OpenLLM-France/wikimedia huggingface dataset:
# Math contest preparation
## Contests

Each country typically has its own set of contests. For high school, these usually include one national Mathematics Olympiad and one or more qualifier contests intended to help select students to invite to the national Olympiad. The top six students of every country are then invited to participate in the International Mathematics Olympiad (IMO).

### List of contests

In the United States:
Middle School
* Math Superbowl - A math contest for students in 4th, 5th and 6th grade
* MathCounts - A national middle school math contest
* AMC 8 - The American Mathematics Contest for students in 8th grade and below
* Purple Comet
High School
* AMC 10 - The American Mathematics Contest for students in 10th grade and below
* AMC 12 - The American Mathematics Contest for students in 12th grade and below
* AIME - The American Invitational Mathematics Examination, qualified for through the AMC 10/12
* USAMO - The United States of America Mathematics Olympiad, qualified through the AIME and the AMC 10/12
Undergraduate
* Putnam - A contest based on high school mathematics as well as first year calculus and algebra
More Listings:
http://k12mathcontests.wikispaces.com/
http://homeschoolmathcontests.com/

## Books

There are many problem solving books available for students. The list is broken up into three levels by difficulty. Most of these books can be purchased online.
Math Contest Books

### Beginner

Art of Problem Solving, Volume 1, by Richard Rusczyk
To practice math facts - KENKEN squares challenge you to think spatially while practicing math facts. www.kenken.com

### Intermediate

Art of Problem Solving, Volume 2, by Richard Rusczyk
The Art and Craft of Problem Solving, by Paul Zeitz

### Advanced

Problem-Solving through Problems, by Loren C. Larson
Problem Solving Strategies, by Arthur Engel

## Problems

http://www.mathinee.com
http://www.aplusclick.com/grade15.htm

## Online Help

http://www.khanacademy.org/
http://www.edugain.com
http://www.artofproblemsolving.com
http://www.totalgadha.com
# Mathematical Methods in Physics/Wave equation

v=λf
# Mathematical Methods for Engineers II/Lecture 1
## Ordinary Differential Equations

Given initial values
* $u(t=0)$
What is the equation associated with evolution?
* There can be a large number of equations
Linear equation:
* $u'=au\;$
    $a\;$ - scalar
    $a={\frac {\partial f}{\partial u}}$
N x N matrix
* $u'=Au$
* Know all the constants
* Symmetric matrices associated with real eigenvalues
* Negative eigenvalues mean the solution decays
The constant $a$ can be complex
* Convection term may not be symmetric

### Non-stiff Ordinary Differential Equations

* $u'=4u$
* Equations relatively easy to solve
* Use explicit methods
** Compute $u_{n+1}$ directly from $u_{n}$ and $f(u_{n},t_{n})$
*** Calculate from formula
** Fast methods of calculation
** Types of methods
*** Euler
**** Minimum accuracy
**** First order
*** Families of methods
**** Adams-Bashforth
***** Multi-step method
**** Runga-Kutta
***** Half-steps to calculate $u_{n+1}$
***** ODE45 in Matlab
****** Fourth order Runga-Kutta
****** Varies $\delta t$ based on behavior
****** The code uses internal checks to estimate the error
****** Relative accuracy of $10^{-3}$
****** Absolute accuracy of $10^{-6}$

### Stiff

* $u(t)=e^{-t}+e^{-99t}$
** $e^{-t}$ control $u$ but $e^{-99t}$ control $\delta t$
* Stiff problems arise in process where there is a dynamic range in rates
* Ill-conditioned
* Implicit methods
** Formula involves the previous value and slope
** The equation can be non-linear
** Methods are not as fast
** Types of methods
*** Backward Euler
*** Families of Methods
**** Adams Moulton
**** Backward differences
***** ODE15s in Matlab
****** Varies $\delta t$
Trade-off of speed versus stability

