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Internet Technologies/The Internet

The Internet is a worldwide collection of computer networks that began as a single network that was originally created in 1969 by ARPA (Advanced Research Projects Agency), a U.S. government agency that was far more interested in creating projects that would survive a nuclear war than in creating anything useful for the civilian population.

In its original form, ARPANET, the U.S. government hoped to create a network of computers that would allow communication between government agencies and certain educational centers that would be able to survive a nuclear explosion. It is doubtful that the original founders of ARPANET foresaw what we now know as "the Internet." From its humble beginnings as a military project, the ARPANET grew slowly throughout the 70's and 80's as a community of academics accomplished the truly monumental task of hammering out the building blocks of this new, open, modular conglomeration of networks.

In addition to the U.S. ARPANET, other countries also developed their own computer networks which quickly linked up to ARPANET, such as the UK's JANET (1983 onwards), and Australia's ACSnet (mid-1970s until replaced). Connecting these together would help develop a global internetwork.

The various protocols, including IP, TCP, DNS, POP, and SMTP, took shape over the years, and by the time the World Wide Web (HTML and HTTP) was created in the early 90's, this "Internet" had become a fully functional, fairly robust system of network communication, able to support this new pair of protocols which eventually turned the Internet into a household word.

While a large portion of users today confuse the Web with the Internet itself, it must be emphasized that the Web is only one type of Internet application, and one set of protocols among a great many which were in use for over a decade before the Web entered into the public awareness.

The Web is a subset of the Net. Email is not a part of the Web, and neither are newsgroups, although Web designers have developed web sites through which users, the world over, commonly access both of these much older forms of Internet media.

While the Net is a largely abstract phenomenon, it cannot (at least, not yet) be accurately equated with the concept of "cyberspace" as depicted in science fiction. If "judgement day" were to occur as depicted in the latest "Terminator" film, much of the Internet would survive it, but most of the electrical and data infrastructure by which we access the net would not. The line which currently demarcates the "digital divide" would shift dramatically to a point where it would leave only a small segment of humanity in virtual touch. This limitation, however, will slowly be overcome as wireless technologies continue to proliferate and wired technologies become increasingly cheaper.

In March 1972 ARPA became known as DARPA, the Defense Advanced Research Project Agency, and then went back to ARPA in February 1993 and back to DARPA in March 1996 and has been ever since. It was originally created as ARPA in 1958 in response to the launching of Sputnik. The launch of Sputnik made America realize that the Soviet Union could exploit military technology. DARPA has contributed to the creation of ARPANET as well as the Packet Radio Network, the Packet Satellite Network and the Internet. As well as research into the Artificial Intelligence field commonly referred to as AI. By the late 1970's the Department of Defense had adopted BSD UNIX as the primary operating system for DARPA.

title: Internet Technologies/The Internet


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Puzzles

Foreword
There are many books in the market nowadays that have written about the puzzles BUT most of the books only dealt with narrow scope of that particular puzzles only.

For this Wikibook, it is the intention of the contributors to give the readers some tidbits/history and examples related to that puzzles mentioned and of course there are some puzzles which provided entertainment / interactive question for readers themselves at the end of the page. If you got stuck after trying, it wouldn't hurt to take a peek on how to solve the puzzles itself (after all puzzles is supposed to be fun).

Hence all said, please enjoy these puzzle collection, avoid any frustration, and fight boredom.

Games & Graphical Puzzles

 * /Two-player games/
 * /Chess puzzles/
 * /Tower of Hanoi/
 * /Seven Bridges of Königsberg/
 * /Four colour map/
 * /Bongard problems/
 * /Subdivisions/

Grid Puzzles

 * /Symbols/
 * /Shading/
 * /Segregation/
 * /Stripe/

Language puzzles

 * /Analogies/
 * /Odd-one-out/
 * /Rebus/
 * /Riddles/
 * /Word-In-Word/

Mathematical puzzles

 * /Action sequences/
 * /Analytical puzzles/
 * /Arithmetical puzzles/
 * /Bertrand’s Box/
 * /Decision puzzles/
 * Geometric puzzles
 * /Luoshu Squares/
 * /Number sequences/
 * /Set theory puzzles/
 * Statistical & combinatorics puzzles

Logic puzzles

 * /Logic puzzles/
 * /River Crossing/
 * Rubik's cube (3x3x3)

Real life problems

 * How do you ... ?
 * Lateral puzzles
 * Non-scientific puzzles
 * Physics puzzles

About puzzles

 * /Puzzles in science/
 * /Solving puzzles/

Puzzle resources

 * Jim Loy's Puzzle Pages
 * Riddles–Wu:Riddles
 * Aha! Puzzles - Original creative puzzles by Lloyd King
 * Puzzles from the Princeton undergraduate mathematics student society.
 * rec.puzzles Archive
 * ResultsAbout Riddles: Collection of links to other riddle web sites.
 * Mathpuzzle: Puzzle blog of Ed Pegg Jr.
 * PuzzlePicnic: Hundreds of deduction puzzles.
 * Puzzles.com

Puzzles

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

title: Puzzles


text:
Talk:Puzzles

I think that the section "statistical puzzles" should rather read "probability puzzles" since this describes the nature of the contributed riddles more precisely (and there are really few statistical puzzles out there going beyond probability theory). However, it seems a bit tedious to make the change because of the references already in place -sboehringer

It's really nice to see so much interest! I'll try to put up some more cool puzzles (and of course I'd love to have some more puzzles put up by other people so that I can also try to solve a few :) Thomas

Suggestion: I think once we have more than 20 or so problems we should split them up into subcategories. Thomas

Suggestion: I think it will be easier to create for each puzzle an own solution page and put a link at the bottom of each puzzle. doopdoop

 * I agree, maybe we should have (at least) two levels of hierarchy in our book: 1. subcategories which contain a list of puzzles for each type 2. a page for each puzzle + an 'official solution' page for this puzzle (the talk page of a puzzle could be used to discuss clarifications, alternate solutions, ...) Thomas
 * Suggested structure (partially inspired by the rec.puzzles archive -> now implemented)

 * What about the classical n-queens or traveling salesman problems?

--Eibwen 07:10, 1 Oct 2004 (UTC)

Overview

 * Two 4's equals 64?: solved
 * Knights, Knaves & Spies: solved
 * Knights, Knaves & Spies II: solved
 * Lying about your Age: solved
 * 12 coins: solved
 * Sharing Milk: solved
 * The Burning Island: solved
 * Crossing the River: solved
 * Crossing the River II: solved
 * Connecting Stars: solved
 * Getting out of Prison: solved
 * Three Daughters: solved
 * Weighings once more: solved
 * Rubber band: solved
 * Digits of the Square: solved
 * Hats: solved
 * Three Knights: solved
 * Pizzas: solved
 * Luxury Cars: solved
 * Connecting Utilities: solved
 * Yet another Weighing: solved
 * Escaping from Prison: solved
 * Scales and Weights: solved, open for better solutions
 * Two Boys and a River: open
 * The Pentagon: open
 * Boy, Girl, and a Dog: open
 * Barrel of Ale: open

Note: even if a problem is solved, you should try and solve it without looking at the solution on the talk page. That way we increase the chance of getting alternative solutions!

I've implemented the structure suggested by doopdoop. Every problem now has it's own problem page and solution page. Also, I think we can use a problem's talk page to vote on the difficulty (say from 1-10, where 1=very easy to 10=(almost) impossible). Thomas

Self-created puzzles
I presume that we're allowed to put puzzles that we created ourselves onto the page, right? Or not? Eric119 21:49, 11 Oct 2003 (UTC)

 * Absolutely! I think that's at least as interesting as gathering the 'standard' puzzles that are out there. Thomas

 * Only as interesting? Surely it's more interesting.  If we were only going to copy other sites/books, what would be the point? -- Smjg 15:13, 13 July 2005 (UTC)

Naming Conventions
I would like to suggest that we start adding a "- Puzzle" to the title of Puzzle pages. This would avoid naimng conflicts with other Wikibooks and furthermore make it more easy to detect new and open puzzles in the Recent changes. Thomas
 * Hi, I am new here (in fact I just created my account), but I'd suggest to put "Puzzle:" to the front, like in the pages of Cookbook. It should help to keep books together, and I wonder why this is not a standardized policy on Wikibooks yet... --Andreas Ipp 14:59, 8 Jan 2005 (UTC)
 * A little late for that? --Divinity 17:27, 19 Jun 2005 (UTC)

 * Not at all. Better late than never.  I hereby propose a hierarchy, so that the names'll look like this:
 * Puzzles - contents page
 * Puzzles:Logic puzzles - section page
 * Puzzles:Logic puzzles:Knights, Knaves & Spies - puzzle page
 * Puzzles:Logic puzzles:Knights, Knaves & Spies:Solution - solution page
 * And get the navigation header on every page while we're at it. Moreover, there are even some pages that have pathologically meaningless titles - just look at Puzzles:Lateral puzzles for instance.  Let's get cleaning at once!  (I've already done puzzles 5 and 7 there, so you can see what I mean.  But still, shouldn't they all have more descriptive titles?) -- Smjg 15:26, 13 July 2005 (UTC)
 * So to implement these ideas, you move the pages and redo all the links? Borbrav 18:01, July 14, 2005 (UTC)

 * Yes. I've started on it.  We can all work on it.  And while we're at it, we should make sure all pages have the navigation header, and that the navigation header has a line below it. -- Smjg 10:32, 22 September 2005 (UTC)

Some pages are acquiring poorly laid out navigation headers, like this

 * Puzzles | Puzzles:Logic puzzles | Puzzles:Logic puzzles:Knights, Knaves & Spies | Solution

That's something else to fix in the process. It should look like this:

 * Puzzles | Logic puzzles | Knights, Knaves & Spies | Solution

-- Smjg 18:02, 22 September 2005 (UTC)

I've just created some navigation header templates, which we could use to make life easier. So now we can do

 * etc. up to hc-navhead6.
 * etc. up to hc-navhead6.
 * etc. up to hc-navhead6.

A little less cumbersome than doing it manually, don't you think?

