OpenLLM-France/wikimedia huggingface dataset:
# Factorial function/Increasing/10! geq e^(11)/Estimate with exponential function/Exercise

a) Prove that for $x\geq 1$ the estimate
    $\int _{1}^{\infty }t^{x}e^{-t}dt\leq 1\,$
holds.
b) Prove that the function $H(x)$ defined by
    $H(x)=\int _{1}^{\infty }t^{x}e^{-t}dt\,$
for $x\geq 1$ is increasing.
c) Prove that $10!\geq e^{11}+1$.
d) Prove that for the factorial function for $x\geq 10$ the estimate
    $\operatorname {Fac} \,x\geq e^{x}\,$
holds.
# Introduction to Non-Genetic Darwinism

Introduction to Non-Genetic Darwinism
Although this course is nearly complete, feel free to help out! You are encouraged to add or edit lessons.
The aim of the course is to discuss the possibility of applying evolutionary principles to other fields, including fields outside biology. We discuss the principles of self-organization down to the Physical Laws that regulate it, then give numerous examples of how Darwinism is being used. We argue that the term for such applications should be "Non-Genetic Darwinism." A discussion of relevant topics is presented.

## Lessons
### Conventional Darwinism

* Lesson 1: Darwin's Theory of Natural Selection
* Lesson 2: Classical Darwinism in Biology
* Lesson 3: Darwinism, Culture and Philosophy

### Non Conventional Darwinism

* Lesson 4: Physics of Self-Organization
* Lesson 5: Complexity Theory
* Lesson 5: Immune System Darwinism
* Lesson 6: Neural Selection
* Lesson 7: Non-Biological Darwinism
* Lesson 8: Conclusion

## Instructors

* AFriedman 15:10, 22 February 2009 (UTC)
* Graeme E. Smith 16:36, 22 February 2009 (UTC)

## Links

* Resources for Research
# Geometric series/Real/Definition

For every $x\in \mathbb {R}$, the series
    $\sum _{k=0}^{\infty }x^{k}$
is called the geometric series in $x$.
# Geometry

Hello, and welcome to Wikiversity's online geometry course!

## Course Description

A course in plane and solid geometry will investigate the basic concepts of Euclidean geometry. Undefined terms and axioms will be presented and used to prove conjectures. The properties of two- and three-dimensional shapes will be explored. Students will also work with coordinate geometry, including transformations. The goal of this course is not only to master the facts of geometry necessary for advanced courses but also the techniques of deductive mathematical proofs as well.

## Curriculum

One lesson should be learned every weekday. Chapter 1 ~ Essentials of Geometry Chapter 2 ~ Reasoning and Proof Chapter 3 ~ Parallel and Perpendicular Lines Chapter 4 ~ Triangles Chapter 5 ~ Similarity Chapter 6 ~ Trigonometry Chapter 7 ~ Quadrilaterals Chapter 8 ~ Properties of Circles Chapter 9 ~ Measuring Length and Area Chapter 10 ~ Surface Area and Volume of Solids Chapter 11 ~ Final Exam

## Homework assignments

Homework will be assigned after most class sessions at the bottom of the page. Homework will be emailed the day after you complete your assignment. Homework will be graded for completeness and correctness. A student can receive up to 3 points for a question. Two points will be awarded for attempting to solve a problem. A third of the assigned problems will be graded for correctness, with an additional point given for the correct answer. No credit will be given for problems not solved. Therefore, every problem should be attempted. As we are more interested in learning methods of solving problems than in answers, all work involved in solving a problem must be shown for credit to be received.

## Tests, quizzes, and exams
### Tests

Tests are given after every chapter and must be completed within 45 minutes. Tests are out of 100 points. To be granted access to the test. All homeworks must be handed in on time. Except for 2, if you wish

### Quizzes

One quiz may be given a chapter, depending on the difficulty. Quizzes are given 15 minutes to complete. Half the homework, minus 2 of them, must be handed in to access the quiz.

