OpenLLM-France/wikimedia huggingface dataset:
# Ideas in Geometry/Instructive examples/Lesson 4: Algebraic Geometry

The equation of a line is L(x)=mx+b, where m is the slope and b is the y-intercept.
The equation of a parabola is P(x)=ax^2+bx+c.
A line that is tangent to a parabola goes through the parabola at exactly one point.
To find P(x)=L(x), we can set P(x)-L(x)=0. This equation will have 2 roots because the answer will be a quadratic since a quadratic minus a line equals a quadratic of some sort. THESE ROOTS MUST BE THE SAME, so P(x)-L(x)=(x-c)^2.
Example 1: Find the line tangent to y=x^2-3x+1 at the point x=3.
Solution 1:
P(x)-L(x)=(x-c)^2
x^2-3x+1-L(x)=(x-3)^2
-3x+1-L(x)=-6x+9
L(x)=8-3x
Example 2: Find the line tangent to y=x^3-3x^2+4x-1 at the point x=0.
Solution 2:
x^3-3x^2+4x-1-L(x)=x^2(x-c)
4x-1-L(x)=0
L(x)=4x-1
# Ideas in Geometry/Instructive examples/Lesson 6: Introduction to City Geometry

Introduction to City Geometry
In City Geometry, we have points and lines, just like in Euclidean Geometry. However, since we can only travel on city blocks, the distance between points is computed in a bit of a strange way. We don't measure distance as the crow flies. Instead we use the Taxicab distance:
Definition: Given two points A=(ax, ay) and B=(bx, by), we define the Taxicab distance as dT(A,B) = │ax-bx│+│ay-by│
Triangles: Triangle look the same in City Geometry as they do in Euclidean Geometry. Also, you measure the angles in exactly the same way. However, there is one minor hiccup. The lengths of the sides of each of these triangles are a little odd.
Circles: Circle is the collection of all points equidistant from a given point. So it City Geometry, we must conclude that a circle of radius 2 would look like a diamond two points away from the center.
Example: Will just bought himself a brand new gorilla suit. He wants to show it off at three parties this Saturday night. The parties are being held at his friends' house: The Antidisestablishment (A), Hausdorff (H), and the Wookie Loveshack (W). If she travels from party A to party H to Party W, how far does he travel this Saturday night?
Solution: We need compute
Let's start by fixing a coordinate system and making A the origin. Then H is (2, -5) and W is (-10, -2). Then dT (A,H) = │0-2│+│0-(-5)│
and
dT (H,W) = │2-(-10)│+│-5-(-2)│
Will must trudge 7 + 15 = 22 blocks in his gorilla suit.
Midset Definition: Given two points A and B, their midset is the set of points that are equal distance away from both A and B.
-Michelle Hur
# Ideas in Geometry/Instructive examples/Lesson twenty Eight: Fields

Lesson Twenty Eight: Fields Section 4.3
We know a set of numbers can include any type of digit. We know there are set of numbers that are related to each other for example, the set of rational numbers, the set of negative numbers, the set of positive integers, the set of all integers. Depending on how the elements of the set are related to each other, we may also be able to describe some sets as fields. Now, not all sets are fields, but all fields are sets. In order for a set to be a field, certain things must be true about the elements.
A field is a set of numbers with binary operations, addition and multiplication, that upholds to specific axioms. The more familiar fields include the field of real numbers, the field of fractions, and the field of constructable numbers.
For a set of numbers to be considered a field, four properties must be true for the numbers in the set:
1. For all pairs of numbers, we'll just say "x,y" in the field, their sum, so x+y, must also be in the field. In other words the field, F, is closed under addition.
2. For all numbers in the field, "x", there is an additive inverse, "-x", in the field. So, x is any element of F, x + (-x) = 0 and (-x) is an element of F. In other words, any number in the field, it's negative is also in the field.
3. For all pairs of numbers, "x,y", in the field, the product of the numbers, "x * y", is also in the field. In other words, F is closed under multiplication.
4. For every number in the field, "x", there exists a multiplicative inverse, x$^{-1}$, such that x$^{-1}$ * x = 1 and x$^{-1}$ is an element of F.
When determining if a set of numbers is a field, simply test the elements of the set for the axioms listed above.
Example: Is the set of natural numbers a field?
N= {0,1,2,3,4,...}
Test the first axiom: Is the set of natural numbers closed under addition? yes.
0+1=1 and 1 is an element of N also, 2+3=5 and 5 is an element of N
The second axiom: Is the additive inverse of each element also in the set of natural numbers? no.
2 is an element of N, however -2 is not an element and therefore set N is not a field
Example: Fractions
Q= {-1,...-1/2,...,-1/4,...,0,...,1/4,...,1/2,....,1,...}
All numbers can be written as a fraction, for example 3= 3/1.
Test axiom one: Is set Q closed under addition? yes.
1/2 + 1/4 = 3/4 and 3/4 is an element of Q. also, 3/1 + 5/3 = 14/3 and 14/3 is an element of Q.
Test axiom two: Does each element of Q have an additive inverse in the set? yes.
-1/2 + 1/2 = 0 and both -1/2 and 1/2 are in set Q. also, -3 + 3 = 0 and both -3 and 3 are in set Q.
Test axiom three: Is set Q closed under multiplication? yes.
1/2 * 1/3 = 1/6 and 1/6 is also in set Q. Each number can be written as a fraction, and because both negative and positive fractions are included in set Q, all products will also be elements of Q.
Test the fourth axiom: Is there a multiplicative inverse for every element of Q? yes.
4/5 * 5/4 = 1 and both 5/4 and 4/5 are in set Q. All fractions are included, therefore the multiplicative inverses will always exist.
# Macro Strategies to Enable Occupation/Health project
## Proposal

