Added config, toc, ex1, ex6 statphys, basic anim.

_config.yml

+# Book settings
+# Learn more at https://jupyterbook.org/customize/config.html
+
+title: Open textbooks demonstration
+author: Timon Idema
+logo: tudelft.png
+copyright: Delft University of Technology, CC BY-SA 4.0
+
+# Only build files in the ToC to avoid building README, etc.
+only_build_toc_files: true
+
+# Force re-execution of notebooks on each build.
+# See https://jupyterbook.org/content/execute.html
+execute:
+  execute_notebooks: force
+
+# Define the name of the latex output file for PDF builds
+latex:
+  latex_documents:
+    targetname: book.tex
+
+# Add a bibtex file so that we can create citations
+bibtex_bibfiles:
+  - references.bib
+
+# Sphinx, for html formatting. Needs checking version.
+sphinx:
+  config:
+    html_js_files:
+    - https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js
+
+# Information about where the book exists on the web
+repository:
+  url: https://gitlab.tudelft.nl/opentextbooks/open-textbooks-demonstration/  # Online location of your book
+  # path_to_book: docs  # Optional path to your book, relative to the repository root
+  branch: master  # Which branch of the repository should be used when creating links (optional)
+
+# Add GitHub buttons to your book
+# See https://jupyterbook.org/customize/config.html#add-a-link-to-your-repository
+html:
+  use_issues_button: true
+  use_repository_button: true
+  comments:
+    hypothesis: true # Hypothesis for comments

_toc.yml

+# Table of contents
+# Learn more at https://jupyterbook.org/customize/toc.html
+
+format: jb-book
+root: index
+parts:
+  - caption: Demonstrating markdown files
+    numbered: True # Only applies to chapters in Part 1.
+    chapters:
+    - file: content/Exercise_set_1
+  - caption: Demonstrating Jupyter notebooks
+    numbered: True
+    chapters:
+    - file: content/Exercise_set_6
+    - file: content/Basic_animation_demo.ipynb
+    
\ No newline at end of file

