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General Chemistry/Liquids

Liquids at a Molecular Level
Liquids have some intermolecular bonding, but it isn't as strong as bonding in a solid. As a result, the molecules are close together, but they are not tightly packed. Instead, they are free to slide past each other. Liquids occur at temperatures above the melting point of a substance, but below its boiling point. At the melting point, the molecules are moving slow enough to form rigid bonds and become a solid. At the boiling point, the molecules are moving so fast that they cannot form any bonds and become a gas.

Characteristics of Liquids
Liquids have definite volume, but indefinite shape. They are free to form droplets and puddles when they are not inside a container. When a liquid is inside a container, it will take its shape. Unlike gases, a liquid will not change its volume to spread out and completely fill a container. There is enough intermolecular bonding to give liquids a definite volume.

Liquids are fluid, able to flow and take any shape. This occurs due to the weak intermolecular bonding that allows the molecules to slide past each other freely. As a result of being fluid, liquids exhibit many interesting properties that solids do not, including capillary action and diffusion.

Liquids, like gases, undergo diffusion when mixed. This can be seen by adding food coloring to water. Different liquids, when added, will chaotically spread out and mix together. Diffusion will occur faster when the liquid is warmer because the increased kinetic energy allows the molecules to move faster and collide more frequently.

Liquids are usually considered incompressible. The molecules are already close together, so it is difficult to compress them any more. Under very high pressures, liquids will actually compress, but not very much.

Liquids, unlike gases, have a distinct surface—they need not take their container's shape. This allows the formation of droplets and puddles.

Cohesion and Adhesion
The molecules of a liquid are attracted to each other. This is called cohesion. Molecules like methane are non-polar, so they are held together only by van der Waals forces. These molecules will have minimal cohesion. In contrast, water molecules use hydrogen bonding, so they display strong cohesion. A cohesive liquid will form more spherical droplets and have much higher surface tension.

Adhesion is the attraction of a liquid molecule to its surroundings. Adhesive liquids will demonstrate capillary action. They are also more "wet". Mercury is very cohesive, but not adhesive. As a result, it doesn't leave behind residue as it rolls across a surface. Water, on the other hand, is much more adhesive. When water rolls across a surface, it wets that surface because some of the molecules adhere to it.

Surface Tension and Capillary Action
When water drops are on an impermeable (waterproof) surface, they tend to form beads. This is due to its surface tension. Liquid molecules pull at each other, and as a result they decrease their surface area. The molecules at the boundary of the liquid are pulled in, causing a droplet shape. When water is on a permeable surface, it spreads out, as can be seen with water on a paper towel. This capillary action explains how water in the ground reaches the top of trees that are hundreds of feet tall.

Pressure
Liquids will distribute pressure evenly. This concept, known as Pascal's Law, is crucial for equipment like hydraulic brakes. It is a result of their incompressibility.

Liquids will evaporate. Although the average kinetic energy of the molecules is too low to overcome bonding and become a gas, individual molecules will occasionally have above-average energy and break free from the surface of the liquid. The molecule then escapes to the gas phase. At the same time, however, a gas molecule may hit the surface of the liquid and slow down enough to join the liquid. A glass of water left outside in the sun will eventually become empty. The sunlight adds energy to the molecules, allowing some to escape as a gas. Eventually, all molecules will escape. The tendency of a liquid to evaporate depends on its intermolecular forces. Volatile liquids tend to evaporate quickly have relatively weak intermolecular forces keeping the molecules together, making it easier for them to escape the liquid phase. Conversely, non-volatile liquids do not evaporate to any visible extent due to the presence very strong intermolecular forces.

The evaporation increases with temperature. It can be measured by vapor pressure, the amount of pressure exerted by the evaporated gas above the liquid's surface. Vapor pressure increases with temperature, and once it reaches the pressure of the surrounding atmosphere, the liquid will boil. Vapor pressure also depends on the intensity of intermolecular forces in the liquid.

Viscosity
Viscosity refers to the liquid's resistance to flow. For example, maple syrup has a relatively high viscosity when compared to water because maple syrup flows much slower than water, which flows relatively quickly and easily. The difference in viscosity between these two liquids is due to the attractive forces within the specific liquid. In order to flow, molecules must roll and move over each other. A solution with low attractive forces would allow the molecules to move in a more free and easy manner, decreasing the viscosity.

In most cases, the viscosity of a liquid decreases as the temperature of a liquid is increased. Increasing the temperature of a liquid causes the molecules to have a higher kinetic energy. This increase in kinetic energy breaks down the intermolecular forces present in the liquid. Since viscosity is dependent on these attractive forces, the viscosity will decrease when the kinetic energy is increased.

title: General Chemistry/Liquids


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General Chemistry/Solids

Characteristics of Solids
Shape and volume are both definite in solids. Although solids have a rigid shape, a large amount of force can cause deformation to the structure of a solid. There are three types of deformation:

Most materials are capable of all three types of deformation. Small amounts of stress cause elastic deformation, but large amounts will cause plastic deformation. In the event of repeated deformation or tremendous stress, brittle deformation occurs.

Solids are incompressible. Solids may break or deform under stress, but they tolerate little compression. For instance, a wooden plank will break if force is applied, but it will not compress like a sponge. The only reason sponges compress is because they contain air pockets and undergo elastic deformation. Otherwise, solids will not compress. At the molecular level, this happens because the intermolecular bonds do not change size without breaking.

Some solids, usually metals, have properties like ductility and malleability. A ductile material can be stretched into long, thin wires. A malleable substance can be hammered into very thin sheets. Gold and copper are some of the most malleable and ductile substances known. These properties occur as a result of the metallic bonding.

Solids at the Molecular Level
Solids occur when there is enough intermolecular bonding to hold the molecules of a substance into a relatively rigid structure. The molecules are close together, and their movement is restricted to vibration. Solids occur at the lowest temperatures and highest pressures. As the temperature of a solid increases, so does the kinetic energy of its molecules. At the melting point, the molecules have enough energy to overcome their bonds and melt into a liquid. Likewise, a liquid will freeze once its molecules are not moving fast enough to avoid strong intermolecular bonds.

Compounds that have ionic bonding or metallic bonding are most likely to be found in the solid phase due to their high melting points. Also, covalent network substances (like diamond or quartz) are solids because the atoms are secured with covalent bonds, requiring extreme amounts of energy to separate them.

Types of Solids

 * Crystalline solids have a molecular structure with a specific geometric shape. The solid has a specific melting point at which all molecules begin to break free of their bonds. Substances like salt, diamond, and quartz are crystalline solids.  These solids usually form by cooling a liquid slowly, so that the molecules have time to arrange themselves in a crystalline structure as their bonds form.
 * Amorphous solids have a molecular structure with no specific shape. The solid melts over a range of temperatures because the amount of energy needed to break the bonds varies from molecule to molecule. Substances like coal and glass are amorphous.  Amorphous solids usually form when a liquid is cooled quickly, so there is no time for the molecules to arrange themselves into a crystal.

Crystalline solids are typically harder and more rigid. Coal and diamond are both made from elemental carbon, but coal is amorphous and diamond is crystalline. Because of its crystal structure, diamond is one of the hardest substances known, whereas coal can be scratched away with a fingernail. The crystal structure also explains diamond's brilliant, transparent appearance. Coal is black and dull because the disorder of the atoms does not allow light to pass.

Packing and Unit Cells
In crystalline solids, the atoms are arranged in a specific pattern. The smallest repeating part of this pattern is called the unit cell. The unit cell may have more atoms than the empirical formula of a substance because the geometric shape may require several atoms. In the case of sodium chloride, the empirical formula contains only two atoms, but the unit cell has 27 atoms.

The molecules of a solid are close packed. They arrange themselves in the densest shape possible. Usually, two different patterns occur.
 * Face-centered cubic or FCC
 * Hexagonal close-packed or HCP

FCC crystals have three alternating layers, described as ABCABCABC (every third layer is the same). The layers are arranged so that each unit cell is halfway between the two unit cells above or below it. HCP crystals have two alternating layers, described as ABABABAB (every other layer is the same).

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

title: General Chemistry/Solids


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Non-Programmer's Tutorial for Python 2.6/Induction

Simple Programs
Python is such a simple language even a non-programmer could understand it. Here are some examples:

This program prints "Hello, World!" on the screen. Even longer programs can be easily understood

Weird Features
Some weird features of Python include the fact that grouping is shown by how indented a line is. For example,

is not the same as:

Instead, some languages prefer to have everything written like this:

In other languages, you can organize it in any way you want. It's different in Python.


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Mac OS X Tiger/Utilities/Grab

Take screenshots the hard way!

It's just easier to press cmd-shift-3.

title: Mac OS X Tiger/Utilities/Grab


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A-level Chemistry/OCR (Salters)/Isomerism

Geometric isomerism
Geometric isomerism, also known as cis-trans isomerism, is commonly observed in alkenes.

Cis is Latin for "on this side of" and refers to the isomer that has both substituents on the same side of the carbon-carbon double bond.

Trans is Latin for "across" and refers to the isomer that has the substituents on opposite sides of the carbon-carbon double bond.

