m248Week_1_2.ipynb

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   "cell_type": "markdown",
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   "source": [
    "![image](JMUlogo.png)   \n",
    "\n",
    "> # Math 248 Spring 2021\n",
    ">                                                      \n",
    "> # Computers and Numerical Algorithms                                                                                                     \n",
    "> ## Instructor: Hala Nelson\n",
    "___\n",
    "                                                                                           \n",
    "> Course Objectives\n",
    ">-----------------\n",
    ">\n",
    ">*This is not a computer science class.* Math 248 is a keystone course for those who wish to specialize in applied or computational mathematics, and also reinforces and advances\n",
    "concepts from the calculus sequence, linear algebra and differential equations (238 or 336), and probability and statistics. This course covers a wide swath of mathematical territory.\n",
    ">-   Understand both the power of computing and its limitations (storage,\n",
    "    etc).\n",
    ">\n",
    ">-   Translate an algorithm into a program.\n",
    ">\n",
    ">-   Learn how to solve mathematical problems numerically and\n",
    "    computationally.\n",
    ">\n",
    ">-   Differentiate between analytical, numerical and computational\n",
    "    solutions of mathematical problems.\n",
    ">\n",
    ">-   Quantify errors and their sources.\n",
    ">\n",
    ">-   Construct sequences to approximate solutions of mathematical\n",
    "    problems (iterative methods, polynomial approximations, *etc.*).\n",
    "    Convergence/divergence, rate of convergence/divergence and error\n",
    "    analysis.\n",
    ">\n",
    ">-   Understand the difference between linear and nonlinear problems.\n",
    "    Linearizing.\n",
    ">\n",
    ">-   Discretize continuum quantities and problems (derivatives,\n",
    "    integrals, differential equations, *etc.*).\n",
    ">\n",
    ">- Build confidence and understanding in using the computer as an\n",
    "    efficient mathematical tool.\n",
    ">\n",
    ">- Gain a working knowledge with Python 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notes for Weeks 1 and 2\n",
    "\n",
    "1.  **Python 3**\n",
    "    - We will code using Python 3. We will be setting up our own Jupyter\n",
    "    notebooks. We will submit our notebooks on Github.\n",
    "    \n",