### Exams

An exam is given half-way through the program and at the end. Exams are given 60 minutes to complete. Exams will be given after you complete half, and then all the tests.
# Geometric series/Real/Convergence/Absolutely/Fact/Proof

For every $x$ and every $n\in \mathbb {N}$ we have the relation
    $(x-1){\left(\sum _{k=0}^{n}x^{k}\right)}=x^{n+1}-1\,$
and hence for the partial sums the relation (for $x\neq 1$ )
    $s_{n}=\sum _{k=0}^{n}x^{k}={\frac {x^{n+1}-1}{x-1}}\,$
holds. For $n\rightarrow \infty$ and $\vert {x}\vert <1$ this converges to ${\frac {-1}{x-1}}={\frac {1}{1-x}}$ because of fact and exercise.
# Geometrical optics

Describing light propagation in terms of rays.
Ray - idealized geometrical model of light.
Law of refraction possible to use for reflective surfaces, curved surfaces can be modeled by ray tracing.
Shell's law can show deflection of a light ray while refraction.
Lenses - devices which produces converging or diverging light rays during refraction. In general two types: convex and concave lenses.
Focal point can be modeled by lensmaker's equation, prediction of how images can be produced by lens formula.
Reflectivity between two materials possible to calc by Fresnel equations.
# Geometry/Chapter 1
## Lessons

* Lesson 1 - Identifying Points, Lines, and Planes.
* Lesson 2 - Use Segments and Congruence
* Lesson 3 - Midpoint and Distance
* Lesson 4 - Measure and Classify Angles
* Lesson 5 - Describe Angle Pair Relationships
* Lesson 6 - Classify Polygons
* Lesson 7 - Find Perimeter, Circumference, and Area
# Midpoint & Distance
## Formulas

Midpoint: $(x2+x1/2,y2+y1/2)$
Distance:$\surd (x2-x1)^{2}+(y2-y1)^{2}$

## Midpoint

Midpoint: a point that is in the middle of the line joining two points.
Example:
If C is in the middle of A (5,4) and B (2, 1)
(5+2/2, 4+1/2) | 5+2 = 7/2 = 3.5 and 4+1 = 5/2 = 2.5 that means C is (3.5,2.5)
Now You Try:

## Distance

Distance: The Difference Between 2 Points/coordinates
1. What Would The Distance Be Between (3,7) and (-1,7)
√(-1-3)^2 + (7-7)^2 then √(-4)^2 + (0)^2 and now when you add, it's √16, and √16 is 4.
2. What Would The Distance Be Between (4,6) and (2,8)
√(2-4)^2 + (8-6)^2 then √(-2)^2 + (2)^2 and now when you add, it's √8 then simplified then its 2√2, that's your answer!
Now You Try:

## Sources

* ↑ "Midpoint Formula - Formula, How to Find Midpoint? Examples". Cuemath. Retrieved 2022-09-22.
* ↑ "Distance Formula - Derivation, Examples, Types, Applications". Cuemath. Retrieved 2022-09-22.
# Geometric series/Real/Convergence/Absolutely/Fact

For all real numbers $x$ with $\vert {x}\vert <1$, the geometric series $\sum _{k=0}^{\infty }x^{k}$ converges absolutely, and the sum equals
    $\sum _{k=0}^{\infty }x^{k}={\frac {1}{1-x}}\,.$
# Geometry/Chapter 10

Oops! These lessons haven't been taught yet. Come back soon! AvidInsight
Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6
# Geometry/Chapter 1/Lesson 1

In geometry, the words, point, line, and plane are undefined terms. These words do not have formal definition, but there is agreement about what they mean.
* Key Concept
* Undefined Terms
* Point A point has no dimension. It is represented by a dot.
* Points can be named like: Point A, Point B, etc.
* Line A line has one dimension. It is represented by a line with two arrowheads, but it extends without end.
* Through any two points, there is exactly one line. You can use any two points on a line to name it.
* Plane A Plane has two dimensions. It is represented by a shape that looks like a floor or a wall, but it extends without end.
* Through any three points not on the same line, there is exactly one plane. You can use three points that are not all on the same line to name a plane.
* Football Field: The dots on the football field can be seen as a point. The lines on the football field can be seen as the geometric undefined term, line, and the football field itself can be interpreted as a plane.
Collinear points are points that lie on the same line. Coplanar points are points that lie in the same plane.