Rotation around an alkene double bond is restricted

In alkenes, there is no free rotation about the double bond, unlike in alkanes. Consequently, groups attached to a double bonded carbon cannot exchange places. Therefore, the cis and trans isomers are separable compounds because they cannot interconvert.

Alkenes such as ethene (shown to the right) have a carbon-carbon double bond. In such a double bond, there is significant electron density above and below the plane of the bond. Rotation around the bond is greatly restricted by a large energy barrier. For rotation to occur, groups attached to one of the double-bonded carbons would have to temporarily occupy this high electron density region, resulting in very high repulsion between the electrons in the group and the electrons in the double bond.

Sometimes cis and trans isomers can interconvert, but this usually requires UV light to provide the energy to overcome the high rotational energy barrier.

Rotation around an alkane single bond is free
In alkanes, the situation is different. There is free rotation about the carbon-carbon bond because there are no regions of electron density above and below the bond that repel rotating groups. Whereas alkenes have cis and trans isomers, alkanes have eclipsed and anti conformers. Unlike geometric isomers, conformers can interconvert with ease and cannot normally be isolated from each other — they are both molecules of the same compound, just in different rotational orientations.

Optical isomerism
For compounds to exhibit optical isomerism, they need to have two non-superimposable mirror images.

For the purposes of this A-level, that means tetrahedral carbon with four different groups attached.

Condition for optical Isomer
the molecule must have a chiral center, each isomer is the mirror image of other


text: User talk:Yurik

title: User talk:Yurik


text: User:Yurik

title: User:Yurik


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SuperCard Programming/Tips & Tricks/Stacks as document templates

= Stacks as documents =

One approach is to store your template as a user prop and write it out when you need a new document.

storeDoc below is run once when you are preparing your application: on storedoc answer file "Choose a template to use:" if it is "" then exit storeDoc put it into tFile open file tFile read from file tfile until end close file Tfile define the UDoc of this proj set the uDoc of this proj to it end storeDoc

newDoc when you want a new document: on newDoc ask file "Name your doc:" if it is "" then exit newDoc put it into tFile put the fileType into toldType set the fileType to RUNXMDOX --Or your standalone's creator and file Type open file tfile write the uDoc of this proj to file tfile close file tfile set the fileType to toldType

set the itemdel to colon put last item of tfile into tWindowName set the name of wd 1 of proj tFile to tWindowName

open proj tFile end newDoc

With bundled apps it would also be possible to just store a template somewhere in the bundle and copy it out when you need a new project.

Obviously things can get a bit more complex if you want to open an untitled document which works like a standard document and needs to be explicitly saved.

Keith's update of Graham Samuel's notes on standalones useful: []


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User:Whiteknight/New Book Guide/Print and PDF Versions

Print Versions
A print version has a singular purpose: to be printed. A printable version is typically not intended to be read in the web browser, but instead to be printed onto actual paper. For that reason, many of the templates that are used on print versions look lousy on the web browser, but look great when printed. Wikis present duality: On the internet they are very flexible, dynamic, and easy to edit. However, without some special effort, they tend to produce books which look lousy when printed. Printable versions of the book are very valuable to ensure it can reach the largest possible audience, but require special care to minimize author effort and maximize aesthetics.

A printable version which is difficult to update and maintain will fall back from the bleeding edge of the most recent version of the book. The result is a printable version which never reflects the most recent fixes and additions, and therefore is an anchor to prevent the book from growing. Also if you create a boring and repetitive task, such as having to make all edits twice (once for the wiki and once for the printable version), authors are going to be less likely to do both and may be less likely to do either. What's needed is a way to automatically fold all changes made on the wiki into the printable version with a minimum of repetitive effort from the authors and editors. A little bit of work upfront preparing things like navigation templates, print versions, and collections can help to automate this process and keep all versions of the book aligned.

Navigation Templates
Navigation templates often use colors and HTML/CSS formatting that doesn't always translate well to a printed medium. If your book has large navigation templates, it might be worthwhile to make them "disappear" in the printed version. This can be accomplished in one of several ways:

 * 1) Use  in the template to prevent it from being printed
 * 2) *Pros: Doesn't print, can be used on any page (so individual chapters can be printed without the navigation template).
 * 3) *Cons: Appears on the printable version, so it can cause worry. Even though it appears on the screen, it doesnt get sent to the printer, decreasing the relationship between "what you see" and "what you get". Also, may still appear in a PDF generated using the collections extension (more testing is needed to confirm this).
 * 4) Use parser functions to make the template invisible on the printable version page
 * 5) *Pros: Don't appear on the printable version pages at all.
 * 6) *Cons: Can be difficult to program them correctly. Templates will still appear on individual chapters, which means if you print an individual chapter you will see the templates. Templates generated in this way are also not portable between books, or even between multiple print editions in the same book.
 * 7) Use Category:Exclude in print
 * Pros: Won't appear in PDFs or publish-on-demand books generated through the collections extension.
 * Cons: Will appear in normal print versions, and PDF versions generated by hand.
 * 1) Use printable template substitutions
 * 2) Pros: Allows templates to be formatted differently on-wiki and in generated collections.
 * 3) Cons: Doesn't have any effect in normal printable versions, or hand-generated PDF versions.

In reality, no single solution above is useful in all cases, and a combination of them is typically needed. It's important to keep print versions, PDF versions, and collections in mind when creating your new book because these are the most common vectors through which readers will be exposed to your book once it is written.

Cover Pages
A cover page is certainly optional, but it adds a certain professional look to a book that is hard to beat. Besides the printable and PDF versions, the cover page might never be seen at all on Wikibooks, so authors tend to view it as "out of sight, out of mind".

Some publishers may prefer a "cover image", which will be dependent on the form factor used by the publisher. Since we only use PediaPress right now for print-on-demand publishing, and since they don't currently allow custom cover art, this point is basically moot. However, if a PDF of a book is taken to a different publisher, different rules and capabilities may apply. For printable versions and PDFs creating a cover page using HTML and wikitext is usually sufficient and easy to do once and forget about. For other applications such as publishing, different rules and requirements might be made that can't be easily done on the wiki.

Licensing
In printed versions it is of paramount importance to include a copy of the GFDL. This can be accomplished by adding this template to the beginning of the book (right after the cover page):

And adding this to the end of the book:

= GNU Free Documentation License =

Failure to take these easy steps could cause large problems, not only for you as an author, but for the entire Wikibooks project. Notice that the GFDL is automatically included in a collection.

Creating a Print Version
Creating a print version can be a difficult task. However, several Wikibooks users have created automated print version creator tools. These tools frequently require either the use of custom User JavaScripts or the use of external programs (most of the external programs for the purpose are written in Perl).

If you would like to use a custom User JavaScript for the purpose, I have written a tool for the creation of print versions:

Note: You won't be able to see this tool until you install the custom javascripts. Instructions to installing the javascripts are located at User:Whiteknight/Javascripts

PDF Versions
There are three different schools of thought to the creation of a PDF version:

 * 1) Direct conversion of the printable version into a PDF, typically though some sort of PDF creation software.
 * 2) Translation of the text and the formatting to LaTeX, and then creation of a PDF.
 * 3) The use of an automatic translator program, to convert Wiki syntax directly to a PDF, or to LaTeX and then to PDF.

The first approach relies on the MediaWiki software to convert the Wiki to HTML, and then the converter program to create the PDF. There are many free options to perform this conversion, and many professional software packages as well. It is important to remember that if you are using a "Print to PDF" converter, that you modify your print options to remove unnecessary page headers and other artifacts.

The second approach is the most time-consuming and also the most difficult to keep up to date. However, the benefit to this is that the book has available both a LaTeX version and a PDF version, which can be downloaded independently. This can be the most difficult option, especially if the authors of the book are not familiar with LaTeX formatting.

The third option is to use some sort of automatic converter program to convert the Wiki syntax into an appropriate form. The problem with this option, while it could conceptually be the easiest to use, is that no suitable converter software programs have been created for this purpose. There are programs in the works, of course, and dedicated volunteers are always working to improve these packages.

A PDF version is the easiest version for a person to download and read. PDF versions can be read offline, and unlike a web browser, PDF versions are typically WYSIWYG, which means that the formatting does not magically change when you print it. As a caveat, remember that PDFs are static files that are not amenable to easy editing. Also, if the PDF is generated by hand and not through the collections extension, it can be hard to update or reproduce.

Collections
Collections are easy to make, often by directly copying the TOC of the book and making a few minor formatting changes. Like a printable version, collections use pages on the wiki directly and are therefore kept up to date with all changes made to pages in the book. Collections can be used to create PDF versions of the book, but also for print-on-demand publishing from PediaPress. Automated tools such as my Visual Book Designer gadget can be used to create collections automatically from an outline or an existing book TOC. This feature is under active development still, so there are some bugs and limitations with it.

Because Collections stay updated with the most recent changes on the wiki (like print versions) and can be easily downloaded and distributed (like PDF versions), and because they have the added benefit of print-on-demand publishing, they are probably going to become the primary method of organizing and printing books in the future. Because the interface isn't quite as polished as I would like, and because it's not obvious enough how to get a PDF from a book to a new user, I'm not ready to say that print versions and PDF files need to be phased out yet, but it's definitely going to happen eventually.