    "    - **Program flow**: Always make sure you understand the *input* and *output* of a program before writing it or creating the algorithm.\n",
    "    \n",
    "    -   Object Oriented and Interpreted Language.\n",
    "    \n",
    "    -   **Libraries**: numpy, matplotlib, pandas, seaborn, os (interacts with operating system), urllib (interacts with the rest of the rest of the internet), scipy, scikit learn (machine learning model), tensor flow (deep learning).\n",
    "\n",
    "    -   Data types, classes, objects, dictionaries, data frames.\n",
    "\n",
    "    -   while loop and for loop\n",
    "\n",
    "    -   if statement\n",
    "\n",
    "    -   Initiating lists, vectors and matrices.\n",
    "\n",
    "    -   Adding onto lists.\n",
    "\n",
    "    -   functions and methods.\n",
    "\n",
    "    -   Good names for your variables and your files.\n",
    "\n",
    "2.  **What are the main topics in Calculus I and II?**\n",
    "- Sequences and series of numbers.\n",
    "- Sequences and series of functions. \n",
    "- Limits.\n",
    "- Functions.\n",
    "- Continuity. \n",
    "- Differentiation\n",
    "- Integration.\n",
    "- Fundamental theorem of calculus: Ties up the concepts of the limit, derivative and integral together, where the derivative is an inverse opeartion to the integrals.\n",
    "- Most important application of calculus: The max and min happen at points where $f'(x)=0$. Make sure you know your chain rule to calculate derivatives in Calculus.\n",
    "\n",
    "3.  **What is the language of Linear Algebra?**\n",
    "- Vectors.\n",
    "- Matrices. \n",
    "- Tensors.\n",
    "- Vector spaces.\n",
    "- Linear transformations.\n",
    "- We will see important Matrix Decompositions (eigenvalue decomposition, singular value decomposition).\n",
    "\n",
    "4.  **What are differential equations (ordinary and partial) useful for?** \n",
    "- Modeling phenomena from the real world.\n",
    "\n",
    "5.  **What does probability quantify?** \n",
    "- Randomness and uncertainty. \n",
    "- How do you generate random numbers sampled from various distributions in Python?\n",
    "\n",
    "6.  **Calculus II Topic: Sequences of real numbers:**\n",
    "\n",
    "    -   Definition: A sequence of real numbers $\\{a_n\\}$ is a function\n",
    "        $a: \\mathbb{N}\\to\\mathbb{R}$ (it has infinitely many terms that\n",
    "        can be listed $a_1=a(1), a_2=a(2), \\dots, a_n=a(n),\\dots$).\n",
    "\n",
    "    -   Possible behaviors: divergence to $\\infty$, divergence to\n",
    "        $-\\infty$, convergence to a limit $L$ (see next item), limit\n",
