OpenLLM-France/wikimedia huggingface dataset:
# Science: A Field Of Wonder/Characteristics of Scientists and How Do Scientists Think
## Characteristics of Scientists

Scientists must possess certain attitudes or ways of thinking to be successful in making scientific investigations. To think like a scientist, you need to have the following:
* Curiosity or inquisitiveness. Scientists never stop learning. They show interest and pay particular attention to objects of events. They ask questions and seek answers.
* Creativity. Scientists are sensitive to problems and can generate original ideas. They are able to find new and alternative answers to a problem.
* Humility. Scientists are humble. They admit that they are not free from committing errors . They recognize that they may be better ideas and realize that there are individuals whom they may have to consult to consult to arrive at correct observations and conclusions.
* Critical-mindedness. Scientists base suggestions and conclusions on evidence. They prefer accuracy of facts and reliability of sources of information.
* Intellectual honesty. Scientists give a truthful report of observations. They do not withhold important information just to please others.
* Resourcefulness. Scientists think of possible alternative solutions to problems they are working on. They find alternative materials to be used for their experiment.
* Objectivity. Scientists do not allow their feelings and biases to influence recording of observations, interpretation of data, and formulation of conclusions.
* Patience. Scientists spend time or days of work to finish a task and get an accurate result.
* Careful judgement. Scientists do not easily jump to conclusions. Their judgement is based on facts and reliable information.
* Rationality. Scientists believe that in this world, things happen for a reason. They only accept facts and statements that are supported by proofs.

## How Do Scientists Think?

You can do what scientists do. Scientific thinking, also commonly called science inquiry or the scientific method, is a process for both asking and answering questions about the universe. This is used by all kinds of scientists to investigate and answer questions. The scientific method involves the following:
* Using the senses and scientific equipment to make careful observations about the environment.
* Asking specific questions about observations that can be answered, using the tools of science.
* Forming hypotheses that explain what is observed.
* Testing hypotheses through repeated experiments and other tests and through collecting and recording data.
* Analyzing and drawing conclusions from the data
* Asking new questions, making new observations, and forming new hypotheses based on these findings
Science inquiry depends on critical thinking skills. This involves keeping one's mind open to new ideas. Wanting to investigate rather than accepting explanations of others, exemplifies scientific thinking.

#### Science Inquiry Process

Below is a process that most of the scientists follow to answer questions and make new discoveries.
# Science: A Field Of Wonder/Introduction

What is science? How is science learned? What does "doing science" mean? How is science done? What tools are needed to do science? How are scientific investigations done? By discovering the answers to these questions you will better appreciate what science truly is.
Everyone should realize the contributions of science and scientists to society. The technological advancement that you are enjoying today is the outcome of researches in science and discoveries by scientists. Young people like you should be encouraged to be interested in science or science-related fields in order to build the country's human resources to a level that can change the country toward economic progress. As you go through this introduction, try to see how well you can answer each of ther questions posted earlier. Moreover, see how your answer could influence the way you view the present-day world.

#### Science and Technology

The word science comes from the Latin term scientia, which means "to know". Science refers to an organized body of knowledge, which people have learned and gained through the use of scientific processes. Furthermore, science is often described as any systematic field of study.
The application of scientific knowledge to practical purposes is called technology or applied science. Technology comes from the Latin words techne, meaning "craft or skill" and logia, meaning "study."
The study of science and technology is very important because it deals with the improvement of the quality of life.
An example of this is a modernized tricycle or E-trike which eliminates the effects of noise and air pollution.
Science and technology provide so much impact on our lives. However, their negative effects cannot be ignored.. For instance, soil erosion, waste management, flooding, new diseases, and other health-related problems are the consequences of the processes and products of science and technology. Aside from these threats to individuals and the surroundings, world-related concerns are also present. An example is the hole in the ozone layer of the atmosphere due to the chlorofluorocarbons (CFC) from aerosols and refrigerants. The issue on global warming, the changes in climate patterns, and the rise in sea level around the world are other examples of environmental problems caused by some products and processes of science and technology.
It is now a challenge for humans like you, equipped with scientific knowledge and skills, to be able to decide wisely whether a particular process or product of science and technology can serve as a risk or a support to human lives.
# Science: A Field Of Wonder
## Table of Contents
### Preface