content/Exercise_set_1.md

+(ch:chapter1)=
+# Large numbers
+
+<!--
+Possible to add learning goals in an admonition box like this:
+```{admonition} Learning goals
+After reading this chapter, you will be able to
+* ...
+``` -->
+
+(sec:Oxygen_in_Box)=
+## Probability
+
+Imagine that we could label and track the oxygen molecules in the air,
+and that we would label two of them inside a classroom. In the corner of
+the classroom is a box with a volume of about $0.1\%$ of the total
+volume of the room. After some time someone takes a snapshot of where
+the molecules are at that point in time.
+
+1.  Assuming that the two molecules can be anywhere with equal
+    probability, what would be the probability that they would both be
+    inside the box?
+
+2.  What would be the probability that all the oxygen molecules would be
+    inside the box? (assume for simplicity that there are $10^{25}$
+    oxygen molecules in the room)
+
+3.  If the answer under b) was expressed as a fraction, then the
+    denominator should be a large number. Compare this number to the
+    total number of grains of sand on Earth ($\mathcal{O}(10^{18})$) and
+    the total number of elementary particles in the visible Universe
+    (roughly $10^{70}$ plus or minus a few orders of magnitude) and
+    comment.
+
+4.  Imagine that the distribution of oxygen molecules would completely
+    randomise every hour, would you be afraid that this situation would
+    occur during the lifetime of the universe? (around $10^{14}$ hours)
+
+5.  Even if the position of the molecules would randomize every
+    femtosecond, show that it would not matter for the previous answer.
+
+6.  A thousand proteins of a certain kind are located inside a cell.
+    What would be the probability that they would all be in a small
+    corner of the cell, with a volume of about $1\%$ of the total
+    volume, under the same assumptions as before? Which assumption would
+    be troublesome and why? (give at least two reasons)
+
+(sec:Central_limit_theorem_dice)=
+## Probability density distributions
+
+A person throws with a perfect dice, i.e. each possible outcome
+$x \in \{1,2,\ldots ,6\}$ has probability $P(x)=\frac{1}{6}$.
+
+1.  Calculate the expectation value of the outcome $\mu$. What is the
+    most likely outcome? What is the standard deviation $\sigma$? What
+    is $\sigma/\mu$? Draw the distribution.
+
+2.  Do the same but now for two dice (so for $P(X_1+X_2 = y)$, where
+    $y\in \{2,3,\ldots,12\}$). Divide the standard deviation $\sigma_2$
+    by the standard deviation $\sigma$ for 1 dice, and check that the
+    number is close to $\sqrt{2}$.
+
+3.  Do the same as in b) but now for three dice. Be welcome to estimate
+    the standard deviation, instead of calculating it.
+
+4.  Do the same but now for $N=100$ dice. Determine the standard
+    deviation. A sketch of the distribution with the appropriate
+    standard deviation would suffice.
+
+5.  Do the same as in d) but now for $N=10^{12}$ dice.
+
+(sec:Orders_of_magnitude)=
+## Orders of magnitude
+
+1.  Estimate the number of water molecules inside a cell. Be welcome to
+    pick convenient numbers, as long as the order of magnitude is
+    correct. (Computer simulations typically can handle several
+    thousands of particles, or an order of magnitude more if run on a
+    cluster for high-performance computation)
+
+2.  Estimate the number of cells inside the human body.
+
+3.  Estimate the number of lipid molecules inside a single cell
+    membrane.
+
+4.  Estimate the number of microbes on our skin.
+
+(sec:Emergent_behavior)=
+## Emergent behavior
+
+Are the following phenomena emergent or not? If so, explain where they
+come from (i.e. mention a lower level phenomenon / microscopic
+mechanism, or multiple levels).
+
+1.  Temperature
+
+2.  Brownian motion
+
+3.  The elasticity of a cell membrane
+
+4.  Cell division
+
+5.  Thoughts
+
+6.  Music
+
+7.  Awareness
+
+(sec:Notes_Central_limit_theorem)=
+## Useful notes and equations
+
+A probability density function should be normalized:
+
+$$
+  \int \limits_{-\infty}^{\infty} P(x) dx = 1.
+$$ (eq:pdf_normalized)
+
+For simplicity we consider a probability density function of a single stochastic variable
+$X$ with a continuous set of potential outcomes $X=x$, but it could be
+generalized to multiple variables and discrete sets.
+
+The $n^{\mathrm{th}}$ moment of this distribution is defined as
+
+$$
+  \langle x^n \rangle \equiv     \int \limits_{-\infty}^{\infty} x^n P(x) dx.
+$$ (eq:moments)
+
+The first and second moment are particularly useful, and yield the mean
+$\mu$ and the standard deviation $\sigma$ of the distribution,
+
+$$
+  \mu = \langle x \rangle
+$$ (eq:mean)
+
+and
+
+$$
+  \sigma = \sqrt{ \langle x^2 \rangle - \langle x \rangle^2 }.
+$$ (eq:stdev)
+
+The Fourier transform of $P$ is known as the characteristic function of
+$P$,
+
+$$
+  G(k) \equiv \int P(x) e^{ikx} dx,
+$$ (eq:characteristic_function)
+
+and the Taylor expansion of
+$G(k)$ yields the moments of $P$. We will not use the characteristic
+function in this course, although it is useful if one wants to derive
+the central limit theorem, given below {cite:p}`van1992stochastic`.
+
+### Central limit theorem (a short version)
+
+Given that $P(x)$ has a mean $\mu$ and a standard deviation $\sigma$,
+one can derive that the probability density function of the sum of many
+outcomes of $X$ is a Gaussian distribution. Defining the sum of $n$
+outcomes as $X_1+X_2+ \ldots + X_n = Y$, then
+
+$$
+  P(Y=y) \propto e^{-\frac{(y-n\mu)^2}{2n\sigma^2}}
+$$ (eq:clt)
+
+with standard
+deviation $\sigma_y = \sqrt{n} \sigma$ and mean $\mu_y = n \mu$. This is
+independent of the form of the distribution of $X$, as long as $n$ is
+'large'. What is called large may depend somewhat on the distribution,
+but usually, the number $10^{23}$ is more than sufficient.
+
+Another
+property of $P(y)$ is that the standard deviation becomes negligible
+compared to the mean, $\sigma_y / \mu_y \propto 1/\sqrt{n}$, such that a
+sample of $Y=y$ will almost certainly have the mean value as the
+outcome. This is one reason why the Gaussian distribution is so
+extremely important in the field of statistics. It appears everywhere,
+and tends to describe the properties of systems of many degrees of
+freedom (the velocity distribution in a gas, density fluctuations in a
+fluid, spatial fluctuations in a membrane, the 'shape' of a flexible
+polymer &c.).
+
+## References
+```{bibliography}
+:style: unsrt
+:filter: docname in docnames
+```