## Example 1 Name points, lines, and planes

DEFINED TERMS In geometry terms that can be described using known words such as point or line are called defined terms.
* Key Concept
* Defined Terms: Segments and Rays
* Line AB and points A and B are used here to define the terms below.
* Segment The line segment AB, or segment AB, consists of endpoints A and B and all points on line AB that are between A and B. Note that line AB can also be named line BA.
* Ray The ray AB consists of the endpoint A and all points on line AB that lie on the same side of A as B. Note that ray AB and ray BA are different rays, since the vertex, or endpoint, is the first letter in naming a ray.
* Opposite Ray - If C is in between A and B, then CA and CB are opposite rays. Opposite rays are two rays that have the same endpoint, but go in different directions.
* Segments/rays are collinear if they lie on the same line. Opposite rays are collinear as well. Lines, segments, and rays are coplanar if they lie in the same plane.
# Informal learning activities/eB

Beings & Behaviourː {{{1}}}__
This template abbreviates initial letter heading code within Beings & Behaviour files.
# Informal learning activities/eQ

Buildings & Placesː {{{1}}}__
This template abbreviates initial letter heading code within Buildings & Places Extra files.
# Informal learning activities/eS

Things and Bitsː {{{1}}}__
This template abbreviates initial letter heading code within Things and Bits files.
# Informal learning activities/eL

Extra Living Thingsː {{{1}}}__
This template abbreviates initial letter heading code within Extra Living Things files.
# Informal learning activities/dW

Women & Menː {{{1}}}⇒ {{{2}}}__  O ther initialsː
This template abbreviates main headings within the Men & Women Extra files.
# Informal learning activities/eM

Men & Womenː {{{1}}}__
This template abbreviates initial letter heading code within Men & Women files.
# Informal learning activities/eP

Places & Buildingsː {{{1}}}__
This template abbreviates initial letter heading code within Places & Buildings files.
# Informal learning activities/dS

Things and Bitsː {{{1}}}⇒ {{{2}}}__  O ther initialsː
This template abbreviates main headings within Things and Bits files.
# Informal learning activities/eD

Extra Bits & Thingsː {{{1}}}__
This template abbreviates initial letter heading code within Extra Bits & Things files.
# Informal learning activities/eW

Women & Menː {{{1}}}__
This template abbreviates initial letter heading code within Women & Men Extra files.
# Digital Media Concepts/Afghanistan

Kabul is the capital of Afghanistan.
# Digital Media Concepts/Amazon Echo
## Amazon Echo
### Introduction:

Amazon Echo is a smart home product, that is hands free and controlled by saying “Alexa.” There are two colors the Echo is available in black or white. The Amazon Echo is 9.3 inches tall, 3.3 inches wide and weighs 37.5 oz. The device is Wi-Fi and Bluetooth compatible. It comes with a 2.5-inch bass speaker and a 2.0-inch high note speaker. Also included with the Amazon Echo would be the 6-ft. power adaptor and an instruction guide.

### Features:

Like how Siri works you say a command or ask a question and the device will deliver the request. The device can talk back to you, play music, put reminders, turn off lights, put a movie on T.V., get local news, weather and other informational request. Allowing the Echo device to give all this information there are a lot of third parties involved. There is also a third party called the Alexa app that goes with the Echo device, that gives off helpful, funny, and important information. Such as Uber, Pandora, 7-minute workouts, Domino’s pizza, Capitol one bank, stocks and many other applications.