* Preface

### Introduction

* Introduction
* Limitations of Science: Believe It or Not
* Branches of Science
* Characteristics of Scientists and How Do Scientists Think
* About The Laboratory

### First Unit (Matter)

* First Unit Opener

#### Chapter 1 (Mixtures and Their Characteristics)

* Homogeneous and Heterogeneous Mixtures
* Separating Mixtures

### Second Unit (Living Things and Their Environment)

* Second Unit Opener

#### Chapter 2 (Different Systems of the Human Body)

* Integumentary System
* Musculo-Skeletal System
* Digestive System and Excretory System
* Respiratory System
* Circulatory System
* Nervous System and Endocrine System

#### Chapter 3 (Diversity of Animals)

* Vertebrates
* Invertebrates

#### Chapter 4 (Diversity of Plants)

* Spore-bearing Plants
* Cone-bearing Plants

#### Chapter 5 (Interactions in the Ecosystem)

* Tropical Rainforests
* Mangrove Swamps
* Coral Reefs
# School Science/Winkler test for dissolved oxygen

The Winkler test is used to determine the level of dissolved oxygen in fresh water samples. What follows is a set of instructions on how to perform the test.

## Materials
### Stage 1

* Manganese(II) sulfate 48%
* Potassium iodide 15% in potassium hydroxide 70%
* Sample of fresh water
* Latex gloves
* Safety glasses

### Stage 2

* Sulfuric acid 60%
* Sodium thiosulfate 0.31%
* Starch making up solutions 0.1%
* Burette
* Burette stand
* 10 ml pipette and pipette filler
* 100 ml conical flasks
* Filter paper
* Latex gloves
* Safety glasses

## Method
### Stage 1

Collect and label water samples in 25 ml stoppered bottles. (Two samples per location are required for Biological Oxygen Demand testing.)
Add 0.1 ml of manganese(II) sulfate solution, and mix carefully, without letting in air. Add 0.2 ml of alkaline potassium iodide, and again mix without letting in air. A pinky-brown precipitate should appear. At this point the sample may be stored for later analysis in the laboratory.

### Stage 2

Add 0.3 ml sulfuric acid to each sample, and mix. Allow the sample to stand for two minutes. If the precipitate does not dissolve into iodine solution, add a further 0.1 ml acid. Fill the burette with thiosulfate solution and adjust to zero (or note the burette reading). Transfer 10 ml of the sample to a conical flask, and add a few drops of starch solution. The subsample should turn blue. Titrate the subsample with thiosulfate until it turns clear. (You may find the endpoint easier to see if the conical flask is stood on a sheet of filter paper.) Record and repeat the titration.

## Notes

Each milliliter of thiosulfate titer is equivalent to 0.1 mg of oxygen in the 10 ml subsample. Thus 1 ml of thiosulfate is equivalent to 1 mg oxygen per 100 ml fresh water.
To determine five-day Biological Oxygen Demand (BOD$_5$), several dilutions of a sample are analyzed for dissolved oxygen before and after a five-day incubation at 20 degrees Celsius (68 degrees Fahrenheit) in the dark. In some cases the sample must be provided a source of oxygen-using bacteria, called "seed", in order to obtain results. The difference in DO and the dilution factor are used to calculated BOD$_5$. The resulting number (usually reported in parts per million or milligrams per Liter) is useful in determining the relative organic strength of sewage or other polluted waters.
The BOD$_5$ test is an example of analysis that determines classes of materials in a sample.
Instrumental methods for measurement of Dissolved Oxygen have widely supplanted the routine use of the Winkler test, although it is still widely used to check instrument calibration.

