text:
User talk:Guido~enwikibooks

Hey, thanks a lot for your help in the German textbook, especially German: Appendix 7. When I created the page, I was hoping to get people to add to that page bit by bit, not completely write a list of names. I changed the format a bit to make it smaller, but otherwise, you did a great job. I look forward to seeing your contributions in this German textbook and using the names in the appendix you wrote. - SamE 04:46, 15 Aug 2004 (UTC)
 * By the way, thanks for your work on German:Beginner Lesson 3. It's good to have someone else actually writing content. - SamE 04:57, 15 Aug 2004 (UTC)

I'm perfectly OK with you putting your name on German: Contributors. You wrote enough in lesson 3 and appendix 7 to be worthy of mentioning. My part of the contributors page isn't that clear: I'm not actually teaching anyone German outside of this site, but rather using my past German classes to decide how to teach Level I.

'Dieser-forms' are dieser, diese, dieses, diesen, etc. I was going to teach how to say "This soup tastes delicious.", or "This bread tastes bad." I was also hoping to incorporate jeder-forms (the same thing) and, going along with last lesson, to say 'every day', 'every week', etc. I had to wait till this lesson because those are in accusative case. I was also going to introduce stuff like " Der ist für mich." This lesson is going to be the largest lesson to date. Thanks for getting that started. - SamE 15:10, 15 Aug 2004 (UTC)

Copyright problem with Image:1e comm.png
Thanks for uploading Image:1e comm.png. The Wikimedia Foundation is very careful about what Wikibooks includes because of copyright law, and requires that we maintain a strict copyright policy. Image:1e comm.png and other files you uploaded may soon be deleted unless we can determine the copyright holder and status. The copyright holder is usually the creator, the creator's employer, or the last person who was transferred ownership rights. Please take the time to read Media to learn more about what copyright information is required to satisfy our requirements and remember to include this important information for every file that you upload in the future as well. If you have any questions, feel free to contact me, or ask another Wikibookian at the help desk. Thank you.

See for a complete list of your uploads which may get deleted soon.

– Mike.lifeguard  | talk 00:43, 21 September 2007 (UTC)

Your account will be renamed
Hello,

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

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

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

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:11, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:00, 19 April 2015 (UTC)

title: User talk:Guido~enwikibooks


text:
Statistics/Summary/Range

Range of Data
The range of a sample (set of data) is simply the maximum possible difference in the data, i.e. the difference between the maximum and the minimum values. A more exact term for it is "range width" and is usually denoted by the letter R or w. The two individual values (the max. and min.) are called the "range limits". Often these terms are confused and students should be careful to use the correct terminology.

For example, in a sample with values 2 3 5 7 8 11 12, the range is 11 (|12|-|2|+1=11) and the range limits are 2 and 12.

The range is the simplest and most easily understood measure of the dispersion (spread) of a set of data, and though it is very widely used in everyday life, it is too rough for serious statistical work. It is not a "robust" measure, because clearly the chance of finding the maximum and minimum values in a population depends greatly on the size of the sample we choose to take from it and so its value is likely to vary widely from one sample to another. Furthermore, it is not a satisfactory descriptor of the data because it depends on only two items in the sample and overlooks all the rest. A far better measure of dispersion is the standard deviation (s), which takes into account all the data. It is not only more robust and "efficient" than the range, but is also amenable to far greater statistical manipulation. Nevertheless the range is still much used in simple descriptions of data and also in quality control charts.

The mean range of a set of data is however a quite efficient measure (statistic) and can be used as an easy way to calculate s. What we do in such cases is to subdivide the data into groups of a few members, calculate their average range, $$\bar{R} $$ and divide it by a factor (from tables), which depends on n. In chemical laboratories for example, it is very common to analyse samples in duplicate, and so they have a large source of ready data to calculate s.

 * $$s= \frac {\bar{R}}k $$

(The factor k to use is given under standard deviation.)

For example: If we have a sample of size 40, we can divide it into 10 sub-samples of n=4 each. If we then find their mean range to be, say, 3.1, the standard deviation of the parent sample of 40 items is approximately 3.1/2.059 = 1.506.

With simple electronic calculators now available, which can calculate s directly at the touch of a key, there is no longer much need for such expedients, though students of statistics should be familiar with them.

{tBookCat}}

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

title: Statistics/Summary/Range


text:
User:LuciferBlack

w:User:LuciferBlack

title: User:LuciferBlack


text:
Talk:European History/The Crises of the Middle Ages

Sources anyone???
Do you not source things in wikibooks? Methinks this is not the best.

 * Agreed and I also think comments should be signed either by the author or by a bot.  Does anyone know why wikibooks has different standards to wikipedia? LookingGlass (discuss • contribs) 06:56, 15 February 2014 (UTC)

Avignon Papacy
I'm thinking this should be split into multiple sections in some fashion... that's a somewhat large lump of text to read.

I'm going to try this format for now, and will be expanding on the papal paragraphs at some point. I also added a bit on the black death and spoke about french control of their land after the 100 years.

Hundred Years War
I expanded the HYW section a little bit.

John Wycliff(e)
I see from some research that there's some debate as to the correct spelling of his name; however, I suggest that the writers of this text pick one, as it's inconsistent within this module and the next. -Byaina 17:27, 26 July 2006 (UTC)

Dealing with bias - NPOV
In line with comments above re Sources, I am concerned about how the Neutral Point of View issue (see: NPOV https://en.wikipedia.org/wiki/Wikipedia:Neutral_point_of_view) is dealt with on Wikibooks. Without a requiremet for both sources and a NPOV I cannot see how these books will not come to merely either reflect one bias or become incoherent.

For instance, in this Introduction it is stated that:
 * "The turn of the first millennium saw renewed growth and activity, as kings and cities consolidated their authority and began to repopulate lands left empty by Rome's decline."

This cause-effect conclusion seems to be belied by the next sentence which notes that over the previous century saw:
 * "Warmer weather after 900 allowed more land to be brought into food production."

It seems reaonable to conclude that the cause of the renewed growth was climatic not political. A further possible interpretation, that this growth and activity was due to technology is then given:
 * "This was aided by the arrival in Europe of the horse collar from Asia, which increased crop yields by allowing plows to be drawn by horse, rather than by slower oxen.".

We are then informed that:
 * "Despite many local wars and disputes between knights, the High Middle Ages, from 1000-1250, saw growing populations and prosperity"

However I understand that warfare in these times was generally limited, with battles being formal affairs not total warfare involving civilian populations.