### Set Up:

The first part of the set-up is to download the Alexa app. It is free to download with iOS and Android services. Once you open the Alexa app you need to sign into your Amazon account. So, you can activate the device you want to work. There are multiple devices to choose from such as Amazon Echo, Echo Dot, Tap, and Echo Show. After you have chosen the right device, picking a language is the next step. Next, plug in your brand-new Echo and an orange ring light at the top of the device should light up, if the orange ring light does not show, press the single dot at the top of the device and hold it for five seconds. This action button should put Alexa in setup mode and you may continue. If you downloaded the Alexa app on your phone or pc you now need to connect the app to same Wi-Fi network that the Echo device is on which is called “Amazon-2Q3,” the last three digits will always be different. You should see a list of all your home Wi-Fi networks that are available connect to yours. Once you are connected Alexa will let you know that the Echo is ready and the orange light will turn off. The final setup part is a video that pops up on the Alexa app explaining some of the basics of the Echo device. You can also change the command from Alexa to whatever you desire. Your Echo is now setup and ready for use.
# Lectures

While lectures may be less popular in college classrooms than in decades past, they are still very popular between universities and the public. Consider the following examples.

## Public lectures

"In our automated lives, we generate and interact with unprecedented amounts of data. This sea of information is constantly searched, catalogued, analyzed and referenced by machines with the ability to uncover patterns unseen by their human creators. These new insights have far reaching implications for our society. From our everyday presence online, to scientists sequencing billions of genes or cataloging billions of stars, to cars that drive themselves – this series of six lectures will explore how the confluence of humans, data and machines extends beyond science – raising new philosophical and ethical questions."
"Since September 1922, Steward Observatory has been hosting public evening lectures in astronomy. The lectures begin at 7:30 p.m. and are held in Room N210 of Steward Observatory, 933 N. Cherry Ave., Tucson. AZ 85721(unless otherwise noted.) Following all Monday evening talks, the Raymond E. White, Jr. Reflector in the historic Steward Observatory dome will be open for public viewing of the night sky (weather permitting). All of the lectures and the use of the telescope are free of charge and open to the general public."

## Classroom lectures

"Lectures are a very common (I could safely generalize and say even the most common) method of teaching at the university level. This does not mean that there are no labs, seminars, discussion sessions, group projects etc. It only means that if we look at the academic schedule of most disciplines, the majority of the booked times are under the heading “lecture”. During these lectures, the teacher imparts information on a specific topic to a group of students. What happens is known as “information transfer”: the teacher shares her knowledge with the students, who take notes and can ask questions whenever something is not clear. At the end of the session, the teacher and the students are in possession of the same amount and quality of information about the specific topic – the transfer of information has been completed."
# Lecture

This Education resource is a "stub". Learn how you can help Wikiversity to develop it.
A lecture is an oral presentation intended to convey information or teach people about a particular subject. Lectures are often given, for example, by university or college teachers.
A group of lectures can make up a course, specifically a lecture course. According to Wikipedia, there are various types of courses, and lecture course is one type of course.

## Related readings
### Wikipedia

* Course (education) - this Wikipedia article specifically mentions lectures and how they relate to courses.

### External

* Lecturing Effectively
# Lecture as performance

"Lecture as performance" refers to the bringing together of dramaturgy and pedagogy in the context of lectures. Thus, lectures can be approached as a drama, and dramatic theories and techniques can be utilised to facilitate affective, social, and intellectual engagement with the topic.
# Integration/Substitution/Fact

Suppose that $I$ denotes a real interval, and let
    $f\colon I\longrightarrow \mathbb {R}$
denote a continuous function. Let
    $g\colon [a,b]\longrightarrow I$
be a continuously differentiable function.
    $\int _{a}^{b}f(g(t))g'(t)\,dt=\int _{g(a)}^{g(b)}f(s)\,ds\,$
# Integration/Substitution/General examples/Example

Typical examples, where one sees immediately that one can apply substitution, are
    $\int g^{n}g',$
with the primitive function
    ${\frac {1}{n+1}}g^{n+1}$
or
    $\int {\frac {g'}{g}},$
with the primitive function
    $\ln g.$
# Integration/Substitution/Remark