I've used it on Puzzles/Logic puzzles/Gold Coins. But I suppose we don't need to go through the ones we've already fixed changing them to use this template quite yet. Note that they automatically include the horizontal line - hopefully this'll see the end of people omitting it. -- Smjg 18:06, 12 January 2006 (UTC)

Bot spec
I've written the following specification, which should enable User:Tsca.bot to get to work. I suggest that this stays here for a few days, giving people time to suggest changes to the spec, before the bot starts work. -- Smjg 17:52, 3 February 2006 (UTC)

Pass 1: Fix the page titles
Starting from the main Puzzles page, follow the links. Move each page to its correct title if it isn't already, using the displayed text of the link by which the page was reached.

For example, the page linked as Two-player games from the main Puzzles page shall become Puzzles:Two-player games. The page linked as Picking Game under that page shall become Puzzles:Two-player games:Picking Game.

Special cases to observe:

 * 1) Ignore navigation header links (see below) during this stage of the process.
 * 2) If a colon appears in the text of a link, ignore all text preceding the colon when generating the new page name.
 * 3) If the link text begins with a lowercase letter, change the first letter to uppercase when generating the title.  For example, Puzzles:Arithmetical puzzles:Three Daughters:Solution not Puzzles:Arithmetical puzzles:Three Daughters:solution.
 * 4) If the text of a link contains the word solution, then use Solution by itself as the name at that level rather than the whole text of the link.
 * 5) If two or more pages link to the same page (either directly or via redirects), then go by the link on the first page that was encountered.  For example, some puzzles have hint pages as well as the solution page, and have both hint and solution links from the main puzzle page.  The hint page may also have a solution link.  Invariably, you will reach the main puzzle page before the hint page.  Consequently, the solution page will be a child page of the main puzzle page, not of the hint page.
 * 6) Two pages, namely Number sequences and Riddles, display several puzzles at once, each with its own solution page.  I'm not sure how the solution pages should be named at the moment.  Meanwhile, I suggest that we skip processing these pages, and then maybe we can deal with them later.

Pass 2: Tidying up the pages
Once the pages are at their correct titles, the bot can then work at tidying up the pages themselves. On the main Puzzles page, I believe the only thing that needs doing is to update the links. On the pages within the book, there is the following work to do:

 * 1) Make sure every page has a navigation header.  Use the hc-navhead2, hc-navhead3, etc. templates, replacing any manually typed header that may be present on the page.  It is sufficient to check whether the page begins with a link back to Puzzles, and if so, delete the whole line.  Any horizontal line immediately below the nav header should also be removed, since the hc-navhead templates automatically include one.
 * 2) Apart from that which is in the navigation header, there should be no repetition of the puzzle title at the beginning of the page content as is present on some of the How do you ... ? pages.
 * 3) Adjust all links to point to the pages by their new, hierarchical names, and make the display text exactly match the final part of the title.
 * 4) Link text should be non-bold.

Changes
If you wish to propose or discuss any changes or additions, please do so here.

Recent attempts
Withinfocus, who added cleanup-NC, obviously didn't practise what the notice preaches by looking at this talk page. As it happens, at least two users - Think Fast and SBJohnny - have undertaken to implement the slashes convention, while at the same time failing to agree on other common-sense conventions ("Logic puzzles" vs. "Analytical Puzzles"). There are also plenty of other cleanups that could be done to the page titles as well as making them use slashes. -- Smjg 12:20, 26 November 2006 (UTC)
 * Hah, I just saw this little dig even though I added that template many months ago. The addition of the template was perfectly valid. Should the naming convention need to be discussed it would be done here as it was in some form above. Flagging a poorly-organized book was my goal and that's what happened, therefore there was nothing I "didn't practice" and my actions are correct. My addition of the template does not require discussion, only the implementation of the naming change does. I'm writing this so that if others notice it they won't be afraid to mark books that need cleanup. This is an implementation of policy and all books should be well-formed here at Wikibooks. The naming suggestions above need improvement in many ways so that colon convention can be avoided, but that will be tackled when a user who knows categories and the slash convention well feels like taking the effort to reorganize here. I unfortunately do not have the time currently. -within focus 17:00, 17 April 2007 (UTC)

Just to clarify, the system that has been mostly followed is that section titles ("Logic puzzles", etc.) are in sentence case, but individual puzzle titles are in title case. This makes a little sense, ISFA one might think of puzzle titles as like titles of a book, song, film, etc. whereas section titles are just descriptive phrases used to group the puzzles. But is it ideal?

It gets even more tricky when you consider that puzzles within Puzzles:Chess problems, and possibly a few others, have more or less descriptive titles rather than titles in the style of the others, and generally have puzzle titles in sentence case.

What are we going to do then? Before we do any more page moving, we should all agree on a convention for capitalising titles. We should also decide what to do with Puzzles:Number sequences, which currently has the puzzles all on one page and each solution on a page of its own. -- Smjg 18:06, 27 November 2006 (UTC)

Non-scientific puzzles
There are some logical puzzles that are too simple to be called logical, or non-solveable, or too contradictory, but interesting nonetheless. I added a new section, Non-Scientific Puzzles. --Divinity 18:24, 19 Jun 2005 (UTC)

New Link Under Puzzle Resources
I added this link to a lot of riddles however the answeres aren't necessarily given to you so for a lot of them you might need to figure them out or check the Wu Forum however these are a lot of great riddles.* Riddles–Wu:Riddles I also added this link which has a wide variety of puzzles *Jim Loy's Puzzle Pages--71.234.101.173 19:39, 14 February 2007 (UTC)

Some pages don't seem to belong
Is this supposed to be a book of puzzles, a book about puzzles or a book of links to puzzles? I'd think the former. In this case, some of the pages seem out of place:

 * Puzzles/Bongard problems and Puzzles/Sudoku are web links to puzzles. The former has a bit of information on what Bongard problems are, but that's an aside.  Of course, if somebody wants to create some puzzles of these kinds to publish in this book, that's fine.

 * Puzzles:Rubik's cubes and the other bullet points under Puzzles don't seem to make sense to have here. Of course a web page can present an applet for the user to play Rubik's cube or any mechanical puzzle, but Wikibooks isn't really the place for this.  You could argue that the right thing to have here is puzzles on how to construct specific Rubik's Cube patterns or perform specific manoeuvres, but that's still probably not the right title for such a section.

-- Smjg 18:16, 25 March 2007 (UTC)

I agree, they do not belong here.

I will try to reorder or remove them.

Zezen (discuss • contribs) 08:26, 4 July 2020 (UTC)

Wikiversity Contributor Needs Material on "Puzzles"!
I intend to read ALL of the previous discussion before I start serious editing. I agree that there is a need to overhaul the available material, so I intend to join in the discussion here.  New Wikibooks User: Ray Calvin Baker (discuss • contribs) 23:07, 31 October 2012 (UTC)

title: Talk:Puzzles


text:
US History/European History

The peoples of Europe have had a tremendous effect on the development of the United States throughout the course of U.S. history. Europeans "discovered" and colonized the North American continent and, even after they lost political control over its territory, their influence has predominated due to a common language, social ideals, and culture. Therefore, when endeavoring to understand the history of the United States, it is helpful to briefly describe their European origin.

Ancient Greece

 * See also: Ancient History/Greece

The first significant civilizations of Europe formed in the second millennium BCE. By 800 BCE, various Greek city-states, sharing a language and a culture based on slavery, pioneered novel political cultures. In the Greek city of Athens, by about 500 BCE, the male citizens who owned land began to elect their leaders. These elections by the minority of a minority represent the first democracy in the world. Other states in Greece experimented with other forms of rule, as in the totalitarian state of Sparta. These polities existed side by side, sometimes warring with each other, at one time combining against an invading army from Persia. Ancient Athens is known for its literary achievements in drama, history, and personal narrative. The individual city-states did not usually see themselves as a single entity. (The conqueror Alexander the Great, who called himself a Greek, actually was a native of the non-Greek state of Macedon.) The city-states of Greece became provinces of the Roman Empire in 27 BCE.

Rome

 * See also: Ancient History/Rome

The city of Rome was founded (traditionally in the year 753 BCE). Slowly, Rome grew from a kingdom to a republic to a vast empire, which, at various points, included most of present-day Britain (a large part of Scotland never belonged to the empire), France (then known as Gaul), Spain, Portugal, Italy, Greece, Turkey, Iraq, Palestine (including the territory claimed today by the modern state of Israel), Northern Arabia, Egypt, the Balkans, and the entire north coast of Africa. This empire was maintained through free-born or adoptive citizenship, citizen education and indoctrination, a large and well-drilled army, and taxes directed by a large bureaucracy directed by the emperor. As each province produced more Roman citizens, the state became hard to maintain. Whole kingdoms in the north and east, and the invading peoples we know as the Germanic tribes (the Ostrogoths and Visigoths and the Franks) sat apart from the system.

After the death of one emperor in 180 CE, power struggles between the army and a succession of rulers of contested origins produced anarchy. Diocletian (243 - 316) reinstated the Empire by 284. Rome regained territory until 395, when the Empire was so large that it had to be divided into two parts, each with a separate ruler. The two halves sat uneasily together. The East, which considered itself the heir of Alexander the Great, spoke Greek or a dialect, while the West spoke Latin. The Eastern Empire survived until 1453, but the system to maintain the Western Empire broke apart. Plagues and crop failures troubled the world. In 476, Germanic tribes deposed the boy who was then the Emperor. Roman roads fell into disrepair, and travel became difficult. Some memories remained in the lands which had once known Roman rule. The supreme rulers of various tribes called themselves king, a distortion of the Roman word Caesar.

The Roman Empire to the Holy Roman Empire
After Rome's fall, monks from Ireland (which had never known Rome) spread Catholic Christianity and the culture and language of the Western Roman Empire across Europe. Catholicism eventually spread through England (where the Germanic tribes of the Angles and the Saxons now lived)and to the lands of the post-Roman Germanic tribes. Among those tribes, the Franks rose to prominence.

Charlemagne (742 - 814), the King of the Franks, conquered great portions of Europe. He eventually took control of Rome. The senate and the political organs of Rome had disappeared, and Charlemagne did not pretend to become the head of the Church. Charlemagne's domain, a confederation of what had been Roman Gaul with Germanic states, was much smaller than Diocletian had known. But prestige came with identity with the past, and so this trunk of lands became The Holy Roman Empire. Charlemagne's descendants, as well as local rulers, took their sanction from the Church, while the Church's pope influenced both religious and political matters.

