{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this exercise, we'll do calculations on many numbers at once. Python provides the numpy library for that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "%matplotlib notebook\n",
    "from matplotlib import pyplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Use `np.arange(..., ...)` to create a vector from `0` up to and including `5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = None\n",
    "\n",
    "print('x: ', x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Extract `1` from all the numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = None\n",
    "print('y: ', y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Take the square root of all these numbers, either using `** 0.5` or `np.sqrt( ... )`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = None\n",
    "print('y: ', y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the square root of `-1` is not defined, and hence the result is *not a number* (nan).\n",
    "\n",
    "The cell below will make a plot of `x` and `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pyplot.plot(x, y)\n",
    "pyplot.xlabel('x')\n",
    "pyplot.ylabel('y')\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You have learned to use `numpy` for so called vector operations, these are mathematical operations on many numbers as well. This field is called *linear algebra*, and is a usefull field on its own, in particular often used in artificial intelligence."
   ]
  }
 ],
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