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User talk:Hedwig0407~enwikiversity

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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 Hedwig0407. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Hedwig0407~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:11, 19 April 2015 (UTC)

title: User talk:Hedwig0407~enwikiversity


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User talk:Stefan Kögl

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
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Good luck! -- sebmol ? 08:25, 21 August 2006 (UTC)

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

title: User talk:Stefan Kögl


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User talk:Tarabishy.md

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional editing help.

You will find more resources at the Community Portal. If you want to ask a question, visit the Study help desk, the Colloquium, IRC channel or ask me personally on my talk page.

Good luck! -- sebmol ? 08:25, 21 August 2006 (UTC)

title: User talk:Tarabishy.md


text: User:Gurch

title: User:Gurch


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User talk:Gurch

Gah!
It's a Gurch! robchurch | talk 13:09, 24 August 2006 (UTC)

title: User talk:Gurch


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User:Gurch/monobook.css

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Units, significant figures, and standard procedures

This lesson is a part of the School of Physics

In order to understand physics and work with physical theory accurately, there must first be a consistent understanding of the conventions and procedures of working out quantities and numbers.

Units
Most quantities that can be measured must be expressed in the correct units. The unit differentiates between whether one is talking about a measure of time, or a measure of distance, or several other fundamental types of observables that have come to light during our study of the universe.

Standard Prefixes
You already use units in everyday conversation. When you want to purchase something, the price of the item is measured in some combination of monetary units. In the U.S., these units are usually dollars and cents. In this system, a dollar is equivalent to 100 cents, although very few people would pay for an item using hundreds of cents. The American dollar is a simple example of a multiplicative unit. When reading the price of an item that costs more than 99 cents, you will most likely read it in terms of dollars, as that is the most convenient term to use. Seldom is the case where one reads an item priced at 10 dollars as being "a thousand cents".

Similarly, scientists must use appropriate types of scale when talking about large and small quantities. You would not want to talk about the mass of the Earth in the same unit as the mass of a few subatomic particles, for example, unless making a pointed comparison. One of the technical reasons for this is simple accuracy. It is just not feasible to be as accurate in talking about the mass of the Earth as one would be in measuring the mass of a few salt crystals. While the salt crystals can easily be measured to the nearest gram, the Earth's mass to the nearest gram is changing constantly (due to atmospheric evaporation and bombardment by radiation, particles, and tiny meteorites).

Scientists have developed a standard for referring to large and small quantities of units by referring to them as multiples of powers of ten. Each power is referred to by appending a prefix to the standard unit. The most common prefixes are listed below:

In terms of dollars and cents, we would then call a dollar a hectocent and if we used c as the unit abbreviation for cents, we would write 200 c = 2 hc. We generally don't go around talking about dollars and cents in this manner, but these prefixes are great way to quantify the myriad units we will encounter in the physical sciences. You may already be familiar with the kilogram as a unit of mass, and from the list above, you know that each kilogram is 1000 grams. You might purchase a few kilograms of cement or add a few grams of salt to a recipe, but you wouldn't want to add a few kilograms of salt to a recipe. This is again just an example of what physicists call order of magnitude.

Types of Units
The units of length and distance may seem obvious to you from everyday experience, but there are many other important units (ie., how would you measure the color of an object? We will learn more about color when we study electromagnetism), and there are ways of relating what may seem like completely different types of units to each other in a standard manner, including time and distance. Finding out that some units are really just products or multiples of some familiar unit is part of the allure of discovering new physics.

Units, most often the SI Unit Standard signify first and foremost what the quantity is relevant to. All SI units can themselves be expressed in terms of the seven SI base units below:

 * length, measured in metres, expressed as the symbol m
 * mass, measured in kilogrammes, expressed as the symbol kg
 * time, measured in seconds, expressed as the symbol s
 * electric current, measured in amperes, expressed as the symbol A
 * temperature, measured in kelvin, expressed as the symbol K
 * amount of substance, measured in moles, expressed as the symbol mol
 * luminous intensity, measured in candela, expressed as the symbol cd

The bold script indicating the symbols above is for emphasis; no special format is required when hand-writing these quantities provided that they are written clearly and in the correct case as shown.

There are many other SI units which have their own symbol, but every one of them is a shorthand for some product of the base units shown above (or equivalently, a product of other SI units which themselves are equivalent to some other product of base units, and so on). SI units are given their own symbol for two reasons; firstly, that the product they represent might be long and awkward to write, and secondly that units relevant to important scientific discoveries may be renamed and given a symbol of their own to honour their creator if the theory which uses them is a particularly significant discovery.

Writing Units
Many units belonging to quantities we can measure in physics are products of other units. As you know from mathematics, a product can include dividing one term by another - and from the Law of Indices we can also show that this is equivalent to multiplying the numerator by a negative power of the denominator. So, as an example, if we take a measurement of the velocity of an object, we express this in metres per second which we can write as:

 * $$m / s$$

Or equivalently as:

 * $$ms^{-1}$$

According to the the BIPM (Bureau Internationale de Poids et Measures), the international authority responsible for standardising systems of measurement, either of these methods is acceptable in scientific literature as long as the form of the unit is clear and unambiguous.

Significant figures and Uncertainty
We will frequently be using measured quantities (which will be expressed as some number or collection of numbers) in equations and formulas in order to relate them to quantities we wish to predict the value of. In all of these cases, it will be very important to pay attention to the precision of the numbers that we have actually measured, as it is very easy to get lots of meaningless numbers from applying basic formulas, all the while forgetting that we did not measure the observables with the precision that we are getting out of blindly applying the formulas.

Instrument Precision
As an example, when you measure the length of something short with a ruler, you may notice that between the centimeter marks, there are ten marks, allowing you to eyeball measurements like 2.64 cm. However, note that the 0.04 cm in the previous measurement is not a precise measure (it is not infallible). The ruler does not give markings down to hundredths of a centimeter; you can really only say that "It looks like the length is 2.64, but my instrument can only report the length as being between 2.60 and 2.70 cm somewhere close to that measurement." You have no hard evidence to support the 0.04; you only hypothesize that its somewhere around the 4 hundredths mark. It could actually be near the 3 hundredths mark or near the 5 hundredths mark, if there were such markings, but it definitely would not be around the 6 hundredths mark. All numerical measurements have this sort of error involved and scientists include the instrumental precision in every measurement by using the notation $$2.64 \pm 0.01$$ cm which means the object you measured is between 2.63 and 2.65 centimeters in length. That is definitely a statement you can support using your ruler. More advanced instruments also have statistical fluctuations in either the property they are measuring or the process/physical properties of the parts being used to measure the phenomenon and they all report (either live or in the manual) statistical uncertainty. Check your scale at home for its uncertainty. While you may expect your scale to tell whether you have sneakers on or not, it may not be able to tell whether you got a haircut today.

Unqualified measurements, those without explicit errors written in, are usually assumed to have a unit error in the most precise digit unless otherwise stated. Ie., if you see a measurement given as 5.4 g, it is usually meant as a shorthand for $$5.4 \pm 0.1$$ g.

Significant Figures
As we have seen above, all instruments have some finite precision. Significant figures are a method of keeping track of the order of magnitude of the error involved in a calculation. For example, You might read 3.26 cm off of a ruler. We say that such a measurement has 3 significant digits, which means all 3 digits present were measured on the ruler, implying the last digit, 6, is uncertain by some amount.

Suppose you measure something to be 0.05 cm using the same ruler. This measurement has only one significant digit (we didn't measure those two zeroes; they are only placeholders, an artifact of our decimal system), and it is uncertain, making it a very weak measurement (you wouldn't use this type of ruler to measure the thickness of paper). If you are ever confused about whether the digits in a measurement are significant and the context does not specify, simply write the measurement in scientific notation. The number of digits in the multiple of the power of ten are the number of significant digits. Above, 0.05 cm becomes 5 x 10-2 cm, with one significant digit.

Addition and Subtraction
For simple calculations, it is important to recognize that you can't get more information from a formula than the information contained by the weakest measurement you put into the formula. Ie., if you measure one object with a normal centimeter ruler and a larger object with a meter ruler, the smallest marking of which is one centimeter, and then add the lengths together, you should not expect to get a length that is precise down to the hundredth of a centimeter. Why not? Because you don't know how many hundredths of centimeters may be present in the length of the larger object. It could be anywhere from none at all to hundreds, which would make your overly precise sum quite nonsensical. This yields the following rule when dealing with addition: The result of an addition or subtraction of two measurements is only as precise as the least precise of the two measurements.

For example, if we have 3.4 g of water and 5.504 g of salt, we expect to get 8.9 g of salt water when we mix them together, not 8.904 g. We do not know what's going on in the hundredths and thousandths place of the mass of the water, only that it's between 3.3 g and 3.5 g of water that we have. For all we know, we may get 8.813 g of salt water as measured by a more precise instrument. As you can see, the 0.004 g carries no useful information.

Multiplication and Division
For reasons similar to the above, if one is taking the product or quotient of two numbers, the result is always rounded to the precision of the least precise measurement involved. Suppose a car is measured by a radar gun to be travelling at 10 m/s (accurate to the nearest meter per second), and you time the car as taking 10.7 seconds to go between point A and point B at that speed. As we will learn later, we can get the distance travelled by the car by multiplying the speed by the time taken. We do this and get 107 m. Rounding to account for the least precise measurement, which only has 2 significant digits, we get 110 m as the approximate distance between A and B. In this last value, note that the trailing 0 is only a placeholder and is not significant.

''Some texts will denote whether the trailing zeroes are significant or not by placing a decimal point after the last zero. This can get rather pedantic, so whenever the trailing zero is significant, we will simply alert the reader to the precision of the measurement, as in the radar gun measurement above.''