Creating Collections
Collections can be created in two different ways:

 * 1) Go to every page that you want in the collection and click the "Add wiki page" link on the left-hand side of the page. Repeat this for all pages in the book. Once you have added all the pages to the collection that you want, go to Special:Collection to save it, convert it to PDF or ODT, or purchase a Print-on-demand copy from PediaPress.
 * 2) Create a wiki page using a particular syntax. This syntax is similar in some regards to how TOCs are created, but it's probably too simplistic to serve as a TOC by itself.

Luckily, my Visual Book Designer is already equipped to create Collections pages from an outline or from an existing book TOC. Load the book into the gadget (click File -> Load TOC to get an existing book), and then click File -> Save (as personal collection) or File -> Save (as community collection) to create the collection page.

Loading Collections
To load an existing collection, go to the collection page and click the "Load collection" link on the left side bar. If you already have an active collection, you will be given the option to overwrite your collection with the saved collection, or to append one to the other.


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User:Whiteknight/New Book Guide/Child Versions

What is a Child Version?
A typical wikibook is going to have a large number of pages, not all of which are needed for a single course of study. Consider the Calculus book: Calculus is typically broken up into multiple semesters of study. Students only need to learn about certain sections in each course, and any additional materials (even if they fall under the umbrella of "calculus") are just wasted in a printed book.

A child version, in essence, is a reuse of existing book pages in a second printable version. The pages in the primary printed version are rearranged, and unnecessary chapters are removed, in order to put the focus on a particular subset of the available information.

Print Versioning
Print versioning is a verb that I use to describe the act of creating multiple print versions (child versions) of a book to suit different needs of the target audience. Consider the Control Systems book. The topic of Control Systems (or, more generally, "Control Engineering") is typically broken down into sub-sections based on the length of the class (semester, trimester, year), and the level of the students. For instance, in my university, this topic was broken down into 3 semesters, and each semester used a different textbook!

Textbooks also need to follow certain standards. At the university level, things are a little more lax, but at the grade school level, there are clear standards in place that need to be met for a textbook to be considered as an acceptable text. Unfortunately for Wikibooks, these standards vary from place to place, and it would be impossible to write separate books on the same topic for different localized sets of standards. However, There are some good alternatives:

 * 1) Break material down into atomic chunks, and list a "suggested reading order" for each different localized set of standards.
 * 2) Create separate Tables of Contents (TOC) and separate print versions for each new localization, transcluding pages from a "master work" containing all pages.

The second option is the best, and makes the best use of the wiki software. In this way, we only need to write all the content of the book once, and people can then prepare individual TOCs and print versions to suit their specific needs.

Creating Child Versions
Creating a child version is typically as easy as copying your existing printable version to a new page, and rearranging the pages as necessary. Sometimes it is useful to create some meta-content pages for the child version, to specify what kinds of materials do and don't belong in that child version. Occasionally, it can be a good idea to create a separate TOC for the child version, although any inter-page navigation that your book uses (forward and back links) won't function properly in your child versions.

Reading and Writing Versions
For a book that is sufficiently old and established, it might be worthwhile to create versions of the book that are specifically designed to be read, but not edited. The raw content pages can be transcluded into a "formatting page", which contains necessary formatting to make the content more aesthetically appealing. To my knowledge there are currently no books that use this practice, although Several books attempted it in the past.


text:
Cookbook talk:Garlic Bread

More traditional recipe
It would be good if someone could add a more traditional recipe without all this cheesy crap (is that an American thing?) Nil Einne 01:50, 17 May 2007 (UTC)

Good point. Plus instructions without mentioning 'microwave'. I imagine every American house must have a microwave yet in countries where people eat properly, are healthy rather than obese and enjoy cooking you will not find a microwave!

title: Cookbook talk:Garlic Bread


text:
User:Chowbok/monobook.css

a.extiw { color: green !important; }

title: User:Chowbok/monobook.css


text:
Cookbook talk:Cardamom

you should distinguish between green & black cardamom – they are completely different!

title: Cookbook talk:Cardamom


text:
User talk:Nonenmac

Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
 * To learn the wiki-markup-language syntax, see Help:Editing.
 * You should sign your name on Talk and vote pages using four tildes, like this: ~~~~
 * There is a box at the top of the edit window that will insert this, too; it looks like part of a signature.
 * Remember to conduct any editing experiments in the sandbox.
 * You can tell the community something about yourself in your userpage.
 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

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 06:43, 17 May 2007 (UTC)

Combinatorics
I noticed your edits on the Combinatorics page. Do you have any suggestions on the table of contents the book should have. Regards--Shahab (talk) 12:35, 21 September 2008 (UTC)

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We sent you an e-mail
Hello ,

Really sorry for the inconvenience. This is a gentle note to request that you check your email. We sent you a message titled "The Community Insights survey is coming!". If you have questions, email surveys@wikimedia.org.

You can see my explanation here.

MediaWiki message delivery (discuss • contribs) 18:48, 25 September 2020 (UTC)

Flora of New York/sn
Having spent the best part of a morning trying to figure out WHERE this was leaking a SPAN tag, I had to conclude it's too convoluted to be maintained. Please rewrite or simplify this template so it can be maintained by others. More complete documentation would also be helpful. Thanks. ShakespeareFan00 (discuss • contribs) 12:41, 25 November 2023 (UTC)

 * I've changed the way that I do synonym lists and have been slowly replacing the /sn templates with special-purpose templates for each taxon type. I'll put more effort into the change-over, but it will still take a while. Nonenmac (discuss • contribs) 21:53, 25 November 2023 (UTC)

title: User talk:Nonenmac


text:
User talk:58.173.0.5

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 07:06, 17 May 2007 (UTC)

title: User talk:58.173.0.5


text:
The Poetry of Gaius Valerius Catullus/Preface

This book is designed to introduce people to the poems of Gaius Valerius Catullus, an influential and gifted poet. Formatted as a Wikibook, its strength lies in the influx of ideas from a global perspective to provide the best critical analysis of Catullus and his Carmina possible. We hope that you find the content interesting and informative to your purposes. The poems here have the original Latin and an English translation, combined with notes about the poem, vocabulary, and links to other resources on the net. Contextual allusions are explained to create a vivid picture of Roman life and all of its specifics.

None of the notes or translations are copyrighted and can be used without consequence. You are also invited to contribute to the pages here and to be bold in making changes and suggestions. This book is constantly growing and developing, to encompass a global community of scholars here at Wikibooks.

Catullus is a common first choice for students of Latin. His poems are concise and elegant and not laden with unnecessarily complex grammar and vocabulary. But more importantly, he is a fun loving personality, who wrote about many themes as common today as they were then; love, betrayal, friendship, and rivalry. He is also one of the few writers of whom a nearly complete body of work has survived, the Carmina. While this may not have been the original order that Catullus intended, it tells us a rich and fluent story of his experiences, something like an ancient stream of consciousness and internal thoughts. This is a valuable window into the life of a fascinating man.

His works are also valuable for their literary excellence. Catullus was of the era of “Golden Latin”, considered in the past to be the pinnacle of Roman literature. He has also been classed with the Latin “Neoterics” or “poetae novi” as Cicero degradingly called them. These were young poets and writers who broke away from the conventions of long epics and historical writing to try to express themselves through short, light hearted verses about the ordinary concerns of the average man. Horace, Ovid and Propertius were also part of this new literary revolution. Whilst epic and historical narratives are important resources for a historian, it is the complaints and celebration of an ordinary man that speaks across the millennia. Lust for a beautiful girl, a sinking feeling of despair and a tortured mind, forced to accept the truth are as relevant to modern humankind as they were to the Ancient Romans. Many of the techniques and ideas in Catullus’s poetry are still common in today’s popular writing.

Enjoy reading!


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Set Theory/Introduction

Many mathematics students have trouble understanding why set theory is important since their introduction to mathematics is usually based on arithmetic and algebra, rather than calculus. To understand why set theory is important, we should look at the fundamental question of what mathematics is. The engineer's viewpoint of mathematics is that it is a tool to solve problems, the scientist uses it to describe reality, the statistician uses it to build models, but what is mathematics to the mathematician?

Who Cares?
Descartes said it well when he said that "mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency." In mathematics, we have a fully formalized discipline - there is no subjectivity, because everything is based upon rules and definitions. While these rules are taught to children as the immutable "way that mathematics works," they are in fact only conveniences. Any defined set of rules is a valid construct in mathematics, but some (the ones that are studied) are more interesting than others. For instance, if we were to redefine equality of numbers so that any two numbers were equal, we would have a well defined system, but there are very few interesting things to say about it, since every proposition is true in such a system.

To answer our second question, then, mathematics is the building of interesting systems. We are still left with a confusion about why we would discuss this particularly in the context of set theory, which leads us to some history of the concept. In the middle of the 19th century, mathematics was formless and void—the Greek concept of rigorous proofs had been displaced by vagueness, and the rigor of a coherent set theory was still in the future. It was around this time that De Morgan and Boole began to write about logic, as a branch of mathematics. This was important to mathematics, because until this point, mathematical proofs were convincing arguments, but were not formalized.