Project Proposal – 15% As part of your project team you will generate and submit a 3000 word project proposal. The proposal is the written statement that captures the project background, justification and the plan of how the project will proceed. Your proposal should conform to the guidelines and you should review the project proposal criteria. The proposal is due Thursday 24th July.
This assignment relates to learning outcome 2.

## Report

As part of your project team you will write a 6000 word project report that will outline the entire project process from scoping through to the final outcomes/deliverables. It will follow a recommended proforma (see guide), which includes an executive summary, and recommendations. Supplementary documents to be submitted include the project logbook. You are encouraged to review the marking criteria. Due September 15th
This assignment relates to learning outcomes 2, 4, 5 & 6.

## Presentation

At the 2014 Graduating students’ conference to be held over 2 days during the Week of November 17th (TBC), you will participate in an oral presentation, which outlines the entire project process from initial scoping through to final outcome. Faculty staff and agency sponsors are invited to attend. You are required to both participate as a presenter and an audience member for the duration of the conference to support your peers. Prior to the conference you are required to submit a 450 word abstract that briefly outlines the content and intent of the session (see other hurdles). Each presentation will be 30 minutes and will include approximately 5-10 minutes for question/audience participation. You are encouraged to review the marking guide for this assignment.
This assignment relates to learning outcome 2, 4, 5, 6.
# Machine learning/Unsupervised Learning

Unsupervised learning is a type of machine learning algorithm used to draw inferences from datasets consisting of input data without labeled responses.
The most common unsupervised learning method is cluster analysis, which is used for exploratory data analysis to find hidden patterns or grouping in data.

## Clustering

Problem statement:
* Given some data, $D=({\boldsymbol {x}}_{1},{\boldsymbol {x}}_{2},\cdots ,{\boldsymbol {x}}_{n})$, identify groups (clusters) of data points and assign each point to one of the groups (clusters)
* The clusters are identified using a measure of similarity which is defined upon metrics such as Euclidean or probabilistic distance.
* Points inside each cluster has a higher measure of similarity than data in any other cluster
Clustering methods :
| Method | Comment |
| K-means clustering | Partitions data into k distinct clusters based on the distance to the centroid of a cluster Find the cluster centers that minimized the sum of distances for all the data points |
| Hierarchical clustering | Builds a multilevel hierarchy of clusters by creating a cluster tree |
| Gaussian mixture models | Models clusters as a mixture of multivariate normal density components |
| Self-organizing maps | Uses neural networks that learn the topology and distribution of the data |

# Index

Special:Prefixindex/Machine learning/Unsupervised Learning/
# Machine learning/Unsupervised Learning/K-means Clustering

K-means is a method of clustering which is an unsupervised learning problem.
* In this method the number of clusters is an input to the algorithm (hyper-parameter).
* K-means method is a greedy algorithm. It is a special case of expectation maximization (EM) algorithm, in which we try to find maximum likelihood expectation (MLE).
* K-means algorithm is not guaranteed to converge to the global mean of the loss function (sum of Euclidean distances from each cluster center). The global minimum problem is an NP hard problem.

### Relation to Gaussian Mixture Model (GMM):

* GMM is a more probabilistic approach to clustering.
* Expectation maximization (EM) algorithm is used to find a good gaussian mixture model to cluster the data.

# Intuition

Data points in each cluster are closer to the center of each cluster than the center of other clusters.