The substitution is applied in the following way: suppose that the integral
    $\int _{a}^{b}f(t)\,dt$
has to be computed. Then one needs an idea that the integral gets simpler by the substitution
    $t=\varphi (s)\,$
(taking into account the derivative $\varphi '(s)$ and that the inverse function $\varphi ^{-1}$ has to be determined). Setting $c=\varphi ^{-1}(a)$ and $d=\varphi ^{-1}(b)$, we have the situation
    $[c,d]{\stackrel {\varphi }{\longrightarrow }}[a,b]{\stackrel {f}{\longrightarrow }}\mathbb {R} .$
In certain cases, some standard substitutions help.
In order to make a substitution, three operations have to be done.
* Replace $f(t)$ by $f(\varphi (s))$.
* Replace $dt$ by $\varphi '(s)ds$.
* Replace the integration bounds $a$ and $b$ by $\varphi ^{-1}(a)$ and $\varphi ^{-1}(b)$.
To remember the second step, think of
    $dt=d\varphi (s)=\varphi '(s)ds\,,$
which in the framework "differential forms“, has a meaning.
# Integration/Substitution/dx version/Fact/Proof

Because of fact, we have
    $\int _{\varphi ^{-1}(a)}^{\varphi ^{-1}(b)}f(\varphi (s))\varphi '(s)\,ds=\int _{\varphi {\left(\varphi ^{-1}(a)\right)}}^{\varphi {\left(\varphi ^{-1}(b)\right)}}f(t)\,dt=\int _{a}^{b}f(t)\,dt\,.$
# Integration/Function with positive derivative/Extrema of partial areas/Exercise

Let
    $f\colon [0,1]\longrightarrow \mathbb {R} _{+}$
be a differentiable function with $f'(x)>0$ for all $x>0$. For what points $t\in [0,1]$ does the area of the hatched surface have a local extremum? Is it a minimum or a maximum?
# Integration/Polynomial/x^m (1-x)^n/Formula/Exercise

Show by induction over $n$, using integration by parts, that
    $\int _{0}^{1}x^{m}(1-x)^{n}dx={\frac {m!n!}{(m+n+1)!}}\,$
holds.
# Integration/Substitution/Fact/Proof

Since $f$ is continuous and $g$ is continuously differentiable, both integrals exist. Let $F$ denote a primitive function for $f$, which exists, due to fact. Because of the chain rule, the composite function
    $t\mapsto F(g(t))=(F\circ g)(t)\,$
has the derivative $F'(g(t))g'(t)=f(g(t))g'(t)$. Therefore,
    $\int _{a}^{b}f(g(t))g'(t)\,dt=(F\circ g)|_{a}^{b}=F(g(b))-F(g(a))=F|_{g(a)}^{g(b)}=\int _{g(a)}^{g(b)}f(s)\,ds\,.$
# Integration/Substitution/dx version/Fact

Suppose that
    $f\colon [a,b]\longrightarrow \mathbb {R}$
is a continuous function, and let
    $\varphi \colon [c,d]\longrightarrow [a,b],s\longmapsto \varphi (s),$
denote a bijective continuously differentiable function.
    $\int _{a}^{b}f(t)\,dt=\int _{\varphi ^{-1}(a)}^{\varphi ^{-1}(b)}f(\varphi (s))\cdot \varphi '(s)\,ds\,$
# Helping Give Away Psychological Science/Resources

HGAPS is finding new ways to make psychological science conferences more accessible!
Here are examples from APA 2022 and the JCCAP Future Directions Forum. Coming soon... ABCT! ~ More at HGAPS.org ~
* /Suicide
* /Bullying
* /Sexual Assault
* /Substance Abuse
* /Grief & Loss
* /Romantic Relationships
* /Annotated List of Where and How to Find a Therapist
# Helping Give Away Psychological Science/Resources/Bullying/Isolation and Loneliness

HGAPS is finding new ways to make psychological science conferences more accessible!
Here are examples from APA 2022 and the JCCAP Future Directions Forum. Coming soon... ABCT! ~ More at HGAPS.org ~
Dealing with feelings of loneliness, isolation, and depression
Feelings of loneliness and isolation are a normal part of the human experience,
* Dealing with depression and loneliness
* Loneliness and isolation
* Loneliness
# Helping Give Away Psychological Science/Resources/Grief & Loss