    "        does not exist (in which case it has subsequences whose behavior\n",
    "        is identified).\n",
    "\n",
    "    -   Convergence of a sequence $\\{a_n\\}$ to a limit $L$: Given\n",
    "        $\\epsilon>0$ there is an $N$ such that for all $n>N$,\n",
    "        $|a_n-L|<\\epsilon$.\n",
    "\n",
    "7.  **Finite sums: Summation formulas** (note that if the index starts\n",
    "    somewhere other than $1$ you have to make appropriate adjustments):\n",
    "\n",
    "    -   Sum of numbers: $\\sum_{i=1}^ni=\\frac{n(n+1)}{2}$\n",
    "\n",
    "    -   Sum of squares: $\\sum_{i=1}^ni^2=\\frac{n(n+1)(2n+1)}{6}$\n",
    "\n",
    "    -   Sum of cubes: $\\sum_{i=1}^ni^3=\\frac{n^2(n+1)^2}{4}$\n",
    "\n",
    "    -   Sum of geometric series: $\\sum_{i=1}^nb^i=\\frac{b^{n+1}-1}{b-1}$\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Answer the following, do research if you need to:\n",
    "\n",
    "1.  What is an algorithm? What is the difference between an algorithm\n",
    "    and a computer program?\n",
    "\n",
    "2.  Why is Python a high level language? Why is it interpreted? What is\n",
    "    Machine Language? Python is an object oriented language so what is object oriented?\n",
    "\n",
    "3.  What is a transistor? Why is it important for building and enhancing\n",
    "    computers?\n",
    "\n",
    "4.  How small is the smallest transistor ever invented?\n",
    "\n",
    "5.  What is a semiconductor? Why is it important for building and\n",
    "    enhancing computers?\n",
    "\n",
    "6.  Why was the development of the RAM revolutionary for the development\n",
    "    of the modern computer?\n",
    "\n",
    "7.  Why is there now so much research about quantum computing?\n",
    "\n",
    "8. Calculate the following sum analytically $\\sum_{k=6}^{50}k^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming\n",
    "\n",
    "1.  Write a program that lists all the positive multiples of $5$ less than 200.\n",
    "\n",
    "2.  Write a program that computes the following limit $\\lim_{n\\to\\infty}\\frac{n^3-2n^2+1}{3n^3-4n+9}$. Make a plot showing the convergence of the sequence $\\left\\{\\frac{n^3-2n^2+1}{3n^3-4n+9}\\right\\}_{n=1}^\\infty$ to this limit as $n\\to\\infty$.\n",
    "\n",
    "3.  *Write a program that tells you the least $n$ so that the sequence $a_n=\\frac{n^2}{2n^2-1}$ is within distance $0.000001$ of its limit*. Is this sequence fast to converge or slow? Compare to the above problem.\n",
    "\n",
    "4.  Write a program that calculates the following sum $\\sum_{k=6}^{50}k^2$.\n",