Georg Cantor asked some very puzzling questions about infinity that undermined some very obvious notions. For instance, he started to claim that there was more than one infinity, and that they were different sizes. The furor and disputes, which were partially caused by ambiguousness in Newton's works concerning infinity and infinitesimals, led to a formalization of what numbers are. Because of this, all of modern mathematics was re-built using set theory, so that all of modern mathematics is in some sense just applications of the notion of a set.

What is a Set?
Before commencing our study of sets, we will comment on what a set is, and why they are used in mathematics. In many ways, a set is the simplest possible conceptual object, from which the rest of mathematics can be rigorously developed. It is conceptually easiest to start where set theory does. Everything in set theory is formed based on the empty set, denoted $$\emptyset$$ or $$\{\} \,$$. Other sets can contain the empty set, so that the set $$\{\emptyset\}$$ is a simple set containing only the empty set. We can build sets of varying complexity based on this idea; $$\{\emptyset,\{\emptyset\}\}$$ would be a set containing two items: the empty set, and the set containing the empty set.

Halmazelmélet/Bevezetés

title: Set Theory/Introduction


text:
Statistical Analysis: an Introduction using R/Chapter 3

Models
Anscombe?

 * R topics: user functions & grouping using curly braces

The Role of Assumptions
Imagine that we have some observations, and we want to use them to conclude something about the world around us. Statistics can help us in the common case when the observations are composed of a systematic component combined with random chance effects. A classic "toy" example is that of dice. Let us say that we wish to analyse the following result, obtained by rolling a die five times.

Although as a general rule, your first step should be to plot your data, there is little point in this instance. The dataset is so small that we can get a feel for it by just inspecting the numbers. The main striking feature is that we seem to have a preponderance of 6's, although this could, of course, be due to chance.

We could just treat the sequence {2,3,6,6,6} as a unique, arbitrary sequence of events. But this is rather pointless: data is usually analysed in order to seek general patterns, and by generalizing, increase our understanding. In this case, we might wish to use the result to decide whether the die is loaded in favour of sixes, and so if it can be relied upon to play a game.

Naively, we might hope to analyse this with a completely open mind; to approach the situation with no prior assumptions. A moment's thought should reveal this is impossible. For example, imagine that the die was a fraudster's dream: a sophisticated miniature machine that could be pre-programmed to give a particular sequence of numbers each day. If could, for example, be programmed to give a 2, followed by a 3, then three 6's, and spend the rest of the day rolling 1's. In this case, the results tally exactly with what we have observed, but they do not tell us anything about the subsequent behaviour of the die. Although it explains the data perfectly, most people would (quite reasonably) adopt the prior assumption that the "miniature machine" explanation was highly unlikely.

This is, of course, an extreme example, but it illustrates the point. Whether or not we realise it, we always examine data with prior notions of what is a reasonable explanation and what is not. Statistical analysis is the process of formalising these explanations, then using the data to choose between them. A good way to do this is by describing the assumptions that we have made in each case. For example, the following two assumptions are common to nearly all explanations that we might want to test.

 * The Assumption of Honesty : We assume that the data has been collected and reported “honestly”. This might not be the case if the data has been deliberately altered, or certain values have been “censored”. In our toy example, this might happen if say, the first four rolls were all 1's but the observer discarded these because this seemed an "unusual pattern”. Although dishonesty might seriously alter our conclusions, all we can do is to assume it has not taken place.

 * The Assumption of Random Error : We assume that the data have been affected by a process of “random chance”, causing the results to vary from one instance to the next in an unpredictable manner. In this case of the die, small changes in the way in which it is thrown and its subsequent tumbling and contact with the surface combine to produce one of six outcomes. Statisticians often (somewhat confusingly) refer to this process of chance as the source of “error” in the data. Describing the way in which chance works usually entails a whole set of other assumptions, which is the focus of   Chapter 3.

Making the assumptions clear
The problem with making any assumptions is that they are just that: assumptions. They may or may not not be true. When trying to convince others with our analysis, we are asking them to take our assumptions on trust. For this reason we should try to make widely accepted assumptions and, more importantly, ensure they are completely explicit. That way, others can decide for themselves if the analysis is to be trusted. We can encapsulate this most easily and concisely by formulating a model of the underlying process.

Modelling reality
A common way of understanding the world around us is to describe it in terms of a model. The more

Many basic statistics books teach simple tests, such as the t-test or sign-test. These are all based on an underlying model.

So what does an appropriate model look like? There are various ways in which we can

Some verbal models
Testing a particular model. We can easily disprove this by a single observation. However, we can never prove it. This turns out to be generally true. It is impossible to prove that something is the case, because there could always be a
 * Model 1 — a completely biased die : the die always gives a 6 when thrown. No extra assumptions are needed here, and in this extreme case, there is no error process.

 * Model 2 — a fair die: Here is a more complicated model, with the following assumptions
 * Each roll has 6 possible outcomes, with a number from 1-6 selected each time. This is sampling "with replacement". Defines the set of possibilities (the sample space)
 * The assumption of independence: one roll does not tell us anything extra about what will happen on a subsequent roll.
 * The assumption of homogeneity: the chance of any outcome is the same for each roll
 * Fairness: There is an equal chance of any of the 6 being chosen each number being equally probable. The

If the model contains an element of chance, how can we know whether ***

Once we have our models, we could either
 * try to disprove this model (although, because in this case there is always a slight chance of 6 in a row, we can never completely
 * compare the models in order to find out which is better

The simplest is simulation (compare to likelihood)

Simulating a model
One of the major ways in which we can use models is simulation. This will be a major way in which models are explored in this book. To do so, we need to convert the various models described above into simulations. The "fair die" model above provides a good, simple example. We will convert this model to a simulation in R. This involves learning a little about how R deals with numbers, so you should check that you are comfortable with the idea of functions in R, as described previously.

Sampling with replacement - describe here the idea of using random sampling for simulation

 * Statistical_Analysis:_an_Introduction_using_R/R/Random sampling

Testing Models
We can try to disprove a particular model, or select between different models using some informed judgement

Various ways to test a model. E.g. compare results from the simulation with the observed ones

We now have a simple method of simulating data produced by the model. How can we

Now that we can simulate How do we ***. We are unlikely to get exactly the sequence we observed. A classic method is to use a sample statistic. If we got 3 fives or 3 ones we would also be surprised. Link to idea of probability space.

The sample statistics

To calculate our sample statistic, we first need a way of counting the frequency of each number in a vector. R provides function called tabulate which does exactly that. We can then use the function max to find the most frequent

Now we can apply this to our model, 1000 times

You should be able to see that there are a smattering of 1’s,

Prelude to introducing the concept of probability.


text:
Belarusian

Belarusian is an East Slavic language spoken by over 9 million people as a first language in Belarus and in other countries. The languages most similar to Belarusian are Russian, Ukrainian and Polish. At first, Russian, Ukrainian and Belarusian were considered during the Kievan Rus era (c. 862- c. 1240) as one common language known as Old Russian or Old East Slavic. Slowly, the languages evolved due to subjugation from Polish-Lithuania as well as the Austrian empire, which is marked by a large number of Polish (and other loan words) words in Ukrainian and Belarusian. Belarusian exists in two forms, official and classical. This is due to the 1933 reform of the Belarusian language, which was not recognized by all Belarusians. The official (post-reform) language is dominant in Belarus while the classical (pre-reform) variety is maintained mainly by Belarusian emigrants in European and American countries. The official language is often referred to as наркамаўка "narkamauka" (i.e. the language of the narkam - narodnyi kamisaryiat, the soviet executive body that carried out the 1933 reform) while the classical variant is called тарашкевiца "tarashkevitsa" (the language of Bronislav Tarashkevich, who adopted the classical grammar and spelling of the language).

Belarusian historically had three alphabets: Cyrillic, almost identical to Russian, which is the official alphabet; Latin, similar to Polish or Lithuanian, which used to dominate in Polish-dominated Belarus during the interwar era, was never popular among Belarusians and is very rarely used even today; and Arabic, which was used by Muslim people during the Mongolian era (1240-1480) and by Muslims is now a kind of curiosity.

This book is based on Cyrillic "narkamauka" modern spelling reform of 1933, though we shall pay attention to spelling and grammar peculiarities of the classical variant.

Belarusian (sometimes obsoletely called Byelorussian or Belorussian, meaning "White Russian") can be a very tricky language to learn, especially if you don't have at least a basic knowledge of either Russian or Ukrainian. However, if you do know some Russian or Ukrainian, you'll be surprised how similar they are as they share the same alphabet (with a few cosmetic differences among themselves), the same grammatical rules, pitfalls, and a common history among them.

Table of Contents
Lesson 1 - The Alphabet

Lesson 2 - This is ...

Lesson 3 - Pronouns; Who/What is this?

