the columns of A are $$c_1,c_2 \cdots c_n$$, where each $$c_i$$ is an m-dimensional vector then,

 * $$\hbox{C}(A) = \{\mathbf{v} \in \mathbb{R}^m : \mathbf{v} = \mathbf{\alpha_1 c_1 + \alpha_2 c_2 + \cdots \alpha_n c_n},\ \alpha_i\in \mathbb{R}\}$$

The column space is thus essentially built out of the columns of the matrix. It is the linear span of the columns and in that capacity is also a vector space with the standard operations. (Recall that span of any collection of vectors is always a vector space). Also as the columns are vectors in the m - dimensional space so the column space is naturally a subspace of $$\mathbb{R}^m$$.

Clearly if we let,

$$x = \begin{pmatrix} \alpha_1\\ \alpha_2\\ \vdots\\ \alpha_n \end{pmatrix} $$

then we can say that,

$$Ax = \begin{pmatrix} c_1 & c_2 & \ldots & c_n \end{pmatrix} \begin{pmatrix} \alpha_1\\ \alpha_2\\ \vdots\\ \alpha_n \end{pmatrix} = \alpha_1c_1 + \alpha_2c_2 + \ldots + \alpha_nc_n $$

Hence our definition can be modified to,
 * $$\hbox{C}(A) = \{\mathbf{v} \in \mathbb{R}^m : \mathbf{v} = \mathbf{Ax},\ x\in\mathbb{R}^n \}$$

This gives us the idea that the column space is precisely the set of transformed vectors by the action of multiplication by the matrix.

Basis for the column space
We shall now prove a theorem regarding the basis for the column space of a matrix. This constructive proof will also allow us to state a very important theorem called the rank-nullity theorem as a corollary.

Theorem: The columns of the m x n matrix A corresponding to the basic variables form a basis of the column space of A.

Proof: First note that the column space of A is formed by the span of all the columns, $$c_1,c_2$$...$$c_n$$. If we take the basis of the null space of A as outlined previously, then as

$$v_1 \in \hbox{Null Space}(A)$$

so $$Av_1$$=0. But this shows us that the column associated with $$v_1$$ is a linear combination of the columns associated with the basic variables. (Note that the contribution of the other free variable columns is 0 and that of the $$v_1$$ linked column is 1.) In this way all the free variable associated columns are linear combinations of the basic variable associated columns. So all the basic variable linked columns span the entire column space.

Now suppose that the row echelon form of $$A$$ is $$U$$, and if we take the basic variable columns the submatrix obtained from A is $$A_1$$ and that obtained from U is $$U_1$$. Clearly $$U_1$$ is the row echelon form of $$A_1$$ (see exercises) and so the two share the same null space. Now $$U_1$$ has only basic variables associated with it because we take only basic variables from A to A1 and so its nullity is zero. This tells us that $$U_1 x = 0$$ has only the trivial solution. Hence $$A_1 x = 0$$ also has only the trivial solution and so its nullity is zero as well. It follows that the columns of $$A_1$$ which were the basic variable linked columns of A are linearly independent.

Thus the basic variable columns are both linearly independent and spanning as a result of which they form a basis of the column space. Q.E.D

Let us look at an example:

Suppose $$A = \begin{pmatrix} 1 & 2 & 0 & 2 & 5 \\ -2 & -5 & 1 & -1 & -8 \\  0 & -3 & 3 & 4 & 1 \\  3 & 6 & 0 & -7 & 2 \end{pmatrix}$$

The first step involves reducing A to its row echelon form U.

Now $$U = \begin{pmatrix} 1 & 0 & 2 & 0 & 1 \\ 0 & 1 & -1 & 0 & 1 \\  0 & 0 & 0 & 1 & 1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

We encircle the first non zero entries in each row by brackets:

$$U = \begin{pmatrix} (1) & 0 & 2 & 0 & 1 \\ 0 & (1) & -1 & 0 & 1 \\  0 & 0 & 0 & (1) & 1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

Clearly the basic variables are $$x_1, x_2$$ and $$x_4$$ and the free variables are $$x_3$$ and $$x_5$$.

So by the theorem, the basis of the column space of A consists of the columns $$c_1, c_2$$ and $$c_4$$ and is given by:

$$\Bigg\{ \begin{pmatrix} 1\\ -2\\  0\\  3 \end{pmatrix},\begin{pmatrix} 2\\ -5\\  -3\\  6 \end{pmatrix},\begin{pmatrix} 2\\ -1\\  4\\  -7 \end{pmatrix} \Bigg\}$$

Note that the nullity of A is 2 which is equal to the difference between the total number of columns and the number of elements in the column space.