I am left with the impression that the narrative of the book is more important than the facts. While the repository of facts provided is helpful in a sense these are available through wikipedia, generally without the interpretative narrative. The result seems to me to be to encourage the distribution and acceptance of a vanilla history that supports the status quo of the culture distributing it. If that is not the objective then I suggest the minimum standards of the sister project be applied here too. LookingGlass (discuss • contribs) 07:30, 15 February 2014 (UTC)


text:
User:Dysprosia~enwikibooks/cologneblue.css

td.top { background-color: #ce6163; color: white; margin-top: 4px; margin-bottom: 4px; padding-top: 0; padding-bottom: 0; text-transform: uppercase; font-family: Verdana, Arial, sans-serif; font-size: 8pt; } td.top a { font-family: Verdana, Arial, sans-serif; background-color: #ce6163; color: white; text-decoration: none; font-size: 10pt; } a { color: #446688; } a.external { color: #336644; } a:visited { color: #8D0749; } a.printable { text-decoration: underline; } a.stub { color:#772233; text-decoration:none; }


text:
Conlang/Advanced/Grammar/Alignment/Trigger

Trigger systems are apparently found only in conlangs, inspired by the applicativization systems of Austronesian languages like the Filipino language Tagalog.

In the case systems of English and other Indo-European languages, there's typically a subject (agent of the action), a verb (action) and an object or several objects (patient(s) of the action). Trigger languages on the other hand divide things into agent, patient and other objects.

The differences between "trigger languages" and "nominative/accusative languages" are:

 * What the sentence is about (the emphasis so to speak) is lexicalized, although still pragmatic -- This is called the trigger, focus or topic of a sentence.
 * The trigger can be the agent or the patient or perhaps have any other theta role, so calling the triggered argument "subject" does not make sense.
 * Such languages need no explicit passive voice because they can do this with triggers: for instance,
 * I-TRG drink-TRG=AGT milk-PAT ( I drink milk.)
 * I-AGT drink-TRG=PAT milk-TRG (I drink milk . / Milk is drunk by me).

Triggering works as follows: Every argument of the sentence is marked for its role (agent, patient, other objects). The triggered argument is marked on the verb. In Carsten Becker's conlang Ayeri, perhaps the best known trigger conlang, trigger and case marker change places.


text:
User:Carsten Becker

My Homepage (in German)

title: User:Carsten Becker


text:
Introduction to Paleoanthropology/Definition

To effectively study paleoanthropology, one must understand that it is a subdiscipline of anthropology and have a basic understanding of archaeology dating techniques, evolution of cultures, Darwinian thought, genetics, and primate behaviours.

There is a long academic tradition in modern anthropology which is divided into four fields, as defined by Franz Boas (1858-1942), who is generally considered the father of the Anthropology in the United States of America. The study of anthropology falls into four main fields:
 * 1) Sociocultural anthropology
 * 2) Linguistic anthropology
 * 3) Archaeology
 * 4) Physical anthropology

Although these disciplines are separate, they share common goals. All forms of anthropology focus on the following:
 * Diversity of human cultures observed in past and present.
 * Human beings in all of their biological, social, and cultural complexity.
 * Many other disciplines in the social sciences, natural sciences, and even humanities are involved in study of human cultures.
 * Examples include: Psychology, geography, sociology, political science, economics, biology, genetics, history and even art and literature.

Sociocultural anthropology/ethnology
This field can trace its roots to processes of European colonization and globalization, when European trade with other parts of the world and eventual political control of overseas territories offered scholars access to different cultures. Anthropology was the scientific discipline that searches to understand human diversity, both culturally and biologically. Originally anthropology focused on understanding groups of people then considered "primitive" or "simple" whereas sociology focused on modern urban societies in Europe and North America although more recently cultural anthropology looks at all cultures around the world, including those in developed countries. Over the years, sociocultural anthropology has influenced other disciplines like urban studies, gender studies, ethnic studies and has developed a number of sub-disciplines like medical anthropology, political anthropology, environmental anthropology, applied anthropology, psychological anthropology, economic anthropology and others have developed.

Linguistic anthropology
This study of human speech and languages includes their structure, origins and diversity. It focuses on comparison between contemporary languages, identification of language families and past relationships between human groups. It looks at:
 * Relationship between language and culture
 * Use of language in perception of various cultural and natural phenomena
 * Process of language acquisition, a phenomenon that is uniquely human, as well as the cognitive, cultural, and biological aspects involved in the process.
 * Through historical linguistics we can trace the migration trails of large groups of people (be it initiated by choice, by natural disasters, by social and political pressures). In reverse, we can trace movement and establish the impact of the political, social and physical pressures, by looking at where and when the changes in linguistic usage occurred.

Archaeology
Is the study of past cultures through an analysis of artifacts, or materials left behind gathered through excavation. This is in contrast to history, which studies past cultures though an analysis of written records left behind. Archaeology can thus examine the past of cultures or social classes that had no written history. Historical archaeology can be informed by historical information although the different methods of gathering information mean that historians and archaeologists are often asking and answering very different kinds of questions. It should be noted that recovery and analysis of material remains is only one window to view the reconstruction of past human societies, including their economic systems, religious beliefs, and social and political organization. Archaeological studies are based on:
 * A specific methodology to recover material remains including excavation techniques, stratigraphy, chronology, and dating techniques
 * Animal bones, plant remains, human bones, stone tools, pottery, structures (architecture, pits, hearths).

Physical anthropology
Is the study of human biological variation within the framework of evolution, with a strong emphasis on the interaction between biology and culture. Physical anthropology has several subfields:
 * Paleoanthropology
 * Osteometry/osteology
 * Forensic anthropology
 * Primatology
 * Biological variation in living human populations
 * Bioarchaeology/paleopathology

Paleoanthropology
As a subdiscipline of physical anthropology that focuses on the fossil record of humans and non-human primates. This field relies on the following:

Evolution of hominids from other primates starting around 8 million to 6 million years ago. This information is gained from fossil record of primates, genetics analysis of humans and other surviving primate species, and the history of changing climate and environments in which these species evolved.
 * Understanding Human Evolution:

Evidence of hominid activity between 8 and 2.5 million years ago usually only consists of bone remains available for study. Because of this very incomplete picture of the time period from the fossil record, various aspects of physical anthropology (osteometry, functional anatomy, evolutionary framework) are essential to explain evolution during these first millions of years. Evolution during this time is considered as the result of natural forces only.
 * Importance of physical anthropology

Paleoanthropologists need to be well-versed in other scientific disciplines and methods, including ecology, biology, anatomy, genetics, and primatology. Through several million years of evolution, humans eventually became a unique species. This process is similar to the evolution of other animals that are adapted to specific environments or "ecological niches". Animals adapted to niches usually play a specialized part in their ecosystem and rely on a specialized diet.
 * Importance of related disciplines

Humans are different in many ways from other animals. Since 2.5 million years ago, several breakthroughs have occurred in human evolution, including dietary habits, technological aptitude, and economic revolutions. Humans also showed signs of early migration to new ecological niches and developed new subsistence activities based on new stone tool technologies and the use of fire. Because of this, the concept of an ecological niche does not always apply to humans any more.

