OpenLLM-France/wikimedia huggingface dataset:
# Waves/Geometrical Problems

Waves : Geometrical Optics 1 - 2 - 3 - 4 - 5 - 6 Problems

### Problems

Figure 3.14: Refraction through multiple parallel layers with different refractive indices.
Figure 3.15: Refraction through a $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ prism.
Figure 3.16: Focusing of parallel rays by a parabolic mirror.
Figure 3.17: Refraction through a wedge-shaped prism.
* The index of refraction varies as shown in figure 3.14:
** Given $\theta _{1}$, use Snell's law to find $\theta _{2}$.
** Given $\theta _{2}$, use Snell's law to find $\theta _{3}$.
** From the above results, find $\theta _{3}$, given $\theta _{1}$. Do $n_{2}$ or $\theta _{2}$ matter?
* A $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ prism is used to totally reflect light through $90^{\circ }$ as shown in figure 3.15. What is the minimum index of refraction of the prism needed for this to work?
* Show graphically which way the wave vector must point inside the calcite crystal of figure 3.3 for a light ray to be horizontally oriented.
* The human eye is a lens which focuses images on a screen called the retina. Suppose that the normal focal length of this lens is $4{\mbox{ cm}}$ and that this focuses images from far away objects on the retina. Let us assume that the eye is able to focus on nearby objects by changing the shape of the lens, and thus its focal length. If an object is $20{\mbox{ cm}}$ from the eye, what must the altered focal length of the eye be in order for the image of this object to be in focus on the retina?
* Show that a concave parabolic mirror focuses incoming rays which are parallel to the optical axis of the mirror precisely at a focal point on the optical axis, as illustrated in figure 3.16. Hint: Since rays following different paths all move from the distant source to the focal point of the mirror, Fermat's principle implies that all of these rays take the same time to do so (why is this?), and therefore all traverse the same distance.
* Use Fermat's principle to explain qualitatively why a ray of light follows the solid rather than the dashed line through the wedge of glass shown in figure 3.17.
* Test your knowledge of Fermat's principle by finding the value of $y$ for which $t$ is a minimum in equation (3.14). Use this to derive Snell's law.
Waves : Geometrical Optics 1 - 2 - 3 - 4 - 5 - 6 Problems
# Waves/Geometrical optics Introduction

Waves : Geometrical Optics 1 - 2 - 3 - 4 - 5 - 6 Problems
As was shown previously, when a plane wave is impingent on an aperture which has dimensions much greater than the wavelength of the wave, diffraction effects are minimal and a segment of the plane wave passes through the aperture essentially unaltered.
This plane wave segment can be thought of as a wave packet or ray consisting of a superposition of wave vectors very close in direction and magnitude to the central wave vector of the wave packet. In most cases the ray simply moves in the direction defined by the central wave vector, i. e., normal to the orientation of the wave fronts.
However, this is not true when the medium through which the light propagates is optically anisotropic, i. e., light traveling in different directions moves at different phase speeds. An example of such a medium is a calcite crystal. In the anisotropic case, the orientation of the ray can be determined once the dispersion relation for the waves in question is known, by using the techniques developed in the previous section.
If light moves through some apparatus in which all apertures are much greater in dimension than the wavelength of light, then we can use the above rule to follow rays of light through the apparatus. This is called the geometrical optics approximation.
This approximation can be applied to any wave theory.
Waves : Geometrical Optics 1 - 2 - 3 - 4 - 5 - 6 Problems
# Web Development/What is web development?