    "\n",
    "5.  Write a program that generates a random number between $0$ and $1$.\n",
    "\n",
    "6.  Write a program that generates a random number between $11$ and $24$.\n",
    "    \n",
    "7.  Write a Python class that defines instances with your name, your jmu eid, your phone number.\n",
    "        \n",
    "8.  Write a dictionary containing your name, jmu eid, major, phone number, then create a data frame for your dictionary.\n",
    "\n",
    "9.  We can change instances in our classes into dictionaries using the .__dict__ method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Say Hello 10 times ;)\n",
    "\n",
    "In the print function, we use \\n to go to the next line. Check the print function documentation for other options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "Hello\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Hello\\n'*10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program A: All possible nonnegative multiples of 5 less than or equal 200."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200]\n",
      "\n",
      " The type of the list object that we created and filled up with multiples of 5 is:\n",
      " <class 'list'>\n",
      "\n",
      " The shape of the list object is:\n",
      " (41,)\n",
      "\n",
      " The type of list_changed_to_array is:\n",
      " <class 'numpy.ndarray'>\n",
      "\n",
      " The shape of the new array object is:\n",
      " (41,)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# initiate an empty list then append it with multiples of 5 \n",
    "list=[]\n",
    "for i in range(0,201,5):\n",
    "    list.append(i)\n",
    "print(list)\n",
    "\n",
    "print('\\n The type of the list object that we created and filled up with multiples of 5 is:\\n',type(list))\n",
    "print('\\n The shape of the list object is:\\n',np.shape(list))\n",
    "\n",
    "list_changed_to_array=np.array(list)\n",
    "\n",
    "print('\\n The type of list_changed_to_array is:\\n',type(list_changed_to_array))\n",
    "print('\\n The shape of the new array object is:\\n',np.shape(list_changed_to_array))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program B: Computing and visualizing the limit of a convergent sequence.\n",
    "\n",
    "Write a program that computes the following limit\n",
    "        $\\lim_{n\\to\\infty}\\frac{n^3-2n^2+1}{3n^3-4n+9}$. Make a plot\n",
    "        showing the convergence of the sequence\n",
    "        $\\left\\{\\frac{n^3-2n^2+1}{3n^3-4n+9}\\right\\}_{n=1}^\\infty$ to\n",