We round to 110 m in order to give the correct impression of the uncertainty of the result. The value of 107 m has 3 significant digits, misleading one to believe there is only an error in the units place. If one looks at the possible range of distances (from 95.4 m to 118.8 m using the lowest possible and highest possible values for the underlying measurements, respectively), one sees how inaccurate that would be.


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Talk:Units, significant figures, and standard procedures

Begin...
Right, I've set out the basics of SI measurement. I referenced it to the NIST, which is American, but the more proper reference I think would be the BIPM. However, I don't speak French. User:guillom, do you think that you could check for any inconsistencies against the resolutions of the CGPM and perhaps put a bit of spiel in english about the whys and wherefores of the SI unit standard?

What else...

 * Products and fractions of units
 * Meaning of significant figures and the practice of abbreviating a given value to the minimum accuracy of the original information
 * A.O.B

Sojourner001 11:00, 21 August 2006 (UTC)

Prefixes
Not entirely happy about the section on prefixes. Is it really necessary, particularly at the start of the lesson? I don't know about anyone else, but I don't use unit prefixes much at all; it's both clearer and easier to work with units in standard form. Just because many (often poor) textbooks have them, doesn't mean they're useful or relevant. Sojourner001 11:03, 22 August 2006 (UTC)

Hello, It is very important for the beginning student to have a table to translate these common prefixes into scientific notation. It also acts as a point of familiarity, as the student may already be familiar with centimeters, decibels, kilowatts, and so forth in their everyday life, and here they see them again, only completely explained and put into context. We are not going to have exercises on trivial things like this, but it's good for the student who may want to translate something in the real world into the units we will be using for their own exploratory purposes. The student should never feel that physics is disconnected from the real world around them. The unit prefixes also highlights the part played by order of magnitude in calculations and measurement. A student can usually tell the great difference between a kilogram and a gram, and when one would use one over the other, but just talking about measuring using multiples of 103 versus 10 isn't really a good connection to everyday experience. Ron 12:51, 22 August 2006 (UTC)


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User:Robchurch/monobook.css

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User:BlankVerse

You can check me out at WikiPedia:User:BlankVerse. You can contact me at WikiPedia:User talk:BlankVerse.

b c i m mw n q s sp v w / evo wt wikia / ss

Beta Wikiversity

 * beta:User:BlankVerse
 * http://beta.wikiversity.org/wiki/User:BlankVerse

My other Wikipedia user pages

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English Wikiversity statistics
At , July, 2024 (UTC): pages,  articles,  files,  users &  admins; version

 * At 08:44, Jan 16, 2007 (UTC): 19,712 pages, 1,526 articles, 750 files, 5,387 users & 14 admins; version 1.10alpha (r19302)
 * At 09:05, Oct 16, 2007 (UTC): 40,731 pages, 5,730 articles, 3,253 files, 14,594 users & 22 admins; version 1.12alpha (r26409)

title: User:BlankVerse


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User talk:BlankVerse

BlankVerse 12:52, 21 August 2006 (UTC)

You can contact me at WikiPedia:User talk:BlankVerse. BlankVerse 12:52, 21 August 2006 (UTC)

title: User talk:BlankVerse


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Wikiversity:Courses

There is nothing that prevents Wikiversity participants from leading and attending "courses" within Wikiversity. Wikiversity participants will do what they think is best for the project, and for many people education implies "courses". However, conventional courses typically imply certified teachers at accredited institutions in classes that exist for a specified duration and including a fixed group of students who are graded and earning credits towards a degree. Wikiversity does not have conventional courses. At best, Wikiversity can have non-conventional "wiki-courses".

Outside the Wikiversity context

 * Hierarchical meaning: a course can denote a learning object with a large level of granularity. That means it is relatively large and consists of many learning objects with smaller granularity. Depending on the nomenclature being used, smaller units at the next level might be "lessons", "modules" or "sessions", but other terms could also be used. In some educational institutions, "modules" have larger granularity than "courses" - i.e. one module may contain more than one course. A course in this sense is typically delivered over a period of time, with its constituent units being delivered at particular points during that period.
 * Evaluative meaning: the word "course" may also emphasize the evaluative side of education. Institutions of higher education may attach credit points, grades or other systems of evaluation to courses. However this is not always the case. Sometimes modules are the unit for evaluation, and sometimes stand-alone examinations which have no direct association with any particular course.

Inside the Wikiversity context
Within Wikiversity, the word "course" only has a hierarchical meaning (see WV:policy proposal on structural nomenclature). The Wikimedia board has explicitly guided Wikiversity away from offering courses which include Wikiversity-offered evaluations coupled to earning credit towards a degree.

A possible exception might be when the evaluative component is in fact provided by an accredited educational institution which explicitly makes use of a specific Wikiversity course. Such an arrangement might allow students to use Wikiversity as a medium for providing course content for use by a credit-awarding institution. Note: this is hypothetical; however courses at real institutions do seem to have made use of Wikiversity as a space for sharing some of their work.

Where are the courses?
The wiki user interface is not well-suited for conventional courses and the Wikimedia Foundation Board of Trustees has directed the Wikiversity community away from courses (the Board's comments). Wikiversity participants are encouraged to innovate and create learning experiences that take full advantage of the wiki format for online community interactions. Non-traditional Learning Projects and other projects oriented towards learning about conventional course subjects are encouraged within Wikiversity. See: Learning.

There is danger in using the word "course" in the names of Wikiversity pages. Visitors to Wikiversity are likely to assume that "course" means conventional course. It is better to not include "course" in Wikiversity page names. You can describe a Wikiversity learning project as a "non-conventional course" when you are describing the features of a "wiki course".

title: Wikiversity:Courses


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Add a description of this department here. If possible, it's probably also good to relate this department to other departments, schools, and/or portals within Wikiversity.

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Wikiversity talk:Main Page/Design

Previous discussion of 1st new design moved to Wikiversity talk:Main Page/Design 1

General comments about design can be discussed here or on the Main talk page.

title: Wikiversity talk:Main Page/Design


text:
User talk:Trevor MacInnis/MainPage

Hey, I like this a lot - much friendlier. There are little tweaks all over the place (like overlapping boxes, and links i would change) but, overall, I like it. Cormaggio 15:06, 21 August 2006 (UTC)
 * Yeah, it involves some knowlege of CSS, and mine is very limited, but I'll try to clean a few things up. Any suggestions on what to put where? What should have its own box and what should go in the sidebar? - Trevor MacInnis 15:12, 21 August 2006 (UTC)
 * I'm not sure anything here should go in the sidebar - I'd keep everything in place (maybe change a few links here and there, but that's rather trivial). The main thing is the right hand side boxes are overlapping with the top and left hand side boxes - this needs to be fixed. And for what it's worth, I'm told that the top-right of a page is where the eye goes first - so maybe there needs to be something here about the content of Wikiversity? Like in Wikipedia, for example, where you can find a link to the various subject portals, perhaps? Thanks for working on this, though :-). Cormaggio 15:36, 21 August 2006 (UTC)
 * 'k, think I've fixed the overlapping (just a note, I'm not sure if its part of what you meant but the right side should overlap the orange header) - Trevor MacInnis 15:48, 21 August 2006 (UTC)

upper right overlap
The two different colors still overlap when I browse with FireFox on my Mac. --JWSchmidt 23:05, 21 August 2006 (UTC)
 * Same problem with Safari browser. --JWSchmidt 23:07, 21 August 2006 (UTC)

 * Sorry, but just to clarify, the blue column on the right is intended to overlap the orange headerbox. The small area where the two intersect forms a separate area for information, in this case I've put some main categories (Category:Engineering and Technology, etc), but pretty much anything can go there (originally I had a second search box and article count there). - Trevor MacInnis 23:17, 21 August 2006 (UTC)

 * I suppose most people viewing the page will be young and have good eyesight. Personally, I need all the help I can get. I prefer the highest contrast possible for text. Personal preference: stick with something like Main Page. If there is large amounts of text on a colored background, do something like make the text bold so that it shows up. --JWSchmidt 00:19, 22 August 2006 (UTC)

 * I've used more muted colors, is that any better? - Trevor MacInnis 15:09, 22 August 2006 (UTC)

I didn't know the right hand box was meant to overlap with the top one - I don't really like that design, personally. Also the right-hand side box overlaps with the globe icon (in my browser - Safari). On a positive note, I like the move of the sister projects to the bottom of the page - that's better. Cormaggio 10:05, 23 August 2006 (UTC)

 * Yeah the globe icon was altered to do that too, see:[[Image:Browser.jpg]]. There are a bunch of them you can see in use at the Italian Wikipedia Main Page. - Trevor MacInnis 14:03, 23 August 2006 (UTC)

I've been an outspoken critic of the Italian Wikipedia's new main page design (which I did convince them to improve slightly), and I'm not a fan of this design either (no offense). The current version is rather plain, but it's entirely usable. In this proposed design, the layout and content are virtually identical, but everything is jarringly over-styled. To me, it makes the page seem less inviting and more difficult to read. Also, as explained in this discussion, displaying the date and time on a relatively static page (one that isn't edited often) doesn't work well (due to caching). —David Levy 01:59, 24 August 2006 (UTC)

Possible design adjustments
In context of the above criticism by David Levy: I think this design can be more friendly than the current bland front page. Trevor, while I do find this design rather busy in first version and just a little busy now, your responsiveness to comments and skill makes me trust that it is ready to go to the front page and develop nicely.