Summary
The following topics were covered:
 * Introduced field of physical anthropology;
 * Physical anthropology: study of human biology, non-human primates, and hominid fossil record;
 * Placed paleoanthropology within overall context of anthropological studies (along with cultural anthropology, linguistics, and archaeology);

Further modules in this series will focus on physical anthropology and be oriented toward understanding of the natural and cultural factors involved in the evolution of the first hominids.


text: Category:Book:Introduction to Paleoanthropology


text:
Outdoor Survival/Shelter

Helpful Hints
Shelter will keep you out of the elements and help prevent hypothermia. It will provide shade in the heat. It also has an important positive psychological effect.

 * Bring a cheap, lightweight tent with you whenever you go hiking, even if you are not staying the night. Consider a "tube tent," for example...such a tube can be constructed by gluing (with waterproof glue) the long edge of a thin tarp or plastic drop cloth to the matching edge, creating a tube of-sorts. To use, simply string the string from one end of the tube through the other end, and tie the ends between two trees. If you are injured in the wilderness, such a shelter can be easy to erect quickly. When injured (particularly in cold weather) proper shelter can be essential for your survival.

 * A lean-to can be made by lashing a stick between two trees, then leaning more sticks on it to form a triangular structure. It can be improved by insulating it with evergreen boughs, branches and leaves, or snow. Alternatively just lay sticks against a log and fill with an cover with insulation. Remember add as much insulation as possible.

 * Get your body off the ground. Build an insulating pad between your body and the earth using sticks, pine boughs, leaves, etc. You should have twice as much insulation below you as above you.

 * Make the inside of your shelter as small as you can in cold conditions with lots of insulation

 * Building a fire reflector (a wall of sticks, rocks, etc.) will improve a lean-to by reflecting the fire's warmth back into the open side of the lean-to.

 * Bring one or two metallic rescue blankets wherever you go. They are useful for building shelters, reflectors, and water collectors, and you can even cook with them.

 * In snowy conditions, build a quinzhee.

 * One shelter that has worked very well in the past, is a lean-to shelter, it is fairly easy to construct, and is very effective.

Shelter for Survival
In the average consideration of survival it often seems shelter is overlooked, or at least taken for granted and misplaced on the scale of priorities.

It is always good to remember the "rule of threes": "A person can survive for three minutes without air, three hours without shelter, three days without water, three weeks without food."

While not absolute these guidelines are reasonable and appropriately stress the need for shelter. Protection from the elements comes second only to breathing.

Quick thoughts about the conditions under which three hours of exposure is a generous life-expectancy should immediately clarify that when shelter is most needed it may be most difficult to find or create.

Levels of shelter: Clothing and basic tools Minimal short-term protection Long-term protection A recent engineer by the name of Howard "Chubby" Fultz has developed an idea that could revolutionize outdoor survival. It is commonly referred to as "The Chubby Dome." The official name is "CD320." Although still in the developing stages, The Chubby Dome offers a fresh water supply, food storage, power, shelter, and a small bathroom.

Clothing:

Dress in Layers!

The first level of shelter to consider is that of clothing. Simply put, you have to be able to "walk home" in the clothing you have on or at hand. Take a hard look at the difference between what you want to wear and what you should have for all possible conditions.

Waypoints where additional resources are available (camp, basecamp, your car) can certainly be the initial target of any self-extraction. Such caches then cover situations of different scope ~what's on your person will get you back to camp, what's at camp will get you to your car, etc.

The concept of walking home may sound out of place, but there is a distinction between being lost and/or injured, and simply being in a difficult spot for an indefinite period of time. As a rule, if you are lost or injured do not wander -get yourself found-.

A minimal set of equipment should be incorporated into one's wardrobe. Without the ability to make fire and cut things -right now- you're not even trying to be prepared and will be hard-pressed to spend anything but a summer night outdoors safely.

Other Wikibooks

 * Debris Hut Construction from the Self-Reliance Handbook

title: Outdoor Survival/Shelter


text:
Geographic Information Systems

Introduction
GIS is an organised collection of computer programs, computer, geographic data, and people.This definition gives you the components that make up GIS.People who know how to use computer(hardware)and programme(software)to provide information (from geographic data) are able to solve a problem or answer a specific question.

What is GIS?
Geographic Information Systems provide a method for integrating and analyzing spatial (digital map based) information such as "where is the nearest movie theater?" alongside related non-spatial information (what movies are playing there?). GIS have three major capabilities (computer mapping, spatial analysis and spatial database) and can operate on a range of platforms (desktop/laptop computer, Internet, PDA, etc.). Many people are becoming far more familiar with seeing the results both textually - for example when their phone shows them the nearest pub - and on open map systems such as Google Maps. Where in the past people had to literally use pencils and string on a paper map to find their nearest school, a computer can do this now extremely quickly an accurately, as long as all the information has been entered correctly in the first place.

In a broader context, GIS involves people and often brings a philosophy of change. For example, in 1994, the New York Police Department introduced GIS to locate crime 'hot-spots', analyze underlying problems and devise strategies and solutions to deal with the problems. Since 1993, violent crime has dropped by two-thirds in New York City. This strategy, known as COMPSTAT, has expanded to cities and jurisdictions across the United States and around the world.

GIS Software
One leading GIS software vendor is ESRI, based in Redlands, California, which offers ArcGIS for the desktop, ArcGIS Server for Internet mapping, ArcPad for PDAs and a range of other products and services for developers. Other popular GIS software packages are available from Cadcorp, Intergraph, MapInfo, Manifold and Autodesk. ERDAS Imagine, ENVI, Idrisi, and PCI Geomatica are geared towards remote sensing i.e. analysis of satellite/aircraft images. There are many third-party extensions and utilities for ArcGIS and other GIS and raster software platforms. Currently, open source GIS software options can be chosen from the first OS GIS package GRASS, recent open source options are DIVA GIS, QGIS, and uDig. There are efforts underway, through the Open GIS Consortium to provide interoperability among spatial data formats and software. The leading contender for spatial data storage is another open source package called PostGIS, which is a spatial extension to the open source database PostgreSQL.

What Is Topology?
Topology is the branch of mathematics concerned with spatial properties in special the continuous deformations of objects, such as deformations that involve stretching (but no tearing or gluing) and how they connect together. In geography this is an indispensable tool for map-making in expressing relevant geographic information, especially in topological maps.