The Row Space
The row space, as, the name suggests is the space built out by the rows of the matrix. Given an m x n matrix A the row space of A, denoted by RS(A), is defined as the collection of all the vectors formed by linear combinations of the rows of A.

More precisely if the rows of A are $$r_1,r_2$$...$$r_m$$, where each $$r_i$$ is an n-dimensional vector then,

 * $$\hbox{RS}(A) = \{\mathbf{v} \in \mathbb{R}^n : \mathbf{v} = \mathbf{\alpha_1 r_1 + \alpha_2 r_2 + \cdots \alpha_m r_m},\ \alpha_i\in \mathbb{R}\}$$

The row space is thus the linear span of the rows and so is also a vector space with the standard operations. It is a subspace of $$\mathbb{R}^n$$.

Basis of the row space
The basis of the row space of A consists of precisely the non zero rows of U where U is the row echelon form of A. This fact is derived from combining two results which are:
 * 1) R(A) = R(U) if U is the row echelon form of A.
 * 2) The non zero rows of a matrix in row echelon form are linearly independent.

The proofs are outlined in the exercises.

Let us look at an example:

Suppose $$A = \begin{pmatrix} 1 & 2 & 0 & 2 & 5 \\ -2 & -5 & 1 & -1 & -8 \\  0 & -3 & 3 & 4 & 1 \\  3 & 6 & 0 & -7 & 2 \end{pmatrix}$$

If we take its row echelon form then we have,

$$U = \begin{pmatrix} 1 & 0 & 2 & 0 & 1 \\ 0 & 1 & -1 & 0 & 1 \\  0 & 0 & 0 & 1 & 1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

The first three rows are non zero and so the basis of the row space is: $$\{(1,\ 0,\ 2,\ 0,\ 1),(0,\ 1,\ -1,\ 0,\ 1),(0,\ 0,\ 0,\ 1,\ 1) \} $$

Rank of a matrix
Notice that in our example the basis of the row space has 3 elements which is the same number as that in the basis of the column space which we derived earlier. This is not a coincidence. It is in fact always true that the number of elements in the basis of the row space and that in of the column space is equal. The steps in the reasoning are as follows:
 * 1) The number of non zero rows in U is equal to the number of pivots (or leading non zero entries in each row) in U.
 * 2) The number of basic variables by their definition equals the number of pivot containing columns (and so equal the number of pivots).
 * 3) By the previous theorem the number of basic variables equals the number of elements in the basis of the column space.
 * 4) It follows that the bases have equal number of elements.

This unique number of elements in the two bases is called the rank of the matrix. Clearly since the rows of a matrix are the columns of its transpose, so a matrix and its transpose have the same rank. The rank of a matrix A is often written as Rank (A) just as the nullity is written as Nullity (A).

The rank nullity theorem
We now proceed to a very important theorem of linear algebra, called the rank nullity theorem. Another form of this theorem will appear in the chapter on linear transformations. The theorem, in our context, is :

For an m x n matrix A,  Rank (A) + Nullity (A) = n = Number of columns of A

The logic behind this theorem is clear. The rank, as we have seen earlier, corresponds to the number of basic variables and the nullity to the number of free variables. Since any column is either basic or free (but not both) obviously the theorem is true.

Readers acquainted with the first isomorphism theorem of groups can note that this theorem can be related with it. We shall later see how this is done.

Exercises
1. Evaluate bases for the column and row spaces for:
 * 1. $$\begin{pmatrix}

2 & 1 & -2 \\ 1 & -2 & 1 \\  -3 & 1 & 1  \end{pmatrix} $$
 * 2. $$\begin{pmatrix}

-2 & -1 & 4 & 2 \\ 1 & -2 & 1 & 1 \\  -3 & 3 & -5 & -3 \end{pmatrix} $$
 * 3. $$\begin{pmatrix}

1 & 1 & 1 \\ 1 & 0 & 1 \\  0 & 1 & 1 \end{pmatrix} $$

2. Show that if A is an m x n matrix then the row space of A coincides with that of its row echelon form U.

 * Hint: Prove that an elementary row transformation on any row of A doesn't alter the fact that it is a linear combination of the rows of A.

3. Show that the non zero rows of a matrix in row echelon form are linearly independent.

 * Hint: Suppose $$\alpha_1r_1+\cdots \alpha_mr_m=0$$ where $$\alpha_i$$ are scalars and $$r_i$$ the non zero rows. Now if the first pivot occurs at the (1,j)th position of the matrix then the jth component of each row other then of $$r_1$$ is 0. So $$\alpha_1$$ is zero. Similarly all other $$\alpha_i$$'s are also necessarily zero.