## Euler's method

* Construction of method:
${\frac {u_{n+1}-u_{n}}{\Delta t}}=f(u_{n},t_{n})=au_{n}$
$u_{n+1}=(1+a\Delta t)u_{n}\;$
$u_{n}=(1+a\Delta t)^{n}u_{o}\;$
* Test of stability
$|1+a\Delta t|\leq 1$
Limit when $a\Delta t=2\;$
Too big a time step results in an estimated value with too great a difference

## Backward Euler method

* Construction of method:
${\frac {u_{n+1}-u_{n}}{\Delta t}}=f(u_{n},t_{n+1})=au_{n+1}$
$(1-a\Delta t)u_{n+1}=u_{n}\;$
$u_{n}=\left({\frac {1}{1-a\Delta t}}\right)^{n}u_{o}$
* Test of stability
Absolutely stable
Growth factor is always less than one
# Mathematical Methods in Physics
## Content
### Second order differential equations

* Introduction to 2nd order differential equations
* Solution of homogeneous equations with constant coefficients
* Solution of inhomogeneous equations with constant coefficients
* Singularities and series solutions
* Frobenius method

### Special functions

* Cylindrical and spherical coordinates
* Boundary value problems
* Sturm-Liouville problem
* Legendre polynomials
* Bessel functions
* Associated Legendre functions
* Spherical harmonics
* Neumann functions
* Modified Bessel functions
* Fourier-Legendre series
* Asymptotic behaviors of certain special functions

### Complex functions

* Complex numbers
* Basic operations with complex functions, analytic functions
* Cauchy theorem
* Singularities
* Taylor and Laurent series
* Residue theorem and applications
* Complex functions

### Partial differential equations

* General definition
* Separation of variables method
* Wave equation
* Laplace and Poisson equations
* Diffusion equation
* Helmholtz equation
* Continuum eigenvalue spectrum

### Green functions

* For Sturm-Liouville operators
* For 2 dimensions
* For initial value problems
* For boundary value problems
* Solution of higher-order differential equations
* Reduction to canonical form
# Northern Arizona University/Environmental Ethics/Journals/What is Fate?

What is fate?
Is it a coincidence of occurrences that we humans attempt to add some sort of significance to or is there some kind of blueprint that connects life to the universe and fate is simply the universe filling gaps where necessary for life to continue, perhaps through some method of odds or probability (after all, was Edison not the only person inventing the lightbulb?). I think of John Muir's life and I imagine what shape our world would have had he not have gone blind. Would someone else have come to fill that evolutionary niche and preservation as we know it would exist or would we have turned this great nation into an exacerbated Easter Island? Would Theodore Roosevelt still have enacted the Antiquities Act of 1906 were it not for the advice and dialogue with John Muir? Would Gifford Pinchot have exercised his concept of conservation to "conservatively" timber old growth forests from the northern mountaintops of California? Would we have national parks today?
# Northern Arizona University/Environmental Ethics/Journals/The Howl of the Wolf

If there is such a thing as Gaia or Earth itself being an organism with all of its biota being the different organs that make up the whole, are some of us humans nothing more than a cancerous cyst? Some people see working for the earth as a responsibility to the land and themselves. How often does a hard day's work seem rewarding of itself? I have never met such grounded individuals as those who find meaning in their relationship with the earth and one another. Their energy sort of describes their story as one can get a sense that of the balance these people find in life.
When I think of a serene mountainside or an untouched riverbank I imagine what Jesus and Buddha must have been thinking when they would retreat to nature to discover their relationship to the cosmos. What clarity and simplicity that can be found in the wilderness! To become the Witness as opposed to telling the world what it is. To observe history, the present, and the unknown all in one place, all in one moment. The wilderness is a place that makes use of all known and unknown senses to all living creatures.
In nature there is no room to frustrate any of the mechanics that aid in its continuation. The delicate balances of the natural world depend on all the elements and the processes that have created and maintained much of what exists on this planet to remain untampered by Human's concept of time. The natural world itself does not know time. Much of the animal kingdom do not know what time is. Only Human's interpretation seems to be at fault for the many miscalculations of our world. To think that we can put characters that we call numbers to represent an eternity of prior and continued existence is beyond any realm that a human being can experience. Isn't that what we attribute to be the duty of God? When did humans decide to take matters into their own hands? Was this the fault of Eve? Do we blame some ancient relative for inventing Human's first tool? Where did we go wrong and how do we begin the process of damage control? Can we control the damage we've made for the biological sphere by which we inhabit?
# Northern Arizona University/Environmental Ethics/Journals/Thoreau and His Great Experiment