While keeping the design elements similar as they are now, here a couple of possibilities for improvement (and you might want to try this is in a second sandbox page):
 * change the center column green color to the same tan color on the sides.
 * eliminate the extra layer of blue background that "shadows" the middle column boxes
 * make all box lines thinner and perhaps as thin as on the main page to go with the side bar thin lines
 * make some of the text just a little less bold
 * the date time could go -- a little graphic could go there as holder for some neat future function (unless one is thought up).
 * just for looksee, if you do a second page, you could try reintroducing a little bit of curve at the main box corners, but only as much as on the left sidebar - a hint. I realized earlier that it was not the presence of rounding but the larger amount of it in previous design that seemed to be off.

The edits I made recently were in attempt to eliminate minor problems and help the page go through community review. If you don't like them, please revert. Reswik 02:41, 24 August 2006 (UTC)

Thanks!
- Thanks for the great design, hope it gets implemented soon. Keep up the good work! Rayshan 14:32, 24 August 2006 (UTC)

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Topic talk:Department of Sociology

Links for Wikibooks not yet created
These links don't seem to be needed on the front page, so saving the list here:

To be developed:
 * Contemporary Social Issues
 * Delinquency and Crime
 * Demography
 * Environmental Sociology (or Human Ecology)
 * Gender Stratification
 * Global Inequality
 * History of Sociology
 * Medical Sociology
 * Organizational Sociology (or Industrial Sociology)
 * Race & Ethnicity
 * Social Class
 * Social Policy
 * Social Movements
 * Urban Society

title: Topic talk:Department of Sociology


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Basic thermodynamics

Part of the School of Physics

''This class provides a basic overview requiring very little prior mathematical knowledge besides basic algebra. For a more involved discussion of thermodynamics which includes detailed derivations of these laws from first principles, please see the class page Statistical mechanics.''

Thermodynamics is the study of temperature, chemical energy, and the properties of matter as a consequence of its atomic structure. In the discipline of thermodynamics, two areas of interest are most significant: macroscopic thermodynamics, which deals with the properties of bulk matter; that is, large quantities of matter on a 'human' scale of understanding, and statistical mechanics, which relates the macroscopic behavior of matter to microscopic behavior.

Heat and Temperature
First of all, we must make clear some important definitions which may be different to the kind of language you are used to. In normal conversation, the words heat and temperature are used interchangeably. To 'warm' or 'heat' something up is to increase its temperature. One might say 'that fire has a lot of heat in it'.

In physics however, the word heat has a very distinct meaning. Heat is a form of energy which is held in matter by the constant jostling of its particles. In macroscopic thermodynamics, heat can be thought of as a massless, invisible substance that can flow from one region to another, but it is very important to remember that this is NOT a real or accurate description of heat, merely a tool to help you visualise how matter and the energy contained within it behaves in the 'real world' as we see it. In reality, heat is an effect of the movement of particles - whether they be atoms, ions, molecules, electrons, photons or any kind of fictional 'magic' particle you could care to imagine. Particles transfer heat between one another by colliding with one another, and over time this will cause heat to flow around in large bodies of matter where it allowed to.

Heat is represented in a formula by the symbol Q, and its units, like other forms of energy, are Joules, which have the symbol J

Example: The amount of heat in an object is measured in an experiment to be ten Joules; so we would write this result as Q = 10J

Temperature, on the other hand, is one of a number of measurements we can make, called thermodynamic variables, of real systems that we study using the laws of thermodynamics.

Thermodynamic variables
Thermodynamic variables are those properties of a real system which can be observed by simple apparatus on a scale that can be readily understood by human beings. These contrast with statistical variables which by and large are estimations and inferred quantities relevant to the atoms within a material, whose existence is not relevant to macroscopic thermodynamics. At this point we make no hypothesis whatsoever on the nature of the material itself, as the laws of macroscopic thermodynamics are concerned only with large quantities of (usually) homogenous matter.

Temperature
Temperature is an physical measurement expressing how much heat is present within a substance. Temperature is measured with a thermometer calibrated to one or more temperature scales. Three temperature scales are Fahrenheit, Celsius and Kelvin.

States and State Diagrams
When physicists talk about the state of a thermodynamic system, what they mean is that the system has precise or 'well-defined' thermodynamic variables. That is to say, the system's pressure, volume and temperature are fixed at that point in time - we call this an equilibrium state. Only equilibrium states can be studied with basic thermodynamics - states where these variables are not changing at this precise moment in time. If these properties are changing, it no longer makes any sense to say that the system has a particular temperature, because energy will be moving around the system in ways that cannot be precisely measured. Similarly with pressure and volume; these cannot be precisely defined for a changing system because not every particle in the system is 'aware' of their current value, and certain areas of the system may behave as though the system has different pressure and volume.

Therefore, if we want to study a system which we know is changing in time, we must consider it to be a succession of equilibrium states - we pretend that instead of changing smoothly, the system jumps instantaneously between very many slightly different equilibrium states as it goes from its initial state to its final state.

The state diagram
It follows from the above statements that if a system has precisely defined thermodynamic variables, they can be plotted on a graph. An example, the P-V diagram, is shown below:

Source:

Source:

The Gas Laws
The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. It is a loose collection of rules developed between the late Renaissance and early 19th century. Early gas laws were:
 * Boyle's law - the product of the volume and pressure of a fixed quantity of an ideal gas is constant, given constant temperature
 * Charles's law - at constant pressure, the volume of a given mass of a gas increases or decreases by the same factor as its temperature increases or decreases
 * Gay-Lussac's law - the ratio between the combining volumes of gases and the product, if gaseous, can be expressed in small whole numbers

These were combined to form the combined gas law:

 * $$\frac {P_1V_1} {T_1} = \frac {P_2V_2} {T_2}$$

Avogadro's law (1811) surmises that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. All four laws were generalized into a the simplified ideal gas law:

 * $$\qquad\qquad P V = n R T$$

where:
 * P is the pressure in pascals
 * V is the volume in cubic metres
 * n is the number of moles of gas
 * R is the ideal gas constant (8.3145 J/(mol K))
 * T is the temperature in kelvins.

The Ideal Gas
The Ideal Gas is a simple model for a gas derived from the gas laws above. The Ideal Gas Equation relates pressure, temperature and volume in all possible combinations for a model gas which has the following properties, making it unlike the 'real' thing:
 * The particles in the gas have no size
 * The particles in the gas do not interact - that is, they cannot 'bounce off' one another, only the walls of the container, and do not exert any forces on one another

As a consequence of these points, further properties emerge that are still important in themselves:
 * The gas never changes phase (never liquefies or alters its properties) and cannot chemically react

The Ideal Gas is described by a single equation:

PV=NRT

Where:
 * P=Pressure in Pascals (Pa)
 * V=Volume in cubic metres (m^3)
 * T=Temperature in Kelvin (K)

N is the number of moles of gas in the volume R is a constant, the Molar Gas Constant. This is not important to know the details of at this stage, except that is approximately equal to 8.31

From this equation, we note that the product PV is directly proportional to T. This tells us the following about the behavior of gases:
 * If the temperature of the gas remains constant, either P or V can increase provided that the other decreases by the same proportion; you could double the pressure while halving the volume and not change the temperature of the gas, for example
 * If T changes, there are many combinations of P and V that can achieve this. To raise the temperature of the gas you can increase the pressure, decrease the volume, or change both at the same time and achieve the same temperature increase.

We also note that it would in theory be possible to alter the state of the gas by changing the number of particles, N. This is possible, but adding or removing particles involves manipulating chemical potentials, which are part of Statistical Mechanics and rather too complex for this lesson.

Exercise
Consider a sealed box of gas at atmospheric pressure (300 kPa) and room temperature (293 K). The gas is heated by a flame until its temperature is 400K. Calculate the change in pressure, $$\delta P$$. (Click expand for the worked answer)

Book list and study hints
Statistical mechanics

title: Basic thermodynamics


text:
Cell Biology/JWSchmidt

Pep Talks and Orientation
Currently (just starting out!) there is only one person, John Schmidt, who has been working on this Wikiversity learning resource. John Schmidt has a Ph. D. in pharmacology and has published original research in journals such as
 * Cell
 * Journal of Cell Biology
 * The Journal of Biological Chemistry

Review Article in the area of Cell Biology

 * Seminars in Cell Biology

Teaching Experience
John Schmidt has taught biology courses at the undergraduate and graduate levels including: Introductory Biology, Biochemistry, Developmental Biology, Cell Biology, Neurobiology, Physiology and Microbiology.

Education Philosophy
There are a few things people want to know: We can make use of the tools of science to explore these issues as we work towards a coherent and unified understanding of the human condition. A good way to learn science topics is to start with the question about the world that most puzzles you. Wikiversity participants can be a guide to help a student take that first step on their personal journey of learning and then provide help as that journey continues on through the entire scope of human knowledge.
 * Who we are
 * Where we come from
 * Where we are going
 * How to get there

Research Interests

 * The role of synaptic adhesion proteins in learning and memory
 * The role of dis-regulated cell adhesion in cancer
 * Mathematical models of neuronal networks

Contact me
If you have a question about cell biology, leave a message at my user talk page.

title: Cell Biology/JWSchmidt


text: Category:Cell biology subpages

title: Category:Cell biology subpages


text:
User:Bhadani

Bhadani'' He is an administrator of English Wikipedia

title: User:Bhadani


text:
User talk:Bhadani

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional editing help.

You will find more resources at the Community Portal. If you want to ask a question, visit the Study help desk, the Colloquium, IRC channel or ask me personally on my talk page.

Good luck! --HappyCamper 16:34, 21 August 2006 (UTC)

title: User talk:Bhadani


text:
User talk:V2os~enwikiversity

Re: C++
Hello V2os, just wanted to say I agree with your comments regarding the C++ resource on wikiversity. Would you assist me in perhaps developing the resource the way it is intended? i.e. as a hands-on tool rather than providing the user with the theory behind C++.