## References

* Moran, Joseph M.; Morgan, Michael D., & Wiersma, James H. (1980). Introduction to Environmental Science (2nd ed.). W.H. Freeman and Company, New York, NY ISBN 071671020X
* Standard Methods for the Examination of Water and Wastewater - 20th Edition ISBN 0-87553-235-7. This is also available on CD-ROM and online by subscription
# Science: A Field Of Wonder/First Unit Opener

Look around you and observe the things that surround you - the animals and the plants, the concrete buildings, the vehicles, the glass doors and windows, the wooden tables, the clothes you wear, your rubber shoes, books, pen, pad paper, the food you eat, the water you drink, the people around you, and everything in the sky above you. These are forms of matter.
In Unit I, you will learn the types, characteristics, and the ways on how to separate mixtures.
# PyTorch/Tensor
## Tensor

The basic object in PyTorch is tensor. Tensors are similar to numpy matrices with two important additions: they work with CUDA, and they can calculate gradients.
Tensors are created and manipulated similarly to numpy matrices:
All function like np.ones, np.zeros, np.empty and so on, as well as other main functions and arythmeric operators, also present in torch:
For tensors, the function size is a function which returns torch.Size object, rather then a member which is a tuple. It is good, because torch.Size inherits tuple and has some additional operators defined:
The functions sum, mean and so on for tensors return not a number but a zero dimensional tensor. Tensor elements are also zero dimensional tensors rather than numbers:
Instead of numpy's astype, in torch there is a function to
The name is changed because the function to can do more than just change element types. It can also move data to and from CUDA, and it works for the wide range of torch datatypes, including neural networks.

### Tensors and numpy matrices

Since tensors and numpy matrices are so similar, it would be nice if we could convert them to each other. And we, indeed, can. It is as easy as cake. To convert tensor to matrix, just call numpy method. For the opposite, call torch.tensor constructor:

### CUDA

While you can use PyTorch without CUDA, it accelerates the computations by a factor of 10-20.
Before using CUDA, check whether it is available. Type:
If it returned False, you may skip the rest of this section.
You may also check the versions of CUDA and cuDNN library:
Unlike numpy, tensors can be easily moved to and from CUDA memory. In CUDA, you can do almost whatever you can do out of it. If your computer is equipped with CUDA, and you installed the driver (NVIDIA CUDA 10.0 or higher), you can do the following:
On my computer, the time was 0.4 seconds, which is $2.5\times 10^{12}$ multiplications per second.
You can easily move tensors to and from CUDA memory with to method
You cannot mix CUDA and CPU tensors in your expressions:

### Autograd

The autograd module implemented into PyTorch makes calculating gradients via backpropagation a piece of cake. You need to specify the requires_grad parameter ("requires" with -s, "grad" without), and call backward method.
# Python 3: working with files and digital assets/Preliminary/Jupyter
## Jupyterlab
### Start

to start jupyter lab run

## Jupyter Notebook

If you want the classic experience you can install notebook with:

### with
#### Pythons Package Manager
## Jupyter Desktop

You can find the latest version of jupyter Desktop at Github. Jupyter Desktop is an application that supports Windows, Linux and MacOS.

### with
## References

* 1 2 3 "Installing Jupyter - Get up and running on your computer". Project Jupyter. Retrieved August 24, 2023.
* 1 2 "JupyterLab Desktop". Github. Retrieved August 24, 2023.
# Python Beginner to Expert
## Introducing Python

* Origins
* History
* language characteristics, etc.