Web development is the work involved in building a website for the internet (World Wide Web) or intranet (private network). A website can be built from scratch or through What You See Is What You Get (WYSIWYG) Editor. Building a website from scratch is more difficult as it requires skilled individuals to manually create and handle Cascading Style Sheets (CSS), HyperText Markup Language (HTML), programming, web architecture, page structure, java script files and more. Building a WYSIWYG editor is easier as all of the programming and coding is done for you and it although some platforms give you the option to code, it is not needed. Using a WYSIWYG mainly consist of design principles since the coding is developed for you.
Due to the complexity of building websites, web development is divided into two types of functions: front-end and back-end. Front-end web development consists of everything a user can view, hear or interact with on a web page (otherwise known as content) and bridges the gap between web design and back-end development. A front-end web developer normally receives design principles from the web designer and input them into the front-end code so the back-end developer can understand it and build functionality around it. Web Accessibility and web performance are two essential aspects to front-end web development because so much of information is viewed and accessed through mobile devices.
A website or application must be functional or else it will fail. Back-end developers are responsible for the functionality of a website and need to know and understand programming language, databases and server architecture. If a website or application is slow, crashing or throwing errors at users it is likely because of back-end issues.
The intricacy of web development is why most people today are using WYSIWYG’s. It is very difficult to build and maintain a website from the ground up without the bandwidth. WYSIWYG’s enable everyday people to create and manage a website on their own with little to no help or on their own.
Most websites use a Content Management System (CMS) to deliver and store information. Some of the most notable CMS’s are WordPress, SharePoint and Drupal. A CMS is useful when building a website with textual dynamic content. CMS’s are not needed if there is no content to be managed.
# Web Programming/Cordova

Apache Cordova is set a APIs for creating native mobile app using only HTML, CSS, and JavaScript.
* Wikibooks: Android/PhoneGap
* Apache Cordova
* Cordova Tutorial
# Setup a Ubuntu VM with LAMP

* Install VirtualBox
* Install latest Ubuntu server (no GUI) or desktop with Apache/MySQL/PHP
** https://www.digitalocean.com/community/tutorials/how-to-install-linux-apache-mysql-php-lamp-stack-on-ubuntu-14-04
** https://help.ubuntu.com/community/ApacheMySQLPHP
* Optional:
** install guest additions to enable shared clipboard
*** download guest additions iso image: http://download.virtualbox.org/virtualbox/
*** install additions: http://virtualboxes.org/doc/installing-guest-additions-on-ubuntu/
** screen resolution
* Activate user public_html directories: http://kimbriggs.com/computers/computer-notes/linux-notes/apache2-public_html-virtual-directories.file
* Intall and configure phpMyAdmin:
** https://help.ubuntu.com/community/phpMyAdmin
** http://www.liquidweb.com/kb/how-to-install-and-configure-phpmyadmin-on-ubuntu-14-04/
# PHP

CodeIgniter http://www.codeigniter.com/
# Web Development/Why do people develop web pages?

* Section 1.2 — Back to Contents
People develop web pages for two main reasons: personal and professional. This book deals mostly with the latter: a medium to large-sized operation designed to generate income.

### Personal

Many people have set up websites to serve their personal interests. There are a huge number of reasons people do this, from sharing information about themselves, to preaching their beliefs, to putting up a resume to be hired or sometimes people publish virtual journals called "blogs".
Often a number of people collaborate on a website, like a forum, product review, or a blog. That is nonlimited to, social media, podcasts, coding projects, gaming mods, bookmarking sties, social news, media sharing pages, microblogging, social knowledge, and sharing economy websites as well. But, since these sites are not designed for the specific purpose of generating revenue, they are still personal sites.

### Professional

Many businesses (perhaps all someday) have web pages. Some are created simply to get the word out about their business: phone number, address, etc., to increase traffic to its physical location.
Many other companies have websites designed to bring in more income. They act as virtual storefronts, shipping to your doorstep or allowing you to pick up goods in person. This book deals with the development of a professional website created to promote your business.
# Web Programming

Web programming is arguably the most important programming skill today. In this book we will introduce basic web programming concepts and development techniques using HTML, CSS, JavaScript, and PHP.

## Table of Contents

* Web and Web Programming
* HTML
** XHTML
* CSS
** Layouts
* XML
** JSON
** DOM
* PHP
* Forms
* Responsive Web Design
* JavaScript
* AJAX
* Web Services
* Cordova
* Node.js
* Frameworks
* Development Environment Setup
* RSS
# Web Programming/AJAX