Why Is Geospatial Topology Important In A GIS?
Geospatial analysis provides a unique perspective on the world. It is a tool with which to examine events, patterns, and processes that operate on or near the surface of our planet. To have this tool interact with the relevant topological information is a must; providing greater understanding of how rivers flow, weather is affected by terrain, or even how humans and other animals flow or choose a specific habitat. This kind of information can only be gathered and made useful if topological information is present in the GIS.

Spatial Data
Spatial data comes in two major formats, as vector or raster data. The main difference is that a raster is usually a static background picture used to illustrate, whereas a vector is an intelligent ladder of information that can be selected and searched.

Vector (points, lines, polygons)

Vector data often represents anthropogenic (human) features such as roads, buildings, political boundaries (counties, congressional districts, etc.), and other features such as lakes and rivers.

Vector data is scalable without loss of resolution and is generally represented by XYZ points in a Cartesian frame reference.

Raster (grids/images)

Raster data is pixellated data, and the more pixels that map the data, the better the resolution. However, if raster data is enlarged, it simply enlarges the pixels, which then leads to a loss of resolution. There are many moves being made to make raster data more usable/searchable as it is much faster to collect, unlike vectors where each piece of data usually has a manual input origin.

Raster data is usually derived from satellite imagery or aerial photography (known as remote sensing). Ordinary cameras are only sensitive to visible light. Satellite sensors can capture not only visible light, but also the thermal, microwave, infrared or other types of energy emanating from the Earth's surface. This extra data provides information about sea surface temperatures, vegetation, ozone, etc. Remote sensing is also used to study other planets and extraterrestrial bodies, such as Mars.

Data sources
The U.S. Federal Government offers a wealth of spatial data for free or at cost, with major offerings from the United States Geological Survey (USGS), NASA and the U.S. Census Bureau. State governments also serve spatial data through GIS portals such as MassGIS. As well, many local governments have detailed GIS data of tax parcels, roads, buildings, etc. Other governments around the world also offer spatial data, though not necessarily for free. Private industry also offers GIS data, with TeleAtlas/GDT offering a wealth of vector data, while Ikonos and DigitalGlobe (QuickBird) provide high-resolution satellite imagery. Some public-domain data sources are listed at http://visual.wiki.taoriver.net/moin.cgi/EarthMapTool.

title: Geographic Information Systems


text:
High School Mathematics Extensions/Matrices/Solutions

Matrix Multiplication exercises

 * $$\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}1\\2\end{pmatrix} =

\begin{pmatrix}(1 \times 1) + (2 \times 2)\end{pmatrix} = \begin{pmatrix}5\end{pmatrix} $$

 * $$\begin{pmatrix}1\\2\end{pmatrix}\begin{pmatrix}1&2\end{pmatrix} =

\begin{pmatrix} 1 \times 1 & 1 \times 2 \\ 2 \times 1 & 2 \times 2 \\ \end{pmatrix} = \begin{pmatrix} 1 & 2 \\ 2 & 4 \\ \end{pmatrix} $$

 * $$\begin{pmatrix}1/8&9\end{pmatrix}\begin{pmatrix}16\\2\end{pmatrix} =

\begin{pmatrix}(1/8 \times 16) + (9 \times 2)\end{pmatrix} = \begin{pmatrix}20\end{pmatrix}$$

 * $$\begin{pmatrix}a&b\end{pmatrix}\begin{pmatrix}d\\e\end{pmatrix} =

\begin{pmatrix}(a \times d) + (b \times e)\end{pmatrix} = \begin{pmatrix}a \times d + b \times e \end{pmatrix}$$

 * $$\begin{pmatrix}6 + 6b&3 - b\end{pmatrix}\begin{pmatrix}0\\0\end{pmatrix} =

\begin{pmatrix}((6 + 6b) \times 0) + ((3 - b) \times 0)\end{pmatrix} = \begin{pmatrix}0\end{pmatrix}$$

 * $$\begin{pmatrix}0&abc\end{pmatrix}

\begin{pmatrix}a\\0\end{pmatrix} = \begin{pmatrix}(0 \times a) + (abc \times 0)\end{pmatrix} = \begin{pmatrix}0\end{pmatrix}$$

Multiplication of non-vector matrices exercises
1.
 * a) $$n \times m$$
 * b) $$2 \times 4$$

2.
 * a)

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

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

\begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 3\\ 1\\ \end{pmatrix} = $$

\begin{pmatrix} 4\\ 1\\ \end{pmatrix} $$

 * b)

\begin{pmatrix} 3&1\\ 2&8\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1\\ 1\\ \end{pmatrix} = $$

\begin{pmatrix} 3&1\\ 2&8\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 2\\ 1\\ \end{pmatrix} = $$

\begin{pmatrix} 3&1\\ 2&8\\ \end{pmatrix} \begin{pmatrix} 3\\ 2\\ \end{pmatrix} = $$

\begin{pmatrix} 11\\ 22\\ \end{pmatrix}$$

3.
 * $$C =

\begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} = \begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} $$
 * $$D =

\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} = \begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} $$ The important thing to notice here is that the 2x2 matrix remains the same when multiplied with the other matrix. The matrix with only 1s on the diagonal and 0s elsewhere is known as the identity matrix, called I, and any matrix multiplied on either side of it stays the same. That is $$A \times I = I \times A$$

NB:The remaining exercises in this section are leftovers from previous exercises in the 'Multiplication of non-vector matrices' section

3.

C = \begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} \begin{pmatrix} 1&0&0\\ 0&1&0\\ 0&0&1\\ \end{pmatrix} = \begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix}$$

D = \begin{pmatrix} 1&0&0\\ 0&1&0\\ 0&0&1\\ \end{pmatrix} \begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} = \begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} $$ The important thing to notice here is that the 1 to 9 matrix remains the same when multiplied with the other matrix. The matrix with only 1s on the diagonal and 0s elsewhere is known as the identity matrix, called I, and any matrix multiplied on either side of it stays the same. That is $$A \times I = I \times A$$

4. a)
 * $$A^5 =

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -5&18\\ -3&10\\ \end{pmatrix} = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -13&42\\ -7&22\\ \end{pmatrix} = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -29&90\\ -15&46\\ \end{pmatrix} = $$

\begin{pmatrix} -61&186\\ -31&94\\ \end{pmatrix} $$

b)

\begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} \begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} = \begin{pmatrix} (1 \times 3) + (-2 \times 1)&(1  \times 2) + (-2 \times 1)\\ (-1 \times 3) + (3 \times 1)&(-1  \times 2) + (3 \times 1)\\ \end{pmatrix} = \begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} $$

c) $$ \begin{pmatrix} a&b\\ c&d\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} = \begin{pmatrix} (a \times 1) + (b \times 0)&(a \times 0) + (b \times 1)\\ (c \times 1) + (d \times 0)&(c \times 0) + (d \times 1)\\ \end{pmatrix} = \begin{pmatrix} a&b\\ c&d\\ \end{pmatrix} $$
 * $$\begin{pmatrix}