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 V2os. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name V2os~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:10, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:24, 19 April 2015 (UTC)

title: User talk:V2os~enwikiversity


text:
User talk:Pbolgiani

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional editing help.

You will find more resources at the Community Portal. If you want to ask a question, visit the Study help desk, the Colloquium, IRC channel or ask me personally on my talk page.

Good luck! Trevor MacInnis 17:28, 21 August 2006 (UTC)

title: User talk:Pbolgiani


text:
Talk:Naming conventions/Network naming conventions

Votes

 * Reswik 17:34, 21 August 2006 (UTC)

Comments
There are two issues to consider in the current naming proposal: structural and linguistic. I think that this naming system is simpler than the structural aspects of the naming convention proposal and that the language used in the network proposal could invite more creativity in study areas and networking amongst them. In practice, it seems the structural proposal (divisions/subdivision/departments/etc) brings focus onto presenting extra unnecessary departmental structural elements which will detract from focusing quickly on developing learning resources and projects. A networking approach and language could invite a less territorial approach and more collaborative atmosphere to co-creating content. See discussion here for more points:. Reswik 17:39, 21 August 2006 (UTC)


text:
Wikiversity:Network naming conventions

To keep pages of different varieties organized on Wikiversity, a series of naming conventions has been suggested.

This page is proposed as an alternative to the Naming conventions page.

This page proposes a simplified three-level network system for the organization of all Wikiversity content, the network level elements being: school, area and learning project.

For anything not covered on this page, use Wikipedia conventions. Wikiversity has just a few schools. Wikiversity has many topics. A Wikiversity topic can be an area or space or field or sub-field.

Schools
Schools are part of a three-level system for the organization of Wikiversity content.

Schools on Wikiversity are content development projects that organize the efforts of many topic areas. Schools can promote collaboration between Wikiversity participants who are interested in related topics. Some schools at Wikiversity are large organizational units such as life sciences. The main page for schools should link to their smaller study areas. A school does not contain other schools.

More than one Wikiversity school can 'contain' the same topic. Those schools should cooperate to develop the topics that they have in common.

Groups of topics may form interdisciplinary units.

The name for a school page always starts with the School: prefix. For example, School:Life Sciences.

The main page for each Wikiversity school can be started with Template:School boilerplate.

Topic namespace
"Topic" is a generic term at Wikiversity; pages in the Topic: namespace can serve as content development projects for narrow academic topics (similar to Wikipedia "wikiprojects". The "Topic" namespace is for organization of the work of Wikiversity content producers. The names of topic pages always start with the "Topic:" prefix. Example of a topic page: Topic:Cell Biology.

"Topic:" pages can be called "Departments", "Center", "Divisions" or any other term desired by those collaborating in that topic area.

The main page for each Wikiversity department can be started with Template:Department boilerplate.

Learning resources
Learning resources are the lowest level in the hierarchy. Two types of learning resources are lessons and research projects. Lessons and research projects are placed into pages in the main namespace (these page names have no prefix). Learning resource pages are linked to from areas.

More than one Wikiversity "Topic:" page can 'contain' (link to) the same learning resource; content development projects should cooperate to develop the learning resources that they have in common.

Note: learning resources are of two main types, "materials" and "projects"; see Portal:Learning Projects.

Lessons
Lessons are common elements in Learning Resources.

Course numbers should not be used to indicate the name of a lesson. The name of a lesson should describe the topic being taught, so instead of saying "Wiki 101", the name of the lesson should be "Introduction to Wiki". Lesson pages are defined as "main namespace pages that serve to be read and to educate and provide information."

Lessons should be linked to from "Topic:" pages and portal pages. Each lesson should have a unique title, for example The rise of the Roman Empire and The Fall of Rome.

Research projects
Research projects are pages in the main namespace as well, only involve collaborative research to achieve a certain goal. Research projects are one type of Wikiversity learning project.

title: Wikiversity:Network naming conventions


text:
Wikiversity talk:Network naming conventions

Votes

 * Reswik 17:34, 21 August 2006 (UTC)

Comments
There are two issues to consider in the current naming proposal: structural and linguistic. I think that this naming system is simpler than the structural aspects of the naming convention proposal and that the language used in the network proposal could invite more creativity in study areas and networking amongst them. In practice, it seems the structural proposal (divisions/subdivision/departments/etc) brings focus onto presenting extra unnecessary departmental structural elements which will detract from focusing quickly on developing learning resources and projects. A networking approach and language could invite a less territorial approach and more collaborative atmosphere to co-creating content. See discussion here for more points:. Reswik 17:39, 21 August 2006 (UTC)

 * The School>Division>Departmentt>Learning Project hierarchy is just an organizational tool that grew from the needs of the Wikiversity community. During the first few days of Wikiversity, different people were using contradictory categorizations of conventional academic subjects, leading to conflicts. People who are familiar with traditional academic disciplines are going be arriving at Wikiversity in search of pages related to a particular topic of study that they are interested in. They will be able to make use of an easy to navigate hierarchical system that can lead them to the relevant Wikiversity pages. I agree that we want to free Wikiversity participants from the restrictions of conventional categorizations. We are free to create new portals in the "Portal:" namespace. Learning materials can be arranged into any imaginable categories. Groups of related pages in a category can be called an "area", a "faculty", a "college", an "institute", a "program" or anything that you want. Right now we only have a few portals such as Portal:Learning Projects. Each category for an "area", a "faculty", a "college", an "institute" or a "program" can have its own portal. --JWSchmidt 18:41, 21 August 2006 (UTC)


text:
User:JWSchmidt/Sandbox

 * MediaWiki:Sitenotice
 * Wikiversity Reports/rss

other subpages

 * Category:Import backups

Introduction

 * User:JWSchmidt/Introduction
 * Template:Please leave this line alone
 * User:JWSchmidt/Introduction edit
 * Template:Please don't change this page
 * User:JWSchmidt/Introduction explore
 * Template talk:Please don't edit this page

more subpages

 * User:JWSchmidt/Protection
 * User:JWSchmidt/Portal
 * User:JWSchmidt/main page images
 * Category:Import backups
 * User:JWSchmidt/Sociology
 * User:JWSchmidt/links
 * User:JWSchmidt/Semantic prosthetic
 * User:JWSchmidt/history
 * User:JWSchmidt/Blog
 * User:JWSchmidt/Wikiversity:Main Page/Content

Introduction
Need a page for how to do citations and reference lists
 * User:JWSchmidt/Introduction
 * Template:Please leave this line alone
 * User:JWSchmidt/Introduction edit
 * Template:Please don't change this page
 * User:JWSchmidt/Introduction explore
 * Template talk:Please don't edit this page

Wiki Scholar

 * User:JWSchmidt/Wiki Scholar

title: User:JWSchmidt/Sandbox


text:
Help:Bugs

Note: Please don't place actual bug reports here. All software issues and site configuration requests need to be posted at the Wikimedia BugZilla installation, which can be found at http://bugzilla.wikimedia.org.

Found a bug?
This web site is powered by the MediaWiki software, which is the same product that runs our sister projects, Wikipedia, Wikinews, etc. and the Wikimedia Commons. For precise details on what's in use, see the version information.

As with all software, it is quite possible that there are several undiscovered and/or unresolved issues in MediaWiki which might interrupt use of the site at a particular time. If you discover a bug, it's extremely helpful to report it on our bug tracker. Once a report has been filed, the development team can begin to track and address the issue.

Before reporting a bug

 * 1) Check that it's a bug. Make sure that the problem can be reproduced under the same conditions.
 * 2) Check that it's not a known issue. Search the bug tracker using the search tool to avoid posting duplicate bugs.
 * 3) Gather the required information. We'll need to know where the bug happened, what happened (and when it's not obvious, why this is the wrong behaviour) and how to reproduce the problem for ourselves. If the problem requires a particular platform and operating system to reproduce, include this in the report - and make sure you select it when entering the bug.

When reporting a bug
When reporting an issue, provide as much detail as possible, and keep it relevant to the problem. If more than one problem is encountered, and the two are not related, please open separate bug reports for each.

For advice on effectively communicating problems, the following resources might be useful:

 * BugZilla Bug-Writing Guidelines
 * "How to Ask Smart Questions"; a useful guide for communicating problems to technical people
 * "How to Report Bugs Effectively"; an excellent guide on what to include in a bug report

After reporting a bug
Once the bug has been filed, the core developers and other subscribers to the wikibugs-l mailing list will receive email summarising the bug, and several things could happen.

 * One or more fields might be changed to categorise the bug in a more effective manner
 * A developer might assign the bug to themselves
 * The bug might be resolved INVALID or WORKSFORME
 * You might be asked to provide further details of the problem
 * The bug might be resolved FIXED

As the bug reporter, BugZilla will ensure that you are emailed whenever the bug status changes (the aforementioned mailing list also receives such messages) so that you can see what's happening to your bug.

A good percentage of bugs are addressed within a week, and it's not uncommon to spot a bug being corrected a short time after it is reported. More involved reports might be placed on the "back burner" to await further improvements.

title: Help:Bugs


text:
Blender

'''This course isn't complete, it needs some students to enroll to make sure the material written is effective, and in proper order. Please add yourself to the enrolled students section if you are interested.'''

About this Course

This course will guide you through learning how to use Blender to create your own models, animations, games, and more. It will eventually be composed of 15 weeks worth of learning material that will help you develop your skills. It is strongly reliant on the documentation found in Blender 3D: Noob to Pro as it is already a valuable resource that has been proven to help quickly advance skills in Blender.

Learning Challenges Objectives:

To first learn the basics of using the complex blender user interface and basics of 3D computer graphics using learning materials already available. Then to make available a series of challenges - gradually increasing in complexity - that allow the reader to learn how blender can be used creatively to produce astonishing graphics.