Resources:
* Introduction to AJAX
* Ajax with JQuery
Each web applications has at least two parts: a client side and a server side. The client side runs in the browser serving as the user interface of the web app. The server side run on a server, which allows app to implement the business logic and have access to various resources, e.g. the file system, databases, or other services. The interactions between the client side and the server side are in the form of requests and responses. Traditional a request is triggered when the user types a new URL in the address bar or click on the page. The response to the request would be a new page. Before the new page arrives the user has nothing to interactive. Such delays can be caused by network latency or server issues, which are hard to control. To offer good user experience our app should stay interactive at all times. Refreshing the whole page to respond to every request is highly inefficient because often time only a small portion of the page need to be updated.
AJAX stands for Asynchronous JavaScript and XML. It is not a new programming language, but a new way to use JavaScript to exchange data between the client side and the server side in a asynchronous fashion. AJAX is based on standards includes XMLHttpRequest object, DOM manipulation with JavaScript, and XML and JSON.
The following are a few commonly used AJAX methods in JQuery. The load method loads data from a server and puts the returned data into the selected element. The AJAX get and post methods with send the requests using the respective HTTP request types.
The following example show the modified version of our TODO list example using AJAx.
Note the client side uses JavaScript code to load the todo list and send the request for adding a new item in the list. The PHP scripts being requests server as the server side by offering a web API. Each PHP script can be viewed a function, which returns data for each parameter combination. The server scripts are as follows:
# VCE Specialist Mathematics/Authors

    Adrignola
    First authorship: 2010-03-28 15:03
    Contributions: (_ edits, _ pages)
# VCE Specialist Mathematics

The purpose of this text is to produce a reliable and free textbook, specifically tailored toward the needs of students studying VCE Specialist Mathematics in an attempt to gain the Victorian Certificate of Education (VCE). The eventual aim is to provide a practical alternative to standard textbooks, complete with exercises and worked examples.

## Table of Contents

    Authors

### Units 3 and 4: Specialist Mathematics

* Coordinate Geometry
* Circular Functions
* Complex Numbers
* Relations and Regions in the Complex Plane
* Differential Calculus
* Integral Calculus
* Differential Equations
* Kinematics
* Vectors
* Vector Calculus
* Mechanics

### Appendices: Units 3 and 4

* Formulae
* Practice SACS
* Practice Exams
* Common Math Hacks
* Common Exam Mistakes

## Resources
### Internal

* VCE Mathematical Methods
* VCE Chemistry

### External

* VCAA: Specialist Mathematics
* The Art of Problem Solving - Is math class too easy for you? Looking for a greater challenge?
# VCE Physics/Unit 4/AoS 2
## Description from the Study Design

In this area of study students explore the design of major experiments that have led to the development of theories to describe the most fundamental aspects of the physical world – light and matter.
When light and matter are probed they appear to have remarkable similarities. Light, which was previously described as an electromagnetic wave, appears to exhibit both wave-like and particle-like properties. Findings that electrons behave in a wave-like manner challenged thinking about the relationship between light and matter, where matter had been modelled previously as being made up of particles

## In This Area of Study

Template:VCE Physics/Unit 4/AOS 2 TOC

## Comments about this Area of Study

Comments to come.
# VCE Physics/Unit 4/AoS 1
## Description from the Study Design

In this area of study students use evidence from experiments to explore wave concepts in a variety of applications. Wave theory has been used to describe transfers of energy, and is important in explaining phenomena including reflection, refraction, interference and polarisation. Do waves need a medium in order to propagate and, if so, what is the medium? Students investigate the properties of mechanical waves and examine the evidence suggesting that light is a wave. They apply quantitative models to explore how light changes direction, including reflection, refraction, colour dispersion and polarisation.

## In This Area of Study

Template:VCE Physics/Unit 4/AOS 1 TOC

## Comments about this Area of Study

Comments to come.
# VCE Specialist Mathematics/Units 1 and 2: Specialist Mathematics
## Overview
### Assessment

Internally assessed by the institution for an N mark.
# VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics
## Overview
### Assessment
#### Totals

* 14% of Study Score: Unit 3 SACS
* 20% of Study Score: Unit 4 SACS
* 66% of Study Score: End of Year Exams (2)
VCE Specialist Mathematics/Units 3 and 4: Specialist MathematicsUnits 3 and 4: Specialist Mathematics