    "        this limit as $n\\to\\infty$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The length of the list containing the members of the sequence is: 500\n",
      "The numerical (not the analytical) limit is: 0.33266644310970245\n"
     ]
    },
    {
     "data": {
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7S/P1tte1pOd7qp17N1fO0ZGKiJURcRLpy5CRBjZXkD4s7ltJyF0p9+XpL05GqnxHaCQuIT0bu6zKOXxNPSuocU7VcxzH4hJSl70rq9R7SR11fjLST8t8ltRluDN3cbwceH6N13QlCLwC2CN3H62o9r60nPQMaNEepfkxt39pXf8iadYQy7cm3YleZ/+GWO8fSF2Id6sk5H1/A6M/Z4dTGUTpqfaTtB2p+/l4WqDBo86+lfS+fm2ev4Q0YMx1Vdqs7i/6IuKBiPgu6YuL8fwyxGzK8p1AsxYUEaskXU/qGvfJnPakpN+SPhicXCryGeACSd8mBSz/SPpm9eRIv2lXy+eBn0g6gXTxfA1Pj/g5Hvtxk6QTSaPGfZn0jfxGpIv+P0TE+4coe7/ScPBfl9RJ6iI7jfTc2msj4i21ylZZ11pJtwFvl3Qt6Vvwq2sFoRGxQumnAb5CGlXwB0OtX9LZpED8z6QPOPuS3l8vzVl+kdNPlfQ/wPasO2rr5aTubifntppNCuL+Vu9+ZmeQnmn8FrBz4VGyByPietLzN8dJ6iV9+NyHdMf5KbXaq7yhiLhX0teAT0l6nHR835rX+c6RVFrSZ0l3IQZIdyJeRjofR3IXkIi4QdL3gG8p/exFZXTQF1D9blA9biR9+P8X0t2g2yJi1TBlKs4gHesBpZ8zuJXUrXAn0gAyx1YrVMc5dRHwYUl/IA1y0k0KdsbLUaTBYs6TdCrpmGxLCrJOi4iBKnV+JnABaZ9vJj2f+DHSnb0bcrbDgUskPUka2fEh0jOMbwB6I+Jm0t2cDwHnSvoqaZTLT5Laoehs4JuSjiQFjm8lvbcUjar9aziW9EPtv5G0kDQ66AtJgy59mXRMLgAukvQlUlf2zUjd9zeKiE9WW2lEXJDf278v6QjSOfZxUqB/zAjqV7eIWC7pCvJoy6T31iMZ/zuPzyA9130y6dh8GvhWRFS281XSaKy/lPRN0vvdLNJr/7IYPMLwIJI+QOpB8QvSXeS5pC+kzhjnfTCbmsojxXjy5KmxE7VHYjwhp/9TIe0TlEZlKyx7B+lu4VrSt7wLKYxaOMT2D83515C6aO3JOI0OmtNFen7pOtKdi5WkQRmKI8sNUBiRrlR+f9KH4UdIQ+H/AfhoYflplEbMq1aXvF9XkwKaALqGaZf353y/r7Js0P6ThidfRHr28aFcxwWlMnvnNlhDusP1wirtuhfpG/JHcl33KbdNeX9ZdzTEJXm+PA3k5dNJwe0KUlfLH5OGkx+2vWq063TS3Z7bSefe9UB3ad+HPUakbr+X5PPj76TuvkcAGuIYrVOfnF4Zxv5u0jm3CPiXUp5B7TrMufAc0p3VBxg8ku8ShhmdMqc9kzSMfaWNlpMGyNhliG0OeU6R3je+TfrQfi+p2+YbGTzKZq32qVbvasfoBaRA7V7SObmYNFJu1RGHSUHfyfnYrSEFjucC/1jKtzPpg/uDpNE2rycFA88s5Jmfz79HST0WdsnrO6qQZ/1c7i7Se8PXST9NMeL2p8pIvVR/n+skdRe/L+/jX4D9Sm3w2dxWa3PdfsEQI6rmcluSgpf7clv/GnjlcMeoxroGKJ3bVBkNlPSlwUA+BpXn6waVrXFeHFiljdc51/L8R0lfSN1HOpePozDycs73bNK5XHm9LgHOBF40zHn8atJgMXeQ3jNuI/0cyobDtZEnT54iXVzNzMzMWpmke0h3kY5qdl3MzCY7PxNoZmZmZmbWRhwEmpmZmZmZtRF3BzUzMzMzM2sjvhNoZmZmZmbWRhwEmpmZmZmZtREHgWZmZmZmZm3EQaCZmZmZmVkbcRBoNgaSBiR9qtn1AJB0saSjmrj91ZJe3cDtXSfpHeO4vjHVX9L+kpaMV33MzFqZr3/r1OEoSRc3sw7joVHHtbydRn+GMAeBViDpOZJ+KOmu/GK8XdLZkjZodt2mCkkhaddSWstcSMciIjaNiN+PdT2S5kt6vI7tvSgivp/LdOW2nT3a7Y5X/c1s8vH1b+JNpeufpNMkndLsekwlvgY3noNAKzofuBN4PvAM4NXABYCaWSkzM7MJ5uuf2QSQtH6z62DVOQg0ACTNIF38ToyIByJZHhEnRsSjhXxvlnSlpPsl3SCpu7SegyTdIulBSd+RdKak0/Kyde7WSDpQ0uLCfIekr0i6TdK9kn4h6XmF5QOS/kfSjyU9lLe1oFSHt0paJOmB/K3uwsKyf5Z0WV73LZI+JqnqRb5Q3/dLujnv888kbTVEO75Y0i8l3SfpVkmfkjQ9L/tLznZh/qb5FEnfAv4Z+K+cdlNhXf8u