## Structured Python

* Intro to shell
* Intro to IDLE
* Words about other development environments
* Basic syntax
* Built in types
* Assignment statements
* Arithmetic
* Math functions
* Lists and dictionaries
* Program flow Control statements
* iterators
* practice problems
* Debugging techniques

## Python for shell scripting

* String processing (re module)
* OS commands
* Example scripts
* practice problems

## Python for web programming

* Example scripts
* Practice problems

## Survey of web frameworks

* Django
* Zope
* flask
# Downloading Files
## Installation of packages
### In the command terminal

If you're using the command terminal from your operating system. You can download the required packages by writing the commands:
# Python 3: working with files and digital assets/Image/EXIF data
## Requirement
### Retrieval of data

Code Snippet:

### Retrieval of GPS Location

Code snippet:

## Footnotes

* 1 2 "image exif information tutorial.ipynb". Gist. Retrieved 2023-07-12.
# Ordinary Differential Equations/d'Alembert

The d'Alembert's Equation, which is sometimes called the Lagrange equation was solved by John Bernoulli before 1694, and d'Alembert studied its singular solutions in a 1748 publication. It is essentially an equation of the form
$y=xf(y')+g(y')$
Where $f$ and $g$ are functions of $y'$.
Take the derivative
$y'=f(y')+(xf'(y')+g'(y'))y''$
Now write this equation as
${\frac {dx}{dy'}}-{\frac {f'(y')}{y'-f(y')}}x={\frac {g'(y')}{y'-f'(y')}}$
Then it is a linear equation with dependent variable x and independent variable <amth>y'</math>.
# Ordinary Differential Equations:Cheat Sheet

* Few Useful Definitions
* Solving First Order Ordinary Differential Equations
* Solving Second Order Homogeneous Ordinary Differential Equations
* Solving Second Order Inhomogeneous Ordinary Differential Equations
* About the Book
Few Useful Definitions →
# Ordinary Differential Equations:Cheat Sheet/Second Order Inhomogeneous Ordinary Differential Equations
## General Form

$p(D)y=g(x)$, where $p(D)$ is a polynomial differential operator of degree $2$ with constant coefficients.

### General Form of the Solution

General solution is of the form $y(x)=y_{c}(x)+y_{p}(x)$
where
$y_{c}(x)$ is called the complimentary solution, and is the solution of associated homogenous equation, $p(D)y=0$.
$y_{p}(x)$ is called the particular solution, obtained by solving $p(D)y_{p}=g(x)$

## Methods to find Complimentary Solution

Methods to solve for complimentary solution is discussed in detail in the article Second Order Homogeneous Ordinary Differential Equations.

## Methods to find Particular Solution
### Guessing method or method of undetermined coefficients

Choose appropriate y_p (x) with respect to g(x) from table below:
| $g(x)$ | $y_{p}(x)$ |
| $ae^{bx}$ | $Ae^{bx}$ |
| $a\cos {\alpha x}\pm b\sin {\beta x}$ | $A\cos {\alpha x}\pm B\sin {\beta x}$ |
| $a_{0}+a_{1}x+\cdots +a_{n}x^{n}$ | $A_{0}+A_{1}x+\cdots +A_{n}x^{n}$ |
Find $p(D)y_{p}(x)=g(x)$, equate coefficients of terms and find the constants $A$ and/or $B$ and/or $A_{0},A_{1},\cdots ,A_{n}$. If it leads to an undeterminable situation, put $y_{p}(x)=x\times y_{p}(x)$ until it’s solvable.

### Variation of parameters

This method is applicable for inhomogeneous ODE with variable coefficients in one variable.
Suppose two linearly independent solutions of the ODE are known. Then
$y_{p}(x)=-y_{2}(x)\int {y_{1}(x)g(x) \over W_{y_{1},y_{2}}(x)}dx+y_{1}(x)\int {y_{2}(x)g(x) \over W_{y_{1},y_{2}}(x)}dx$

### Solving by Laplace Transforms

When initial conditions are given,
* Find Laplace Transform of either sides (See notes in earlier chapter for few common transforms)
* Isolate F(s)
* Split R.H.S. into partial fractions
* Find inverse Laplace Transforms.