After reading through the first few chapters of Henry David Thoreau's Walden, I admire his approach in running an experiment on himself to pursue the origin of virtue. Is it possible that with everything that has been incorporated in our lives and the superfluous complexities that have accompanied our progression through time enable us to understand and see virtue? His case seems to stand on the grounds of getting back to the basics.
When I look out at today's cultural setting it would seem that we are moving backwards by moving forwards. It would seem that we are exacerbating an end by a manufactured means. Rather than individuals pursuing independent spiritual freedoms and sharing in that experience with others we are merely synthesizing a spiritual polymer to create a manufactured soul! The dividing lines between the upper echelons of society and those falling behind are creating an illusory mode of social acceptance. If you purchase a product and display its name for the world to see then somehow that is supposed to give the purchaser a sense of societal acceptance. Yet spiritually they have sacrificed a personal part of their being in order to separate a piece of their identity onto a product that does not breath or live. Strip a person naked of all material possessions and what does one have left?
# Northern Arizona University/Environmental Ethics/Journals/Trash Day

I felt something odd come over me today. I was on my way to treat a friend to breakfast when an obstacle appeared in our path. It seems as though a trash can had been emptied all around the entrance area of the Campus Store. I felt compelled to pick up the trash when at some point I froze. I thought to myself, "this isn't my job. someone else gets paid to deal with this."
Out of self-interest I picked up a few pieces of plastic until there were only paper products left scattered among an area of roughly 12 ft².
Is it not my responsibility to stop and aid in whatever clean-up efforts are required of me? Am I not an able man who can bend over? Am I not capable of work?
This responsibility manifested within a place where my soul reaches outward into a space I do not own nor control. I can attempt to but will only fail when faced with the limitations of the boundaries that the Divine has set for me.
Yet, rather than pick up the remaining trash that was still sitting on the lightly frosted concrete, I felt a sense of freedom. I had the choice to walk past it within the rights of "it's not my job".
I feel that traces of guilt are building up. Small doses that grow...I must root this before it grows further. Perhaps the weeds of my conscience will sprout up from time to time but nothing that will require much effort to clean up.
Is ignorance truly Bliss? I would argue...
# Northern Arizona University/Environmental Ethics/Journals/Virtue

After reading the last portions of Thoreau's Walden I am left with a ponderation of virtue. A classic cliché that I hear is "It's not the destination, it's the journey." How true is the experience of pursuing virtue opposed to attaining it? In our experience as sentient beings we attempt to make reason of our existence and the purpose behind it all. While reason can explain a lot in our existence it cannot predict much of anything! Perhaps this is where the limitations of science begin to feel their ceiling. We, as a species, seek so tirelessly a way to justify the means of our existence. We battle for and manufacture whatever pittance we can muster up to justify our lives in a manner that science, however ideal in its nature, can suggest to us the correct course of our behavior and actions. We live in an "economically-based society" that runs its whole operation based upon equations and theories that have not be proven to work. Yet we trust that this system built of imaginary mathematics will give us the very means to our fulfilled ends. We trust without knowing what trust is. We act without knowing what action is. We base our observations on previous interpretations without pursuing our own understanding of what life entails.
# Northern Arizona University/Environmental Ethics/Journals/Virtue by Virtue