1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} a&b\\ c&d\\ \end{pmatrix} = \begin{pmatrix} (1 \times a) + (0 \times b)&(0 \times a) + (1 \times b)\\ (1 \times c) + (0 \times d)&(0 \times c) + (1 \times d)\\ \end{pmatrix} = \begin{pmatrix} a&b\\ c&d\\ \end{pmatrix}$$

d)
 * $$A =

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&4\\ 1&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} $$

e) As an example I will first calculate A2
 * $$A^2 =

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} \begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix}^2 \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1^2&0\\ 0&2^2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&4\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&8\\ 1&4\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -5&18\\ -3&10\\ \end{pmatrix} $$ Now lets do the same simplifications I have done above with A5-
 * $$ A^5 =

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix}^5 \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1^5&0\\ 0&2^5\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&32\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&64\\ 1&32\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -61&186\\ -31&94\\ \end{pmatrix} $$

f)
 * $$ A^{100} =

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix}^{100} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1^{100}&0\\ 0&2^{100}\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&1267650600228229401496703205376\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2535301200456458802993406410752\\ 1&1267650600228229401496703205376\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -2535301200456458802993406410751&7605903601369376408980219232254\\ -1267650600228229401496703205373&3802951800684688204490109616122\\ \end{pmatrix} $$

Determinant and Inverses exercises
1.
 * $$ \det(A) = \frac{2}{5} \times \frac{5}{2} -\frac{2}{3} \times \frac{3}{2} = 0$$

The simultaneous equation will be translated into the following matrices $$ \begin{pmatrix}\frac{2}{5}&\frac{2}{3}\\ \\ \frac{3}{2}& \frac{5}{2}\end{pmatrix} \begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}0\\0\end{pmatrix}$$ Because we already know that
 * $$ \det(\begin{pmatrix}\frac{2}{5}&\frac{2}{3}\\ \\ \frac{3}{2}& \frac{5}{2}\end{pmatrix}) = 0$$

We can say that there is no unique solution to these simultaneous equations.

2. First calculate the value when you multiply the determinants

\det( \begin{pmatrix} a&b\\ c&d \end{pmatrix} ) \det( \begin{pmatrix} e&f\\ g&h \end{pmatrix} ) = $$

(ad - bc)(eh - fg) = $$

adeh - bceh - adfg + bcfg $$ Now let's calculate C by doing the matrix multiplication first

\det( \begin{pmatrix} a&b\\ c&d \end{pmatrix} \begin{pmatrix} e&f\\ g&h \end{pmatrix} ) = $$

\det( \begin{pmatrix} ae+bg&af+bh\\ ce+dg&cf+dh \end{pmatrix} ) = $$

(ae + bg)(cf + dh) - (af + bh)(ce + dg) = $$

aecf+bgcf+aedh+bgdh-afce-bgce-afdg-bhdg = $$

bgcf+aedh-bgce-afdg $$ Which is equal to the value we calculated when we multiplied the determinants, thus
 * det(C) = det(A)det(B)

for the 2×2 case.

3.
 * $$A =

\begin{pmatrix} a&b\\ c&d \end{pmatrix} $$

\det(A) = ad - bc $$
 * $$A' =

\begin{pmatrix} c&d\\ a&b \end{pmatrix} $$

\det(A') = cb - da $$

-\det(A') = -(bc - ad) = ad - bc $$ Thus det(A) = -det(A') is true.

4. a)
 * $$A = P^{-1}BP$$
 * $$\det(A) = \det(P^{-1})\det(B)\det(P) =$$
 * $$\det(P^{-1})\det(P)\det(B) =$$
 * $$\det{(P^{-1}P)}\det(B) =$$
 * $$\det{(I)}\det(B) =$$
 * $$\det(B)$$ as det(I) = 1.

thus det(A) = det(B) b) if $$A^k=0$$ for some k it means that $$\det(A^k)=0$$. But we can write $$\det(A^k)=\det{(A)}^k$$, thus $$\det{(A)}^k=0$$. This means that $$\det(A)=0$$.

5. a)
 * $$A^5 = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} = $$

(\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix})( \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix}) \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} = $$

\begin{pmatrix} -5&18\\ -3&10\\ \end{pmatrix} \begin{pmatrix} -5&18\\ -3&10\\ \end{pmatrix} \begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} = $$

\begin{pmatrix} -5&18\\ -3&10\\ \end{pmatrix} \begin{pmatrix} -13&42\\ -7&22\\ \end{pmatrix} = $$

\begin{pmatrix} -61&186\\ -31&94\\ \end{pmatrix} $$

b)
 * $$P^{-1} =

\frac{1}{1} \begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} = \begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} $$

c)

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&4\\ 1&2\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} $$

d)
 * $$A^5 = $$

(P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} P)^5 = $$

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

P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} I \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} I \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} I \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} I \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} P = $$

P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix}^5 P = $$

P^{-1} \begin{pmatrix} 1^5&0\\ 0&2^5\\ \end{pmatrix} P = $$

P^{-1} \begin{pmatrix} 1&0\\ 0&32\\ \end{pmatrix} P = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&32\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&64\\ 1&32\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} -61&186\\ -31&94\\ \end{pmatrix} $$ We see that P and it's inverse disappear when you raise the matrix to the fifth power. Thus you can see that we can calculate An very easily because you only have to raise the diagonal matrix to the n-th power. Raising diagonal matrices to a certain power is very easy because you only have to raise the numbers on the diagonal to that power.

e) We use the method derived in the exercise above.
 * $$A^{100} = $$

(P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} P)^{100} = $$

P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix}^{100} P = $$

P^{-1} \begin{pmatrix} 1^{100}&0\\ 0&2^{100}\\ \end{pmatrix} P = $$

P^{-1} \begin{pmatrix} 1&0\\ 0&2^{100}\\ \end{pmatrix} P = $$

\begin{pmatrix} 3&2\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2^{100}\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3&2^{101}\\ 1&2^{100}\\ \end{pmatrix} \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} = $$

\begin{pmatrix} 3-2^{101}&3\times2^{101}-6\\ 1-2^{100}&3\times2^{100}-2\\ \end{pmatrix} $$


text:
Esperanto/Appendix/Web resources

Tools For Learning Esperanto

 * Interactive Telephone Reseller Training
 * Free online Esperanto courses and learning resources
 * Esperanto Department at Wikiversity
 * Free text-only Esperanto course
 * Free online Esperanto flashcard sets on Quizlet (user-generated)

Online Books About Esperanto

 * [[Image:Wikibooks-logo.svg|text-bottom|14x14px]] Esperanto: A Complete and Comprehensive Grammar
 * The Esperanto Teacher, A Simple Course for Non-Grammarians at Project Gutenberg
 * The Esperanto Book by Don Harlow
 * Esperanto: A Language for the Global Village by Sylvan Zaft
 * About Language Problems by Claude Piron
 * Plena Manlibro de Esperanta Gramatiko- An online Esperanto grammar, in Esperanto.