4. Combine the above two results to show that the non zero rows of a matrix in its row echelon form U form a basis of both R(A) and R(U).

5. Show that a n order square matrix is invertibile $$\iff$$ its rank is n $$\iff$$ R(A) = C(A) = $$\mathbb{R}^n$$ $$\iff$$ Ax = b has a unique solution for each m dimensional vector b.

6. Show that if A is a m x n and B a n x p matrix then:
 * 1. C(AB) $$\subseteq $$ C(A).
 * 2. R(AB) $$\subseteq $$ R(B).

 * Hint: For (1) note that $$\{ABx : x\in\mathbb{R}^p\}\subseteq\{Ay : y\in\mathbb{R}^n\}$$ and for (2) note that $$R(AB) = C((AB)^T) = C(B^TA^T) \subseteq C(B^T) = R(B)$$

7. A submatrix of a matrix A is a matrix obtained by deleting some rows and/or columns of A. Show that for every submatrix C of A, we have Rank (C) $$\le$$ Rank (A).

 * Hint: Consider a matrix B formed by deleting rows of A not in C. Then Rank (B) $$\le$$ Rank (A) and Rank (C) $$\le$$ Rank (B).

8. Show that a m x n matrix A of rank r has at least one r x r submatrix of rank r, that is, A has an invertible submatrix of order r.

 * Hint: Let B be the matrix consisting of r linearly independent row vectors of A. Since Rank (B) = r so we can take r linearly independent vectors of B to get an r x r invertible submatrix C.

title: Linear Algebra/Column and Row Spaces


text:
User:Jdlambert

Sandboxing... Electronics Engineering Technology

title: User:Jdlambert


text: User talk:209.168.175.253

title: User talk:209.168.175.253


text:
Talk:Adventist Youth Honors Answer Book/Vocational/Typewriting

If this is a 1929 Honor, where were these parts on a 1929 typewriter? k. Line-finder control l. Paper centering scale m. Cardholder o. Pitch selection lever

(BTW, I am having way too much fun)

 * The honor was originally introduced in 1929, but like most honors, it was updated as time went by. I have a feeling it was reintroduced in 1986, and it may have been updated then.  Typewriters were almost dead in 1986, but I do remember trying to buy a ribbon for one in 1987.  The PC revolution was underway, but it had not yet completely supplanted our old friend.  I think the last nail in the typewriter's coffin was the affordable laser printer, circa 1995. It would certainly be interesting to see the original honor requirements. --Jomegat 21:16, 22 May 2007 (UTC)


text:
User:Komislaw

Rozdział 1 - Formatowanie tekstu
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Donec euismod sem eu dolor. Phasellus auctor gravida velit. Praesent ante enim, porttitor ac,  hendrerit  a, dapibus in, elit. In hac habitasse platea dictumst. Vivamus dolor nulla, cursus nec, venenatis a, tincidunt sed, diam.

Rozdział 2 - Hasła

 * Haslo : element bezpieczeństwa systemu rozpoznania - obcy / swój - między innymi w operacjach szpiegowskich, wojskowych lub innych niejawnych np. hasło - odzew
 * Hasło 2 : klucz zabezpieczający dostęp do informacji lub urządzenia np. PIN

Lista numerowana

 * 1) Punkt pierwszy
 * 2) Punkt drugi
 * 3) Podpunkt pierwszy do punktu drugiego
 * 4) Podpunkt drugi
 * 5) Punkt trzeci

Wypunktowanie

 * Punkt 1
 * Punkt 2
 * Podpunkt 1
 * Podpunkt 2
 * Punkt 4

title: User:Komislaw


text:
User talk:198.215.16.159

Please stop deleting content from Raising Cattle. --Whiteknight (talk) 19:44, 22 May 2007 (UTC)

 * I have blocked you for 1 day. Please do not delete any more content. --Whiteknight (talk) 19:56, 22 May 2007 (UTC)

title: User talk:198.215.16.159


text: User:Turelion

title: User:Turelion


text:
User talk:Thinknscience

Test Message
This will create your talk page.

Pete 20:22, 22 May 2007 (UTC)

Test 2
This is the second test.