The result of political stability was technological advance. After the year 1000, Western Europe caught some of the East's discoveries, and invented others. In addition to vellum, Europeans now started making paper of rags or wood pulp. They also adopted the wind and water mill, the horse collar (for plows and for heavy weights), the moldboard plow, and other agricultural and technological advances. Towns came into being, and then walled cities. More people survived, and the knights and kings over them grew restive.

Viking Exploration of North America
In the eighth century, pushed from their homes in Scandinavia by war and population expansion, Norsemen, or Vikings, began settling parts of the Faeroe, Shetland, and Orkney Islands in the North Atlantic. They went where ever treasure was, trading as far as Byzantium and Kiev in the East. In the West they raided from Ireland and England down to the Italian peninsula, sailing into a port, seizing its gold, and murdering or enslaving its people before fleeing. They began settling Iceland in approximately 874 CE. A Viking called Erik the Red was accused of murder and banished from his native Iceland in about 982. Eric explored and later founded a settlement in a snowy western island. Knowing that this bleak land would need many people to prosper, Eric returned to Iceland after his exile had passed and coined the word "Greenland" to appeal to the overpopulated and treeless settlement of Iceland. Eric returned to Greenland in 985 and established two colonies with a population of nearly 5000.

Leif Erikson, son of Erik the Red, and other members of his family began exploration of the North American coast in 986. He landed in three places, in the third establishing a small settlement called Vinland. The location of Vinland is uncertain, but an archeological site on the northern tip of Newfoundland, Canada (L'anse aux Meadows) has been identified as the site of a modest Viking settlement and is the oldest confirmed presence of Europeans in North America. The site contains the remains of eight Norse buildings, as well as a modern reproduction of a Norse longhouse. But the settlement in Vinland was abandoned in struggles between the Vikings and the native inhabitants, whom the settlers called Skraelingar. Bickering also broke out among the Norseman themselves. The settlement lasted less than two years. The Vikings would make brief excursions to North America for the next 200 years, though another attempt at colonization was soon thwarted.

By the thirteenth century, Iceland and Greenland had also entered a period of decline during the "Little Ice Age." Knowledge of their exploration, in the days before the printing press, was ignored in most of Europe. Yet the Vikings are now considered the true European discoverers of North America. The influence of their people outlasted even the terrible raids, and their grandchildren became kings and queens. For example, a branch of Viking descendants living in France, the Normans, conquered England from the Anglo-Saxons in 1066.

The Great Famine and Black Death
The Little Ice Age led to European famines in the years 1315-1317 and in 1321. In the year 1318 sheep and cattle began to die of a contagious disease. Farmers could not support the growing population. And then, in 1347, some Genoese trading ships inadvertently brought a new, invasive species of rat to Europe. These rats carried bubonic plague.

Plague was also called the Black Death, from the darkened skin left after death and from its deadly reach. It had three strands: bubonic, pneumonic, and septicemic. In bubonic plague fleas carried by the rats would leave their hosts and bite people. The masses of bacteria would flow through the human system, killing cells and leaving their refuse in lymph nodes in the armpit, groin, and neck. These nodes would swell and turn black, creating bubos. Infection could also spread into the lungs, so that a person might cough or sneeze the germ into the air. This created pneumonic plague, spreading disease into spaces where people gathered and where rats dared not go. It also spread through contamination of food. The last form of disease, and its most deadly, was septicemic. This attacked the blood, leaving stretches of pale skin looking black, and killing the person within hours.

Surviving laws of cities and guilds regulate public cleanliness and penalize adulteration of food. They cannot show how strictly these laws were applied. And they show no knowledge, of course, of germ theory and the need for sterilization. Older systems such as the few public baths which remained from the days of colonial Rome were seen as sinful and dangerous, invitations to the plague. The dwelling places of survivors of pre-Christian Rome, the Jews who were forced to live apart, were attacked by mobs who attributed the Black Death to their poisoning Christians' wells.

The responses to plague can be seen in the records left by survivors -- one third of the population of Europe died in repeated waves of disease -- and in the subsequent changes in society. Airplanes and satellites show the foundations of plague-era towns which were emptied by the disease. In just one square mile of pre-plague Europe there are reports of there being 50,000 people. In large cities, families would flee or lock themselves away, trying to keep themselves from death. Other families were locked in by city authorities. This is the beginning of the modern system of quarantine. Some branches of the family would not be among those so helped. The Black Death seemed erratic, sometimes taking people deemed good and pious, sometimes not. One priest or church prelate might die, and another survive. And a living priest might give no aid to other survivors. Some critiques of the Church which had become spread through most of Europe date from this era.

Although some lands became waste through lack of tilling, those people who survived grasped the property of those who had not. Europe then had a land-based economic system. Rich people became richer. There began a labor shortage: the farmers who survived needed hands to take in their crops. The wages of farm hands began to rise. In the surviving towns they needed people to guard the gates: in the courts they began to look for rising young men. Cities became more powerful in the depleted lands, and authority grew more centralized.

Education
During the Middle Ages Western society and education were heavily shaped by Christianity as expressed through the Roman Catholic Church. Towns, courts, and feudal manors had their priests, monasteries and nunneries had their scriptora or libraries, and after the 11th century CE, a few cities had Universities, schools to educate men to be high-ranking clerics, lawyers, or doctors. Where children had schools, their parents paid a fee so that they might learn Latin, the language St. Jerome had used for his translation of the Bible. Latin was the language of the Church. It was also learned, along with military tactics and the rules of chivalry, by men who trained to be knights. A smattering of Latin was necessary, along with Math, even for the elementary schools which sprang up in some cities. There both boys and girls were taught literacy and math, prerequisite for acceptance as an apprentice in many Guilds. Latin across Europe created a European-wide culture: a doctor from Padua could talk to his fellow from Oxford in Latin.

As in the Greek and Roman eras, only a minority of people went to school. There were not enough books, little travel, and no means of spreading standardized education. Schools were attended first by persons planning to enter religious life. Occasionally a cleric would reach out to educate a very bright peasant boy. This was one of the few ways peasants could rise in the world. But the vast majority of people were serfs who served as agricultural workers on the estates of feudal lords. They were, in effect, tied to the fate of the land. From the serf up to some high princes, the vast majority of people did not attend school, and were generally illiterate.

In the rise of the Universities in the 11th century, the Church translated several manuscripts of the ancient Greek writer Aristotle into Latin. From Aristotle's emphasis upon human reason, philosophy and science, and the Church's emphasis upon revelation and the teachings of Christ, medieval scholars developed Scholasticism. This was an philosophical and educational movement which attempted to integrate into an ordered system both the natural wisdom of Greece and Rome and the religious wisdom of Christianity. It was dominant in the medieval Christian schools and universities of Europe from about the middle of the 11th century to about the middle of the 15th century, though its influence continued in successive centuries. The idea of Man in the middle of ordered nature, and yet dominant over nature, bore fruit in the observation of natural phenomena, the beginnings of what the Western World knows as science. It also led to the exultation of system over observation, and the persistence of the Ptolemaic theories such as geocentrism among formally educated people.

Noble girls were sometimes sent to live in nunneries in order to receive basic schooling. Nuns would teach them to read and write and the chores necessary to run their establishments, including spinning and weaving. (Cloth-making was a major national industry in the Middle Ages.) They taught them their manners and their prayers. Some of these girls later became nuns themselves.

Christianity, Islam, Judaism
During the centuries after the fall of Rome, various flavors of Christian churches spread from Northern Africa and Armenia westward. This changed after Mohammed established Islam in 610 CE. Like Christianity, it spread through conversion and conflict. At its height it was also a faith of Europe, from Spain to Albania and Bosnia and their sister states. Both Prince and Caliph held that their state must have one faith, and no other belief was encouraged. When Jerusalem was reconquered by the Seljuq Turks, Christians were no longer able to go on religious pilgrimages to the Holy City.

At the end of the eleventh century, Pope Urban II inaugurated the Crusades, urging Western European kings and great nobles to begin what would be a century and a half of warfare. Christian armies fought first to reconquer and then to hold part of the Kingdom of Jerusalem. The Crusaders ultimately failed in the face of resurgent Muslim forces. Western Europeans within Church and State argued for and against the Crusades.

Despite the failure of the Crusades, militant Western Christianity persisted in Spain in an effort known as the Reconquista (the "reconquest"), which purged the land of the Muslims who had arrived there in 711. By the fifteenth century, the Muslims were confined to the kingdom of Granada, which bordered the Mediterranean Sea in the southern side of the Iberian Peninsula. Granada finally fell in 1492 to the Spanish Christians, ending the reconquista.

Rome had destroyed Israel in 70 CE, but allowed a remnant of her people to survive. Fortified by rabbinic culture and centered on the Torah, they became a resilient group. They survived as the known world became Christian. They spread, as traders, through East and West. However, Christian relationships with Jews were punctuated by hatred. They were held to be guilty of Jesus' death, and they were supposed to be evil because they had not converted to Christianity. They were forced into the notorious ghettos, usually built on waste or undesirable land. They were forced to wear strange clothing which marked them off, and to pay heavy taxes. Christians spread rumors that Jewish officials sometimes kidnapped and killed young boys for their sacrifices. Sometimes a mob might break into the ghetto, killing some people. Individuals were sometimes forced to convert. One of the effects of European nationalism was the expulsion of a country's Jewish population. England was the first, in the 13th century; later, a reviving France; later still, Spain and Portugal. Some men crewing the ships in the Age of Exploration were Jews, often practicing their faith in hiding.

For a period in the late Twelfth century there two sets of Popes, a line in Rome and another in the French city of Avignon under the sway of that Court. In reaction against this, the Church centralized its powers in parallel to what nations were doing. There had been dissension before, in medieval England's Lollards and later with the Czech priest John Hus. However, it was only in an age after the printing press, when people began printing the Bible in their own languages, when Martin Luther founded the Protestant church. England's King Henry VIII, who had won the title "Protector of the Faith" for a work defending the Pope, later left it to become the head of the Church of England. This division of Western Christianity created religious minorities, who were persecuted throughout Europe. Among these were the Pilgrims, who helped settle America.

The Renaissance

 * See also: European History

Another, more humble result of the plague was the accumulation of rags left over from clothing. These were quickly used to make paper. Books were very rare during the Middle Ages, and the monks who made them chained them to their shelves. It took one year for a man to make one book. In that climate Bibles took priority: we have only one copy of Democritus's most famous work surviving from this period. As rag paper replaced velum, books began to become more plentiful. The supply was augmented by Europe's adoption of Johannes Gutenberg 's fixed-type printing press in the 15th century.