# Algorithm

Assume that the number of clusters is given by $k$ and the cluster centers are shown with $\mu _{1},\mu _{2},\cdots ,\mu _{k}\in \mathbb {R} ^{d}$.
We define a loss function for clustering and try to minimize it through the following greedy algorithm.
The loss function is defined as
$L=\sum _{j=1}^{k}\sum _{i}a_{ij}||x_{i}-\mu _{j}||^{2}~~~{\text{where}}~~~a_{ij}=\left\{{\begin{aligned}1&~~{\text{if }}x_{i}{\text{ assigned to }}j\\0&~~{\text{else}}\end{aligned}}\right.$
Minimize $L$ with respect to $a$ and $\mu$ by following these two steps until convergence is achieved:
* Choose optimal $a$ for fixed $\mu$ by assigning $x_{i}$ to the nearest $\mu _{j}$$a_{ij}=\left\{{\begin{aligned}1&~~{\text{if }}j={\arg \min }_{l}|x_{i}-\mu _{l}|^{2}\\0&~~{\text{else}}\end{aligned}}\right.$
* Choose optimal $\mu$ for fixed $a$ by updating $\mu _{j}$ to be the empirical mean of the points assigned to each cluster$\mu _{j}={\frac {1}{n_{j}}}\sum _{i:~x_{i}{\text{ in j}}}x_{i}{\text{ where }}n_{j}=\sum _{i=1}^{m}a_{ij}={\text{number of data points assigned to j}}$

# Justification

In this section, we show that choosing cluster center, $\mu _{j}$, according to step 2 of the algorithm minimized loss function for a fixed set of assignment factors ($a_{ij}$)
In order to find the minimum value of loss function ($L$) as a function of $\mu _{j}$, we find the point for which the gradient of the function is zero
$\nabla _{\mu _{j}}L=0$Therefore, we have
${\begin{aligned}\nabla _{\mu _{j}}L=&\sum _{i}a_{ij}\nabla _{\mu _{j}}(x_{i}-\mu _{j})^{T}(x_{i}-\mu _{j})\\=&\sum _{i}a_{ij}\nabla _{\mu _{j}}(x_{i}^{T}x_{i}-2\mu _{j}^{T}x_{i}+\mu _{j}^{T}\mu _{j})\\=&\sum _{i}a_{ij}(-2x_{i}+2\mu _{j})=0\end{aligned}}$Getting rid of the factor of 2 in the last expression we have $\mu _{j}\sum _{i}a_{ij}=\sum _{i}a_{ij}x_{i}~~~\Rightarrow ~~~\mu _{j}={\frac {\sum _{i}a_{ij}x_{i}}{\sum _{i}a_{ij}}}$We also have $n_{j}=\sum _{i=1}^{n}a_{ij}=\#\{i:x_{i}{\text{ is assigned to }}j\}$, which simplifies $\mu _{j}$ to$\mu _{j}={\frac {1}{n_{j}}}\sum _{i:~x_{i}{\text{ in j}}}x_{i}$
# Machine learning/Classification algorithms

Classification is a subcategory of supervised learning problems.

## k-nearest neighbor

* a simple classification algorithm
* Intuition: Find the majority vote in the training data
* This is a discriminative model, meaning that there is no way to generate the training data points

### Algorithm

* Define some distance metric or similarity metric. The simplest case is Euclidean distance.
* Given some input point $x$, find the $k$'th nearest neighbors from the training set.
* Do a majority vote between these nearest neighbor list and classify the input point as the category with highest number of vote.

### Probabilistic interpretation

Consider the classification output as a random variable $y$. Define probability of $y$ given input $x$ and training data $D$ is
$P(y|x,D)={\text{fraction of points }}x_{i}{\text{ in }}k{\text{-th nearest neighbor points to }}x{\text{ such that }}y_{i}=y$The output of the classification is
${\hat {y}}=\arg \max _{y}P(y|x,D)$Read more about probabilistic interpretation here:
* https://www.cc.gatech.edu/~afb/classes/CS7616-Spring2014/slides/CS7616-13a-PKNN.pdf
# Machine learning/Statistics Fundamentals

Point estimation is the process of calculating a statistic from a sample dataset.
* A point estimator is any function for a sample.
* Therefore, any statistic is a point estimator
Methods of finding point estimations
* Method of Moments
* Maximum Likelihood Estimators
* Bayes Estimators
* Maximum a posteriori estimator