Software to Learn Esperanto

 * Kurso de Esperanto, an interactive course in 25 languages to learn Esperanto (freeware)

Online

 * Lernu!
 * Retbabilejo.net to practice your esperanto speaking with microphone with other esperanto speakers.

Other
IRC: ##esperanto on irc.freenode.net

Jabber: esperanto@conference.jabber.org (For more information on this, see Kiel uzi Jabber)

MSN: Add "tuj@lernu.net" to your user list (interfaces with the chatroom at Lernu!)

title: Esperanto/Appendix/Web resources


text:
User:Wjgilmore~enwikibooks

Apress' (http://www.apress.com/) Open Source Editorial Director, and an all-around PHP maniac. Learn more about me at my Web site (http://www.wjgilmore.com/)

title: User:Wjgilmore~enwikibooks


text:
Talk:Hebrew

The discussion here should be focused on the Hebrew cover page only. You can discuss the contents of the course here.

title: Talk:Hebrew


text:
Talk:ASP.NET

new version is 2.0 Beta

Links not working, ) is included giving wrong url
The links (in brackets) are not working as the closing bracket is included in the url.

Looking at the editing instructions briefly it seems that you should include these in double square brackets to make them in to proper links.

Don't include language-specific features
I think that VB features such as the lack of a multiline comment delimiter should be taken to the Visual Basic .NET article.

 * I think that we should include both languages. --Mplogan 23:11, 11 Feb 2005 (UTC)

 * ASP.Net is a web programming model that uses different languages for the CodeBehind. We should try not to dive into the language-specific parts of the ASP.Net programming model, rather we should look at ASP.Net from a broader perspective like the usage of the various contorls, web.config, web.sitemap and other such stuff.
 * - Arunreginald 08:32, 15 May 2006 (UTC)

Learning the languages is part of the point
Discussing ASP.NET w/o discussing VB.NET and C#.NET is worthless. The point of the book should be to teach the languages along with the best practices for coding ASP.NET web apps. A book that merely discussed the life-cycle of development patterns of ASP.NET apps w/o the specifics of language would be too abstract to have any value for most. The idea, I think, is to create a useful introductory text. --wheat 02.16.05

Problems in the code
I am still learning ASP.NET, but I am very familiar with C#, and the code given in this article is most definitely not C# code.

Please quote an example of the book's C# code that is wrong. I can find no fault with the C# code in this book yet. All examples are given in both C# and VB.Net, are you sure you're not confusing the VB.Net code with C#?

ASP to ASP.NET 1.0/1.1 to ASP.NET 2.0
There are three versions 'in the wild' which need explaining - and ASP.NET 1.0/1.1 is also different from ASP.NET 2.0 as well. A basic section on installation would help BY VERSION along with a conversion section.

One aspect that I have found confusing is the deployment to make a designed web available under a public IIS. aspnet_regiis -i anyone?

Probably an explaination of the .NET paradigm would be of benefit. ASP.NET is just an application of the .NET paradigm to ASP

Contributors list
I am removing the contributors list from the main page, I dont think it's appropriate for people to be signing the content modules. If you want to talk about the authors either do it here on the discussion page, or create a special page for it at ASP.NET/Authors. I am copy+pasting the contributors list here, in case somebody wants to move them to a better place. --Whiteknight (Page) (Talk) 14:33, 17 August 2007 (UTC)

 * --Jaq316 12:10, 8 May 2006 (UTC) Jaq316 added the "Links about ASP.NET Providers section under Related Links
 * --Mplogan 00:28, 21 Feb 2005 (UTC) Michael Logan is currently working on upgrading this page along with several other topics.

title: Talk:ASP.NET


text:
Introduction to Paleoanthropology/Dating Techniques

Having an accurate time scale is a crucial aspect of reconstructing how anatomical and behavioral characteristics of early hominids evolved.

Researchers who are interested in knowing the age of particular hominid fossils and/or artifacts have options that fall into two basic categories:
 * Relative dating methods
 * Chronometric dating methods

Relative dating methods
Relative dating methods allow one to determine if an object is earlier than, later than, or contemporary with some other object. It does not, however, allow one to independently assign an accurate estimation of the age of an object as expressed in years. The most common relative dating method is stratigraphy. Other methods include fluorine dating, nitrogen dating, association with bones of extinct fauna, association with certain pollen profiles, association with geological features such as beaches, terraces and river meanders, and the establishment of cultural seriations. Cultural seriations are based on typologies, in which artifacts that are numerous across a wide variety of sites and over time, like pottery or stone tools. If archaeologists know how pottery styles, glazes, and techniques have changed over time they can date sites based on the ratio of different kinds of pottery. This also works with stone tools which are found abundantly at different sites and across long periods of time.

Principle of stratigraphy
Stratigraphic dating is based on the principle of depositional superposition of layers of sediments called strata. This principle presumes that the oldest layer of a stratigraphic sequence will be on the bottom and the most recent, or youngest, will be on the top. The earliest-known hominids in East Africa are often found in very specific stratigraphic contexts that have implications for their relative dating. These strata are often most visible in canyons or gorges which are good sites to find and identify fossils. Understanding the geologic history of an area and the different strata is important to interpreting and understanding archaeological findings.

Chronometric dating methods
The majority of chronometric dating methods are radiometric, which means they involve measuring the radioactive decay of a certain chemical isotope. They are called chronometric because they allow one to make a very accurate scientific estimate of the date of an object as expressed in years. They do not, however, give "absolute" dates because they merely provide a statistical probability that a given date falls within a certain range of age expressed in years. Chronometric methods include radiocarbon, potassium-argon, fission-track, and thermoluminescence.

The most commonly used chronometic method is radiocarbon analysis. It measures the decay of radioactive carbon (14C) that has been absorbed from the atmosphere by a plant or animal prior to its death. Once the organism dies, the Carbon-14 begins to decay at an extremely predictable rate. Radioactive carbon has a half-life of approximately 5,730 years which means that every 5,730 years, half of the carbon-14 will have decayed. This number is usually written as a range, with plus or minus 40 years (1 standard deviation of error) and the theoretical absolute limit of this method is 80,000 years ago, although the practical limit is close to 50,000 years ago. Because the pool of radioactive carbon in the atmosphere (a result of bombardment of nitrogen by neutrons from cosmic radiation) has not been constant through time, calibration curves based on dendrochronology (tree ring dating) and glacial ice cores, are now used to adjust radiocarbon years to calendrical years.