There had been earlier leaps in culture, including the wave of population and technological adaptation in the 12th century. This left its mark in increased population and the Roman Catholic Church's adoption of Aristotle. Yet the press made it possible for knowledge to have a foothold in society. Inventions in one place could be explained and adopted across a continent. The Greeks fleeing the fall of Byzantium brought their knowledge of ancient Greek culture to the West. The Bible, the basic book of Christendom, could be pored over by laypeople, and reading it could be learned by more people than ever before. Learning was no longer solely the province of the Church.

If the Bible was first off of the presses, pseudo-science and science followed soon after. The European witch trials were one result of the new medium. The questioning of scientific consensus was another. Andreas Vesalius published his observations about the circulatory system. Books discussing the theories of Nicolaus Copernicus and Galileo Galilei demolished the old geocentric theory of the cosmos. The arts were not neglected. Giorgio Vasari's biographical Lives introduced such new artists as Leonardo Da Vinci and Michelangelo Buonarroti to the larger world.

A later time called this growth of knowledge the Renaissance. They said it began in the Italian city-states, spreading throughout most of Europe. The Italian city of Florence was called the birthplace of this intellectual movement.

Books spread the Crusader's newly found experience and knowledge of the Mediterranean, a region whose technology was at that time superior to that of western Europe. Books written about traders, adventurers, and scholars spread knowledge of Chinese technology such as gunpowder and silk. They spread writings of the ancient world which had been lost to Europe, and nurtured a taste for new foods and flavors. They spread pictures of ancient Greek statues, Moorish carpets, and strange practices.

In the fifteenth century, the Mediterranean was a vigorous trading area. European ships brought in grains and salts for preserving fish, Chinese silks, Indian cotton, precious stones, and above all, spices. White cane sugar could be used to preserve fruit and to flavor medicine. Cinnamon was medicine against bad humors as well as preservative and flavoring, part of the mysterious poudre douce, and now available even to some European common people.

Toward Nation-States
The great age of exploration was undertaken by nation-states, cohesive entities with big treasuries who tended to use colonization as a national necessity. When such nations as Portugal, England, Spain, and France became stronger, they began building ships.

The Rise of Portugal
The Italian peninsula dominated the world because of its position in the Mediterranean Sea. Universities in Padua, Rome, and elsewhere taught men from East and West. Above all, principalities such as the Republic of Venice and Florence controlled trade. Genoa and Venice in particular ballooned into massive trading cities. Yet there was at yet no nation of Italy, so each city's riches belonged only to that city. Individual cities used their monopoly to raise the price of goods, which would have been expensive in any case, because they were often brought overland from Asia to ports on the eastern Mediterranean. The mad prices, in turn, increased the desire of purchasers to find other suppliers, and of potential suppliers to find a better and cheaper route to Asia.

Portugal was just one of many potential suppliers, with a location which extended its influence into the Atlantic and down, south and east, to Africa. Prince Henry, son of King John I, promoted the exploration of new routes to the East. He planned Portugal's 1415 capture of Ceuta in Muslim North Africa. He also sponsored voyages that pushed even farther down the West African coast. By the time of his death in 1460, these voyages had reached south to Sierra Leone.

Under King John II, who ruled from 1481 to 1495, Bartolomeu Dias finally sailed around the southernmost point of Africa to the Cape of Good Hope (1487-1488). In 1497-1499 Vasco da Gama of Portugal sailed up the east coast of Africa to India.

The Portuguese colonized and settled such islands in the Atlantic as Madeira, Cape Verde, the Azores, and Sao Tome. These islands supplied them with sugar and gave them territorial control of the Atlantic. West Africa was more promising, not only unearthing a valuable trade route to India, but also providing the Portuguese with ivory, fur, oils, black pepper, gold dust, and a supply of dark skinned slaves who were used as domestic servants, artisans, and market or transportation workers in Lisbon. They were later used as laborers on sugar plantations on the Atlantic.

France, England, And The Hundred Years' War
King Harold of England faced William the Norman usurper after defeating the last Viking forces holding the North of England. And when William the Norman became William the Conqueror, he held England by consolidating the nation. His army was ruled from newly built castles, and had the best technology of the time. His sons and their sons fought the original inhabitants of their country in Scotland and Wales, pushing their boarders. They also claimed the right to their ancestral Normandy, in what is now France. (There had long been rivalry between England and France over the wool trade.) By a English king's marriage to an former queen of France, Eleanor of Aquitaine, the king subsequently claimed Aquitaine. During the years of 1337 to 1453, the kings of England claimed the whole of France and beyond, fighting The Hundred Years' War there and in the Low Countries. For some years the English threatened Paris, and there was a question whether the small area of France proper would be entirely conquered. The early stages of the war marked by English victory against a demoralized French people and their Prince. But around 1428, a young peasant girl from Lorriene, France named Joan of Arc approached a garrison of the French army. She told them that Saint Michael, Saint Catherine, and Saint Margaret had told her to lead the army to victory. She said that God had come to her in a dream, and told her how to defeat the English. She claimed that God said Prince Charles of France needed to be crowned in order for France to claim victory over the English. After gaining the new French king, support of the populace, and several key victories, Joan was sold to the English for treason and as an appeasement. Yet France had been renewed. It pushed back against the invaders, and took back most of the land. In the next few centuries it was to remove England from Continental Europe.

The Hundred Years' War devastated both countries. But it ultimately turned both of them into stronger, colonial powers. The Hundred Years' War created opportunities for wealth and advancement for the knights of both countries. The Chivalric code showed great influence during this period. France absorbed Aquitaine, Castile, and Normandy itself, prosperous areas. The twin strokes of the plague and the Inquisition weakened opposition to the French king's rule. And English centralization continued as its own royalty sought service of serf and Baron. A group of new dialects, Middle English, came out of the tug between Norman lord and Anglo-Saxon peasant. If the nation could not get new land in Europe, it could use its ships to sail elsewhere.

Review Questions
1. Explain how one of these late medieval devices affected prosperity: the wind mill; the horse collar; the printing press.

2. How did the plague infect individuals? How did mass death affect society?

3. What was the importance of these four men to the Renaissance? Galileo Galilei, Nicolaus Copernicus, Andreas Vesalius, Leonardo Da Vinci.

title: US History/European History


text:
General Chemistry/Chemical equations

Chemical equations are a convenient, standardized system for describing chemical reactions. They contain the following information.

 * The type of reactants consumed and products formed
 * The relative amounts of reactants and products
 * The electrical charges on ions
 * The physical state of each species (e.g. solid, liquid)
 * The reaction conditions (e.g. temperature, catalysts)

The final two points are optional and sometimes omitted.

Anatomy of an Equation
$$\hbox{H}_{2 (g)} + \hbox{Cl}_{2 (g)} \to 2\hbox{HCl}_{(g)}$$

Hydrogen gas and chlorine gas will react vigorously to produce hydrogen chloride gas. The equation above illustrates this reaction. The reactants, hydrogen and chlorine, are written on the left and the products (hydrogen chloride) on the right. The large number 2 in front of HCl indicates that two molecules of HCl are produced for each 1 molecule of hydrogen and chlorine gas consumed. The 2 in subscript below H indicates that there are two hydrogen atoms in each molecule of hydrogen gas. Finally, the (g) symbols subscript to each species indicates that they are gases.

Reacting Species
Species in a chemical reaction is a general term used to mean atoms, molecules or ions. A species can contain more than one chemical element (HCl, for example, contains hydrogen and chlorine). Each species in a chemical equation is written:

$$\hbox{E}_{x(s)}^y$$

E is the chemical symbol for the element, x is the number of atoms of that element in the species, y is the charge (if it is an ion) and (s) is the physical state.

For example, ethyl alcohol would be written $$\hbox{C}_2\hbox{H}_6\hbox{O}_{(l)}$$ because each molecule contains 2 carbon, 6 hydrogen and 1 oxygen atom. A magnesium ion would be written $$\hbox{Mg}^{2+}$$ because it has a double positive ("two plus") charge. Finally, an ammonium ion would be written $$\hbox{NH}_4^+$$ because each molecule contains 1 nitrogen and 4 hydrogen atoms and has a charge of 1+.

Coefficients
The numbers in front of each species have a very important meaning—they indicate the relative amounts of the atoms that react. The number in front of each species is called a coefficient. In the above equation, for example, one H2 molecule reacts with one Cl2 molecule to produce two molecules of HCl. This can also be interpreted as moles (i.e. 1 mol H2 and 1 mol Cl2 produces 2 mol HCl).

It is important that the Law of Conservation of Mass is not violated. There must be the same number of each type of atoms on either side of the equation. Coefficients are useful for keeping the same number of atoms on both sides:

$$2\hbox{H}_2 + \hbox{O}_2 \to 2\hbox{H}_2\hbox{O}$$

If you count the atoms, there are four hydrogens and two oxygens on each side. The coefficients allow us to balance the equation; without them the equation would have the wrong number of atoms. Balancing equations is the topic of the next chapter.

Other Information
Occasionally, other information about a chemical reaction will be supplied in an equation (such as temperature or other reaction conditions). This information is often written to the right of the equation or above the reaction arrow. A simple example would be the melting of ice.

$$\hbox{H}_2\hbox{O}_{(s)} + heat \to \hbox{H}_2\hbox{O}_{(l)}$$, which could be written as $$\hbox{H}_2\hbox{O}_{(s)} \xrightarrow{heat} \hbox{H}_2\hbox{O}_{(l)}$$

Reactions commonly involve catalysts, which are substances that speed up a reaction without being consumed. Catalysts are often written over the arrow. A perfect example of a catalyzed reaction is photosynthesis. Inside plant cells, a substance called chlorophyll converts sunlight into food. The reaction is written:

$$6\hbox{CO}_2 + 6\hbox{H}_2\hbox{O} + sunlight \xrightarrow{chlorophyll} \hbox{C}_6\hbox{H}_{12}\hbox{O}_6 +  6\hbox{O}_2$$

title: General Chemistry/Chemical equations


text:
French/Lessons/People and things

Nouns are words that represent something perceived or conceived, like an apple or a thought. In French, all nouns have a grammatical gender; that is, they are either masculine (m) or feminine (f).