What is virtue? Is virtue an end result to a means that can come in many forms? Or is virtue the means that leads to an end that forms from many different origins? Being the intellectual animals that we are we often seek answers to many of life's questions. We've searched through science, religion, mythic interpretations, holistic interpretations, and yet we still cannot answer it all. Even the small amount that we've been able to wrap our head around seems to slip into doubt as more time passes. It seems like both the eastern and western traditions alike have tried very different approaches to finding what this Truth is all about. Both seem to come close but nearly miss with maybe an exception or two. How can we raise a global conscious in a time span that needs urgent action when it has taken thousands of years of mistakes of grand and small scales to lead us a millimeter in the right direction? Can we make significant strides and "snap-out" of our cloudy state of mind to focus on the problems that plague us the same way they did those that lived in that distant yet short past?
# Using the All Critical Learning (ACL) Model
### All Critical Learning (ACL) Model

When evaluating complex tasks it is often important to be able to customize the criteria to be evaluated. For this reason, the ACL instrument is often the preferred tool because it allows the user to tailor the evaluation criteria to be evaluated to the situation. The user can select criteria like:
   * What is the immediacy of performance? (How soon will will the task be performed after being trained?)
   * How difficult is the task to perform?
   * How often is the task performed?
   * How critical is the performance?
   * Are there important safety concerns that need special consideration?
   * What are the consequences if the task is not performed correctly?
The ACL Data Analysis Form not only provides a form where you can tailor the evaluation criteria, but it also allows each criteria to be independently evaluated and rated on a scale from 0 to 7 where a higher final rating indicates a greater need for training. The typical rating scales is as follows:
    0 = Not Necessary. No need to consider; already identified as not requiring training.
    1 = Weekly important. These probably don't need to be trained either.
    3 = Important. Consider including as supporting information
    5 = Strongly Important. These should definitely be trained if possible.
    7 = Essential. Must be trained; an absolute must.
When all criteria for a task are graded, the scores are totaled and entered in the last column. In the example there are 9 critera, so the maximum final rating would be 63. (9 criteria times 7 points each = 63 points)
Experts consider the ACL model [also known as the Multiple Factor Model (MFM)] the best model because the user can tailor the evaluation criteria to fit the context for its use. Adding selection criteria makes the instrument harder and more time consuming to use, but it also makes it more accurate when used carefully.
* Advantages
* Evaluation criteria can be tailored to fit the application and context
* Can provide a fairly comprehensive set of data for the task
* Some believe it provides the best analysis of any model
* Disadvantages
* Analysis is time consuming
* Analysis is difficult
* Assigning a weight factor can be difficult and is subjective

### ACL Job Aids

    ACL Data Collection Form
    Instructions for using the ACL Instrument
    All Critical Learning - Practical Exercise

## Navigation

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# Using video/Hangouts on Air

Some interim examples of how I'm using Hangouts on Air can be seen in my YouTube channel
# Using video

We will begin with an open conference - an event to quickly gather perspectives and share skills on the use of video in teaching, learning and assessment. After the conference, this page will become both the proceedings of the event, and an educational resource in its own right.

## Topics

A list of presentations to follow.
If you're working with video, or have a critical insight on the uses of video in education, please list the title of your presentation here, prepare a one page handout, and record a 10 minute presentation.
* Presentations through video - Rick Hayes, Leigh Blackall
* Using video in teaching professional therapy - Colleen Cousins, Nella Charles, Karen Smith and Imogen O'Neill
* Youtube playlists - Rick Hayes and Meri Vukicevic
* Mixed media in assessment - Ruth Ford
* Media production and management in the Faculty of Health Sciences La Trobe University - Brian Dunell, Cameron Grant, Frank Niebling and Leigh Blackall
* Learning in 4 minutes and 12 seconds - Leigh Blackall

## Participation

1pm, 9 May 2014. La Trobe University, HS1203 and live recorded webstream at New date TBA Teachers of Health Professionals
# Using video/Learning in 4 minutes and 12 seconds