6dq8H3+WtGdhmSR9UtLyvC/HMsyHFUnfzt9uPyTpeknvKi1/Q05fLelcScdKGigs/3zep9W57Q4rlX/qW97KcZX04VzH+ySdVGiLDST1SVqRz5WbJe0r6dnAz4HpeTurJR1QY3+WSNo/z1ba9qZc5r9yGy2UdEfe5yWS/mOI9qm7/jnPTvk8Wy3pMuA5pfXVPJcl/WPe79fk+WmSLpT0nVr1M7OJIV//qrXJVLv+DVW3yr6+W+ka+FB+P96mxroOB7qBA/T0dWr604v1eaVr2wpJny2V3VHSBZLukbRM0hc0RJCU63WIpCtyvS6X9ILC8nXupGrwtewoSZdI+pKklZJWSfqopM7cHg/lc/qFpU3PVPocsFrp0Yu9S9uo+VrQ09fP/5S0HLiq1v4NUe96rsFzJP1I0p156pP0jHq2ZVlEePJERABcC/wOeA+wA6DS8j2AVaQ37WnATsB9wG55+T8Dj+R86+X1PAaclpd3AQHMLqzzQGBxYf67wLnALGAD4LPAjcD6efkAcA+wS67D/wPuBzry8r2Bh4A35jpsBuyal70oL1sATAdeANwGvKdGe1TqeymwdV7X2cCFhTwDwKfy/88E7gb+C9gQeCFwK/CfhfxRqU+1dRTSeoDFwEvyfu4DrAael5e/G1gBvCK3U29u66OGOL7vA2bkfd8PWAvskJc9F3gUeGdut92BB4GBQvn9gWeTLravy8f6X6rtWz6ujwELc1s8D7gX6C7s35+BGXl+u0Jd5gOP13G+LgH2H+Lc2hNYDmyX52cBLx9ifSOp/zNJr4Ujcvu/ErgLWDKCc/kg4I68/DPA9cAmzX4f8OSpHSd8/Su3R6W+k/76N1zdCvt6LjAz7+tvgZOHOF9OA04ppR2V63Fwbv+d8/wueflWpHPoA7ne2wKLgE8PsZ0A/gjMyXX/IXDRMO1XvJZV6vT+fNz3Bp4ALs7tsD5wZpXj+hBPn8vdwN+BrjpfCwcCjwPHAhuTz88q+zao7ozsGrxRPkc+l7exOelu/qnNfi+ZTFPTK+Cpdab85vd54E+kAGFFftNUXn5u+c0K+GbljRA4GfhOaflvqfMimLcfwJzC8mnAA4U3hgHguMLyTXKZl+T584Fjauzft8pvEMDHgItr5K/Ud/dC2vNy2rML9alcBN8F3E7hwwPpzf6mwny9F8FrKV2cgf8rbOsi4OhSO93OEEFglf1bBByS//8UcGlp+XcoBIFVyv8I+HK1fcvH9UFgemH5D4FjC8v/SrqIrFda73zGJwicT/rAtBewUR3rG0n9u4FlpWO9kBwEUse5nNO+DVydt7XDWF6/njx5Gv2Er3/l/JX6Tvrr33B1K+zrKwvLPwT8eYjz5TSqB4HXldKuAD6S//848MvS8n+j8EVAle0E8LbC/BuA+4Zpv3IQWK7TCgYH5/tUWWf5XL4MOLLO18KBpC9ENhzmNTeo7ozsGrwvcEtpfa8gfZk9fajtenp6Wg+zLCLuAY4EjpTUAbyddGH7G3AqsD3wWkkfLRSbDvwm/z+bFFgU3TaCKmyf/15d6qGyPulOUcWdhTo/nPNWugB0kb6trLX+10l6ayGtcvEYypIq/88m3cUp2o4UBEQh7ZZS3eu1PXCcpG8U0tYj3dmqbP+pekXEk5KW1lqZpGmki8E7SN/qBukDxJY5y7ZAufzSYt0lfRj497xtkb59++4Q+7AiIp4ozD/M08fpTNK33ccCcyVdAhweEYsZJxExIOlIUoD7A0m/B3ojonyO1jJU/WcDS0vHuniu13suf4P0ofOMiLi+znqZ2Tjz9a+mJVX+n1TXvxHU7c7C/8X3+5G4szRfXM/2wC6S7i8sF+k8qnedo6lXuU5rSmlrqqxzSZX5Slfm4V4LAHdGoSv1KA11Dd4emFNqS0ifbbYmvW5tGA4CraqIWAOcpvQM1Utz8lLSt5rH1Cj2N9JFqGh70h0fSN05IAUfFc8u/F95E58bEStHUW1Ib1RzayxbSvom9EMjXGcX6YJR+R+evhgV3Q50SlLhYvMcBl9kY91iPFmjrp+JiB/WqNOgtlb6JNBZIy+kbp7vJ3WRvD5fNBfx9HMUf8vLiuYU1r8L8CVSN9E/RMQTkn7EMM9h1BIRj+f1fUnSs8jfUgO7Ub09hlO1TET0AX35Q91RwE8o7NcY/I11j/X2heXDnsuSNgZOJ32j/FZJr4+IST+8uNlk5+vfIF1M/utfPXUbqdFcp5aS7ry+YQzbLVtN4ZxSeq5+PHRVmT8//z/cawFG1z4jsRS4OSJeNMHbmdI8MIwBIGnz/IDyjpLWl7SepH8DduTpb3e+Bhym9HD5dKXBPV4haV5efgawr6Tdc/n9SX3Fgae+aV0KHJTL/yPpzlJl+QrSnaXjJW2b6/UsSW+RtGmdu3IccLCkvXMdNssBDMDxwH6S/rWwjzsoD84xhP+SNEvSZqTA5ZKIKH8LCnAeqZ/6kbltng98AvjfQp67WPcifRepm03RscBRkl6qZGNJu+rpB8K/A/RIernSQ+VHkL79qmUzUh/9lcA0SQeRnreo+B6ws6S352MzH3hzqfwTuXxIegPp2YJRkfS6fO6sT+o28nCuH6T