Most nouns that express people or animals have both a masculine and a feminine form. For example, the two words for the cat in French are le chat (m) and la chatte (f).

However, there are some nouns that talk about people or animals whose gender is fixed, regardless of the actual gender of the person or animal. For example, is always feminine, even when it's talking about your uncle;  is always masculine, even when it's talking about your female professor or teacher.

The nouns that express things without an obvious gender (e.g., objects and abstract concepts) have only one form. This form can be masculine or feminine. For example, can only be feminine;  can only be masculine.

Exceptions
There are many exceptions to gender rules in French which can only be learned. There are even words that are spelled the same, but have a different meaning when masculine or feminine; for example, means the book, but  means the pound. Some words that appear to be masculine (such as la photo, which should be masculine but is not because it is actually short for la photographie) are in fact feminine, and vice versa. Then there are some that just don't make sense; la foi is feminine and means faith or belief, whereas le foie is masculine and means liver.

In English, the definite article is always the.

In French, the definite article is changed depending on the noun's: There are three definite articles and an abbreviation. Le is used for masculine nouns, La is used for feminine nouns, Les is used for plural nouns (both masculine or feminine), and L' is used when the noun is singular and begins with a vowel or silent h (both masculine or feminine). It is similar to English, where a changes to an before a vowel.
 * 1) gender
 * 2) number
 * 3) first letter

Unlike English, the definite article is used to talk about something in a general sense, a general statement or feeling about an idea or thing.

Elision
Elision refers to the suppression of a final unstressed vowel immediately before another word beginning with a vowel. The definite articles le and la are shortened to l’ when they come before a noun that begins with a vowel or silent h. When pronounced, the vowel sound is dropped.

Elision does not occur on an aspired h:
 * (le) héros:

In addition to the definite article, elision will also occur with other words, such as que, je, le, ce, ne, and de. The details on these words will be covered in later sections of the book.

In English, the indefinite articles are a and an. Some is used as a plural article in English.

Again, indefinite articles in French take different forms depending on gender and number. The articles un and une literally mean one in French.

une is often (more often than not) pronounced (ewnuh) in poetry and lyric.

Des fils does mean some sons, but is a homograph: it can also mean some threads (when pronounced like ).

Some
Note that des, like les, is used in French before plural nouns when no article is used in English. For example, you are looking at photographs in an album. The English statement I am looking at photographs. cannot be translated to French as Je regarde photographies. because an article is required to tell which photographs are being looked at. If it is a set of specific pictures, the French statement should be On the other hand, if the person is just browsing the album, the French translation is

Plurality, pronunciation, and exceptions
The plural of most nouns is formed by adding an -s. However, the -s ending is not pronounced. It is the article that tells the listener whether the noun is singular or plural.

Most singular nouns do not end in -s. The -s is added for the plural form of the noun. Fils is one exception. Whenever the singular form of a noun ends in -s, there is no change in the plural form.

The final consonant is almost always not pronounced unless followed by an -e (or another vowel). is also an exception to this rule.

Liaison
Remember that the last consonant of a word is typically not pronounced unless followed by a vowel. When a word ending in a consonant is followed by a word beginning with a vowel sound (or silent h), the consonant often becomes pronounced. This is a process called liaison. When a vowel goes directly after un, the normally unpronounced n sound becomes pronounced.

Compare the pronunciation to words without liaison:

Une is unaffected by liaison.

Liaison also occurs with les and des.

As with elision, an aspired h isn't liaised:
 * (les) hangars:

Qu’est-ce que c’est ?
To say What is it? or What is that? in French, is used.

 * is used often to say What…? at the beginning of sentences.

To respond to this question, you say C’est un(e) [nom]., meaning It is a [noun]:

Remember that the indefinite article (un or une) must agree with the noun it modifies:

Il y a
is used to say there is or there are. Il y a expresses the existence of the noun it introduces.

The phrase is used for both singular and plural nouns. Unlike in English (is → are), il y a does not change form.

The -s at the end of the most pluralised nouns tells you that the phrase is there are instead of there is. In spoken French, when both the singular and plural forms almost always sound the same, the article (and perhaps other adjectives modifying the noun) is used to distinguish between singular and plural versions.

A is the present third person singular form of the verb to have, and y is a pronoun meaning there. The phrase il y a, then, literally translates to he has there. This phrase is used in all French tenses. It is important to remember that verb stays as a form of have and not be.

Voici and voilà
Like in English, il y a… is not often used to point out an object. To point out an object to the listener, use, meaning over here is/are or right here is/are, and , meaning over there is/are, or there you have it.

title: French/Lessons/People and things


text:
User talk:Etothex

To Etothex, Greetings.

In re the US History textbook: After Chapter 20 ("Eisenhower, Civil Rights, and the Fifties,") I consider that further chapters need to be added. But the question is- where should the line be drawn? I think that we can have one Chapter on the Vietnam War and the Seventies, and another on Reagan, but that we should end there. Everything after that seems to be too recent to be included. What is your personal opinion, if I may ask? Thanking you, Lord Emsworth 22:23, 4 Oct 2003 (UTC).

 * Sure. I know lots of history books stop at Pres. Carter/Reagan because of several reasons, but maybe we could even get into the Clinton administration a bit. Definitely stop there, though. Current events haven't quite 'aged' enough yet. I just stopped at Eisenhower because I wasn't quite sure what to title them. I mean, I could say "Chapter 21: The Vietnam War and the Sixties", but that suggests everything happened in the sixties and that's just not true. Etothex 07:47, 5 Oct 2003 (UTC)

Hey :) Great start on Vectors! I'd just ask one thing, don't use $$\cdot$$ for multiplication, since that could conceivably be confused with the dot product later. Writing a product without the dot is still pretty clear :) Thanks Dysprosia 08:51, 9 Oct 2003 (UTC)

 * Oh, sure. I'd written it when I was pretty sleepy and too lazy to look up the correct tex syntax for vectors, so I just wrote it out and didn't even think about dot product. :) I might add on trig later, if I feel like drawing some more diagrams. Etothex 02:09, 11 Oct 2003 (UTC)

Just another point, you don't need to variables to get x; you can just go x - if you didn't know already :) Dysprosia 11:13, 14 Oct 2003 (UTC)
 * Hmm, yeah. :) I did it because of the option in prefs for how to display tex syntax, as PNG or text. I've got a small monitor and even on 800x600(versus 1024x768) the text is small...So I kinda like it when I can turn on PNG when I need it. I don't know if anyone else uses this, but I find it convenient. I can switch back if it doesn't work, but otherwise, I'll just keep on doing it. Etothex 23:36, 14 Oct 2003 (UTC)

 * Oh cool! I never really realized that you could do that; it's just easier when I type to just hit ' four times, I'm a lazy typist - I don't see any other real problem with it :) Dysprosia 03:21, 15 Oct 2003 (UTC)

Vocabulary Project
Hi Etothex, since you started the wikibook on German I thought you might be interested in a learnign project I am starting, especially for vocabulary. Please check my page and let me know what you think about it. Get-back-world-respect 19:49, 6 May 2004 (UTC)

title: User talk:Etothex


text:
French/Lessons/Transportation

-uire verbs are conjugated irregularly.

Most verbs form the passé composé with avoir, however there are a small number of verbs that are always conjugated with être. In a general case, these verbs indicate a change in state or position.

List of verbs
The verbs that take être can be easily remembered by the acronym MRS. DR VANDERTRAMP:

Direct objects
These verbs take their conjugated avoir when they are immediately followed by a direct object

For Example,
 * Je suis descendu.

with the direct object mes bagages becomes
 * J'ai descendu mes bagages.

As another example,
 * Je suis monté.

with the direct object mes bagages becomes
 * J'ai monté mes bagages.

As another example, but with ils instead of je,
 * Ils sont sortis.

with direct object leur passeport becomes
 * Ils ont sorti leur passeport.

Subject-past participle agreement
When conjugating with être, the past participles of the above verbs must agree with the subject of a sentence in gender and number. Note that there is no agreement if these verbs are conjugated with avoir.

 * If the subject is masculine singular, there is no change in the past participle.
 * If the subject is feminine singular, an -e is added to the past participle.
 * If the subject is masculine plural, an -s is added to the past participle.
 * If the subject is feminine plural, an -es is added to the past participle.

Indirect object pronoun - to it, to them
The French pronoun y is used to replace an object of a prepositional phrase introduced by à. Note that lui and leur, and not y, are used when the object refers to a person or people.
 * Je réponds aux (à les) questions. - J'y réponds.
 * I respond to the questions. - I respond to them.

Replacement of places - there
The French pronoun y replaces a prepositional phrase referring to a place that begins with any preposition except de (for which en is used). Note that en, and not y is used when the preposition of the object is de.
 * Les hommes vont en France. - Les hommes y vont.
 * The men go to France - The men go there.

Idioms

 * Ça y est! - There we go!, There you have it.
 * J'y suis! - I get it!

 These verbs are conjugated irregularly, and normally follow the -er conjugation scheme. In past participle form, -ir is replaced with -ert for these verbs.

Formation
A common -rir verb is ouvrir:

The noun is derived from ouvrir, and the adjective  is derived from its past participle.

1Mourir is the only -ir verb that takes être as its helping verb in perfect tenses (and therefore agrees with the subject as a past participle in a perfect tense).

The word is also used as a noun, meaning death or dead person, or as an adjective, meaning dead:
 * Le roi est mort. - The king is dead.

The derived word means dying or person who is dying.

Acquis is also a noun, meaning asset.

title: French/Lessons/Transportation


text:
US History/World War I

Europe

In 1815, Europe had united to defeat French Emperor Napoleon. For a century since that time, there had been no major war in Europe. Countries had organized themselves in a complex system of alliances.

After Napoleon's defeat, the United Kingdom, France, Prussia, Russia, and Austria met in Vienna. These nations decided that if power in Europe was balanced, then no nation would become so powerful as to pose a threat to the others. The most important of these were the German Confederation. In 1871, after defeating France and Prussia, several small German nations combined into the German Empire. This upset the traditional balance of power.

German Chancellor Otto Von Bismarck began to construct a web of alliances to protect German dominance. Germany and the United Kingdom were on good terms, as Germany had not built a navy to go up against British sea power. In 1873, Russia, the Austro-Hungarian Empire, and Germany formed the Three Emperors' League. Nine years later, Austria-Hungary, Italy, and Germany formed the Triple Alliance. In 1887, the Reinsurance Treaty ensured that Russia would not interfere in a war between France and Germany.