HGAPS is finding new ways to make psychological science conferences more accessible!
Here are examples from APA 2022 and the JCCAP Future Directions Forum. Coming soon... ABCT! ~ More at HGAPS.org ~
Dealing with a loss from suicide
Grieving from the loss of a loved one or acquaintance due to suicide can be overwhelming and cause feelings of guilt, anger, or confusion. The resources below from the Mayo Clinic details how to deal with emotions that can surface due to the event as well as healthy coping strategies.
https://www.mayoclinic.org/healthy-lifestyle/end-of-life/in-depth/suicide/art-20044900?pg=1
This resource from Harvard also addresses similar coping strategies and suggests as well as how to seek support from others and how to help a friend who might be struggling with a loss due to suicide.
https://www.health.harvard.edu/blog/suicide-survivors-face-grief-questions-challenges-201408127342
Dealing with the loss of a loved one and how to process grief
- http://www.apa.org/helpcenter/grief.aspx
- https://www.helpguide.org/articles/grief/coping-with-grief-and-loss.htm
# Helping Give Away Psychological Science/Public Interests

HGAPS is finding new ways to make psychological science conferences more accessible!
Here are examples from APA 2022 and the JCCAP Future Directions Forum. Coming soon... ABCT! ~ More at HGAPS.org ~
The following is a comprehensive list of the Public Interest pages created by HGAPS:
2017-2018 Year
* Microbiome and Mental Health
* Schizophrenia, Criminality, and its Portrayal in the Media
* Representation of Eating Disorders in To the Bone
* 13 Reasons Why
* Creativity in Bipolar Disorder
# Helping Give Away Psychological Science/Resources/Bullying

HGAPS is finding new ways to make psychological science conferences more accessible!
Here are examples from APA 2022 and the JCCAP Future Directions Forum. Coming soon... ABCT! ~ More at HGAPS.org ~

# Bullying

* http://www.voicesofyouth.org/en/posts/how-to-avoid-being-bullied
* http://www.stompoutbullying.org/information-and-resources/about-bullying-and-cyberbullying/are-you-being-bullied
* https://www.stopbullying.gov/what-you-can-do/teens/index.html
Stop Bullying.gov
* Main page: https://www.stopbullying.gov
* What is bullying and Statistics: https://www.stopbullying.gov/what-is-bullying/index.html
* Roles Kids Play: https://www.stopbullying.gov/what-is-bullying/roles-kids-play/index.html
* Who is at Risk: https://www.stopbullying.gov/at-risk/index.html
* Warning Signs: https://www.stopbullying.gov/at-risk/warning-signs/index.html
* Effects of Bullying: https://www.stopbullying.gov/at-risk/warning-signs/index.html
* Diversity, Race, Religion: https://www.stopbullying.gov/at-risk/groups/index.html
* LGBTQ Youth : https://www.stopbullying.gov/at-risk/groups/lgbt/index.html
George Lucas Educational Foundation:
* Main page: https://www.edutopia.org
* Anatomy of School Bullying: https://www.edutopia.org/article/anatomy-school-bullying-stephen-merrill
* 8 Steps to Combat Bullying: https://www.edutopia.org/blog/8-steps-combat-bullying-epidemic-ann-marie-gardinier-halstead
* Students with disabilities: https://www.edutopia.org/blog/anti-bullying-students-disabilities-maurice-elias
CyberBullying Research Center
* Main page: https://cyberbullying.org
* Statistics: https://cyberbullying.org/statistics
* Bullying laws across U.S: https://cyberbullying.org/bullying-laws
* CyberBulling stories: https://cyberbullying.org/stories
* Report CyberBulling: https://cyberbullying.org/report
CyberBullying Hotline
* Main page: http://www.cyberbullyhotline.com
* Call 1-800-420-1479
/Cyberbullying /Isolation and Loneliness