Syllabus
/Week 1/ - Learn about 3D modelling in general and become familiar with the Blender interface.

/Week 2/ - Adventure further into the blender interface. Learn how to model a house and a simple person.

/Week 3/ - Use modifiers to create a hat for your simple person. Learn about materials, textures, and halos.

/Week 4/ - Become familiar with how Blender organizes data. Model multiple objects to learn about modifiers and other tools.

/Week 5/ - Randomize size, color and position to make a virtual world look realistic

Related resources

 * Get Blender here
 * Blender for Game Graphics and Animation
 * Blender 3D at Wikibooks An extensive learning trail was established there while waiting for Wikiversity to get authorization to proceed.  It is still pretty active.
 * 3D Modelling

/External resources/ - This is a large list of Helpful tutorials, models, textures, and much more. It has been moved to its own page so that it will all fit. Please don't overlook this for information!

title: Blender


text:
Introduction to Calculus/Differentiation

Resources
Wikibooks entry for Differentiation

Prelude
Arithmetic is about what you can do with numbers. Algebra is about what you can do with variables. Calculus is about what you can do with functions. Just as in arithmetic there are things you can do to a number to give another number, such as square it or add it to another number, in calculus there are two basic operations that given a function yield new and intimately related functions. The first of these operations is called differentiation, and the new function is called the derivative of the original function.

This set of notes deals with the fundamentals of differentiation. For information about the second functional operator of calculus, visit Integration by Substitution after completing this unit.

Before we dive in, we will warm up with an excursion into the mathematical workings of interest in banking.

Compound Interest
Let us suppose that we deposit an amount $$A_0$$ in the bank on New Year's Day, and furthermore that every year on the year the amount is augmented by a rate $$r$$ times the present amount. Then the amount $$A$$ in the bank on any given New Year's Day, $$t$$ years after the first is given by the expression

 * $$A=A_0(1+r)^t\,\!$$.

Unfortunately, if we withdraw the money three days before the New Year, we don't get any of the interest payment for that year. A fairer system would involve calculating interest $$n$$ times a year at the rate $$r/n$$. In fact this gives us a slightly different value even if we take our money out on a New Year's Day, because every time we calculate interest, we receive interest on our previous interest. The amount $$A$$ we receive with this improved system is given by the expression

 * $$A=A_0\left(1+\frac{r}{n}\right)^{nt}.$$

With this flexible system, we could set $$n$$ to $$12$$ to compound every month, or to $$365$$ to compound every day or to about $$31536000$$ to compound every second. But why stop there? Why not compound the interest every moment? What is really meant by that is this: as we increase $$n$$ does the value for $$A$$ get ever greater with $$n$$ or does it approach some reasonable quantity? If the latter is the case, then it is meaningful to ask, "What does $$A$$ approach?" As we can see from the following table with sample values, this is in fact the case.

! colspan="2" | $$A_0=1$$, $$r=.025$$, $$t=1$$
 * $$n$$
 * $$A$$
 * 1
 * 1.02500
 * 12
 * 1.02529
 * 365
 * 1.02531
 * 31536000
 * 1.02532
 * 100000000
 * 1.02532
 * 31536000
 * 1.02532
 * 100000000
 * 1.02532
 * 1.02532
 * }

As we can see, as $$n$$ goes off toward infinity, $$A$$ approaches a finite value. Taking this to heart, we may come to our final system in which we define $$A$$ as follows:

 * $$A=\lim_{n\rightarrow \infty}A_0\left(1+\frac{r}{n}\right)^{nt}.$$

Thus we set $$A$$ now not to $$A_0\left(1+\frac{r}{n}\right)^{nt}$$ evaluated for some large $$n$$, but rather to the limit of that value as $$n$$ approaches infinity. This is the formula for continually compounded interest. To clean up this formula, note that neither $$A_0$$ nor $$t$$ "interfere" in any way with the evaluation of the limit, and may consequently be moved outside of the limit without affecting the value of the expression:

 * $$A=A_0B^t\,\!$$,

where

 * $$B=\lim_{n\rightarrow \infty}\left(1+\frac{r}{n}\right)^n.$$

We can see from the form of the expression that $$A$$ increases exponentially with $$t$$ much as it did in our very first equation. The difference is that the original base $$(1+r)$$ has been replaced with the base $$B$$ which we have yet to simplify.

Take a moment to step back and do the following exercises:
 * 1) Without looking back, see if you can write down the expressions that represent
 * 2) *yearly interest
 * 3) *semiannual interest
 * 4) *monthly interest
 * 5) *interest $$n$$ times a year
 * 6) *continually compounded interest
 * 7) Think about how much money you have. Figure out how long you would have to leave your money in a bank that compounds interest monthly before you became a millionaire, with a yearly interest rate of
 * 8) *.02 (common for a savings account)
 * 9) *.07 (average gain in the US stock market over a reasonably long period).

Finding the Base
In order to shed some light on the expression whose value we call $$B$$, we shall make use of the following expansion, known as the Binomial Theorem:
 * $$(a + b)^n = a^n + na^{n-1}b + \frac{n(n-1)}{2}a^{n-2}b^2 + \dots + \frac{n(n-1)(n-2)\dots(n-(k-1))}{k!}a^{n-k}b^k + \dots + nab^{n-1} + b^n.$$

By applying it to our limit, we get

 * $$B=\lim_{n\rightarrow \infty}\left(1+\frac{r}{n}\right)^n = \lim_{n\rightarrow \infty}\left(1+n\left(\frac{r}{n}\right)+\frac{n(n-1)}{2}\left(\frac{r}{n}\right)^2

+\frac{n(n-1)(n-2)}{3!}\left(\frac{r}{n}\right)^3 + \dots\right) =1+r+\frac{r^2}{2}+\frac{r^3}{3!}+\frac{r^4}{4!}+\dots$$.

This last step may seem mystifying at first. What happened to the limit? And where did all of the $$n$$'s go? In fact it was the evaluation of the limit that allowed us to remove the $$n$$'s. More exactly, as $$n\rightarrow\infty$$, so too $$n(n-1)\rightarrow n^2$$, $$n(n-1)(n-2)\rightarrow n^3$$, etc., so that the top left and bottom right of each term cancel to produce the last expression.

Take a moment to look over the following exercises. Take the time to follow the trains of thought that are newest to you.

The Birth of e
Now comes a real surprise. As it turns out, the infinite polynomial above is in fact exponential in $$r$$. That is, $$B = 1+r+\frac{r^2}{2}+\frac{r^3}{3!}+\frac{r^4}{4!}+\dots = b^r$$, for some $$b$$. In order to show this far-from-obvious fact, I offer the following.

 * $$1+r+\frac{r^2}{2}+\frac{r^3}{3!}+\frac{r^4}{4!}+\dots = \lim_{n\rightarrow \infty}\bigg(1+nr\bigg(\frac{1}{n}\bigg)+\frac{nr(nr-1)}{2}\bigg(\frac{1}{n}\bigg)^2

+\frac{nr(nr-1)(nr-2)}{3!}\bigg(\frac{1}{n}\bigg)^3 + \dots \bigg)$$

 * $$ = \lim_{n\rightarrow\infty}\bigg(1+\frac{1}{n}\bigg)^{nr} = \Bigg(\lim_{n\rightarrow\infty}\bigg(1+\frac{1}{n}\bigg)^n\Bigg)^r = \bigg(1+1+\frac{1}{2}+\frac{1}{3!}+\frac{1}{4!}+\dots \bigg)^r$$

To this last infinite series of numbers, define the quantity to be $$e$$:

 * $$e=1+1+\frac{1}{2}+\frac{1}{3!}+\frac{1}{4!}+\dots$$.

$$e$$, an irrational (and in fact transcendental) number, has the approximate value 2.71828, which you may easily verify on a standard pocket or graphing calculator.

There are a few things to think about.
 * 1) The first line in the preceding derivation was motivated by my knowledge of the outcome.
 * 2) Convince yourself that the two expressions are in fact equal to one another.
 * 3) *Evaluate the term $$\frac{nr(nr-1)(nr-2)}{3!}\bigg(\frac{1}{n}\bigg)^3$$ for $$r=.02$$ and $$n=10000$$. How does that compare to $$\frac{r^3}{3!}$$? How about with $$n=10000000$$?
 * 4) Now that you have convinced yourself that I may do it, ask yourself why I would do it.
 * 5) *Using the reverse Binomial Theorem, do you understand how it leads to the next expression?
 * 6) Is the equation $$1+r+\frac{r^2}{2}+\frac{r^3}{3!}+\frac{r^4}{4!}+\dots = \bigg(1+1+\frac{1}{2}+\frac{1}{3!}+\frac{1}{4!}+\dots\bigg)^r$$ something that one would predict merely from the rules of exponents or distribution?
 * 7) What makes certain seemingly uninteresting numbers so profoundly central to mathematics, such as $$0$$, $$1$$, $$\pi$$, and $$e$$?

Back to the Start
From here, everything cascades back to our original goal, namely to find a usable formula for continually compounded interest. $$B = e^r \rightarrow A=A_0(e^r)^t \rightarrow A=A_0e^{rt}$$. And there she is.

Take a moment to do the following exercises.
 * 1) Think about how much money you have. How long will it take to become millionaire if you leave the money in a bank with yearly interest of .025
 * 2) *that compounds interest yearly?
 * 3) *that compounds interest continually?
 * 4) Seeing as the values with and without continually compounded interest are very close to one another, what does that tell you about the two equations used?
 * 5) *Both formulas are of the form $$A=A_0($$_____$$)^t$$. Compare the various values that we have put in this blank, especially the in the equations for yearly and continually compounded interest.
 * 6) *How close in value is $$(1+r)$$ to $$e^r$$? Does that surprise you?
 * 7) *Now look at the infinite series version of the function $$e^r$$. Does it still surprise you that $$(1+r)$$ and $$e^r$$ are so close in value?