Lesson 4 - Adjectives

Lesson 5 - Noun Gender and Number

Lesson 6 - Soft Consonants

Lesson 7 - Yes and No; This and That

Lesson 8 - Possessives; Asking for Definitions, Descriptions and Possession

Lesson 9 - Verbs Conjugation; You - Polite and Familiar

Lesson 10 - Adverbs; Short Answers; Nouns in ок; Verbs in аваць

Lesson 11 - Nouns Singular Genitive

Lesson 12 - Nouns Plural Genitive; Numbers from 1 to 10

Lesson 13 - Genitive of Adjectives and Other Words; Indefinite Words

Lesson 14 - Translating Proper Names; Deriving Adjectives from Nouns; the Second Conjugation of Verbs

Lesson 15 - Personal Names; Nouns Accusative; Likes and Dislikes

/Lesson 16/

Lesson 17 - Past and future tenses

Appendix A: Common phrases

title: Belarusian


text:
Set Theory/Sets

Sets and elements
A mathematical set is defined as an unordered collection of distinct elements. That is, elements of a set can be listed in any order and elements occurring more than once are equivalent to occurring only once.

We say that an element is a member of a set. An element of a set can be anything. It's easiest to begin with only numbers as elements. For that reason, most of the examples in this book will only include numbers, but this is only a technique to make the topic less abstract.

Terminology
For a set $$A$$ having an element $$x$$, the following are all used synonymously:

 * $$x$$ is a member of $$A$$
 * $$x$$ is contained in $$A$$
 * $$x$$ is included in $$A$$
 * $$x$$ is an element of the set $$A$$
 * $$A$$ contains $$x$$
 * $$A$$ includes $$x$$

Notation
We specify a set by specifying its members. The curly brace notation is used for this purpose.

is the set containing 1, 2, 3 as members. Or, {mother, this ipod, my school, the planet Jupiter, 12} is also a set. The curly brace notation can be extended to specify a set by specifying a rule for set membership. ("|" means "such that".)

is again the set containing 1, 2, and 3 as members.

is the set of all natural numbers. This form or representing set can be generalized as:

where $$P(x)$$ is a statement about the variable $$x$$. The set defined by above notation is a set of all objects $$x$$ such that $$P(x)$$ is true. **** (For a concrete example, consider $$A=\Big\{x\in\R:x^2=1\Big\}$$ . Here the property $$P$$ is “$$x^2=1$$” Thus, $$A$$ is the set of all real numbers whose square is one.). EXPLANATION: [A set may be defined by a property. For instance, the set of all planets in the solar system, the set of all even integers, the set of all polynomials with real coefficients, and so on. For a property $$P$$ and an element $$s$$ of a set $$S$$, we write $$P(s)$$ to indicate that $$s$$ has the property $$P$$. Then the notation $$\Big\{s\in S\Big|P(s)\Big\}$$ indicates that the set consists of all elements $$s$$ of $$S$$ having the property $$P$$. The vertical bar | is commonly read as “such that,” and can be also written using a colon instead. So $$\Big\{s\in S:P(s)\Big\}$$ is an alternative notation for $$\Big\{s\in S|P(s)\Big\}$$. For a concrete example, consider $$A=\Big\{x\in\R\Big|x^2=1\Big\}$$. Here the property $$P$$ is $$x^2=1$$. Thus, $$A$$ is the set of all real numbers ($$x$$ of $$\R$$ (i.e. 1)) whose square $$(1^2=1)$$ is one.] ***

A modified epsilon notation is used for set membership. Thus

means that $$x$$ is a member of $$A$$. We can also say that $$x$$ is not a member of $$A$$ :

Characteristics of sets
A set is uniquely identified by its members.

Moreover, the sets $$A,B$$ are said to be equal if and only if every element of $$A$$ is also an element of $$B$$, and every element of $$B$$ is an element of $$A$$.

All the above expressions specify the same set even though the concept of an even prime is different from the concept of a positive square root. Repetition of members is inconsequential in specifying a set. The expressions

all specify the same set.

Sets are unordered. The expressions

all specify the same set.

Sets can have other sets as members. There is, for example, the set

Some special sets
As stated above, sets are defined by their members. However some sets are given names to ease referencing them.

The set with no members is the empty or null set. The expressions

all specify the empty set.

A set with exactly one member is called a singleton. A set with exactly two members is called a doubleton. Thus $$\{1\}$$ is a singleton and $$\{1,2\}$$ is a doubleton.

Subsets
A set $$S$$ is a subset of set $$A$$ if every member of $$S$$ is a member of $$A$$. We use the horseshoe notation to indicate subsets. The expression

says that $$\{1,2\}$$ is a subset of $$\{1,2,3\}$$. The empty set is a subset of every set. Every set is a subset of itself. A proper subset of $$A$$ is a subset of $$A$$ that is not identical with $$A$$. The expression

says that $$\{1,2\}$$ is a proper subset of $$\{1,2,3\}$$.

Power sets
A power set of a set is the set of all its subsets. $$\mathcal P$$ is used for the power set. Note that the empty set and the set itself are members of the power set.

Union
The union of two sets A and B, written $$A \cup B$$, is the set that contains all the members of A and all the members of B (and nothing else). That is,

As an example,

Intersection
The intersection of two sets $$A,B$$, written $$A\cap B$$ , is the set that contains everything that is a member of both $$A$$ and $$B$$ (and nothing else). That is,

As an example,

Two sets are disjoint if their intersection is empty. That is, if $$A$$ and $$B$$ are disjoint sets,

Relative complement
The relative complement of $$A,B$$, denoted $$B\setminus A$$ (sometimes $$B-A$$), is the set containing all the members of $$B$$ that are not members of $$A$$. That is,

As an example,

Absolute complement
If we define a universe, or a set containing all of the elements we wish to consider, then we can discuss the absolute complement of a set. For a universe $$U$$, define the absolute complement of a subset $$A$$ of $$U$$ to be

The absolute complement of $$A$$ is denoted by $$A^C,\complement_U A,\complement A,\overline A$$ (according to the ISO 31-11 standard) if $$U$$ is fixed.

Union and intersection
Based on the preceding definitions, we can derive some useful properties for the operations on sets. The proofs of these properties are left as an exercise to the reader.

The union and intersection operations are symmetric. That is, for sets $$A,B$$

Furthermore, they are associative. That is, for sets $$A,B,C$$

Furthermore, union distributes over intersection and intersection distributes over union. That is, for sets $$A,B,C$$

De Morgan's laws
Two important propositions for sets are De Morgan's laws. They state that, for sets $$A,B,C$$

When $$A$$ is a universe to which $$B$$ and $$C$$ belong, De Morgan's laws can be stated more simply as,

Families of sets
A set of sets is usually referred to as a family or collection of sets. Often, families of sets are written with either a script or Fraktur font to easily distinguish them from other sets. For a family of sets $$\mathfrak{A}$$, define the union and intersection of the family by,

For a family of sets, we say that it is pairwise disjoint if any two distinct sets we choose from the family are disjoint.

Teoria dos conjuntos/Conjuntos

title: Set Theory/Sets


text:
Statistical Analysis: an Introduction using R/Chapter 4

Good likelihood stuff at http://statgen.iop.kcl.ac.uk/bgim/mle/sslike_1.html

Repeat the concept of the likelihood of a set of observations. Models, etc.,

This is a frequentist approach

Prior probability of models: the Bayesian approach


text:
Statistical Analysis: an Introduction using R/Chapter 5

This chapter contains the most "pure maths" concepts of the book. It is intended to demonstrate 3 main concepts of probability, using two complementary graphical methods. This may make it easier to understand the concepts of likelihood and Bayesian techniques used in the next chapter. However, If you already know some probabiltiy theory, or are willing to accept the 3 probabilty concepts below, then you may wish to move on the Chapter 3.

A link to the wiki prob book

 * 1) Mutually exclusive additivity p(a or b) = P(a) + P(b)
 * 2) p(a and b),
 * 3) concept of independence
 * 4) Conditional probability
 * 5) Bayes' Theorem

Methods to use
 * 1) Probability spaces
 * 2) Decision trees

Do this graphically. I have a few ideas of how.

Main text here
etc.

a bit about likelihood & models, as intro to Ch 3

R sections: using R as a calculator - or should this go in a later chapter?

Introduce the idea of classifying prob space using a single sample statistic, thus probability distributions, cumulative distributions, quantiles (use graphs).

Introduce binomial distribution. Don't give formula: link to binomial dist on wikipedia. Produce graph. Some sample statistics can be calculated analytically....

Introduce Poisson distribution


text:
Statistical Analysis: an Introduction using R/Chapter 6

Continuous measures. Histograms.

Normal distribution. Central limit theorem

T distribution (use simulations to sample from normal).


text:
User talk:Fasten/Meta-schoolbook Writer's Guide

= Web =

Schüler als Schulbuchautoren
This article discusses pupils as school book authors, but in primary school (google)

students as authors, class book

 * goole scholar: students as authors, class book (1 result)
 * goole scholar: students as authors (133 results)
 * goole scholar: pupils as authors (3 results)
 * google: students as authors (2,600 results)


text:
Horticulture/Melissa

Melissa a genus of five species of perennial herbs native to Europe and Asia. The name Melissa is derived from a Greek word meaning bee, owing to the abundance of nectar in the flowers which attracts bees.