A short presentation given to the Faculty of Health Sciences at La Trobe University, Bendigo Campus. Points raised include: Professional education is ignoring the impact of Google, Youtube and Wikipedia. That 4 minutes and 12 seconds is a target time frame for teaching through video. That Michael Wesch's video called An Anthropological Introduction to Youtube is a good reference. And that mini lectures and short demos recorded using a mobile phone are a simple place to start for teachers wanting to use video to teach with.
# Using social media for teaching and research/Header

* The University of Canberra (UC) brings you: Social media in teaching and research
* A series of live streamed and recorded seminars demonstrating how people at UC and afield are using social media in their teaching and research.
# Using video/Google Glass in Health

Alexander Hayes, in Association with the University of Canberra's INSPIRE Centre, has been researching the Google Glass phenomenon, interviewing 60 people who are intensively using the technology already. Alex has convened a large conference around Google Glass in Australia, at the INSPIRE Centre on the 12th of May 2014 (webstreamed to Youtube via Hangouts on Air).
An important resource also to refer to is an event that preceded these resources - IEEE ISTAS 2013
# Using the internet for learning and research
## What

The Internet has evolved rapidly, fast becoming a primary source of information for many, on almost any topic. Many people are simply overwhelmed by the quantity of information, and are at a loss on how to make sense of it all. This page sets out a method in which you can harness Internet information for your learning and research.

## Why

Relying on mere search will not bring you information in either a timely or precise way. You must engage with information as it moves if you wish to understand better its context and the effect it has. Following the advice set out here will help you keep on top of new and emerging information, as well as to track it as it evolves.

## How

Creating and involving yourself in an online network is an excellent way to access and keep on top of information. Here, we think of information as a flow rather than a static product. We have broken the steps toward tapping a 'flow' into 3 parts:

### Search

* Use a traditional search, such as google.
* Use google scholar, and include scholar preferences that suit your need (such as your University library and BibliographyManager to import references quickly). Don't just search on google scholar, click on the "cited by" link to see what articles have used this particular reference. Here's a short video tutorial to google scholar.
* How to use Google Blog Search

### Follow

* Take RSS feeds from leading journals (such as Ben's)
* Take RSS feeds from blogs (Again, example of Ben's RSS feed network)
* Video: RSS in Plain English
* How to follow someone on Twitter

### Share

* Socially bookmark significant finds (for example, this might be as varied as the journals Ben is interested in to resources for teaching a biochemistry unit)
* Tweet (or micro blog) links and/or comments on finds (example of Ben's tweets)
* Video: Social Bookmarking in Plain English

### Generate

* Write and discuss information in online collaborative spaces such as wikis
* Write to a blog post comments, notes, thoughts of finds and/or original work (example Skype collobrative discussion, generated blog post, and comments that lead to increasing network)
* Set up a professional blog and youtube channel

### Regenerate

* As you become aware of other work, other individuals online and other resources through the following, sharing and generating steps you will gradually develop, grow, refine and evolve your network.
# Using video/Healthtalkonline

Kath Ryan and I could present something at the FHS Conference on Using Video, about the use of video narratives and people’s experiences of health and illness in teaching and learning. The presentation would be titled Healthtalkonline: A Multimedia Resource for Health Professional Education
A bit about our team - we are currently working on a module about people’s Experiences of Ageing in Australia for the www.healthtalkonline.org (UK) and www.healthtalkonlineaustralia.org (Aus) website. These websites use qualitative research methods to document personal experiences of health and illness and present the research findings online through video. There are over 60 health conditions explored so far, and new topics are being added all the time. Our module on Ageing and others on Depression, Perinatal Mental Health, and Multiple Medicines are among the first modules conducted in Australia. The website is an amazing resource for teaching students and health professionals and we wanted to share it with you at the conference.
Tools to be demonstrated within the presentation include:
* The Healthtalkonline websites
* Use of video narratives in teaching and assignments
* Scrapbook facility for collecting clips
* The teaching and learning area
* Video compilations