Pete 20:22, 22 May 2007 (UTC)

title: User talk:Thinknscience


text:
User:Ssugioka

This is my user page, but I'm not really a user.

title: User:Ssugioka


text:
Talk:Korean/RWP/Lesson 4

Lesson planning
The following words, moved from the lesson plan, may be incorporated into lesson 4 exercises. Rodasmith 21:31, 22 May 2007 (UTC)

ㅔ
Words for practise:

 * Indonesia 인도네시아
 * Ireland 아일랜드
 * Israel 이스라엘
 * Lebanon 레바논
 * Netherlands 네덜란드
 * Serbia 세르비아
 * Slovenia 슬로베니아
 * Venezuela 베네수엘라
 * Berlin 베를린
 * Bern 베른
 * Bombay 봄베이
 * Buenos Aires 부에노스아이레스
 * Denver 덴버
 * Kobe 고베
 * Lome 로메
 * lemondade 레모네이드

 * Rio de Janeiro 리우데자네이루
 * Sarajevo 사라예보
 * Moses 모세
 * Osama Bin Laden 오사마 빈라덴
 * Sadam Hussein 사담 후세인
 * Indiana 인디에나

Possibly nonstandard Korean:
 * mail 메일
 * Belarus 벨라루스

ㅐ
Words for practise:
 * Miami 마이애미
 * Dallas 댈러스
 * San Diego 샌디에이고
 * Taegu 대구 (alternatively: Daegu)
 * dancer 댄서
 * lab 랩
 * Alabama 앨라배마
 * 메릴랜드
 * Nevada 네바다
 * 로드아일랜드

new:
 * IBM 아이비엠
 * Maryland 메릴랜드
 * Rhode Island 로드아일랜드

ㅎ
Words for practise:
 * Bahamas 바하마
 * Hungary 헝가리
 * Doha 도하
 * Hanoi 하노이
 * Harare 하라레
 * Honolulu 호놀룰루
 * Harbin
 * Shanghai 상하이
 * hamburger 햄버거
 * House 하우스 (music genre)
 * 오하이오

New:
 * Idaho 아이다호
 * Ohio 오하이오

ㅈ
Words for practise:
 * Abuja 아부자
 * Nigeria 나이지리아
 * Zambia 잠비아
 * Nanjing 난징
 * bazaar 바자
 * image 이미지
 * 미주리
 * Algeria 알제리
 * Belize 벨리즈
 * Brazil 브라질
 * Niger 니제르
 * Basel 바젤
 * Beijing 베이징
 * Brasilia 브라질리아
 * Geneva 제네바
 * Los Angeles 로스앤젤레스
 * Taejon 대전 (alternatively: Daejon)
 * Zagreb 자그레브
 * engine 엔진
 * garage 개라지
 * Jazz 재즈
 * message 메시지
 * orange juice 오랜지주스
 * Soju 소주 (traditional Korean drink)
 * television 넬레비전
 * Georgia 조지아
 * 루이지애나, 버지니아 (some active).
 * Armenia 아르메니아

new:
 * juice 주스
 * Disney 디즈니
 * GM Daewoo 지엠대우
 * Kim Jong-il 김정일
 * Arizona 애리조나
 * Louisiana 루이지애나
 * Missouri 미주리
 * Virginia 버지니아

title: Talk:Korean/RWP/Lesson 4


text:
Change Issues in Curriculum and Instruction/Other Issues Worth Investigating/19 May, 2007

1. Balanced Constructivism:  Challenging Within Boundaries

2. Learning how to Learn (and Teach):  Experimenting with One's Own Learning (and Teaching) Styles

3. Perspective

4. Reform in Reality:  How can educators' good ideas actually be implemented in the real world?

5. Teachers as Content Authorities:  How can teachers teach effectively without "knowing everything"? What is an appropriate level of student participation in the teaching process? Switching roles (teacher/learner) across a continuum at appropriate times.

6. Linking the Unknown to the Known

7. Educational By-Products:  Learning One Thing After Being Taught Another

8. Maximizing the Effectiveness of Dialogue:  Effectively Using Conversation in Education


text:
User talk:CT1010

I have blocked your account from editing Wikibooks for 2 hours. Please don't post the same message across different pages and user pages on Wikibooks. Many people consider this to be spamming. Also we prefer messages to be in English so that all of our users can understand what is being said. Xania talk 22:31, 22 May 2007 (UTC)

title: User talk:CT1010


text:
User talk:Adriano~enwikibooks

Hello Adriano, welcome to wikibooks! We can create your new book here: Fermat's Last Theorem. I dont know what you mean when you say "it needs to go under the corresponding section to that of the original on Wikibooks.it" Do you mean it needs to have the same category, or that it needs to go on the same bookshelf, or what?