Description
The stems are square, like all other plants in the mint family. The leaves are borne in opposite pairs on the stems, and are usually ovate or heart-shaped and emit a lemony scent when bruised. Axillary spikes of white or yellowish flowers appear in the summer.

Growing conditions
They are very frost hardy plants which prefer full sun or light shade if summers are hot. They are quick growing, and look especially good along paths, herb gardens, or among ferns when grown in pots. Slightly moist, well-drained soil is best. M. officinalis has become naturalised in many parts of the world.

Species

 * ../Melissa axillaris/ (Benth.) Bakh.f.
 * ../Melissa bicornis/ Klokov
 * ../Melissa flava/ Benth. ex Wall.
 * ../Melissa officinalis/ L.
 * ../Melissa yunnanensis/ C.Y.Wu & Y.C.Huang

Uses
The most commonly grown species of this genus is Melissa officinalis. It is native to southern Europe. It can grow up to 1.5 m high and is grown mainly for its lemon-scented leaves. Small white flowers appear in late summer, which attract bees. It spreads rapidly, and can become an invasive species if left unchecked. The leaves can be used for a calming herbal tea, fruit salads, jellies, iced tea, and a substitute for lemon peel in cooking.

Propagation
Propagate from seed sown in spring. Variegated forms are propagated by root division or from young spring cuttings.

title: Horticulture/Melissa


text:
Horticulture/Melissa officinalis

Lemon balm (Melissa officinalis)is a perennial herb in the mint family Lamiaceae, native to southern Europe and the Mediterranean region.

Description
It grows to 70-150 cm tall. The leaves have a lemon scent and taste. At the end of the summer, little white flowers full of nectar appear. These attract bees, hence the genus name Melissa (Greek for 'honey bee'). Its flavour comes from the terpenes citronellal, citronellol, citral, and geraniol. Lemon Balm grows in clumps and spreads vegetatively as well as by seed. In mild temperate zones, the stems of the plant die off at the start of the winter, but shoot up again in spring.

Growing conditions
This herb can be easy to cultivate in United States Department of Agriculture Plant Hardiness Zones 4 to 9. In zone 4, it needs winter mulch and a well-drained sandy soil to survive. In zone 7, it can be harvested through late autumn. It is moderately shade-tolerant, much more so than most herbs. In dry climates, it grows best in partial shade.

Uses
It is used as a flavouring in tisane and ice cream, but its most common use is to make herbal teas. It makes a particularly refreshing iced tea, especially when mixed with other herbs such as spearmint. It is also often paired with fruit dishes or candies.

Lemon balm essential oil is very popular in aromatherapy. The essential oil is commonly co-distilled with lemon oil, citronella oil, or other oils.

The crushed leaves, when rubbed on the skin, are used as a repellant for mosquitos.

Lemon Balm is also used medicinally as a herbal tea, or in extract form. It is claimed to have antibacterial, antiviral properties, and it is also used as a mild sedative or calming agent. At least one study has found it to be effective at reducing stress, although the study's authors call for further research. Its antibacterial properties have also been demonstrated scientifically, although they are markedly weaker than those from a number of other plants studied.

Propagation
It can be easily grown from stem cuttings rooted in water, or from seeds. Under ideal conditions, it will seed itself prolifically and can become a nuisance in gardens.

Harvesting
Harvest fresh, using the leaves.

title: Horticulture/Melissa officinalis


text:
A-level Mathematics/OCR/FP4

Contents

 * 1) /Matrix Algebra/
 * 2) /Vector Product/
 * 3) /Determinants/
 * 4) /Applications of Vector Products/
 * 5) /Inverse Matrices/
 * 6) /Solving Linear Equations/
 * 7) /Eigenvectors/

Formulae
By the end of this module you will have learnt the following formulae:

Eigenvectors

 * $$Mv = \lambda v$$

Where λ is the Eigenvalue and v is the Eigenvector.

title: A-level Mathematics/OCR/FP4


text:
Belarusian/Lesson 1

Belarusian Alphabet
The Belarusian alphabet is based on the Cyrillic writing system. It is virtually identical to the Russian alphabet, differing from it just in a few points:
 * i is used instead of и
 * ў letter, specific to Belarusian, is used to denote short u sound
 * шч combination is used instead of щ
 * ' (апостроф/apostrophe) is used instead of ъ or the hard sign.

The Belarusian alphabet contains 32 letters:

Аа - a - pronounced like a in art

Бб - be - pronounced like b in body

Вв - ve - pronounced like v in van

Гг - he - has no correspondence in English; the voiced analog of х; occasionally pronounced like g in guest

Дд - de - pronounced like d in desk

Ее - e/ye - pronounced, depending on position, either like a long e after consonant as in  Lenin or ye in yes (Initially, after vowel or any of the two signs).

Ёё - o/yo - pronounced, either like o in shore (only after Ч, Ш, Ж or ШЧ)  or yo in York. Either way, always stressed

Жж - zhe - pronounced like s in pleasure

Зз - ze - pronounced like z in zoo

Іі - i  - pronounced like i in machine

Йй - i nieskladovaye "non-syllabic y" - pronounced like y in toy

Кк - ka - pronounced like k in kitten

Лл - el - pronounced like l in lamp

Мм - em - pronounced like m in map

Нн - en - pronounced like n in net; pronounced like a Spanish ñ after i or e.

Оо - o - pronounced like o in sort: usually, but not always stressed

Пп - pe - pronounced like p in park

Рр - er - differs largely from English r sound; similar to Italian r in ridere

Сс - es - pronounced like s in Sun

Тт - te - pronounced like t in top

Уу - u - pronounced like u in put

Ўў - u nieskladovaye "non-syllabic u" - pronounced like the w in know

Фф - ef - pronounced like f in fox

Хх - kha - pronounced harder than English h sound; similar to German ch in Buch

Цц - tse - pronounced like ts as in cats; similar to German z in Zeit or Italian z in canzone

Чч - cha - pronounced like ch in chalk

Шш - sha - pronounced like sh in shelf

Ыы - y - pronounced like y in myth

Ьь - miakki znak "soft sign" - not pronounced: softens previous consonant and, if in any position except the end, separates syllables

Ээ - e - pronounced like e in end: if found after a consonant, it is shorter than the previous "e" mentioned above.

Юю - yu - pronounced like a yu as in "Yugoslavia";

Яя - ya - pronounced, like "ya" in "yard" or "Goya"

NOTE. In tarashkievitsa, letter Ґґ (ge) is also used to denote the sound g (as in english guest). Narkamauka uses г letter instead. The position of ґ in the classical Belarusian alphabet is immediately after г, before д. Thus there are 33 letters in tarashkievitsa. Sometimes in tarashkievitsa combinations ДЖдж and ДЗдз are given the status of letters on their own.

1. Cities
Try to read and recognize the names of some cities. Confer the hint below if you have difficulties. Note that " ́" is a stress sound (which is normally omitted). Also note that proper names in Belarusian, as in most other languages, are capitalized.

Масква́

Ло́ндан

Варша́ва

Амстэрда́м

Стамбу́л

Hint: Maskva (Moscow), Londan (London), Varshava (Warsaw), Amsterdam, Stambul (Istanbul)

2. Animals
Try to read and remember Belarusian names of some animals. Confer the pronunciation hint below if you have difficulties. Pay special attention to the stress - like Russian and Ukrainian, there is no fixed stress position in Belarusian, and stressing the wrong syllable (or even missing out a sign) can create misunderstandings. Virtually every book and dictionary concerning these three languages place an accent in the tonic syllable, so make sure you do the same. Note that о is normally stressed in Belarusian.

кот - a cat (male)

ко́шка - a cat (female)

саба́ка - a dog

каро́ва - a cow

каза́ - a goat (female)

бара́н - a sheep (male)

пту́шка - a bird (general)

варо́на - a crow

саро́ка - a magpie

ка́чка - a duck

жа́ба - a toad

слон - an elephant

Hint: kot, koshka, sabaka, karova, kaza, baran, ptushka, varona, saroka, kachka, zhaba, slon

title: Belarusian/Lesson 1


text:
Finite Model Theory/Logics and Structures

FMT studies logics on finite structures. An outline of the most important of these objects of study is given here.

Logics
The logics defined here and used throughout the book are always relational, i.e. without function symbols, and finite, i.e. have a finite universe, without further notice.

Fragments of FO
The subsequent restrictions can analogously be found in other logics like SO.
 * MFO ...
 * ESO and USO ...
 * FOn ...

Second Order Logic (SO)
Second-order logic extends first-order logic by adding variables and quantifiers that range over sets of individuals. For example, the second-order sentence $$\forall S \, \forall x \, ( x \in S \lor x \not \in S)$$ says that for every set S of individuals and every individual x, either x is in S or it is not. That is, the rules are extended by:
 * If X is a n-ary relation variable and t1 ... tn are terms then X t1 ... tn is a formula
 * If φ is a formula and X a relation variable then $$\exists_X \varphi$$ is a formula

Fragments of Second Order Logic

 * The fragment monadic second-order logic (MSO) only unary relation variables ("set variables")are allowed.
 * The existential fragment (ESO) is second-order logic without universal second-order quantifiers, and without negative occurrences of existential second-order quantifiers.
 * USO ...