Commentary
The formula itself, however, is quite forgettable. In fact, as you may have guessed, the importance of compounded interest pales in comparison to the importance of the ideas we stumbled upon on the way, namely limits and $$e$$. It is these two things that beg for us to go further into the heart of the life and being of functions. That wish is called calculus. And it all starts rather innocently with the derivative…

Notion of secant & slope
Imagine a straight line plotted on square graph paper. For the sake of our discussion, suppose this line goes off your sheet of paper on both sides, and keeps going forever. What can you say about this line? Take your page and look at it. A line might be flat, parallel to the bottom of the page. It might be vertical, parallel to the sides of the page. Or it might lie somewhere between these two extremes, not as flat as the first, and not as steep as the second.

The first thing to understand about 'slope' is that it is a measure of steepness. We often measure slope as a ratio. If you drive 30 kilometers in the timespan of one hour, we say your speed is the ratio of distance over time: 30 kilometers per hour. Similarly, the slope is the change in vertical distance over the change in horizontal distance.

How steep is a horizontal line? Draw a horizontal line, and then place one finger on one end of the line. Take another finger and slowly move it along the line. As you change the horizontal distance (as you move your finger from side to side), you will notice that the vertical distance does not change at all- you don't have to move your finger up or down. The change in vertical distance is always 0, regardless of the change in horizontal distance. So the slope is 0/x where x is the change in horizontal distance (you can choose whatever number you want for this), meaning the slope is 0.

Our flat, horizontal line has a slope of zero - nothing happens to the y's whatever you do to the x's, think of cycling in parts of the Netherlands for example.

A line at 45 degrees to the horizontal (half way between vertical (90 degrees) and horizontal (0 degrees)) has a slope of 1 (this would be a brutal hill for cycling, and very tough on foot). As you increase the horizontal distance by one unit, you also increase the vertical distance by one unit. This makes the slope 1/1=1.

Our vertical line is incredibly steep (and much harder to cycle on). The slope is undefined, and as our line gets closer and closer to vertical, the slope gets bigger and bigger without limit.

The second part of slope captures the idea of direction. Look at your line again. As it goes from left to right, does it go up the page, or down the page? If it was a road going up a hill, would it be hard to follow on a bicycle (going up), or very easy (going down)? This is expressed by saying that a line has a positive slope if, as it goes across, it also goes up, (or as the y's increase, the x's also increase). A line has a negative slope if it goes down as it goes across (or as the y's increase, the x's decrease). As a cyclist, you want a negative slope, unless you're in training.

Definition
Given a function $$y = f(x)$$, we define the derivative $$f'(x)$$ to be

 * $$f'(x)=\lim_{h\rightarrow 0}{\frac{f(x+h)-f(x)}{h}}$$.

This definition is motivated by the proportion $$\frac{\Delta y}{\Delta x}=\frac{f(x+h)-f(x)}{h}$$, which for any h defines the slope of a line, when f is linear. Because of the nature of the calculation, the derivative can be figuratively thought of as the ratio between an infinitesimal dy and an infinitesimal dx and is often written $$\frac{dy}{dx}$$. Both functional notation $$\left ( f'(x) \right )$$ and infinitesimal or Leibniz notation $$\left ( \frac{dy}{dx} \right )$$ have their virtues. In operator theory, the derivative of a function $$f$$ is sometimes written as $$D_x f \,\!$$.

 * 1) Using the definition above, what is $$\frac{d(x^2)}{dx}$$?
 * 2) *Note that this is a short way of asking, if $$f(x)=x^2$$, what is $$f'(x)$$? One may also ask, what is $$[x^2]'$$?
 * 3) If you have trouble remembering the definition of the derivative, it's much more important to know what it means, that is, why it's defined how it is. Remember it like this:
 * 4) *$$f'(x)=\frac{dy}{dx}=\lim_{\Delta x\rightarrow 0}\frac{\Delta y}{\Delta x}=\lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x)-f(x)}{(x+\Delta x) - x}$$.
 * 5) *From this we get the definition as stated above, $$f'(x)=\lim_{h\rightarrow 0}{\frac{f(x+h)-f(x)}{h}}$$.
 * 6) What kinds of functions have derivatives? What would a function need to have, for it not to have a derivative at some point?

Properties
The derivative satisfies a number of fundamental properties

Linearity
An operator $$L$$ is called linear if $$L(f(x)+g(x))=L(f(x)) +L(g(x))$$ and $$L(kf(x))=kL(f(x))$$ for any constant $$k$$. To show that differentiation is a linear operator, we must show that $$[f(x)+g(x)]'=f'(x)+g'(x)$$ and $$[kf(x)]'=kf'(x)$$ for any constant $$k$$.

 * $$[f(x)+g(x)]'=\lim_{h\rightarrow 0}\frac{(f(x+h)+g(x+h))-(f(x)+g(x))}{h}$$

 * $$=\lim_{h\rightarrow 0}(\frac{f(x+h)-f(x)}{h}+\frac{g(x+h)-g(x)}{h})=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} + \lim_{h\rightarrow 0}\frac{g(x+h)-g(x)}{h}=f'(x)+g'(x)$$.

In other words, the differential operator (e.g., $$\frac{d}{dx}$$) distributes over addition.

 * $$[kf(x)]'=\lim_{h\rightarrow 0}\frac{kf(x+h)-kf(x)}{h}=k\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=kf'(x)$$.

In other words, addition before and after doing differentiation are equivalent.

Fundamental Rules of Differentiation
Along with linearity, which is so simple that one hardly thinks of it as a rule, the following are essential to finding the derivative of arbitrary functions.

The Product Rule
It may be shown that for functions f and g, $$[f(x)g(x)]'=f(x)g'(x) + f'(x)g(x)$$. Like the other two rules, this one is not a new axiom: it is directly provable from the definition of the derivative.

$$[f(x)g(x)]' = \lim_{h\rightarrow 0} \frac{f(x+h)g(x+h) - f(x)g(x)}{h} = \lim_{h\rightarrow 0} \frac{f(x+h)g(x+h) - f(x+h)g(x) + f(x+h)g(x) - f(x)g(x)}{h}$$

$$= \lim_{h\rightarrow 0} \left( f(x+h)\frac{g(x+h)-g(x)}{h} + g(x)\frac{f(x+h)-f(x)}{h} \right)$$

$$ = f(x)\left( \lim_{h\rightarrow 0}\frac{g(x+h)-g(x)}{h} \right) + g(x) \left( \lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h} \right) = f(x)g'(x) + g(x)f'(x)$$.

Chain Rule
If a function f(x) can be written as a compound function f(g(x)), one can obtain its derivative using the chain rule. The chain rule states that the derivative of f(x) will equal the derivative of f(g) with respect to g, multiplied by the derivative of g(x) with respect to x. In mathematical terms: $$[ \, f(g(x)) \, ]'=f'(g(x))g'(x).$$ This is commonly written as $$\textstyle \frac{df}{dx} = \frac{df}{dg}\frac{dg}{dx}$$, or more explicitly $$\tfrac{d}{dx}f(x) = \tfrac{d}{dg}f(g(x)) \, \tfrac{d}{dx} g(x).$$

The proof makes use of an alternate but patently equivalent definition of the derivative: $$f'(x) = \lim_{p\rightarrow x}\tfrac{f(p)-f(x)}{p-x}$$. The first step is to write the derivative of the compound function in this form; one then manipulates it and obtains the chain rule.

$$ \begin{align} \left[f(g(x))\right]' & = \lim_{p\rightarrow x}\frac{f(g(p))-f(g(x))}{p-x} \\ & = \lim_{p\rightarrow x} \frac{f(g(p))-f(g(x))}{g(p)-g(x)} \; \frac{g(p)-g(x)}{p-x} \\ & = \lim_{g(p)\rightarrow g(x)} \frac{f(g(p))-f(g(x))}{g(p)-g(x)} \; \lim_{p\rightarrow x} \frac{g(p)-g(x)}{p-x} \\ & = f'(g(x)) g'(x). \end{align} $$

In the third step, the first limit changes from p→x to g(p)→g(x). This is valid because if g is continuous at x, which it must be to have a derivative at x, then of course as p approaches x the value of g(p) approaches that of g(x).

Differentiating a nested function occurs very frequently, which makes this rule very useful.

The Power Rule
We may now readily show the relation $$\frac{d(x^n)}{dx} = n x^{n-1}$$ as follows:

$$\frac{d(x^n)}{dx} = \lim_{h\rightarrow 0}\frac{(x+h)^{n}-x^n}{h} = \lim_{h\rightarrow 0}\frac{(x^n+nx^{n-1}h+\frac{n(n-1)}{2}x^{n-2}h^2+\cdots)-x^n}{h}$$

$$= \lim_{h\rightarrow 0}(nx^{n-1}+\frac{n(n-1)}{2}x^{n-2}h+\cdots)=nx^{n-1}+0=nx^{n-1}.$$

While this derivation assumes that $$n$$ is an positive integer, it turns out that the same rule holds for all real $$n$$. For example, $$\frac{d}{dx}\left[\frac{1}{x}\right]=\frac{d(x^{-1})}{dx}=(-1)x^{-2}=-\frac{1}{x^2}$$.

Take a moment to do the following exercises.
 * 1) Using the $$x^n$$ rule and linearity, find the derivatives of the following:
 * 2) $$x^{14} + 8$$
 * 3) $$3x^2+x^5$$
 * 4) $$\frac{1}{\sqrt{x}}$$
 * 5) What functions have the following derivatives?
 * 6) $$3x^2$$
 * 7) $$15x^{14} + 2x$$
 * 8) $$x^2$$

Exponentials and logarithms
Exponentials and logarithms involve a special number denoted e.