#### Using Convolutions

While solving by Laplace Transforms, if finally $F(s)$ is of the form </math>g(s)h(s)</math>, use property of convolutions that
$L{f(t)*g(t)}=L{f(t)}\cdot L{g(t)}$
and hence $y(x)=g(s)*h(s)$.
← Second Order Homogeneous Ordinary Differential Equations · About the Book →
# Ordinary Differential Equations/Without x or y
## Equations without y

Consider a differential equation of the form
$F(x,y')=0$.
If we can solve for y', then we can simply integrate the equation to get the a solution in the form y=f(x). However, sometimes it may be easier to solve for x. In that case, we get
$x=f(y')$
Then differentiating by y,
${1 \over y'}={df \over dy'}{dy' \over dy}$
Which makes it become
$y=C+\int y'{df \over dy'}dy'$.
The two equations
$x=f(y')$
and
$y=C+\int y'{df \over dy'}dy'$
is a parametric solution in terms of y'. To obtain an explicit solution, we eliminate y' between the two equations.
If it is possible to express
$F(x,y')=0$
parametrically as $x=f(t),y'=g(t)$,
then one can differentiate the first equation:
${\frac {1}{y'}}{\frac {dy}{dt}}=f'(t)$
So that
$y=C+\int g(t)f'(t)dt$
to obtain a parametric solution in terms of $t$. If it is possible to eliminate $t$, then one can obtain an integral solution.

## Equations without x

Similarly, if the equation
$F(y,y')=0$.
can be solved for y, write y=f(y'). Then the following solution, which can be obtained by the same process as above is the parametric solution:
$y=f(y')$
$x=C+\int {\frac {f'(y')}{y'}}dy'$
In addition, if one can express y and y' parametrically
$y=f(t),y'=g(t),$
then the parametric solution is
$y=f(t),$
$x=C+\int {\frac {f'(t)}{g(t)}}dt$
so that if the parameter $t$ can be eliminated, then one can obtain an integral solution.
# Ordinary Differential Equations:Cheat Sheet/Few Useful Definitions
## Wronskian of Two Functions
### Definition

The Wronskian of two functions $y_{1},y_{2}$ is given by
$W_{y_{1},y_{2}}(x)=\left|{\begin{matrix}y_{1}&&y_{2}\\y_{1}'&&y_{2}'\end{matrix}}\right|$

### Useful Facts

* If two functions $y_{1},y_{2}$ are linearly dependent on an interval, then their Wronskian vanishes on that interval.

## Laplace Transforms
### Definition

The Laplace transform of $f$ at a complex number $s\in \mathbb {C}$ is
${\mathcal {L}}\{f\}(s)=F(s)=\int _{0}^{\infty }e^{-st}f(t)\,dt$

### Properties

* Linearity: ${\mathcal {L}}\{af+bg\}=a{\mathcal {L}}\{f\}+b{\mathcal {L}}\{g\}\,$
If $F(s)={\mathcal {L}}\{f\}(s)$ then:
* ${\mathcal {L}}\{e^{at}f(t)\}(s)=F(s-a)\,$ for $s>\alpha +a$
* ${\mathcal {L}}\{f'\}(s)=sF(s)-f(0)$
* ${\mathcal {L}}\{f''\}(s)=s^{2}F(s)-sf(0)-f'(0)$

### Laplace Transform of Few Simple Functions

* ${\mathcal {L}}\{1\}={1 \over s}$
* ${\mathcal {L}}\{e^{at}\}={1 \over s-a}$
* ${\mathcal {L}}\{\cos \omega t\}={s \over s^{2}+\omega ^{2}}$
* ${\mathcal {L}}\{\sin \omega t\}={\omega \over s^{2}+\omega ^{2}}$
* ${\mathcal {L}}\{1\}={1 \over s}$
* ${\mathcal {L}}\{t^{n}\}={n! \over s^{n+1}}$

## Convolution
### Definition

The convolution of $f$ and $g$ is
$f(t)*g(t)=\int _{0}^{t}f(u)g(t-u)dt$

### Properties

Convolution is:
* Associative
* Commutative
* Distributive over addition
First Order Ordinary Differential Equations →
# Ordinary Differential Equations:Cheat Sheet/About the Book

This book summarizes the learning on solving Ordinary Differential Equations, in much less words as possible. Those who are trying to refresh their learning in ODE might find it useful. If you are looking for detailed explanation of content discussed here, please refer to the Wikibook Ordinary Differential Equations, which the author seems to have abandoned halfway, still contains a great deal of useful information in simple words.