Notion
The intention is to extend FO by an infinite disjunction element over a set ψ of formulas (of infinitary logic)

$$\bigvee \psi$$

So the following infinitary logics can be defined
 * $$L_{\infty \varpi}$$ where ψ is an arbitrary set of formulas, e.g. uncountable
 * $$L_{\varpi \varpi}$$ where ψ is a countable set of formulas
 * $$L_{\infty \varpi}^n$$ ...

Definition
syntax ...

semantics ...


text:
Muggles' Guide to Harry Potter/Major Events/Dumbledore's Army

Overview
Dumbledore's Army (D.A.) is the secret Defence Against the Dark Arts group founded by Harry Potter and Hermione Granger, with assistance from Ron Weasley.

Event Details
Professor Dolores Umbridge, Hogwarts' new Defence Against the Dark Arts teacher in Harry's fifth year, only lectures on Ministry-approved theory, which seems entirely based on appeasement and negotiation, from the textbook, and refuses either to teach real defensive magic, or to allow practicing defensive spells. Within the first two weeks of classes, Hermione has seen how stultifying and useless this form of teaching is, and with the assistance of Ron, suggests to Harry that it would be a good idea to have someone teach the students real Defence Against the Dark Arts, rather than the useless "conciliation techniques" currently being taught only through books. When Harry agrees to this, Hermione tentatively suggests that the appropriate teacher would be Harry himself. Harry is surprised when Ron agrees that he is the logical choice.

Although Harry initially feels he is unqualified to teach Defensive Arts to any interested classmates, he reluctantly agrees after Hermione and Ron convince him he has gained considerable knowledge on the subject through their experiences in the past four years. Hermione then invites "a couple of students" to meet at the Hog's Head Inn on their next Hogsmeade weekend to discuss forming a group to learn real Defence Against the Dark Arts. Harry is stunned when Hermione's "couple of students" ends up numbering 25; Hermione simply says "The idea did seem quite popular." The group struggles briefly with a name for themselves, eventually suggesting the nebulous name Defence Association, or D.A. for short.

The members of Dumbledore's Army include: Hannah Abbott, Lavender Brown, Katie Bell, Susan Bones, Terry Boot, Cho Chang, Michael Corner, Colin Creevey, Dennis Creevey, Marietta Edgecombe, Justin Finch-Fletchley, Seamus Finnigan, Anthony Goldstein, Hermione Granger, Angelina Johnson, Lee Jordan, Neville Longbottom, Luna Lovegood, Ernie Macmillan, Padma Patil, Parvarti Patil, Harry Potter, Zacharias Smith, Alicia Spinnet, Dean Thomas, Fred Weasley, George Weasley, Ginny Weasley, and Ron Weasley. Seamus Finnigan is a late-joining member; not present at the initial meeting in The Hog's Head, the first meeting he attended turned out to be the final meeting of the group.

Shortly after the initial meeting, a new Educational Decree is posted by Umbridge banning unapproved student groups. Harry and Ron are convinced that someone has told Umbridge about the DA, but Hermione says nobody could have. She reminded Harry and Ron that she had passed a parchment around that everyone had signed their names on in the meeting. The parchment was jinxed so that anyone who betrayed the group after signing it would break out in severe facial blemishes.

Sirius Black uses the Floo network to speak to Harry about this organization. He reveals that Umbridge's choice of teaching philosophy is because the Ministry is worried that Professor Dumbledore may be trying to raise a private army of students to attack the Ministry itself. Umbridge has been placed at the school as a teacher by the Ministry, and remains loyal to the Ministry. Sirius Black mentions to Harry that he knows that they are starting the Defensive Arts group. He says that a heavily veiled witch that Harry and Hermione had noted was Mundungus Fletcher in disguise, there to keep an eye on Harry's activities for the Order. Sirius passes on a message from Ron's mother forbidding Ron from having anything to do with the DA, and appealing to Harry and Hermione to likewise give up the idea. Sirius himself, however, says he strongly supports the idea of the group.

There is concern for some time as to where the group can have meetings. Various suggestions are made and rejected for practical reasons. Finally, Harry happens to ask Dobby if he knows of a place, and Dobby tells Harry about the Room of Requirement. This is a room which appears when a person really needs it, in the form that the person needs. Harry, Ron, and Hermione pass on the description of the Room to other members of the Defence Association, and then go to the room themselves. When it appears for them, it is perfect, stocked with everything they need for a Defence Against the Dark Arts class. Hermione, who has been unsure about using the Room of Requirement for a meeting place due to its nature, agrees that it is a good idea. At their first full meeting, they change the name of the group to "Dumbledore's Army" to show their loyalty to the Headmaster and to mock the paranoia of the Ministry of Magic, noting that this keeps the same initials, "D.A.", as the initially suggested Defence Association.

Meetings are irregular, as they have to be fit around the three different participating house's Quidditch practices. Hermione provides fake Galleons that allow DA members to send messages. The spell used to do this is a Protean Charm, which Terry Boot says is "NEWT-level magic". For several months, Harry secretly teaches the signed up students from Gryffindor, Ravenclaw, and Hufflepuff. Under Harry's effective tutoring, the D.A. members learn many advanced defensive techniques, starting with the simple disarmament charm and proceeding to the NEWT-level Patronus charm. Neville struggles to learn these charms throughout the meetings, but eventually he becomes very successful. Many of the members of the DA find themselves considering Dumbledore's Army to be like a second family.

Dumbledore's Army abruptly ends in April when D.A. member and Ravenclaw student Marietta Edgecombe willfully reveals its existence to Umbridge. Marietta's mother worked at The Ministry of Magic. Umbridge then sets a raid by her Inquisitorial Squad, comprised of Slytherin students and led by Draco Malfoy, to bring in those behind the DA. Umbridge's attempt to detain members of the Army is thwarted by Dobby, who defies Umbridge's orders and warns Harry. Harry sends the rest of the group away, and is the only group member captured. He is taken to Dumbledore's office, where he finds Dumbledore, along with Umbridge, the Minister for Magic Cornelius Fudge, Percy Weasley (along to record the meeting), and a pair of Aurors, one of whom (Kingsley Shacklebolt) Harry recognizes as being in the Order of the Phoenix.

Umbridge's star witness, Marietta, proves less than useful, as it seems Kingsley has performed a memory charm on her secretly to keep Harry out of trouble. However, the membership list for the D. A. was retrieved by Pansy Parkinson, and the title on the paper, "Dumbledore's Army", causes some consternation. This title allows Dumbledore to claim responsibility for forming the group, thus protecting the students in general and Harry in particular. The Ministry's subsequent attempt to arrest Dumbledore results in his spectacular departure from Hogwarts. Umbridge is appointed Headmistress in his place, but is apparently not able to enter the Headmaster's office.

It is not likely that Umbridge illegally used a truth potion on Marietta to get her to tell the details about Dumbledore's Army because it seems the original impetus had to be Marietta's. For betraying Dumbledore's Army, permanent purple pustules spelling "SNEAK" had erupted across Marietta's face courtesy of Hermione's jinxed parchment.

With the appointment of a competent Defence Against the Dark Arts teacher in Harry's sixth year (Severus Snape), there is little need to re-start Dumbledore's Army. Harry does put out a call to the members of the DA for assistance when he knows Dumbledore will be leaving the school temporarily, but only five members respond: Ron Weasley, Hermione Granger, Luna Lovegood, Neville Longbottom, and Ginny Weasley. Providing them with the remnants of his Felix Felicis luck potion, Harry sets them to watch the Room of Requirement, where Draco has been working, and Severus Snape, who he believes is working with Draco.

In what would be Harry's seventh year, Neville, Luna, and Ginny restart Dumbledore's Army as a means of rebelling against Hogwarts' new emphasis on Dark Arts at the hands of headmaster Snape, Dark Arts teacher Amycus Carrow, and Muggle Studies teacher Alecto Carrow, all of whom are Death Eaters. The DA falls on hard times as its members are hunted down; Luna is captured, Ginny escapes with her family, and Neville's grandmother is targeted in an unsuccessful attempt to put pressure on Neville (although Dawlish, who is sent to capture her, is thwarted, winding up in St. Mungo's). The DA retreat to the Room of Requirement, from which they recruit new members and continue guerrilla raids on the school. When Harry eventually returns to the school to hunt for the final Horcrux, there are many rebelling Hogwarts students in the Room of Requirement. Neville, using the Galleons that Hermione had earlier enchanted to tell about meetings, recalls the rest of the D.A. The members of the Order of the Phoenix come along with them, along with many other wizards, triggering the final, climactic battle.

Notable Consequences
When meeting in the Hog's Head, Harry expresses some doubts that they may be overheard by someone, suggesting that a veiled witch in the corner might be Umbridge. Umbridge is not present, as it turns out, but there are in fact two eavesdroppers: the witch is Mundungus Fletcher, there for the Order of the Phoenix, and also present is Willy Widdershins, the comprehensively bandaged wizard at the bar drinking Firewhiskey, who promptly reports back to Umbridge. It is as a direct result of this meeting that Umbridge causes promulgation of Educational Decree number Twenty-Four which prevents unapproved student groups. This has the side effect of banning the Quidditch teams. The fact that the Slytherin Quidditch team is approved and reforms immediately, while the Gryffindor team is not allowed to reform for a month, is an indication of how Umbridge will tend to abuse her powers.