The development of Atomic Absorption Mass Spectrometry in recent years, a technique that allows one to count the individual atoms of 14C remaining in a sample instead of measuring the radioactive decay of the 14C, has considerably broadened the applicability of radiocarbon dating because it is now possible to date much smaller samples, as small as a grain of rice, for example.

Dendrochronology is another archaeological dating technique in which tree rings are used to date pieces of wood to the exact year in which they were cut down. In areas in which scientists have tree rings sequences that reach back thousands of years, they can examine the patterns of rings in the wood and determine when the wood was cut down. This works better in temperate areas that have more distinct growing seasons (and thus rings) and relatively long-lived tree species to provide a baseline.

Methods of dating in archaeology
Techniques of recovery include:
 * Surveys
 * Excavations

Types of archaeological remains include:
 * Perishable: plant remains, animal bones, wooden artifacts, basketry, and other easily degradable objects
 * Nonperishable materials: stone tools, pottery, rocks used for structures.

Data collection and analysis is oriented to answer questions of subsistence, mobility or settlement patterns, and economy.

Methods in physical anthropology
Data collections based on study of hard tissues (bones and teeth), usually the only remains left of earlier populations, which include:
 * Identification of bones/Which part of skeleton is represented?
 * Measurement of the cranium and other elements of a skeleton. Carefully defined landmarks are established on the cranium, as well as on the long bones, to facilitate standardization of measurements.
 * Superficial examination of bone for any marks (for instance, cutmarks)
 * Further examination using specific techniques:
 * X-ray to identify evidence of disease and trauma in bones
 * DNA extraction to determine genetic affiliations


text: Template:Introduction to Paleoanthropology


text:
Arabic/Arabic sounds

Sounds in both English and Arabic
Most of the sounds in Arabic are also in English and vice versa. For example, the Arabic ba (ب) sounds exactly like the b in English, the Arabic zay (ز), sounds just like the z in English and the Arabic versions of k (ك), m (م), n (ن), f (ف), and j (ج) are all just the same. The counterpart of l (ل) in Arabic, known as laam, is not exactly the same sound as the English one (the Arabic one is pronounced with the tip of the tongue touching the roof of the mouth a bit farther back). The counterpart of r (ر) in Arabic, known as raa, is very different from English r. The Arabic one is trilled (it is a "rolled r").

In addition to the above, the following Arabic sounds also exist in English:

-Thâ (ث) makes the sound "th" (voiceless) as in thin or thick or through.

-Dhâ (ذ) makes the sound "th" (dh) (voiced) as in them or there or the.

-Shîn (ش) makes the sound "sh" as in shoot or shin.

-Tâ marbûta (ة) is usually silent in modern Arabic. In Classical Arabic, it is pronounced t, the same as the letter tâ.

-Hamza (ء) represents the glottal stop. It is pronounced by stopping the flow of breath at the back of the mouth cavity (the glottis). We make this sound when speaking English; we just have no symbol for it in our alphabet. Think of the dash in uh-oh, or the Cockney way of saying British as Bri-ish. However, hamza is also written as a diacritic.

-Yâ (ي) acts just like a y. It can be a vowel (always a long vowel) at the end of a word sounding like î (the "ee" in beet), or it can be a consonant (y). It can be a consonant (as in the y in yes) or a vowel (like the "ee" in beet) in the middle of a word.

Sounds in Arabic only
There are sounds in Arabic hard for English speakers to tell apart. Look at what makes them different.

Like "k" (ك vs ق)
In Arabic, the corresponding letter to q (ق) makes a different sound than the corresponding letter to k (ك), whereas in English they are redundant. The q is further back in the throat while the k is not as in English, k in English is voiceless, while its Arabic counterpart is voiced. So is the Arabic counterpart of q. Kuwait starts with a k. Qatar with a q. Listen to the difference.

Like "h"
The most significant sound that English speakers hear in Arabic are the three corresponding letters to h. The first (ه) is equivalent to the h and is thus very light, almost not heard at all. The noise comes from friction in the upper throat. The second (ح) comes from deep down in the throat, from actual friction from the vocal cords themselves. It sounds a little like blowing warm air on your cold hands or very fine sandpaper. The third (خ) is very rough, almost like collecting phlegm, or exactly like the French r, only if you pronounce it voiceless. It is very similar to the last sound in "Bach."

None of these three sounds have any humming or vowel sound (known as voicing). They are all like a whisper; your vocal cords do not vibrate.

Like "h" but voiced
The ayn (ع) may be difficult to hear and produce because though it is a consonant in Arabic, it sounds like the English a, as in water. It is produced like the y in you, but the constriction is made down in the throat instead of the mouth. It is a little like the sound a doctor asks to hear when looking down your throat. While saying "aaah", pull the back of your tongue back into your throat a bit, with a little squeeze. Similar is the ghayn (غ), which is a rougher version with more of the ch from "Bach", only with vocal cords vibrating. The difference between the last sound in the previous paragraph and the last sound in the first paragraph should be very clear. They are both rough, but one has no vibrating vocal cords while the other has them.

Letters that come in hard and soft varieties
Arabic has hard and soft versions of s, t, d, and th (as there, not thin). Arabic-speakers often refer to their language as the language of Daad (hard d) because it is so hard for foreigners to say it right. However, this refers to the classical pronunciation of Daad (ض) which probably resembled a sound closer to an emphatic z sound (voiced lateral fricative). It can be easier for English-speakers to think of the hard sounds as lower-pitched and the soft sounds as higher-pitched. What complicates matters is that for English-speakers the hard s and the soft s sound the same, but the vowels before and after them are affected by the consonant. To the English speaker, the vowels are different, and the consonant is the same. To the Arabic-speaker the vowels are the same, and the consonant is different.

Partly, it is because Arabic has very few recognized vowel sounds. An a and an e to an Arabic-speaker are usually the same, depending on the dialect. It is one letter pronounced differently depending on what letter comes before or after it.

Also, the hard letters can be hard for even native speakers to say and so are often changed in local colloquial Arabic to something else. For example, the hard d in many areas is pronounced exactly like the z, but it is not formal, proper Arabic.

The soft s, "seen" (س), is pronounced just like the English s (with mouth open, small and weak). The hard s, "sod" (ص), is with the mouth more closed, with a lower pitch, as if you were a big, stalwart man. The easiest way to say it is to make the vowels before and after it lower-pitched and deeper.