During this time the British Queen Victoria built alliances in her own way. During years of relative peace, she had her children marry into many of the royal families of Europe, believing that this would solidify relations among the nations. In the first decade of the Twentieth century the Kaiser and the King of England were cousins through Victoria, as were the Tsar and Tsarina of Russia.

In 1890, Bismarck was fired by Kaiser Wilhelm II, who then began to undo many of Bismarck's policies. He decided to build up a German navy, antagonizing the United Kingdom. He did not renew German agreements with Russia. In 1894, this led Russia to form a new alliance with Germany's rival France.

In 1904, France and the United Kingdom decided to end centuries of bitter enmity by signing the Entente Cordiale. Three years later, those two nations and Russia entered the Triple Entente. Imperial Russia began to build its army, as did Germany and Austria-Hungary.

War Breaks Out
Austria-Hungary was a patchwork of several nations ruled by the Habsburg family. Several ethnic groups resented rule by the Habsburgs. In June, 1914, the heir to the throne, Archduke Franz Ferdinand, traveled to Sarajevo in Bosnia and Herzegovina. A Serbian nationalist named Gavrilo Princip, who hated Habsburg rule, assassinated the Archduke and his wife. This assassination triggered the First World War.

The Austro-Hungarian government decided to retaliate by crushing Serbian nationalism. They threatened the Serbian government with war. Russia came to the aid of the Serbs. To oppose this alliance, Austria-Hungary called on Germany. Kaiser Wilhelm II said his country would give Austria-Hungary whatever it needed to win the war; in effect, a "blank check." In addition to these open agreements, any of these countries might have had secret agreements with other states. The result was almost all of Europe at war, with the largest battlefield ever seen before.

In July, 1914, Austria-Hungary declared war on Serbia. Austria-Hungary, Russia, and Germany began to mobilize their troops. The conflict in Austria-Hungary quickly spread over Europe. In August, Germany declared war on France. The Germans demanded that Belgium allow German troops to pass through the neutral nation. When King Albert of Belgium refused, Germany violated Belgian neutrality and invaded. Belgium appealed to the United Kingdom for aid. The British House of Commons threatened that Great Britain would wage war against Germany unless it withdrew from Belgium. The Germans refused, and the United Kingdom joined the battle. The Central Powers, Germany and Austria-Hungary, were pitted against the Allies, the United Kingdom, Russia, and France.

The Early Stages
German troops entered Belgium on August 4. By August 16, they had begun to enter France. The French Army met the Germans near the French border with Belgium. France lost tens of thousands of men in less than a week, causing the French Army to retreat to Paris. The Germans penetrated deep into France, attempting to win a quick victory.

On August 5, the United States formally declared their neutrality in the war. They also offered to mediate the growing conflict. In the United States, the opinions were divided. Some felt we should aid England, France, and Belgium because they were depicted as victims of barbarous German aggression and atrocities. Others felt we should avoid taking sides.

The Allies won a key battle at Marne, repelling the German offensive. The Germans lost especially due to a disorganized supply line and a weak communications network. The French Army, however, had not completely defeated the Germans. Both sides continually fought each other, to no avail. On the Western Front, Germany and France would continue to fight for more than three years without any decisive victories for either side.

Meanwhile, on the Eastern Front, Germany faced Russia. In the third week of August, Russian troops entered the eastern part of Germany. Germany was at a severe disadvantage because it had to fight on two different fronts, splitting its troops. However, despite Germany's disadvantage, no decisive action occurred for three years.

The United Kingdom used its powerful Royal Navy in the war against Germany. British ships set up naval blockades. The Germans, however, countered with submarines called U-boats. U-boats sank several ships, but could not, during the early stages of the war, seriously challenge the mighty Royal Navy.

The war spread to Asia when Japan declared war on Germany in August, 1914. The Japanese sought control of German colonies in the Pacific. Germany already faced a two-front war, and could not afford to defend its Pacific possessions.

In October, 1914, the Ottoman Empire entered, allying itself with the Central Powers. The entry of the Ottoman Empire was disastrous to the Allies. The Ottoman Empire controlled the Dardanelles strait, which provided a route between Russia and the Mediterranean. The Ottoman sultan declared holy war- jihad- against the Allies. Muslims in the British Empire and French Empire were thus encouraged to rebel against their Christian rulers. However, the Allies' concerns were premature. Few Muslims accepted the sultan's proclamation. In fact, some Muslims in the Ottoman Empire supported the Allies so that the Ottoman Empire could be broken up, and the nations they ruled could gain independence.

The Middle Stages

Between 1914 and 1917, the war was characterized by millions of deaths leading nowhere. Neither side could gain a decisive advantage on either front.

In 1915, the Germans began to realize the full potential of Submarines. German Submarines engaged in official unrestricted warfare, engaging and sinking any ship found within the war zone regardless of the flag flown. Germany's justification for this use of force was that there was no certain method to ascertain the ultimate destination of the passengers and cargo carried by the ships in the war zone, and thus they were all taken as attempts at maintaining the anti-German blockade.

In May, 1915, Italy broke the Triple Alliance by becoming an Allied Power. In October, Bulgaria joined the Central Powers. Each side had induced their new partners to join by offering territorial concessions. Italy prevented Austria-Hungary from concentrating its efforts on Russia, while Bulgaria prevented Russia from having connections with other Allied Powers.

In May, 1916, one of the most significant naval battles in World War I occurred. The Royal Navy faced a German fleet during the Battle of Jutland. The Battle proved that the Allied naval force was still superior to that possessed by the Central Powers. The Germans grew even more dependent on U-boats in naval battle.

In August, 1916, Romania joined the Allies. Romania invaded Transylvania, a province of the Austro-Hungarian Empire. But when the Central Powers struck back, they took control of important Romanian wheat fields.

In 1917, the liberal-democratic government of Russia that was lead by Aleksander Kerensky was over thrown by Vladimir Lenin. When Lenin took over in Russia one of the things he promised was to change world politics. The terms by which Lenin wanted to changed world politics challenged Woodrow Wilson's vision and Lenin's Bolshevik-style revolutions spreading world wide was something that western leaders did not want.

The United States Declares War
Through all of this, America was neutral. It adopted the policy of isolationism because it felt that the increasing colonialism in Europe did not affect North America. There was a strong pacifist strain in American society, as evidenced by such popular songs as "I Didn't Raise My Boy to be a Soldier" and "Don't Take My Darling Boy Away," though at the same time many ethnic groups agitated for involvement. Economic links with the Allies also made neutrality difficult. The British were flooding America with new orders, many of them for arms. The sales were helping America get out of its recession. Although this was good for the economic health of the United States, Germany saw America becoming the Allied arsenal and bank.

On May 7, 1915, the German navy sunk the Cunard Line passenger ship R.M.S. Lusitania, operating under the flag of Great Britain. Of the 1,959 passengers 1200 died, including one hundred twenty Americans. The ship's quick explosion was due to a hidden cargo of American weaponry, a fact the US government denied. Woodrow Wilson's Secretary of State William Jennings Bryan, a pacifist, resigned over Wilson's responsibility for the placement of arms and the consequent inevitability of war. Various American citizens from different ethnic groups put pressure on their government to join the war. However, the US government was calmed by the Germans, who agreed to limit submarine warfare. In 1917, the Germans reinstated unrestricted submarine warfare in order to cripple the British economy by destroying merchant ships, and break the sea blockade of Britain.

On February 24, 1917, the American ambassador received a telegram in London from the British. It enclosed a British-decoded message, originally sent as a ciphered telegram from the German foreign Secretary, Arthur Zimmerman, to the ambassador in Mexico. Zimmerman proposed that the event of the war with the United States, Germany and Mexico would join in alliance. Germany would fund Mexico's conflict with the US: victory achieved. Mexico would then be able to gain their lost territories with Arizona. The message was published in American newspapers on March 1st.

On the evening of April 4, 1917 at 8:30 P.M., President Wilson appeared before a joint session of Congress, asking for the declaration of war to make the world "safe for democracy." He was hoping for a quick resolution of the conflict. Congress complied on April 6, 1917. The United States was at last at war with Germany.

The last American war had been the minor Spanish-American War a generation before. A draft of men above the age of eighteen followed the call to war, but many more volunteered. Men wanted to escape their lives and join the military for a job and an adventure.

The US had to mobilize its military before it could aid the Allies by sending troops. The cadre of the U.S. Army had experience in mobilizing and moving troops from its Mexican expedition, but the Army needed to expand to over one million men, most of which were untrained. This new draft was for a "scientific" army. Military officers were selected by the new "IQ" tests. The new conscripts met en massein embarkation camps in places such as Yahank, New York. Companies exercised together and drilled together. At this time, soldiers were taught techniques such as assembling and disassembling weapons blindfolded. They drilled constantly in formation. There was much amusement at these shaven-headed, first-time solders.

The chorus of a contemporary song went, "Good morning, Mister Zip-Zip-Zip,/ With your hair cut just as short as mine,/ Good morning, Mister Zip-Zip-Zip,/ You're surely looking fine!/ Ashes to ashes, and dust to dust,/ If the Camels don't get you,/ The Fatimas must . . . [Camels and Fatimas were brands of cigarettes.]

Then they went into ships to be transported to Europe. On the battlefield, they were placed in companies with other Americans, rather than being embedded with other nations.

American business and industry became involved as men created more military supplies, and jobs opened for building and designing new materials to be used in battle. However, for purposes of the battle, most of the weapons American soldiers carried had been designed by Europeans. An American-style tank was produced but only came out after the war.

In the same way, the Navy could send a battleship division to assist the British Grand Fleet, but needed to expand. To supply the American forces, new supply lines in France would be needed south of the British and French lines, which meant the U.S. would take over the southern part of the Western Front battle line. The US could and did help the Allies with monetary assistance. Increased taxes and the sale of war bonds allowed the US to raise enormous sums of money. Politicians and celebrities, as well as such movie stars as Charlie Chaplin and Mary Pickford, headed huge patriotic "Bond Rallies," where people were encouraged to buy bonds.