Cho Chang has joined the D.A. largely because Harry was there. Cho makes use of the end of the last D.A. meeting before Christmas to kiss Harry in private. We can see from his response to this, as related to Hermione, that he is extremely unsure of himself around Cho. The continued unapproved meetings of the D.A., in violation of Educational Decree number Twenty-Four, are eventually betrayed, and an attempt is made to apprehend the group. In the end, due to a timely warning from Dobby, the only group member caught is Harry himself. Pansy Parkinson enters the Room of Requirement and retrieves the membership list. Cornelius Fudge has been summoned to witness the bringing of the group to justice; on seeing the membership list heading, his paranoia asserts itself, and he tries to arrest Dumbledore. Dumbledore escapes, dramatically, and Umbridge is appointed Headmistress, although she is never able to get into the Headmaster's office after Dumbledore's departure.

Marietta Edgecombe's defection not only betrayed Dumbledore's Army, but ultimately doomed Harry and Cho Chang's relationship. When Cho defends Marietta's actions and is angry that Hermione secretly jinxed the parchment the D.A. members signed, Harry angrily lashes out, calling Hermione's plan "brilliant." Cho is deeply offended and storms off in tears; she and Harry do not speak to one another for two years.

Unfortunately for Umbridge, students have acquired what she vigorously prevented them from having: Defence Against the Dark Arts knowledge. The D.A. members use their new-found skills on several occasions. When Ron, Ginny, Neville, and Luna are captured by Umbridge's Inquisitorial Squad, they escape with defensive jinxes and hexes. The students use Defensive Arts during the Battle at the Department of Mysteries, fending off Death Eaters until Order of the Phoenix reinforcements arrive. When Draco and his minions attempt to Curse Harry on the Hogwarts Express, D.A. members come to his rescue, jinxing the Slytherins until they are unrecognizable. Members of Dumbledore's Army use what they have learned to assist with the defence of the school at the battle under the Astronomy tower. And it is largely members of Dumbledore's Army who make up the core of the guerrilla resistance against Snape's rule in the seventh book.

For Neville Longbottom the D.A. is a timely opportunity to improve his dueling skills. After the escape of Bellatrix Lestrange from Azkaban, Neville is determined to become proficient in Defence and works very hard at D.A. meetings.

The D.A. is very important to Luna Lovegood who experiences, for the first time, a fellowship with her peers. In Harry Potter and the Half-Blood Prince Luna tells Harry how much she misses the D.A. meetings and what the friendship of the D.A. means to her.

Analysis
Curiously, it is Hermione who takes action against Umbridge by doing the groundwork that results in Dumbledore's Army. Although she started her career at Hogwarts strictly adhering to school rules, she has, over the years associating with Harry and Ron, learned to break them when she believes they are wrong or a nobler purpose is served. In this instance, she not only takes on Umbridge, but the entire Ministry of Magic, who are convinced Dumbledore may be creating a secret wizard army against them.

There are two people in Dumbledore's Army who do not completely seem to belong there. These are Zacharias Smith and Marietta Edgecombe. Smith is confrontational, to the point that at the organizational meeting Fred Weasley feels compelled to threaten him with a pointed metal object that he produces from a Zonko's Joke Shop bag. Smith also does not seem to want to sign the parchment that Hermione passes around, where they swear not to tell anyone about the D.A. Granted, he is not the only one to express reluctance; Ernie Macmillan hesitates, saying he is a prefect, and if the parchment were found... He only signs when Hermione points out that she's not going to leave this bit of parchment lying around. From the beginning, we have a feeling that the D.A. is doomed, that it will accomplish at least some part of its purpose, but will ultimately fall to Umbridge and her cronies; and Zacharias Smith's continuing skepticism makes him a lead candidate for that betrayal.

Marietta is along because Cho is going, and she is always very quiet, limiting her interaction to sighs and non-verbal displays of impatience. When the actual betrayal takes place, we fully expect Zacharias to have been the agent, and are very surprised when it turns out to be Marietta.

Even before Harry gets the teaching up to that level, Hermione is seen doing two NEWT-class spells here. The first is the parchment, on which everyone signs their names at the organizational meeting. As mentioned above, the parchment is charmed so that anyone who betrays the D.A. will break out in horrendous blemishes. When Hermione mentions this to Ron and Harry, after the promulgation of the Educational Decree banning student organizations, they are both very impressed; Ron in particular recognizes that this is very advanced magic. One wonders why Hermione had not told the rest of the D.A. of this charm, once they had all signed; Marietta might have chosen a different course of action had she known that betraying the D.A. to Umbridge would result in her wearing the word "Sneak" across her face for at least a year.

The second is the Galleons; every Galleon has on it a serial number, that of the gnome who cast it. Hermione has made fake Galleons for the D.A., which look like real ones except that the serial number changes to indicate the date and time of the next meeting. When Hermione passes these out at the second regular meeting, everyone present is amazed that she is capable of performing a Protean Charm, it being such advanced magic.

It is noted that Seamus had joined Dumbledore's Army for only its last session before it was discovered and disbanded. This timing is, in fact, rather important. Harry has noted and tried to work around the fact that there are an even number of people (including himself) in the DA; most often, he has the students pair up so they can practice on each other, and as he cannot generally be one of the pairs, as he has to inspect and correct the other students, he often creates a single group of three, Neville, Hermione, and Ron. In the final session, Marietta Edgecombe is not present because she is telling Professor Umbridge about the group; Harry would be much more likely to notice her absence if suddenly he could pair everyone up. Seamus's presence, by keeping the number of working students odd, prevents Harry noticing that Marietta is missing, and thus helps provide the necessary surprise.

Questions

 * 1) What prompts Hermione to form Dumbledore's Army? Why is it kept secret?
 * 2) What are possible reasons Slytherin students were excluded from the group? Is it simply because none of them signed up, or inter-house stereotypes?
 * 3) Why does Professor Dumbledore claim responsibility for having organized the group?
 * 4) Where does Professor Dumbledore go when he eludes the ministry's capture?
 * 5) Why is Harry initially reluctant to teach Defensive Arts?
 * 6) How does Marietta Edgecombe betraying the D.A. contribute to Harry and Cho breaking up?

Greater Picture
In Harry Potter and the Half-Blood Prince, Harry finds out that he and Dumbledore are going to both be leaving the school for a while, and while he cannot be sure what Draco's mission is, or whether he has accomplished it, he has at the very least a great suspicion that it has been completed successfully. Although Dumbledore reassures him that the school is protected by Aurors and members of the Order of the Phoenix, Harry does not feel that is enough. For reasons of his own, he feels that Draco's task may have resulted in an increased danger to Hogwarts in a way that the Order had not anticipated. When appealing to Dumbledore seems ineffective, Harry tries to re-activate the D.A., with very limited success: only Ron, Hermione, Ginny, Neville, and Luna Lovegood come forward. However, the five of them, with a little help from Harry's remaining stock of Felix Felicis potion, manage to turn the tide of the battle.

In Harry Potter and the Deathly Hallows, Neville and Ginny re-activate Dumbledore's army as a means of rebelling against the headmaster, Severus Snape. As there are two other Death Eaters teaching at the school, and the teaching has become a lot darker and more abusive, this is not a complete success. However, the organization is in place, and is working out of the Room of Requirement, when Harry reaches Hogwarts. Additionally, when Neville uses the Galleons to summon the D.A., all of the past members of the D.A. (with the possible exception of Marietta Edgecombe) arrive as well, forming the nucleus of a fighting group that will largely save Hogwarts.

Surprisingly, the choice of which student enters the Room of Requirement when the DA is broken up, to retrieve the parchment with the organization name, is important. Voldemort, when he was at Hogwarts, apparently discovered the Room of Requirement. It seems that most people who discover it are looking for some place to hide something; Professor Trelawney had discovered it when looking for a place to hide her sherry, and the Twins had been looking for a place to hide themselves from Filch, for instance. Voldemort, presumably looking for a place to hide something he had done, had thus managed to open the door onto a warehouse full of a thousand years worth of magical junk. He apparently instructed Draco Malfoy, over the summer, as to how to get into that aspect of the Room. It is in that aspect of the room that Draco was working on his technique for getting Death Eaters into Hogwarts throughout Harry's sixth year. If Draco had ever seen the inside of the room prepared for D.A. meetings, he might have had a better idea of what the room actually was; as it is, though, only Pansy has seen that aspect of the room, and Draco, in his superior way, likely would not bother to ask her what the inside of the room looked like, assuming, once he got instructions on how to enter, that the DA had been practicing in the junk warehouse.


text: Category:Book:Consciousness Studies

title: Category:Book:Consciousness Studies


text: Template:Goodbook/Consciousness Studies

title: Template:Goodbook/Consciousness Studies


text: Category:Book:Formal Logic

title: Category:Book:Formal Logic