Anyway, Once you have the text, it's as easy as clicking "Edit this Page" and pasting it in. any images or broken links that we need to fix, as well as any necessary formatting, can be fixed after the fact. Just let me know what you need, and I'll set you up. You can ask me a question at any time on my user talk page. --Whiteknight (talk) 23:03, 22 May 2007 (UTC)

 * The book looks very good! Do you have a link to the copy on the italian wikibooks? I don't know italian, but i should be able to pick my way through the markup and fix the image sizes and all. Also, we can create an "interwiki" link between the two books, and give you credit as the translator. --Whiteknight (Page) (Talk) 18:26, 25 May 2007 (UTC)

I created a link to the italian book, and I created a link to the english book from the italian version. If you look in the lower-left corner of the page, you will see a link to "Italiano", which will take you to the italian book. I also made a note on the cover of your book that you were the translator. --Whiteknight (Page) (Talk) 02:36, 29 May 2007 (UTC)

 * We have some pages about the markup at Help:Contents/Editing Wikibooks, if you want to look through that. I want to warn you that our help pages are a little old and not always complete. You certainly aren't "bothering" me, you can ask me any question at any time. If you can't find the answers you need in that help page, you can ask me, i'm happy to help. --Whiteknight (Page) (Talk) 18:19, 29 May 2007 (UTC)

Your account will be renamed
Hello,

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

Unfortunately, your account clashes with another account also called Adriano. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Adriano~enwikibooks 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 22:55, 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) 04:29, 19 April 2015 (UTC)

title: User talk:Adriano~enwikibooks


text:
Talk:IB English

Notes on Specific Books
To be honest, I believe having notes to 3 novels is rather pointless for this module. The whole aim of IB is to be "International". This infers that a variety of novels will be focused on throughout the various IB world schools, as the IBO prescribed title list is expansive. Implicitly, this means a minority of schools will have done these 3 novels, and it will only be useful to them. So what are the candidates at the other schools to do? What they've always been doing, using Sparknotes, or paying attention in class. Thus, it would make more sense to take off these links completely. Any comments?

Akademix 23:11, 22 May 2007 (UTC)

title: Talk:IB English


text:
User:Psychless

I usually contribute to the English version of Wikipedia as The Psychless. Please leave all messages on my talk page. I mainly made this account to make sure I have the same username across all projects (well almost) and if I ever wanted to do something on this project.

title: User:Psychless


text:
User:IvanLanin/monobook.css

@import "http://id.wikipedia.org/w/index.php?title=Pengguna:IvanLanin/monobook.css&action=raw&ctype=text/css";

title: User:IvanLanin/monobook.css


text:
Talk:Teaching Assistant in France Survival Guide

does anyone know what the deal is with receiving CAF money? is this possible? it seems like the wiki suggests so, but i have read nothing of it anywhere else in my online readings. —Preceding unsigned comment added by 68.184.33.93 (discuss • contribs) 2007-05-23T11:37:48


text:
User talk:Fatso2424~enwikibooks

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 00:48, 23 May 2007 (UTC)

Your account will be renamed
Hello,

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

Unfortunately, your account clashes with another account also called Fatso2424. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Fatso2424~enwikibooks 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 23:09, 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) 04:59, 19 April 2015 (UTC)

title: User talk:Fatso2424~enwikibooks


text:
Talk:Network Plus Certification/Technologies/Addressing Formats

what portions of a mac address encodes an identifier representing the manufacturer of the card?
 * The first 24 bits do. They are also known as the Organizationally Unique Identifier, or OUI, and are assigned by the IEEE for a hefty fee.  For a smaller fee they will assign an Individual Assignment Block (IAB) which is 36 bits long.  If using an OUI, an organization can use the lower 24 bits of the 48-bit mac address to serialize each NIC, meaning they get 16 million MACs.  If using an IAB, the organization only gets 12 bits to serialize each NIC, meaning they get 4096 MACs. --Jomegat 02:16, 23 May 2007 (UTC)


text:
User talk:FStonier

Hello, welcome to Wikibooks!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 13:19, 29 May 2007 (UTC)

Frank was here!

title: User talk:FStonier


text:
User talk:71.7.60.88

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. --Jomegat 02:08, 23 May 2007 (UTC)

title: User talk:71.7.60.88


text:
User:FStonier

Frank was here!

title: User:FStonier


text:
User talk:203.29.244.7

You have been blocked from editing Wikibooks for a period of one day for vandalizing Of Mice and Men. When you come back, please try to make positive contributions. --Jomegat 03:41, 23 May 2007 (UTC)

Please stop adding nonsense to Wikibooks. It is considered vandalism. --Az1568(Talk) 02:04, 24 May 2007 (UTC)

title: User talk:203.29.244.7