The soft t, ta (ت) is just like the English t, soft and weak, and the hard t "taw" (ط) is deep and strong.

The soft d, del (د) is even softer than the English d, and the hard d, Dod (ض) is very deep and hard.

The soft dh, dhel (ذ), is just like the th in "the", and the hard dh, DHa (ظ) is deep and strong.

Note on transliteration
Since Arabic does not use capital letters, transliterating soft letters usually uses in lowercase, hard letters in uppercase. Transliterating is not an exact science and is never entirely consistent. You are highly recommended to learn the Arabic alphabet because studying Arabic from English letters is terrifically frustrating. The same sound can be written totally differently in English letters.

`Ayn is usually written as ' (with a 6 shape) in English and hamza as an opposite ' (with a 9 shape). `ayn and hamza are often left out when transliterating, especially `ayn at the beginning of a word (as in `iraaq). Ghayn(غ) is written as gh, soft ha as h, khaa (the one in Bach) as kh, and hard ha as "H" (capital h), its sound is exactly like the French r, only that ghayn is not rhotic.

Sounds in English only
In case you mistakenly think that Arabic has more sounds than English, the following sounds do not exist in Arabic, with the sounds that are usually substituted for them in borrowed words.

v (f)

p (b in new loanwords, such as “computer” (كمبيوتر) and f in old loanwords, such as Palaestina (فلسطين))

g (j, gh, q, or k)

r is very close but is always rolled (similar to Spanish r)

As mentioned above, in Arabic the corresponding letter to q (ق) makes a different sound than the corresponding letter to k (ك).

Conclusion
Most sounds in English and Arabic correspond perfectly. Give yourself time to recognize the different sounds of h and the hard and soft letters. And learn the alphabet. The book Alif Baa is one of many introductions to the Arabic alphabet. Much better, take a short course, but make sure it is one that teaches the Arabic alphabet. Those 50 hours it takes you to get comfortable with the alphabet will be endlessly worth it. Plus, if you ever want to learn Persian, Ottoman Turkish, Kurdish, Berber, or Urdu, these languages are also written with the same letters. Some of these languages also have a few extra or modified letters in order to make up for the sounds not available in Arabic but that are found in those languages.

Insha'Allah (God willing) you will learn these sounds with ease.

Gaining proficiency in the sounds
Learning and differentiating those sounds is crucial to having a good Arabic accent. First expose yourself to the sounds, as many hours of the day as possible. If you have audio in Arabic, play it again and again, in the background of your life. You can occasionally also listen to it attentively, but you need to listen to how Arabic is spoken to be able to speak it.
 * 1) Do not imitate sounds without an expert at Arabic sounds. You do not want to learn them incorrectly. Learn them from someone who has proper pronunciation.
 * 2) Because in cartoons, the following letters ح خ ع غ along with others are pronounced very softly, you want be able to pick them up properly. What you need to do is have the sounds pronounced as strongly as possible by an Arabic person, as it is much easier to differentiate the sound when the sound is pronounced strongly. (Make sure they know how to pronounce all letters properly. In any case, all Arabs can pronounce: ح خ ع غ ق ل ر properly.) Then, you will start recognizing the difference. Once you recognize the pronunciation, with the help of an Arabic speaker, pronounce the sounds as strongly (to your mouth the ability to pronounce it properly) but correctly as possible. Once you have a strong pronunciation, your pronunciation will fall in place and the amount of strength you use to pronounce letters will become less, making you sound perfect.
 * 3) Listen to more and more Arabic, while learning grammar and vocabulary, and it will all sink in after a while (especially the vowels), and you will become fluent.

title: Arabic/Arabic sounds


text:
High School Mathematics Extensions/Logic/Solutions

Compound truth tables exercises
1. NAND: x NAND y = NOT (x AND y) 2. NOR: x OR y = NOT (x OR y) 3. XOR: x XOR y is true if and ONLY if either x or y is true.

Produce truth tables for: 1. xyz 2. x'y'z' 3. xyz + xy'z 4. xz 5. (x + y)' 6. x'y' 7. (xy)' 8. x' + y'

Laws of Boolean algebra exercises
1.
 * 1. z = ab'c' + ab'c + abc

\begin{matrix} x &=& ab'c' + ab'c + abc\\ &=& ab'c' + c(ab' + ab)\\ &=& ab'c' + ca \end{matrix} $$
 * 2. z = ab(c + d)

\begin{matrix} x &=& ab(c + d)\\ &=& abc + abd\\ \end{matrix} $$
 * 3. z = (a + b)(c + d + f)

\begin{matrix} x &=& (a + b)(c + d + f)\\ &=& ac + ad + af + bc + bd + bf\\ \end{matrix} $$
 * 4. z = a'c(a'bd)' + a'bc'd' + ab'c

\begin{matrix} x &=& a'c(a'bd)' + a'bc'd' + ab'c\\ &=& a'c(a + (bd)') + a'bc'd' + ab'c\\ &=& a'ca + a'c(bd)' + a'bc'd' + ab'c\\ &=& a'c(b' + d') + a'bc'd' + ab'c\\ &=& a'cb' + a'cd' + a'bc'd' + ab'c\\ \end{matrix} $$
 * 5. z = (a' + b)(a + b + d)d'

\begin{matrix} x &=& (a' + b)(a + b + d)d'\\ &=& (a' + b)(a + b + d)d'\\ &=& (a'a + a'b + a'd + ba + bb + bd)d'\\ &=& (a'b + a'd + ba + b + bd)d'\\ &=& (b(a' + a) + a'd + b + bd)d'\\ &=& (a'd + b + bd)d'\\ &=& a'dd' + bd' + bdd'\\ &=& bd'\\ \end{matrix} $$ 2. Show that x + yz is equivalent to (x + y)(x + z)

\begin{matrix} x &=& (x + y)(x + z)\\ &=& xx + yx + xz + yz\\ &=& x(x + y + z) + yz\\ &=& x + yz\\ \end{matrix} $$

Implications exercises

 * 1) Decide whether the following propositions are true or false:
 * 2) If 1 + 2 = 3, then 2 + 2 = 5 is false because something that's true implies something that's false
 * 3) If 1 + 1 = 3, then fish can't swim is true because 1+1 is not 3
 * 4) Show that the following pair of propositions are equivalent
 * 5) $$x \Rightarrow y$$ : $$y' \Rightarrow x'$$
 * We use truth tables for this
 * The columns in the table are the same for both propositions, thus they are equivalent.
 * The columns in the table are the same for both propositions, thus they are equivalent.

Logic Puzzles exercises
Please go to Logic puzzles.