A government committee to influence the public on the war was formed, the Committee on Public Information or CPI. Among its organs of publicity were the "Four Minute Men," speakers who talked on pertinent subjects on Vaudeville stages, in movie theaters, and in public assemblies. There was also an organization of private citizens formed to root out German sympathizers, the American Protective League. A hit movie, "The Kaiser, the Beast of Berlin," was one hit of 1918. To strengthen the United States in this time of stress, families were encouraged to grow Victory Gardens, and American women and African Americans were encouraged to go into jobs the servicemen had left. This is the beginning of the Great Migration, when Southern African Americans began moving to Northern cities for jobs.

Trench Warfare

The U.S. commander, General John J. "Black Jack" Pershing, faced immense pressure from the British and French governments to use American forces in small units to reinforce depleted British and French units. This was impossible politically. Pershing insisted to General Foch, the Generalissimo of the Allied armies, that the U.S. Army would fight as a single Army. Pershing did not want to give his men to other Allied commanders, many of whose strategies he disagreed with.

The European method of fighting, as it had been since the Boer War, was trench warfare. An army on the French battleground protected itself from the enemy with zigzag trenches, mines, barbed wire, and a line of rifles and machine guns. Between the enemy lines was a contested area, "no man's land." An attempt to advance toward the enemy was met with gunfire. These trenches stalemated military advances, as any man who raised his head from the trenches would be shot. At the Battle of the Somme in 1916, for example, Allied troops suffered 600,000 dead and wounded to earn only 125 square miles; the Germans lost 400,000 men. Rain fell in the trenches. As one song put it, a soldier was "Up to your waist in water, up to your eyes in slush." The damp produced a foot disease known as "trench foot": if untreated, it could rot flesh from the bone. The close, unsanitary conditions of the front lines encouraged fleas and lice, and typhoid, typhus, and dysentery caused deaths unrelated to gunfire. Worst of all, perhaps, was that sometimes the enemy would gas your trench. There was no way to escape, and sometimes no masks to protect you.

First used by the Germans in April 1915, chlorine gas stimulated overproduction of fluid in the lungs, leading to death by drowning. One British officer tended to troops who had been gassed reported that,

quite 200 men passed through my hands. . . Some died with me, others on the way down. . . I had to argue with many of them as to whether they were dead or not.

Chlorine, mustard, and phosgene gas would continue in use throughout the war, sometimes blistering, sometimes incapacitating, and often killing.

The End of the War
Despite the fact that the Germans could concentrate their efforts in one area, the Central Powers faced grim prospects in 1918. Encouraged by the United States joining the war, several nations joined the Allied Powers. The four Central Powers of Germany, the Austro-Hungarian Empire, the Ottoman Empire, and Bulgaria faced the combined might of the Allied Powers of the United Kingdom and the British Empire, Australia, New Zealand, Canada, South Africa, France, Belgium, Japan, Serbia, Montenegro, San Marino, Italy, Portugal, Romania, the United States, Cuba, Panama, Guatemala, Nicaragua, Honduras, Haiti, Costa Rica, Brazil, Liberia, Siam (Thailand) and China (some of the above nations did not support the war with troops, but did contribute monetarily.) The Germans launched a final, desperate attack on France, but it failed miserably. Due to Allied counterattacks, the Central Powers slowly began to capitulate.

Bulgaria was the first to collapse. A combined force of Italians, Serbs, Greeks, Britons, and Frenchmen attacked Bulgaria through Albania in September, 1918. By the end of September, Bulgaria surrendered, withdrawing its troops from Serbia and Greece, and even allowing the Allies to use Bulgaria in military operations.

British forces, led by T. E. Lawrence (Lawrence of Arabia), together with nationalist Arabs, were successful in the Ottoman Empire. About a month after Bulgaria's surrender, the Ottoman Empire surrendered, permitting Allies to use the Ottoman territory, including the Dardanelles Strait, in military operations.

The Austro-Hungarian Empire also decided to surrender in October. The royal family, the Habsburgs, and the Austro-Hungarian government desperately sought to keep the Empire of diverse nationalities united. Though Austria-Hungary surrendered, it failed to unite its peoples. The once-powerful Austro-Hungarian Empire was destroyed by the end of October, splitting into Austria, Hungary, Czechoslovakia, and Yugoslavia.

Germany, remaining all alone, also decided to surrender. President Wilson required that Germany accede to the terms of the Fourteen Points, which, among other things, required Germany to return territory acquired by the Treaty of Brest-Litovsk to Russia and the provinces of Alsace and Lorraine to France. Germany found the terms too harsh, while the Allies found them too lenient. But when German Emperor Wilhelm II abdicated the throne, the new German government quickly agreed to Wilson's demands. On November 11, 1918, World War I had come to an end.

The war had been marked by millions and millions of casualties. The deaths were so wide-spread and so vast that people in England talked of "The Lost Generation." Many died in battle, others died from disease and some even died after when hit with an influenza that spread throughout the whole world in 1918. Destruction of factories and farms, not to mention houses, created economic damage, and was one of the factors creating widespread European starvation during the winter of 1918-1919.

In contrast, damage was low in America. Although America had also suffered from the flu, the war had not touched U.S. shores. For years afterward, in Germany, France, and even British Commonwealth countries such as Canada, you could see men wearing artificial tin faces to hide battle wounds, men who wheezed because of damage from poison gas, and "war cripples" begging with bowls on the street corner. But American men were by-and-large intact. U.S. factories had been fully supplied, and the nation was on a sounder financial footing because of profit from the War.

At the end of the war, as American soldiers returned from Europe, employment rose. Some of the veterans returned to find themselves without homes or jobs. Overseas, some Black men were organized into a top fighting unit. However, Homeland outrage at the success helped to fuel riots in the notorious "Red Summer" of 1919. Each veteran returned with a certificate promising certain monies for their service; however, the certificate could not be cashed in until 1945.

Suffrage For American Women
An after-effect of the employment of women during the war was the Nineteenth Amendment, giving them the right to vote. There had been a Suffrage movement since the nineteenth century. President Wilson and his contemporaries were reluctant, but conceded it as a quid pro quo. After the servicemen had returned, there were still two million more women in the workforce. However, instead of being in factory jobs, they were largely only permitted in "women's work": the "caring professions" such as nurses or teachers, secretaries or "stenographers," and waitresses, cooks, or washerwomen. These jobs paid little, and women were often expected to quit the job when they got married.

Politically active women still remained excluded from local and national power structures. Their voluntary organizations used tactics that advanced modern pressure-group politics. Issues ranged from birth control, peace, education, Indian Affairs, or opposition to lynching. Women in these associations lobbied legislators to support their causes. At the state level women achieved rights such as the ability to serve on juries.

Increasing Racial Tension

A force of African Americans had served in the War:

More than 350,000 African Americans served in segregated units during World War I, mostly as support troops. Several units saw action alongside French soldiers fighting against the Germans, and 171 African Americans were awarded the French Legion of Honor. In response to protests of discrimination and mistreatment from the black community, several hundred African American men received officers' training in Des Moines, Iowa. By October 1917, over six hundred African Americans were commissioned as captains and first and second lieutenants.

Fighting units such as the Harlem Hellfighters proved their mettle. Yet they received no recognition. Upon their return, particularly to the South, they faced resentment and sometimes lynchings.

In 1913, President Woodrow Wilson had segregated the Civil Service, which before had been an employer for black Americans. The war and the Great Migration triggered more oppression and more violence. When Caucasian White Americans were drawn into the army or defense industries, their jobs were sometimes given to black workers, for lower wages. The owners considered this a double good, keeping production going while destroying the workingman unions which agitated for higher pay. But while bosses were dependent, for the moment, on black workers, they did not think they owed anything to these employees.

An influx of unskilled Black strikebreakers into East St Louis, Illinois, heightened racial tensions in 1917. Rumors that Blacks were arming themselves for an attack on Whites resulted in numerous attacks by White mobs on Black neighborhoods. On July 1, Blacks fired back at a car whose occupants they believed had shot into their homes and mistakenly killed two policemen riding in a car. The next day, a full scale riot erupted which ended only after nine Whites and 39 Blacks had been killed and over three hundred buildings were destroyed. The anxieties of war helped fuel violence: Southern and Midwestern war vigilance committees formed the matrix for a revival of the Ku Klux Klan.

The Great Experiment
On August 1, 1917, the Senate voted to send the Eighteenth Amendment to the Constitution to the states for ratification. The vote was bi-partisan, 65 to 20. Section One read, in part, After one year from the ratification of this article the manufacture, sale, or transportation of intoxicating liquors [. . . ] is hereby prohibited. By 1919, the requisite number of states had ratified the Amendment. The Amendment actually came into effect, under its own terms, one year after ratification.

The Temperance movement had been in effect for more than a hundred years, since the Second Great Revival. The late 19th and early 20th century Anti-Saloon League had been successful in turning the discussion from social discouragement of alcohol to legal prohibition of the substance. It was not simply a creature of Protestant or Catholic Churches, but was "united with Democrats and Republicans, Progressives, Populists, and suffragists, the Ku Klux Klan and the NAACP, the International Workers of the World, and many of America's most powerful industrialists including Henry Ford, John D. Rockefeller, Jr., and Andrew Carnegie – all of whom lent support to the ASL's increasingly effective campaign."

But if Prohibition was not a simple reaction to World War I, it drew strength from the conflict. The War was funded by an income tax, thus unlocking saloon profits from the interests of the nation. The Lever Act of 1917, with the aim of feeding soldiers, prohibited grain from being used for alcoholic beverages. There were nationalist concerns, too: the most famous brewers of beer had German last names.

Treaty of Versailles

The Treaty of Versailles was the peace settlement signed after World War One had ended in 1918 and in the shadow of the Russian Revolution and other events in Russia. The treaty was signed at the vast Versailles Palace near Paris - hence its title - between Germany and the Allies. The three most important politicians there were David Lloyd George, Georges Clemenceau, and Woodrow Wilson. The Versailles Palace was considered the most appropriate venue simply because of its size - many hundreds of people were involved in the process and the final signing ceremony in the Hall of Mirrors could accommodate hundreds of dignitaries. Many wanted Germany, now led by Friedrich Ebert, smashed. Others, like Lloyd George, were privately more cautious.

