00_python_in_a_nutshell/00_content_arithmetic.ipynb

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    "**Note**: Click on \"*Kernel*\" > \"*Restart Kernel and Clear All Outputs*\" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *before* reading this notebook to reset its output. If you cannot run this file on your machine, you may want to open it [in the cloud <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-data-science/main?urlpath=lab/tree/00_python_in_a_nutshell/00_content_arithmetic.ipynb)."
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   "source": [
    "# Chapter 0: Python in a Nutshell (Part 1)"
   ]
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   "source": [
    "Python itself is a so-called **general purpose** programming language. That means it does *not* know about any **scientific algorithms** \"out of the box.\"\n",
    "\n",
    "The purpose of this notebook is to summarize anything that is worthwhile knowing about Python and programming on a \"high level\" and lay the foundation for working with so-called **third-party libraries**, some of which we see in subsequent chapters."
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   "source": [
    "## Basic Arithmetic"
   ]
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   "source": [
    "Any computer can always be viewed as some sort of a \"fancy calculator\" and Python is no exception from that. The following code snippet, for example, does exactly what we expect it would, namely *addition*."
   ]
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   "source": [
    "1 + 2"
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   "source": [
    "In terms of **syntax** (i.e., \"grammatical rules\"), digits are interpreted as plain numbers (i.e., a so-called **numerical literal**) and the `+` symbol consitutes a so-called **operator** that is built into Python.\n",
    "\n",
    "Other common operators are `-` for *subtraction*, `*` for *multiplication*, and `**` for *exponentiation*. In terms of arithmetic, Python allows the **chaining** of operations and adheres to conventions from math, namely the [PEMDAS rule <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Order_of_operations#Mnemonics)."
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       "45"
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   "source": [
    "87 - 42"
   ]
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   "execution_count": 3,
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     "data": {
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       "15"
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     "execution_count": 3,
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   "source": [
    "3 * 5"
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       "8"
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   "source": [
    "2**3"
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   "source": [
    "2 * 2**3"
   ]
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   "metadata": {},
   "source": [
    "To change the **order of precedence**, parentheses may be used for grouping. Syntactically, they are so-called **delimiters** that mark the beginning and the end of a **(sub-)expression** (i.e., a group of symbols that are **evaluated** together)."
   ]
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   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "(2 * 2) ** 3"
   ]
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   "source": [
    "We must beware that some operators do *not* do what we expect. So, the following code snippet is *not* an example of exponentiation."
   ]
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   "source": [
    "2 ^ 3"
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   "source": [
    "*Division* is also not as straighforward as we may think!\n",
    "\n",
    "While the `/` operator does *ordinary division*, we must note the subtlety of the `.0` in the result."
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
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     "data": {
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       "4.0"
      ]
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     "execution_count": 8,
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   "source": [
    "8 / 2"
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   "source": [
    "Whereas both `4` and `4.0` have the *same* **semantic meaning** to us humans, they are two *different* \"things\" for a computer!\n",
    "\n",
    "Instead of using a single `/`, we may divide with a double `//` just as well."
   ]
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   "source": [
    "8 // 2"
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   "source": [
    "However, then we must be certain that the result is not a number with decimals other than `.0`. As we can guess from the result below, the `//` operator does *integer division* (i.e., \"whole number\" division)."
   ]
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   "source": [
    "7 // 2"
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   "source": [
    "On the contrary, the `%` operator implements the so-called *modulo division* (i.e., \"rest\" division). Here, a result of `0` indicates that a number is divisible by another one whereas any result other than `0` shows the opposite."
   ]
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   "source": [
    "7 % 2"
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   "source": [
    "8 % 2"
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   "source": [
    "What makes Python such an intuitive and thus beginner-friendly language, is the fact that it is a so-called **[interpreted language <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Interpreter_%28computing%29)**. In layman's terms, this means that we can go back up and *re-execute* any of the code cells in *any order*: That allows us to built up code *incrementally*. So-called **[compiled languages <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Compiler)**, on the other hand, would require us to run a program in its entirety even if only one small part has been changed.\n",
    "\n",
    "Instead of running individual code cells \"by hand\" and taking the result as it is, Python offers us the usage of **variables** to store \"values.\" A variable is created with the single `=` symbol, the so-called **assignment statement**."
   ]
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   "execution_count": 13,
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   "source": [
    "a = 1"
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  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = 2"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After assignment, we can simply ask Python about the values of `a` and `b`."
   ]
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   "execution_count": 15,
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   "source": [
    "a"
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       "2"
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   "source": [
    "b"
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   "source": [
    "Similarly, we can use a variable in place of, for example, a numerical literal within an expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
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     "execution_count": 17,
     "metadata": {},
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   "source": [
    "a + b"
   ]
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   "metadata": {},
   "source": [
    "Also, we may combine several lines of code into a single code cell, adding as many empty lines as we wish to group the code. Then, all of the lines are executed from top to bottom in linear order whenever we execute the cell as a whole."
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   "cell_type": "code",
   "execution_count": 18,
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   "source": [
    "a = 1\n",
    "b = 2\n",
    "\n",
    "a + b"
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   "source": [
    "Something that fools many beginners is the fact that the `=` statement is *not* to be confused with the concept of an *equation* from math! An `=` statement is *always* to be interpreted from right to left.\n",
    "\n",
    "The following code snippet, for example, takes the \"old\" value of `a`, adds the value of `b` to it, and then stores the resulting `3` as the \"new\" value of `a`. After all, a variable is called a variable as its value is indeed variable!"
   ]
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   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = a + b"
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   "cell_type": "code",
   "execution_count": 20,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
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     "execution_count": 20,
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   "source": [
    "a"
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   "source": [
    "In general, the result of some expression involving variables is often stored in yet another variable for further processing. This is how more realistic programs are built up."
   ]
  },
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   "cell_type": "code",
   "execution_count": 21,
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     "data": {
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       "3"
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     "execution_count": 21,
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   "source": [
    "a = 1\n",
    "b = 2\n",
    "\n",
    "c = a + b\n",
    "\n",
    "c"
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