#### Unit 3 SACS
##### Outcome 1: 5.25% of Study Score

* Analysis task 1: 2.45% of Study Score
* Analysis task 2: 2.8% of Study Score

##### Outcome 2: 5.25% of Study Score

* Analysis task 1: 2.8% of Study Score
* Analysis task 2: 2.45% of Study Score

##### Outcome 3: 3.5% of Study Score

* Analysis task 1: 1.75% of Study Score
* Analysis task 2: 1.75% of Study Score

#### Unit 4 SACS
##### Outcome 1: 10% of Study Score

* Application Task: 5% of Study Score
* Tests: 5% of Study Score

##### Outcome 2: 6.7% of Study Score

* Application Task: 6.7% of Study Score

##### Outcome 3: 3.3% of Study Score

* Application task: 1.7% of Study Score
* Tests: 1.6% of Study Score

#### End of Year Exams
##### Exam 1: Tech-Free: 22% of Study Score

* 1 hr: 22% of Study Score

##### Exam 2: Tech-Active: 44% of Study Score

* 2 hrs: 44% of Study Score
# VCE Physics/Unit 4/AoS 3
## Description from the Study Design

A student-designed practical investigation related to waves, fields or motion is undertaken either in Unit 3 or Unit 4,or across both Units 3 and 4. The investigation relates to knowledge and skills developed across Units 3 and 4 and is undertaken by the student through practical work.
The investigation requires the student to develop a question, formulate a hypothesis and plan a course of action to answer the question and that complies with safety and ethical guidelines. Students then undertake an experiment that involves the collection of primary quantitative data, analyse and evaluate the data, identify limitations of data and methods, link experimental results to science ideas, reach a conclusion in response to the question and suggest further investigations that may be undertaken. The student is expected to design and undertake an investigation involving two continuous independent variables. Results are communicated in a scientific poster format according to the template provided on page 13. A practical logbook must be maintained by the student for record, authentication and assessment purposes.

## In This Area of Study

Template:VCE Physics/Unit 4/AOS 3 TOC

## Comments about this Area of Study

Comments to come.
# VCE Physics/Unit 4

Jump to the main table of contents for this book

## Description from the Study Design

A complex interplay exists between theory and experiment in generating models to explain natural phenomena including light. Wave theory has classically been used to explain phenomena related to light; however, continued exploration of light and matter has revealed the particle-like properties of light. On very small scales, light and matter – which initially seem to be quite different – have been observed as having similar properties. In this unit, students explore the use of wave and particle theories to model the properties of light and matter. They examine how the concept of the wave is used to explain the nature of light and explore its limitations in describing light behaviour. Students further investigate light by using a particle model to explain its behaviour. A wave model is also used to explain the behaviour of matter which enables students to consider the relationship between light and matter. Students learn to think beyond the concepts experienced in everyday life to study the physical world from a new perspective. Students design and undertake investigations involving at least two continuous independent variables. A student-designed practical investigation related to waves, fields or motion is undertaken either in Unit 3 or Unit 4, or across both Unit 3 and Unit 4, and is assessed in Unit 4, Outcome 3. The findings of the investigation are presented in a scientific poster format as outlined in the template on page 13.

## Comments

Some text to go here.

## In This Unit
### Area of Study 1 : How can waves explain the behaviour of light?

Template:VCE Physics/Unit 4/AoS 1 TOC

### Area of Study 2 : How are light and matter similar?

Template:VCE Physics/Unit 4/AoS 2 TOC

### Area of Study 3 : Practical investigation

Template:VCE Physics/Unit 4/AoS 3 TOC
# Universal Algebra/Binary relations

Many algebraic varieties that are studied in mathematics have a very important binary relation. In this chapter, we study this case.
Definition (identity):
Let ${\mathcal {A}}$ be an algebraic variety, and let $A$ be an instance of ${\mathcal {A}}$. Suppose that instances of ${\mathcal {A}}$ have a binary operation $*$. Then an identity of $A$ with respect to $*$ is an element $e\in A$ corresponding to a 0-ary operation of ${\mathcal {A}}$ so that the rule $x*e=x$ holds, where $x$ is a variable.
Definition (associativity):
Let ${\mathcal {A}}$ be an algebraic variety whose instances have a binary operation $*$. This binary relation is called associative iff the rule $x*(y*z)=(x*y)*z$ holds for ${\mathcal {A}}$.
Definition (inverse):
Let ${\mathcal {A}}$ be an algebraic variety whose instances have a binary operation $*$ and an identity $e$. An inverse operation is a unary operation $~^{-1}$ on ${\mathcal {A}}$ so that the rule $x*x^{-1}=e$ holds.
Definition (commutativity):
Let ${\mathcal {A}}$ be an algebraic variety with a binary relation $*$. This binary relation is called commutative if and only if the rule $x*y=y*x$ holds.
Proposition (higher associativity):
Let ${\mathcal {A}}$ be an algebraic variety with a binary relation $*$. Suppose $*$ is associative. Then let $A$ be an instance of ${\mathcal {A}}$, and let $a_{1},\ldots ,a_{n}\in A$. Let $w\in D_{1}$ be a word of the first Dyck language $D_{1}$.
# Units of Measurement/Temperature