Differentiating ex
Now, recall that

$$e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots.$$

Using the three basic rules established above we can differentiate any polynomial, even one of infinite degree:

$$\frac{d}{dx}e^x = 0 + 1 + \frac{2x}{2} + \frac{3x^2}{3!} + \frac{4x^3}{4!} + \cdots = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \cdots = e^x.$$

$$e^x$$ is the remarkable function that is its own derivative. In other words, $$e^x$$ is an eigenfunction of the differential operator. Which means that the application of the differential operator on $$e^x$$ has the same effect as multiplication by a real number. For example, these concepts are useful in quantum mechanics.

Differentiating ln(x)
The natural logarithm is the function such that if $$e^y=x$$ then $$y=\ln(x)$$; in other words, it is the inverse function of $$e^x$$. We will make use of the chain rule (marked by the brace) in order to find its derivative:

$$y=\ln(x) \rightarrow x=e^y \rightarrow \frac{dx}{dx}=\frac{d(e^y)}{dx} \rightarrow 1=\underbrace{\frac{d(e^y)}{dy}\frac{dy}{dx}}=e^y\frac{dy}{dx}=e^{\ln(x)}\frac{dy}{dx}=x\frac{dy}{dx} \rightarrow \frac{1}{x}=\frac{dy}{dx}=\frac{d(\ln(x))}{dx}.$$

This conclusion, that the derivative of $$\ln(x)$$ is $$\frac{1}{x}$$, is remarkable: it ties together two seemingly unrelated functions. Be careful, this derivative has definite values only when x > 0! (Examine the $$ln(x)$$ to understand why.)

Exponentials
Supppose we have the function

 * $$y = 3^x \,\!$$

To differentiate this, we rewrite this as
 * $$y = 3^x = \left ( e^{\ln 3} \right )^x = e^{x \ln 3}$$

Since $$\ln 3$$ is a constant,

 * $$\frac{dy}{dx} = e^{x \ln 3} \cdot \ln 3 = 3^x \ln 3.$$

In other words, for a constant a, we have

 * $$\frac{dy}{dx} = a^x \ln a $$ whenever $$y = a^x \,\!$$

This re-enforces the special place that $$e$$ has in calculus - it is the unique number for which the constant $$\ln a$$ is precisely equal to one.

Logarithms
Let us differentiate the function
 * $$y = \log_a x\!$$

We already know how to differentiate $$\ln x\!$$, so let's change it into another form with the base e.
 * $$y = \log_a x = \frac{1}{\ln a} \cdot \ln x.$$

Because $$\frac {1}{\ln a}$$ is a constant,
 * $$\frac{dy}{dx} = \frac{1}{\ln a} \cdot \ln' x = \frac{1}{x\ln a}.$$

In conclusion, for any constant a, the derivative of $$\log_a x\!$$ is $$\frac{1}{x\ln a}$$

Implicit Differentiation
Let's suppose that

 * $$y(x) = \frac{x^3 + x^2 + 1}{2x^5 -x^4 +2} $$

One could find $$\frac{dy}{dx}$$ with the quotient rule, but for more complicated functions, it may be better to use what is called "implicit differentiation".

In this case, we take the logarithm of both sides, to obtain

 * $$\ln y = \ln \left ( \frac{x^3 + x^2 + 1}{2x^5 -x^4 +2} \right )

= \ln \left( x^3 + x^2 + 1 \right ) - \ln \left( 2x^5 -x^4 +2 \right )$$

or, in other words, just simply
 * $$\ln y = \ln \left( x^3 + x^2 + 1 \right ) - \ln \left( 2x^5 -x^4 +2 \right )$$

Differentiating the left and right hand side, we get

 * $$\frac{1}{y} \frac{dy}{dx} = \frac{3x^2+2x}{x^3 + x^2 + 1} - \frac{10x^4 - 4x^3}{2x^5 -x^4 +2 }$$

Now, multiply both sides by y, which we know is just $$y(x) = \frac{x^3 + x^2 + 1}{2x^5 -x^4 +2} $$ to obtain the answer:

 * $${dy \over dx} =  \frac{x^3 + x^2 + 1}{2x^5 -x^4 +2} \left ( \frac{3x^2+2x}{x^3 + x^2 + 1} - \frac{10x^4 - 4x^3}{2x^5 -x^4 +2 } \right )$$

which of course can be simplified further. You should verify that this result agrees with the quotient rule. Differentials of logarithms of functions occur frequently in places like statistical mechanics.

General exponentials and logarithms
Consider the function

 * $$y(x) = u(x)^{v(x)} = e^{v(x) \ln u(x)} \,\!$$

It can be immediately seen that

 * $$y'(x) = u^v \left ( \frac{v}{u} \frac{du}{dx} + \ln u \frac{dv}{dx} \right )

= v u^{v-1} \frac{du}{dx} + u^v \ln u \frac{dv}{dx} $$

Compare this result to the chain rule and power rule results. The first term results in treating v constant. The second term results in treating u constant.

Trigonometric functions
Consider the function $$f(x) = \sin x$$. To find the derivative of $$f(x)$$, we use the definition of the derivative, as well as some trigonometric identities and the linearity of the limit operator.
 * $$\lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \dfrac{\sin(x+h) - \sin x}{h} = \lim_{h \to 0}\dfrac{\cos x\sin h + \sin x \cos h - \sin x}{h}$$

 * $$=\lim_{h \to 0} \cos x \dfrac{\sin h}{h} - \sin x \dfrac{1 - \cos h}{h} = \cos x\left[\lim_{h \to 0} \dfrac{\sin h}{h}\right] - \sin x \left[\lim_{h \to 0}\dfrac{1 - \cos h}{h}\right],$$

and since $$\lim_{h \to 0}\dfrac{1 - \cos h}{h} = 0$$ and $$\lim_{h \to 0} \dfrac{\sin h}{h}=1$$, the above expression simplifies to $$\cos x\!$$.

Thus, the derivative of $$\sin x\!$$ is $$\cos x\!$$.

We perform the same process to find the derivatives of the other trigonometric functions (try to derive them on your own as an exercise). Since these derivatives come up quite often, it would behoove (advantageous to) you to memorize them.

$$\dfrac{d}{dx}\sin x = \cos x$$

$$\dfrac{d}{dx}\cos x = -\sin x$$

$$\dfrac{d}{dx}\tan x = \sec^2 x$$

$$\dfrac{d}{dx}\sec x = \sec x \tan x$$

$$\dfrac{d}{dx}\csc x = -\csc x \cot x$$

$$\dfrac{d}{dx}\cot x = -\csc^2 x$$

Hyperbolic functions
The rules for differentiation involving hyperbolic functions behave very much like their trigonometric counterparts, with the notable difference being in the sign of the derivative. Here,

$$\textrm{sinh}(x) = \frac{e^{x} - e^{-x}}{2} $$

$$\cosh(x) = \frac{e^{x} + e^{-x}}{2} $$

so it can be seen that

$$\frac{d}{dx} \sinh(x) = \cosh(x) $$

and $$\frac{d}{dx} \cosh(x) = \sinh(x) $$


text: Category:Program for entrepreneurship

title: Category:Program for entrepreneurship


text:
User:Hypermorphism

Hello there. I am a mathematics major that is interested in all the physical sciences. I was originally going to major in physics until I attempted to study general relativity and got sucked into majoring in mathematics. I found the physicist-types too vague and hand-wavy in their axioms and the more mathematically minded physicists' descriptions too elegant to ignore. :D

title: User:Hypermorphism


text:
User:Sparkles09

I am an Electrical Engineering student at PSU and quickly becoming addicted to wikipedia. I was hoping to use Wikiversity as a supplement to school and hopefully be able to contribute some once I start classes.

title: User:Sparkles09


text:
User:Lazyquasar~enwikiversity

This is a popular pseudonym for user:mirwin who does not use this handle as a sock puppet or for trolling purposes. Political rabble rousing ... now that is a different story. The proper response to "like it or fork it" is "ok, when it suits me.

title: User:Lazyquasar~enwikiversity


text:
User talk:Lazyquasar~enwikiversity

I currently participate at Wikiversity under this account -->> user:mirwin Messages should be placed on the talk page there. This account is reserved primarily for rabble rousing aimed at forks of convenience and to make wiki stalking a bit difficult if I get tired of interacting with self authorized big wheels.

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 Lazyquasar. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Lazyquasar~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:42, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:14, 19 April 2015 (UTC)

title: User talk:Lazyquasar~enwikiversity


text: Category:Wiki business ventures

title: Category:Wiki business ventures


text:
Grants and fundraising/Wikiversity nonprofit corporation

Participants in the Wikiversity NPC project create a nonprofit corporation (NPC) that will produce Wikiversity content.

Learning project
The Wikiversity NPC learning project allows Wikiversity participants to learn how to create and manage a nonprofit corporation. The corporation will be entirely oriented around the use of MediaWiki technology for the promotion of education.

Business plan
The goal of this nonprofit corporation (note, a name for the corporation needs to be selected) is to hire experts who will be employed to produce learning resources for Wikiversity. The corporation will also hire experts to write grant proposals for both itself and for the Wikimedia Foundation. Any profits made by this NPC will be donated to the Wikimedia Foundation.

November 2007. The Wikimedia Foundation has an illustration project designed to allow people to get paid for creation of “key illustrations” that will be used by Wikimedia wiki projects. If the Wikimedia Foundation is able to support this kind of arrangement for Wikiversity, then a new NPC as proposed here will not be needed.