## Bayes Estimators

Using the Bayesian rule${\begin{aligned}P(\theta |D)&={\frac {P(D|\theta )P(\theta )}{P(D)}}\\&={\frac {P(D|\theta )P(\theta )}{\int P(D|\theta )P(\theta )d\theta }}\end{aligned}}$Where $D=(X_{1},X_{2},\cdots ,X_{n})$ is the sample dataset.
$P(D|\theta )=\prod _{i=1}^{n}P(X_{i}|\theta )$
# Machine learning/Supervised Learning

Supervised learning is a type of machine learning algorithm that uses a known dataset (called the training dataset) to make predictions.
Supervised learning includes two categories of algorithms:

## Classification

* Support vector machines (SVM)
* Neural networks
* Linear classifiers: a group of algorithms such as:
** Logistic regression
** Perceptron
** Fisher's linear discrimination
** Naïve Bayes classifier
* Decision trees: a group of algorithms such as
** Random forest
** Bootstrap aggregation
** Boosting
* Discriminant analysis
* Nearest neighbors (kNN): A Non-parametric and instance-based method used for classification and regression

## Regression

* Linear regression
* Nonlinear regression
* Generalized linear models
* Decision trees: a group of algorithms such as
** Random forest
** Bootstrap aggregation
** Boosting
* Neural networks
# Macro Strategies to Enable Occupation

In this subject you will look beyond the occupational challenges facing individuals and consider the ways in which occupational therapists enable change at the level of the service/organisation, community or population. This is referred to as macro level practice. You will focus on gaining knowledge and developing capabilities for an impending role as a health practitioner in a rapidly changing health and social policy context.

## Objectives

By the end of this subject you should be able to:
* Integrate and apply an understanding of macro level practice approaches (health promotion, capacity building, service development/quality assurance, leadership and project management)
* Apply principles of project scoping to justify, design and propose an ethically considered health project in consultation with an external agency
* Evaluate/analyse projects targeting national health priorities re: occupation, prevention, and project management factors
* Apply principles of project management to implement, evaluate and communicate project processes and outcomes to a range of stakeholders
* Critically reflect on, and apply advanced professional capabilities to successfully lead and influence the project management process, and communicate these in an interactive forum
* Work collaboratively with a range of stakeholders to manage the project process and communicate progress and outcomes
* Provide a coherent statement of the professional capabilities you have developed in relation to the project-based learning experience
* Critically reflect on the personal learning journey throughout the program and generate a plan for continued learning.

## Assignments

* Quiz
* Project based learning assessments
* Population Health Presentation
* Other Hurdle Requirements

## Topics

Throughout the weeks you will apply, critique and reflect upon major subject themes by planning and appraising your own project, and critiquing and reflecting on others' project process and outcomes. The subject topics should be viewed as integrated.
* Introduction and overview (Week 1)
* Project management (Weeks 1-6)
* Health promotion and prevention (Weeks 3-6)
* Leadership & Political skill (Week 4)
* Preparation for contemporary practice (Weeks 8-10)
# Machining

Machining related learning materials may be here.

## Learning resources
### Wikipedia

* Machining
* Lathe
* Milling machine
* Metalworking
* Machinist
* Well drilling
* Machine tool
* Machinist calculator
* Electrical discharge machining
* Electro chemical machining
* Lathe (metal)
* Drilling
* Tap and die
* Grinding machine
* Welding
* Fabrication (metal)

### Learning videos

* Making a BOLT ACTION Pen
* A Career In Machining (1971) (of potential historical interest)
* CNC Machining 30,000 LBS of Steel Per Day
* Prototype Machining from a Garage Shop with Metal Parts Machine
* Making A Toolmakers Mill Vise
* How Experts Made 4Ton Roller For Milling Machine - Machining With The Big Lathe
* Making a Machinist Hammer
* Machining a Custom Motorcycle Axle
* Casting and Machining a Brass Ingot from brass plumbing fittings
* Machining BIG Parts for Caterpillar Construction Machinery & Equipment
* Making Parts for CAT D10 Dozer
* Machining Giant Crankshaft Using Heavy Lathes
* Machining Process of Eccentric Shaft For Stone Crusher Plant on Lathe Machine
# Macro Strategies to Enable Occupation/Health promotion and prevention