The SI unit for Temperature is the Kelvin (K). However, Celsius (°C) is also often used as a measure of temperature. The formula to convert Celsius to Kelvin is K = °C + 273.15, so 25 °C will equal to 298.15 K. 20-22 degrees Celsius is called room temperature, and 0 °C or 273.15 K is called standard temperature.
Fahrenheit (°F) is also a commonly used temperature system in the United States, Palau, and Liberia, and the formula to convert from Celsius to Fahrenheit is F= C*1.8+32. An example would be 32 Celsius times 1.8 is 57.6, and then gets added with 32 to make 89.6 °F.
There are also scales like the Rankine scale, which is the Kelvin version of Fahrenheit, or the Delisle scale that has negative numbers correspond to warmer temperatures.

## Formulas for Conversion

| From row to column | Celsius | Kelvin | Fahrenheit | Rankine |
| Celsius | = | °C+273.15 | °C*1.8+32 | °C*1.8+459.67 |
| Kelvin | K-273.15 | = | (K-273.15)*1.8+32 | K*1.8 |
| Fahrenheit | (°F-32)/1.8 | (°F-32)/1.8-273.15 | = | °F+459.67 |
| Rankine | (°R-459.67)/1.8 | °R/1.8 | °R-459.67 | = |

## Common Temperatures

0 K | -273.15 °C | -458.67 °F is the temperature needed to make absolute zero, the lowest temperature that can theoretically exist. However, it is impossible to get to this temperature as Heisenberg's Uncertainty Principle states that we can know the position or velocity of a particle, but not both. Absolute zero would allow us to know both, which would be impossible.
1 K | -272.15 °C | -457.87 °F is how cold the Boomerang Nebula is, making it the coldest known natural place in the universe.
4.25 K | -268.90 °C | -452.07 °F is the boiling point of helium at standard pressure.
273.15 K | 0 °C | 32 °F is the melting point of pure water, and is also standard temperature.
283.15 K - 285.15 K | 20 °C - 22 °C | 61 °F -71.6 °F is considered to be room temperature.
373.15 K | 100 °C | 212 °F is the boiling point of pure water.
5700 K | 5430 °C | 9800 °F is the temperature of the Earth's core.
5811.3 K | 5537.8 °C | 10000 °F is the average temperature of the sun's photosphere.

## References

* ↑ Helmenstine, Anne (2020-08-10). "What Is Absolute Zero? Temperature in Kelvin, Celsius, and Fahrenheit". Science Notes and Projects. Retrieved 2024-06-02.
* ↑ "Uncertainty principle | Definition & Equation | Britannica". www.britannica.com. Retrieved 2024-06-02.
* ↑ information@eso.org. "The Boomerang Nebula - the coolest place in the Universe?". www.spacetelescope.org. Retrieved 2024-06-02.
* ↑ "Helium - Element information, properties and uses | Periodic Table". www.rsc.org. Retrieved 2024-06-02.
# Units of Measurement/Velocity

The SI unit for velocity is meter per second (m/s). The basic formula to get velocity is distance(m)/time(s).
# University of Alberta Guide

This book is a series of guides that relate to life and education at the University of Alberta. The goal of this book is to introduce guides/notes on courses that can be taken, professors that teach the courses, and otherwise general activities that occur on the University of Alberta campus. Since this is a brand new book, there will not be a lot of content until it becomes more popular and the contributions start to increase. However, in time, this book can become not only a complete survival guide to life at the University of Alberta, but also a template for other universities to start their own guides.

## Courses
### Department of Mathematical and Statistical Sciences

* STAT
** 222

### Department of Computing Science

* CMPUT
** 115
Faculty Arts
* Philosophy
* Classics

## Student Life

* Campus Rec
* Student Union