"aiming to see if the general idea -funneling restricted donations to community members for execution- is workable. To the extent that it does work, it could be very powerful." - Sue Gardner

(Note: I doubt that the grant funders will let you do this. Roadrunner 18:40, 7 January 2007 (UTC))

The corporation will be a strictly educational entity with no purpose other than to advance education as made possible by the Wikimedia Foundation's Wikiversity project.

The corporation will engage in commercial activities such as providing the services of certified educators who specialize in teaching by making use of Wikiversity-derived learning resources. Income derived from fees charged for these services will fund grant writing and the creation of new Wikiversity learning resources.

(Note: This is probably not legally possible. Any funds that you make from for-profit activities will be subject to tax, and if it makes up a large fraction of your income, you will lose your non-profit status.  If you are going to engage in any for-profit activity, it is much simpler to simply create a for-profit corporation.

Non-profit law in the United States allows schools and universities to have non-profit status. The trouble is that they have a rather restrictive definition of school (it has to have a formal curriculum. Simply having classes without a curriculum, will not get you that exemption.

Roadrunner 18:40, 7 January 2007 (UTC)

 * The point is not to create a school. The point would be that there could be charges for services provided by the NPC; if there was any money from those charges above the costs of providing the services the money would go into the mission of the NPC, support for the Wikimedia Foundation's Wikiversity project.)

Research
We need to do research into the history and activities of the Wikimedia Foundation and other education-oriented NPCs.

Interested users
The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this project, you can list your name here (this can help small projects grow and the participants communicate better; for large projects a list of active participants is not needed).
 * User:JWSchmidt - I am interested in the Wikiversity NPC project
 * User:CQ - I want to hear and see Wikiversity Internet Audio and Video
 * User:Roadrunner - I manage a 503(c) non-profit at http://www.gnacademy.org/
 * User:Historybuff - I'm helping to set up Wikimedia Canada
 * Dionysios (talk), Founder of the Wikiversity School of Advanced General Studies, Date: 2007-09-25 (September 25, 2007) Time:  2121 UTC
 * Remi
 * User:Sunflower67

I AM interested... I run an NPO in South Africa


text:
User:NCHE1776

The National Council for History Education is a non-profit corporation whose Board of Trustees is dedicated to promoting the importance of history in schools and in society. The Council is supported by the contributions of individuals and organizations. NCHE links history in the schools with many activities sponsored by state and local organizations. We provide a communications network for all advocates of history education, whether in schools, colleges, museums, historical councils, or community groups.

For more information read our mission statement below.

All who teach history, anywhere along the line from Grade One to graduate seminars, have a friend: the National Council for History Education, founded in 1990 as the successor organization to the Bradley Commission on History in Schools. Until then, we had no equivalent to the National Council of Teachers of Mathematics, the National Council for Geographic Education, or the other discipline-based advocacy groups that bring school and university people together to tackle all the issues that concern them--from curricular design, K to Ph.D., through state, local, and university standards and requirements, teacher education, certification, and professional development, to the implications of the assessment movement, of new technologies, and of school re-structuring.

Each of these issues was directly addressed in 1988 by the 32-page Bradley Commission report, Building a History Curriculum: Guidelines for Teaching History in Schools (revised 2nd Edition © 2000). Each has become more urgent, carrying all kinds of chances for good or bad outcomes, with the emergence of GOALS 2000, the governors' National Educational Goals Panel, the National Council on Standards and Testing, and the National Board for Professional Teaching Standards. Add to these the recurrent American love affair with math, science, technology, and "job-training" as quick fixes for the country's problems. And add on top the needless quarrels among ourselves over diversity vs. commonality, social vs. political, chronology vs. post-holing, "active" vs. "passive" learning, and we historians have, as they say, a full plate before us.

The special prescience of the Bradley Commission on all of these questions was largely due to its diverse membership: historians and classroom teachers of so many different backgrounds, persuasions, and professional experiences. Its special, overriding message, repeated by the National Commission on the Social Studies in its 1989 report, Charting a Course, was the need for much more time in the social studies curriculum, to liberate teachers to offer a better kind of history.

More time, of course, cures nothing by itself, though our opponents love to pretend we think so and that all we want is to force helpless students to "memorize more facts". What, in fact, we do think is what every teacher already knows: that more time is plainly indispensable to learning better history. So what exactly is the "new" and better history that justifies fundamental changes in the conventional social studies curriculum, and probably even bigger changes in the graduate and undergraduate education of those who teach history at any level?

The National Council for History Education, carrying the message from the Bradley Commission and the National Commission on the Social Studies, is pressing for all teachers to be given the chance to offer the sort of history that only a minority have been lucky enough to offer up to now, in courses that:

1. combine an analytical, chronological narrative with frequent pauses for studies in depth, neither of which can do without the insights of the other.

2. deal constantly with the relation between fact and concept, neither of which educates without the other.

3. carry significant, compelling themes and questions from the start of United States and world history down to the present day, frequently responding to the students' challenge: "So what?" 4. demonstrate the interdependence of history and the social sciences, by teaching the concepts of the latter in dramatic historical context. 5. demonstrate the interdependence of history and the humanities, by concurrent studies of literature, philosophy, and the arts. 6. are pluralist, multicultural, inclusive of people of all kinds and conditions in whatever society is under study. 7. provide a sophisticated understanding of the origins, the advances and defeats, the worldwide adventures of the democratic ideas that bind us together as one people. 8. offer many chances for active learning, inquiry and the development of critical, historical habits of the mind. 9. are taught by a wide diversity of pedagogical methods, of the teacher's own choice and design.

On this broad ground, all but a few of those who debate the history/social studies curriculum can come together. Who can still pretend that single-year United States or world history courses, madly rushing from the Ice Age to the Spring prom, allow teachers to do these things? Only more time will let us sweep aside the false conflicts between multicultural and a common civic education, between "memorized" and "issue-oriented" history, between "elite" political history and "egalitarian" social history. And on current issues, only more time can let teachers make clear, for example, that most of the nation's ills are rooted in historical choices and priorities, not to be waved away by a little more math and "work-related" schooling. The National Council for History Education, then, bases its campaign for history on the recommendations of the Bradley and National Commissions. The Council is eager to collaborate with anyone promoting the cause of history. But it is the only comprehensive national organization forthrightly arguing for history as the continuing core of the social studies throughout the grades, integrated with geography and civic instruction, as is the case in other modern democratic nations. We intend to campaign for this in every state and school district in the country.

We believe that the social sciences and current issues, both domestic and global, are best studied in historical context and perspective. We believe that historical study is the precondition for intelligent political and personal judgment and that, in turn, such judgment is the absolute precondition for the political power of the citizen, and the private self-fulfillment of the person. Familiar notions, no doubt, but their implications call for a fundamental reordering of the American curriculum from grade school to graduate school.

It is the mission of the National Council for History Education to see that this happens--not as a top-down imposition, but out of the collaboration of scholars and teachers across all levels of schooling, working together as equals who educate each other at every step of the way.

In Support of History

- NCHE supports history as the core of the social studies in the schools and links it to many pro-history forces and organizations in the profession and the community. American children cannot afford to enter the 21st century ignorant of everything that preceded their own time and ignorant of the history and culture of other nations. An education in history prepares youngsters to understand not only their own society but other societies and civilizations around the world. - NCHE speaks vigorously to policy-makers about the importance of providing enough time in the curriculum for both world and U.S. history and adequate support for good teaching and materials. NCHE encourages regular communication between those who teach history in the schools and those who promote history in the community. - NCHE links history in the schools with many activities sponsored by state and local organizations. It provides a communications network for all advocates of history education, whether in schools, colleges, museums, historical societies, humanities councils, or community organizations. - NCHE membership consists of individuals, not organizations. Members include historians and history teachers, school administrators, authors, publishers, historical association and historical museum personnel, history buffs, in short, anyone who loves history.

title: User:NCHE1776


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User talk:NCHE1776

Will you help me create an article or lesson or something on japan? 68.96.23.7 20:48, 21 August 2006 (UTC)

What specifically were you thinking? If you can isolate a specific topic or episode in the history of Japan; I can better suggest sources, what to keep in mind while developing the lesson plan, etc. in order to make this a good, strong, content founded lesson.

title: User talk:NCHE1776


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User:Reuvenk

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Institutional ethnography

Summary
Institutional ethnography is a research method that emphasizes the study of the social organization of everyday life. This project involves extensive observation of social settings and writing about experiences and events in such.

Institutional ethnography was developed by the Canadian Sociologist Dorothy Smith. This project is based on Smith's writings and Mapping Social Relations by Campbell and Gregor.

Prerequisites

 * Completing an introductory course in Sociology or Anthropology is recommended.
 * Completing the learning project Introduction to ethnography is recommended.
 * Close reading of the WRN Privacy Policy and Wikiversity research ethics pages is required before or early on in the course.
 * If you intend to do social research, reviewing one of these free online courses is recommended:
 * Research Ethics Training Curriculum prepared by Family Health International (FHI).
 * National Cancer Institute Human Subjects Research Tutorial.

Goals
This learning project offers learnings activities to explore the practice of institutional ethnography. After doing these activities, the learner should have started to develop the ability to:
 * take field notes
 * identify ones social location in relation to various social contexts
 * analyze problems that arise in everyday life
 * analyze social groups and processes sociologically
 * organize an ethnography research project

Concepts to learn include: /concepts

Activities

 * Activity 1. Observe how collaborations develop at Wikiversity. Create some wiki pages that promote collaborative learning.
 * Activity 2.
 * etc.

Readings
Each activity has a suggested associated background reading selection.
 * Reading 1.
 * ect.

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User:Nemesis 961

Hi! I'm a junior in high school in California, and am a 15-yr old male (16 on Sept. 7). My interests are science, Java programming, math and roller coasters.

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