On June 28th 1919, the chief Allied and Associated Powers of the United Kingdom, the United States, France, Italy, and Japan met with the Central Powers in France to discuss a peace settlement. British Prime Minister David Lloyd George, American President Woodrow Wilson, and French President Clemenceau were known as "The Big Three." Each of the Allied and Associated Powers had distinct national interests. The UK wanted to keep the Royal Navy supreme by dismantling the German Navy. The British also wished to end Germany's colonial empire, which might have become a threat to the vast British Empire. Lloyd George wanted to be hard on the Germans to bolster his popular support at home in Great Britain. . Italy wanted the Allies to fulfill their promise of territory given to Rome at the beginning of the war. Clemenceau wanted Germany to be brought to its knees so it could never start another war against France. The French also wanted Germany to compensate Paris for damage inflicted on France during the War. Japan had already largely served its interests by taking over German colonies in the Pacific. President Wilson's main goal for the conference was the creation of a "League of Nations." He believed that such an organization was essential to preventing future wars. Many historians believe that Wilson's concentration on the League, forcing him to sacrifice possible compassion toward Germany, helped contribute to the conditions leading to World War II.

The Treaty of Versailles forced Germany to cede Alsace and Lorraine to France, dismantle its Army and Navy, give up its colonial Empire, pay massive reparations to the Allies, and take full responsibility for causing the war. The conference also led to the creation of the League of Nations. The US Senate, however, did not consent to the Treaty, and the European powers were left to enforce its provisions themselves. This eventually led to violations of the treaty by Germany, which then led to the Second World War. The treaty crippled the Weimar Government in Berlin and led to great bitterness in Germany, which helped to strengthen Adolf Hitler's National Socialist, or Nazi Party.

Questions For Review
1. What extended a conflict between Serbians and the Austro-Hungarian Empire into the globe-straddling World War I?

2. How did the advances of technology lead to trench warfare?

3. What in 1914-1915 led to an economic advantage for America from the War? What were the nation's post-war advantages?

4. Listen to songs from this period: "I Didn't Raise My Boy to be a Soldier." "Oh, How I Hate to Get up in the Morning." "Oh! It's a Lovely War." "Over There." "K-k-k-Katy." What is the song's point of view?

title: US History/World War I


text:
Organic Chemistry/Templates

Note table
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Note
note contents go here
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Equations
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Title
CH4 Br- → No reaction
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title: Organic Chemistry/Templates


text:
User:Etothex

Ok, first, I'm a student, so my time is very limited. But I try to check in here as often as possible.

I'm etothex, so what am I interested in? Math+science, but of course I'm not working on those, I'm working on US History. :)
 * Update: Since Lord Emsworth took over US History, I haven't been able to add much to that. Then I started German, though I don't speak it, and Marsh is doing a great job there now. :)

So I'll try to do what I can. Hopefully I can do some stuff on math, too, since I'm at the level of having done most of the courses which have texts here and can write for pretty much all of them.

title: User:Etothex


text:
Discrete Mathematics/Polynomials

Introduction
In this section we look at the polynomial in some commutative ring with identity. What is interesting is that studying polynomials over some commutative ring with identity acts very much like numbers; the same rules often are obeyed by both.

Definitions
A polynomial over some commutative ring with identity R is an expression in the form
 * $$\sum_{j=0}^n a_jx^j; \forall a_j \in R, a_n \not = 0$$

and n ∈ N, and x is some indeterminate (not a variable).

Terminology
Given the first nonzero term in the polynomial, i.e. the term anxn above:
 * an is called the leading coefficient
 * Given 7x3+2x+5, 7 is the leading coefficient
 * the polynomial has degree n
 * 7x3+2x+5, 3 is the degree
 * if an=1 the polynomial is termed monic
 * 7x3+2x+5 is not monic, whereas x4 and x5-3x+2 are monic.

In the above, if ai=0 for all i, the polynomial is the zero polynomial.

Properties
Let R[x] be the set of all polynomials of all degrees. Clearly R is closed under addition and multiplication (although in a non-straightforward way), and thus we have that R[x] is itself a commutative ring with identity.

Assume now R is a field F; we do this so we can define some useful actions on polynomials

Division algorithm
Firstly recall the division algorithm for numbers, that each number can be decomposed into the form
 * n = qk+r

where q is the quotient and r the remainder and r<n.

Now, since we have that F is a field, we can do something similar with the polynomials over F, F[x].

If f(x), g(x) ∈ F[x], with g(x) nonzero:
 * f(x) = q(x)g(x)+r(x)

Again, q(x) is known as the quotient polynomial and r(x) the remainder polynomial. Furthermore, we have the degree of r(x) ≤ degree of f(x)

We perform divisions by polynomial long division. For brevity we omit the xk terms. Here's an example. We divide x3+x+2 by x-1. First write:

\begin{matrix} &   &   &   &   &   &   & \\ 1 & -1 & | & 1 & 0 & 1 & 2 & \\ \end{matrix} $$ Note we place a 0 in any polynomial not present. Now x3/x = x2, so we place a 1 in the second column to get

\begin{matrix} &   &   &   & 1 &   &   & \\ 1 & -1 & | & 1 & 0 & 1 & 2 & \\ \end{matrix} $$ Multiply x2 throughout the divisor x-1 to get x3-x2, which is (1 -1), so write this below like the following:

\begin{matrix} &   &   &   & 1 &   &   & \\ 1 & -1 & | & 1 & 0 & 1 & 2 & \\  &    & | & 1 &-1 &   &   & \\ \end{matrix} $$ Now subtract (1 0) and (1 -1), drop the third 1 to get:

\begin{matrix} &   &   &   & 1 &   &   & \\ 1 & -1 & | & 1 & 0 & 1 & 2 & \\  &    & | & 1 & -1 &   &   & \\  &    & | &   & 1& 1 &   & \\ \end{matrix} $$ Now repeat, but divide by x2 now (since we have subtracted and gotten (1 1) - x2 + x), and continue in the same fashion, to get:

\begin{matrix} &   &   &   & 1 & 1 & 2 & \\ 1 & -1 & | & 1 & 0 & 1 & 2 & \\  &    & | & 1 & -1&   &   & \\  &    & | &   & 1 & 1 &   & \\  &    & | &   & 1 & -1 &  & \\  &    & | &   &   & 2 & 2 & \\  &    & | &   &   & 2 & -2 & \\  &    & | &   &   &   & 4 & \\ \end{matrix} $$ So the quotient is x2+x+2, and the remainder is 4.

Euclidean algorithm
Now we have a working division algorithm for polynomials, the Euclidean algorithm, and hence the gcd of two polynomials can readily be found.

Examples
Let's use a similar example above: what is gcd(x3+x+2, x-1)? We've shown already above that x3+x+2=(x2+x+2)(x-1) + 4

Proceeding in the normal fashion in the Euclidean algorithm
 * x3+x+2=(x2+x+2)(x-1) + 4
 * gcd(x3+x+2, x-1) = gcd(x-1,4)

and the greatest common divisor of any monomial and an integer is clearly 1, so x3+x+2 and x-1 are coprime.

For a second example, consider gcd(x2-1,x2+2x+1)

 * x2+2x+1= (x2-1) *1+ 2x+2
 * x2-1= (2x+2) *x/2+ -(x+1)
 * 2x+2= -(x+1) *(-2)+ 0

Since factors of -1 make no difference, gcd(x2-1,x2+2x+1) is -(x+1)

Irreducibles
We've seen that x3+x+2 and x-1 are coprime; they have no factors in common. So, are we able to determine "prime" polynomials? Indeed we can - depending on the field that the polynomial lies in. We call these irreducibles instead of primes.

Example
Take p(x)=x3 + x2 + 2 over Z3. Now we can factor this polynomial if it has a root - from the factor theorem (which also holds for polynomials over any commutative ring with identity) p(k)=0 means k is a root. So, let's look at the following: Since we're in Z3, we luckily only need to check three values p(0)=2 p(1)=1 p(2)=2 So we have p(x) having no roots - it is irreducible ("prime").

Now observe an interesting fact. Take the exact same polynomial but instead over Z2. The polynomial then is equivalent to
 * x3+x2+0

and thus has root p(0)=0 and thus is reducible but over Z2

So the reducibility of the polynomial depends on the field it is in.

Showing irreducibility
The general procedure to show a polynomial is irreducible is: effectively a proof by cases.
 * observe its degree
 * identify possible factorizations
 * eliminate these factorizations

For example, consider the polynomial q(x)=x4+x+2 in Z3. To prove it is irreducible, observe that q(x) could be factorized in the following ways:
 * 1) linear, irreducible cubic
 * 2) linear, linear, irreducible quadratic
 * 3) linear, linear, linear, linear
 * 4) irreducible quadratic, irreducible quadratic

So we can prove 1, 2, 3 by showing it has no linear factors. 4 is a little more difficult. Let us proceed to show it has no linear factors: Observe
 * q(0)=2
 * q(1)=1
 * q(2)=2

So q has no linear factors. Now, we need to show that q is not the product of two irreducible quadratics.

In Z3, we have the quadratics
 * {x2,x2+1,x2+x,x2+x+1,x2+x+2,x2+2,x2+2x,x2+2x+1,x2+2x+2}

We can identify the irreducible quadratics easily by inspection. We then obtain
 * {x2+1, x2+x+2, x2+2x+2}

If we can show that neither of these polynomials divide q(x)=x4+x+2, we have shown q(x) is irreducible.

Let us try x2+1 first.
 * $$\begin{matrix}

&  &   &   &   &   & 1 & 0 & 2 \\ 1 & 0 & 1 & | & 1 & 0 & 0 & 1 & 2 \\  &   &   &   & 1 & 0 & 1 &   &   \\  &   &   &   &   &   & 2 & 1 & 2 \\  &   &   &   &   &   & 2 & 0 & 2 \\  &   &   &   &   &   &   & 1 & 0 \\ \end{matrix}$$ We have a remainder, so x2+1 doesn't divide q. On dividing the other polynomials, we all get a remainder. (Verify this for yourself as practice).

So q(x) is irreducible in Z3.

Modular arithmetic and polynomials
Since we have a working polynomial division and factor theorem, and that polynomials appear to mimic the behaviour of the integers - can we reasonably define some sort of modular arithmetic with polynomials?

We can indeed. If we have a field Zp[x] and we wish to find all the remainders (remember, these remainders are polynomials) on dividing by some polynomial m(x), we can do so by polynomial long division.

If m(x) is irreducible, then the set of remainders as above forms a field.

title: Discrete Mathematics/Polynomials