{
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   "source": [
    "# Excercise I - Python Essentials\n",
    "\n",
    "The purpose of this exercise is to get familiar with pure Python, meaning that you don't need any third-party libraries such as NumPy for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Mathematical operations\n",
    "\n",
    "Calculate the following mathematical expressions for a predefined value of x:\n",
    "\n",
    "a) $x^2$\n",
    "\n",
    "b) $\\sqrt{(x^2 + y^2)}$\n",
    "\n",
    "c) $\\frac{1}{x^y}$\n",
    "\n",
    "d) $\\sum_{x=1}^5 x^3 - 2x$ (Hint: Use a [for loop](https://docs.python.org/3/tutorial/controlflow.html#for-statements) and sum to a variable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "for x in 1, 2, 3, 4, 5:\n",
    "    a = x**3 - 2*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Lists"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a list of numerical values called *numbers*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "numbers = [1, 4., 2.5, 3, 10.]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) What is the difference between the first and the last entry?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Calculate the sum of numbers and call it `summe` (Hint: You can use a [for loop](https://docs.python.org/3/tutorial/controlflow.html#for-statements) again)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'summe' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-75e858c309b4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0msumme\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m20.5\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Well done.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Try again.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'summe' is not defined"
     ]
    }
   ],
   "source": [
    "# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\n",
    "if summe == 20.5:\n",
    "    print(\"Well done.\")\n",
    "else:\n",
    "    print(\"Try again.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Calculate the mean of numbers and call it `mean` (Hint: with [`len()`](https://docs.python.org/3/library/functions.html#len) you can get the number of items in a list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\n",
    "if mean == 4.1:\n",
    "    print(\"Well done.\")\n",
    "else:\n",
    "    print(\"Try again.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Do all entries in `numbers` have the same type? You can check the type of a Python object with `type(object)` and convert integers to floats with `float(1)` for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "e) Create a new list `numbers2` with floating points only using a [list comprehension](https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Dictionaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Write a Python script to generate a dictionary where the keys are numbers between 1 and 15 (both included) and the values are square of keys. (Hint: [Dictionary documentation](https://docs.python.org/3/tutorial/datastructures.html#dictionaries))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Iterate over the dictionary and print key, value pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Define a function called `std` which calculates and returns the standard deviation of a list of numbers. (Hint: Maybe you can reuse some of the code you wrote in exercise 2?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\n",
    "if std([1,4,1,0]) == 1.5:\n",
    "    print(\"Well done.\")\n",
    "else:\n",
    "    print(\"Try again.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Define the piecewise function `N` expressed as:\n",
    "\n",
    "$$\n",
    "N(x) = \\left\\lbrace\\begin{array}{ll}\n",
    "0, & x < 0\\\\\n",
    "x, & 0\\leq x < 1\\\\\n",
    "2-x, & 1\\leq x < 2\\\\\n",
    "0, & x \\geq 2\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "Hint: Use an [if statement](https://docs.python.org/3/tutorial/controlflow.html#if-statements)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Write a Python function called `swap` to reverse a string. (Hint: `[::-1]`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\n",
    "if swap(\"1234abcd\") == \"dcba4321\":\n",
    "    print(\"Well done.\")\n",
    "else:\n",
    "    print(\"Try again.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**BONUS questions**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Write a function to count the upper and lower case letters in a given string.\n",
    "\n",
    "```\n",
    "Sample String : 'The quick Brown Fox'\n",
    "Expected Output : \n",
    "No. of Upper case characters : 3\n",
    "No. of Lower case Characters : 12\n",
    "```\n",
    "\n",
    "Hint: Maybe some of these [string methods](https://docs.python.org/3/library/stdtypes.html#string-methods) are useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Write a function called `unique`, to find the unique values in a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your answer here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check if your answer is correct (*DO NOT CHANGE THIS CELL*)\n",
    "if unique([1,2,3,3,3,3,4,5]) == [1, 2, 3, 4, 5]:\n",
    "    print(\"Well done.\")\n",
    "else:\n",
    "    print(\"Try again.\")"
   ]
  }
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