## Author's Notes

I'm an amateur in ODE, and have presented information I know in the best way possible, in least words as possible. It's more of a reference book than a textbook. It surely has errors all over, please feel free to correct it.

## Sources

* Ordinary Differential Equations
* MIT 18_03S10 - Linear Differential Operator

## Roadmap

* Write content
* Create template to be present near each subheading, with links to relevant article and/or Wikipedia Page
# Ordinary Differential Equations:Cheat Sheet/First Order Ordinary Differential Equations
## Linear, Inhomogeneous Type
### General Form

${dy \over dx}+p(x)y=q(x)$

### Solution

$y(x)={\int u(x)q(x)dx+C \over u(x)}$, where
* $C$ is a constant and
* $u(x)=e^{\int p(x)dx}$

## Separable
### General Form

${dy \over dx}=g(x)h(y)$

### Solution

Rearrange to get ${dy \over h(y)}=g(x)dx$, and integrate

## Bernoulli's
### General Form

${dy \over dx}+p(x)y=q(x)y^{n}$

### Solution

Substitute $v=y^{1-n}$

## Exact Equations
### General Form

$M(x,y)dx+N(x,y)dy=0$, with ${\partial M \over \partial y}={\partial N \over \partial x}$

### Solution

Solution is of the form $F(x,y)=C$, a constant, where $F_{x}=M$ and $F_{y}=N$

## Approximation Methods

Let $y'=f(x,y),y(0)=y_{0}$

### Euler's Method

Euler's method with step size $h$ is given by:
$y_{n+1}=y_{n}+hf(x_{n},y_{n})$.

### Improved Euler's Method

Improved Euler's method with step size $h$ is given by:
$y_{n+1}=y_{n}+{\frac {h}{2}}\left[f(x_{n},y_{n})+f(x_{n+1},{\bar {y}}_{n+1})\right],{\bar {y}}_{n+1}=y_{n}+hf(x_{n},y_{n})$.

### Runge-Kutta Method of Fourth Order

For step size $h$,
$y_{n+1}=y_{n}+{\frac {h}{6}}\left[k_{1}+2k_{2}+2k_{3}+k_{4}\right]$, where
* $k_{1}=f(x_{n},y_{n})$
* $k_{2}=f(x_{n}+{\frac {h}{2}},y_{n}+{\frac {h}{2}}k_{1})$
* $k_{3}=f(x_{n}+{\frac {h}{2}},y_{n}+{\frac {h}{2}}k_{2})$
* $k_{4}=f(x_{n}+h,y_{n}+hk_{3})$
← Few Useful Definitions · Second Order Homogeneous Ordinary Differential Equations →
# Ordinary Differential Equations/Trajectories
### Orthogonal Trajectory

Let A be a family of curves. Then B is an orthogonal trajectory of A if every member of B(also a family of curves) cuts every member of A at right angle.It is important to note that we are not insisting that B should intersect every member of A but if they intersect, the angle between their tangents, at every point of intersection, is ${\pi }/2$

## Example

Every straight line passing through origin is a normal to every circle having origin as the center. Hence they are orthogonal trajectories of each other.

## Steps to find orthogonal trajectory

* let f(x,y,c)=0 be the equation of the family of curves, where c is an arbitrary constant.
* Differentiate the given equation with respect to x and then eliminate c.
* replace $dy/dx$ by $-dx/dy$
* Solve the obtained differential equation. You will get the required orthogonal trajectory.