Viewing health through a prevention and health promotion lens and applying this thinking can reflect a micro and/or macro level approach. In MSP we will take the opportunity to think 'macro'. How can our actions as health professionals - experts in occupation and its relationship to health and wellbeing - take on a more population rather than individual focus. How can we promote health by tackling the determinants of health (individual and social) environments, policy, personal skills, community action, and reorienting health services.
During this week you will be encouraged to think about prevention and health promotion. You will attend or access the scheduled lecture. During this lecture we will set out your task to explore a population health strategy (a project) with the dual aim of:
Firstly, understanding how others have tackled the health burden at a population level, and
Secondly, thinking about the strengths and limitations of the projects that others have scoped and devised to address identified needs.
Instructions for this week
1. Listen to this podcast with Evelyne DeLeeuw - where she talks with Tracy Fortune about why health promotion, and, why OT?
# Instructional design/ARCS IMDesign

| 1. ID Home | 2. Introduction | 3. Learner Analysis | 4. Information Design & Motivational Design | 5. Are You Ready? | 6. How Others Did It? |
test
# Instructional design/ARCS Try It

| 1. Introduction | 2. ARCS | 3. Learner Analysis | 3. Information Design & Motivational Design | 5. Are You Ready? | 6. Evaluation |

## Problem

The principal of the rural Alaska school was very impressed with the workshop you designed and how students were motivated during the workshop. Now that the school started to offers online high school courses, you are considered to lead the design and development for the same content; however, this time the delivery is changed to a 30-minute self-running module with the same audiences (Grade 9) who are enrolled in the distant program but live in remote villages in the same state.
Your task is to apply motivational information design strategies based on the learners' learning-style preferences as to include
* at least 2 strategies that gain the student’s attention in e-learning,
* at least 2 strategies that establish relevance to the student in e-learning,
* at least 2 strategies that boost the confidence of the student in e-learning, and
* at least 2 strategies that increase the student's satisfaction in e-learning.
Please also explain the reasons why a typical motivational information design strategy is chosen and give evidence from the case. In order to consider the background and context of the instruction as well as the analysis results of the learner in your design (i.e. the learning-style preference), please refer to the previous case scenario.
Name:
Description of your lesson:
A1:
A2:
Evidence:
R1:
R2:
Evidence:
C1:
C2:
Evidence:
S1:
S2:
Evidence:
| 1. Introduction | 2. ARCS | 3. Learner Analysis | 3. Information Design & Motivational Design | 5. Are You Ready? | 6. Evaluation |
# Instructional design/ARCS Evaluation

| 1. Introduction | 2. ARCS | 3. Learner Analysis | 3. Information Design & Motivational Design | 5. Are You Ready? | 6. Evaluation |

## Rubrics

Once you complete the final task, please refer to the rubric below for quality assurance. You need to score at least 75% (3 out of 4) or higher in order to pass.
| CATEGORY | 4 | 3 | 2 | 1 |
| Content | All content is in your own words and is accurate. | Almost all content is in your own words and is accurate. | At least half of the content is in your own words and is accurate. | Less than half of the content is in your own words and is accurate. |
| Motivational Information Design Strategies | All the applications of the motivational information design strategies in each area of attention, relevance, confidence, and satisfaction are appropriate. | Most applications of the motivational information design strategies in each area of attention, relevance, confidence, and satisfaction are appropriate. | At least half of the applications of the motivational information design strategies in each area of attention, relevance, confidence, and satisfaction are appropriate. | Less than half of the applications of the motivational information design strategies in each area of attention, relevance, confidence, and satisfaction are appropriate. |
| Grammar and Spelling | No spelling or grammatical mistakes with a lot of text. | No spelling or grammatical mistakes with a little text. | Three spelling or grammatical error. | Five or more than five spelling and/or grammatical errors. |
| Clarity and Neatness | All elements are easy to read and all elements are so clearly written, labeled, or drawn. Your peer instructional designer could create the presentation if necessary. | Most elements are easy to read and all elements are so clearly written, labeled, or drawn. Your peer instructional designer might be able to the presentation if necessary. | Elements are hard to read with rough drawings and labels. Your peer instructional designer might ask a lot of questions. It might be hard for him to create this presentation. | Elements are hard to read and one cannot tell what goes where. It would be impossible for Your peer instructional designer to create this presentation without questions. |
# Instructional design/ARCS Introduction

◀ ID Homepage
| 1. Introduction | 2. Learner Analysis | 3. Information Design & Motivational Design | 4. Are You Ready? | 5. How Others Did It? |
This lesson includes the following components:
* preview Keller’s ARCS Model of Motivational Design and the role of a learner analysis.
* viewing provided examples that present the choices of information design strategies with regards to attention, relevance, confidence, and satisfaction perspectives in Keller’s Motivational Design Model.
* Draft a paper prototype plan within a given e-learning project scenario and defined characteristics of the targeted audience.
* Review a completed sample solution to the scenario.
Let's get started!