2mC5p+5orWNdK0kXnqbaV9MrcZhuSuog8VNjGWJ0LbAr8Zz6XXk56xg+o+1w+jvRcxftJXY/6VWMgAjObOL7+DWkqXP/qqdtI3QU8R6mXTb3OAOYpDSC0kdKAYM+RtNcY6rEIWCBpS6VBURYOV6BOb87n8nRJ7yQ9935WXvY1hn4tNMK5wPqSjpT0jHyebCvpLQ2sw6TnINAq1pIeWv4J6eHblaRudP9R+TYuIi4kPbB9DOlZqztJb9ab5uWXAv8BnJLXsRfw/dJ2DiA9tP4A8FXWfRP+d+AmYEDSQ8A1wNuo/g3iOiLiPNKH6s/nOtyU60FEXJu3fViu+wrSXZgtq6yq6EzSB4HbSQ9z718tU0Q8QLqb9nrSQ+gXkN70v1rI1gt8Tnmkq5x2LOnCcL+k6/K6Tga+THpm7D7S82f/ReoaRF7vN0nPSdxNOnaXDrEPpwN/ID1I/TfSwAdPdd2IiFtI7fxZ0rH5OOlCW+nOcUGe/yPp2O9L7W5H9ZiV13cf6Vh0kp7RICJuJn1g+WNuk3cPt7KIeITUPt/LZXpJ3Ua+keu7inRs9htDnYvbu5/0bMY78j58AzihlK3muSzpPaTnMN4ZEU9ExJmkY/ldFUY/M7OG8PWvtkl//auzbiN1CukO3Kpc92HftyPiLuC1pC9Yl5D27WxKI0uP0LGkwYNuIY3Ced4Y1lX0v8BHSefqp4G3RsStMPxroRHy3frdSZ9lbsz1vISn79xbHSoPPJtNCKUfU10vIg5sdl1GSlIX6ZmO7SKiWveXKU3S94CHIqKn2XUxM5tsfP0zs1bmO4FmBkDuJrR57ia0gDRq2feaXS8zMzMzG18eGMbMKl5D6n6zEan7zcER8avmVsnMzMzMxpu7g5qZmZmZmbURdwc1MzMzMzNrIw4CzczMzMzM2siUfSZw5syZ0dXV1exqmJnZBLvyyivviYjhhrq3bDyujw8//DCbbLLJ8BknCe9Pa/P+tDbvT2urdY2cskFgV1cXixYtanY1zMxsgkla2uw6TCbjcX0cGBhg/vz541OhFuD9aW3en9bm/Wltta6R7g5qZmZmZmbWRhwEmpmZmZmZtREHgWZmZmZmZm3EQaCZmZmZmVkbcRBoZmZmZmbWRhwEmpmZmZmZtREHgWZmZmZmZm3EQaDZJNDf38+mm26KJE+eptw0c+ZM+vv7m/0yMzMzaxtT9sfirXUccsghnHjiiUREs6tiZi1o1apVHHTQQQB0d3c3uTZmZmZTn+8EtqFG31U64YQTHACa2ZDWrl1Lb29vs6thZmbWFnwncBLr7+/nIx/5CKtWrWp2VczMxmzZsmXNroKZmVlbcBDYwvr7+/nABz7Aww8/3OyqmJlNuDlz5jS7CmZmZm3B3UFbQH9/PzNnzlynG+X+++/vANDM2sIGG2zAwoULm10NMzOztuAgsAnKQd/+++/vLp1m1rZmzJjBqaee6kFhzMzMGsTdQRvEI2TaeNh000058cQT/WHZzMzMzEbNQeAEO+SQQzjhhBOaXY2W4ADGzMzMzKz5HAROkMkQ/E2bNo0PfOADHH/88c2uipmZmZmZNYiDwHHW39/PQQcdxNq1axu2TQdzZmZmZmZWLweB4+j1r389l1xyybiv190ozczMzMxsvHh00HEyXgHgjBkzOPPMM4mIp6aHHnrIAaCZmZmZmY0L3wkcB6MNAN2N08zMzMzMGs1B4BiNNADcaKONOOWUU3xnz8zMzMzMmsJB4BgccsghdQeADv7MzMzMzKwVOAgcpf7+/rp+AsLBn5mZmZmZtRIHgaN08MEHD5tn99135+KLL25AbczMzMzMzOrj0UFHob+/n9WrVw+ZxwGgmZmZmZm1IgeBo/CRj3xkyOUOAM3MzMzMrFU5CByhQw45hFWrVtVcvskmmzgANDMzMzOzluUgcAT6+/s58cQTh8xz0kknNag2ZmZmZmZmI+cgcAR6e3uJiJrLP/jBD3oUUDMzMzMza2kOAkdg6dKlNZfNmDGD448/voG1MTMzMzMzG7mGBYGS9pJ0k6TFko6osnyBpKslXSVpkaRd6y3bKNOnT6+57Otf/3oDa2JmZlNFHddHSfpGXn61pJeXlk+X9GdJ5zau1mZmNpk1JAiUNB04Dtgb2AF4p6QdStkuAV4SES8FDgJOGUHZhnjiiSdqLnM3UDMzG6k6r3F7A3Pz1AOcUFr+EeCGCa6qmZlNIY26E7gTsDgibo2ItcBZwIJihohYHU8/cLcJEPWWbYT+/n4kVV3W2dnZ4NqYmdkUUc81bgFwRiSXA8+StA2ApNnAG8hfnJqZmdWjUUHgtsDthfnlOW0QSW+RdCNwHuluYN1lc/me3JV00cqVK8el4hW1BoWRxMKFC8d1W2Zm1jbqucYNledrwOHAkxNUPzMzm4LWa9B2qt1CWyeiioizgbMl7QYcDby+3rK5fB/QBzBv3rzaw3iOQq1BYSLCXUHNzGy06rnGVc0j6Y3Aioi4UtL8ITci9ZC6kjJr1iwGBgZGXtOC1atXj3kdrcT709q8P63N+zM5NSoIXA5sV5ifDdxRK3NEXCrpuZJmjrTsRKh0Ba12J9BdQc3MbAzqucbVyrMv8CZJ+wAbAZtJOjMi9i9vpPwl6fz588dU6YGBAca6jlbi/Wlt3p/W5v2ZnBrVHfQKYK6k7SVtAOwHnFPMIOl5yg/d5ZHPNgBW1VN2orkrqJmZTZB6rnHnAO/Jo4S+CnggIu6MiE9GxOyI6MrlflktADQzMytryJ3AiHhc0qHABcB04NSIuE7SwXn5icC/kS5yjwGPAO/IA8VULduIelcsW7asarq7gpqZ2VjUeX08H9gHWAysAd7brPqamdnU0KjuoETE+aQLWTHtxML/XwK+VG/ZRtpiiy1YtWrVOukzZsxoQm3MzGwqqeP6GMCHhlnHADAwAdUzM7MpqGE/Fm9mZmZmZmbN5yCwDvfee++I0s3MzMzMzFqVg8A6zJkzZ0TpZmZmZmZmrcpBYB322Wcf8sClT+no6PDIoGZmZmZmNuk4CBxGf38/p59++qCfiJDEAQcc4JFBzczMzMxs0nEQOIze3l7WrFkzKC0iOP/8pg1WamZmZmZmNmoOAodR6zcCa6WbmZmZmZm1MgeBw/CgMGZmZmZmNpU4CBzGwoUL6ejoGJTmQWHMzMzMzGyychBYh4033vip/2fMmEFfX58HhTEzMzMzs0lpvWZXoJX19/fT09MzaGCYRx55pIk1MjMzMzMzGxvfCRxCtZFB16xZQ29vb5NqZGZmZmZmNjYOAofgkUHNzMzMzGyqcRA4BI8MamZmZmZmU42DwCF4ZFAzMzMzM5tqHAQOobu7m76+Pjo7O5FEZ2enRwY1MzMzM7NJzaODDqO7u9tBn5mZmZmZTRm+E2hmZmZmZtZGHASamZmZmZm1EQeBw+jv76erq4tp06bR1dVFf39/s6tkZmZmZmY2an4mcAj9/f309PQ89YPxS5cupaenB8DPCZqZmZmZ2aTkO4FD6O3tfSoArFizZg29vb1NqpGZmZmZmdnYOAgcwrJly0aUbmZmZmZm1uocBA5hzpw5I0o3MzMzMzNrdQ4Ch7Bw4UI6OjoGpXV0dLBw4cIm1cjMzMzMzGxsHAQOobu7m76+Pjo7O5FEZ2cnfX19HhTGzMzMzMwmLY8OOozu7m4HfWZmZmZmNmX4TqCZmZmZmVkbaVgQKGkvSTdJWizpiCrLuyVdnaffSXpJYdkSSddIukrSokbV2czMzMzMbKppSHdQSdOB44A9gOXAFZLOiYjrC9luA14TEfdJ2hvoA3YuLH9tRNzTiPqamZmZmZlNVY26E7gTsDgibo2ItcBZwIJihoj4XUTcl2cvB2Y3qG5mZmZmZmZto1FB4LbA7YX55TmtlvcBPy/MB3ChpCsl9dQqJKlH0iJJi1auXDmmCpuZmZmZmU1FjRodVFXSompG6bWkIHDXQvIuEXGHpK2AiyTdGBGXrrPCiD5SN1LmzZtXdf1mZmZmZmbtrFF3ApcD2xXmZwN3lDNJejFwCrAgIlZV0iPijvx3BXA2qXvphOvv76erq4tp06bR1dVFf39/IzZrZmZmZmY2YRoVBF4BzJW0vaQNgP2Ac4oZJM0BfgK8OyJuLqRvIukZlf+BPYFrJ7rC/f399PT0sHTpUiKCpUuX0tPT40DQzMzMzMwmtYYEgRHxOHAocAFwA/CDiLhO0sGSDs7ZPg3MAI4v/RTELOAySX8B/gicFxG/mOg69/b2smbNmkFpa9asobe3d6I3bWZmZmZmNmEa9UwgEXE+cH4p7cTC/+8H3l+l3K3AS8rpE23ZsmUjSjczMzMzM5sMGvZj8ZPNnDlzRpRuZmZmZmY2GTgIrGHhwoV0dHQMSuvo6GDhwoVNqpGZmZmZmdnYOQisobu7m76+Pjo7O5FEZ2cnfX19dHd3N7tqZmZmZmZmo9awZwIno+7ubgd9ZmZmZmY2pfhOoJmZWRNJ2kvSTZIWSzqiynJJ+kZefrWkl+f07ST9StINkq6T9JHG197MzCYjB4FmZmZNImk6cBywN7AD8E5JO5Sy7Q3MzVMPcEJOfxz4WES8EHgV8KEqZc3MzNbhINDMzKx5dgIWR8StEbEWOAtYUMqzADgjksuBZ0naJiLujIg/AUTEQ6Tf4d22kZU3M7PJyc8EmpmZNc+2wO2F+eXAznXk2Ra4s5IgqQt4GfCHahuR1EO6i8isWbMYGBgYU6VXr1495nW0Eu9Pa/P+tDbvz+TkINDMzKx5VCUtRpJH0qbAj4HDIuLBahuJiD6gD2DevHkxf/78UVW2YmBggLGuo5V4f1qb96e1eX8mJ3cHNTMza57lwHaF+dnAHfXmkbQ+KQDsj4ifTGA9zcxsCnEQaGZm1jxXAHMlbS9pA2A/4JxSnnOA9+RRQl8FPBARd0oS8L/ADRHx1cZW28zMJjN3BzUzM2uSiHhc0qHABcB04NSIuE7SwXn5icD5wD7AYmAN8N5cfBfg3cA1kq7KaUdGxPkN3AUzM5uEHASamZk1UQ7azi+lnVj4P4APVSl3GdWfFzQzMxuSu4OamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBNfT399PV1cW0adPo6uqiv7+/2VUyMzMzMzMbs/WaXYFW1N/fT09PD2vWrAFg6dKl9PT0ANDd3d3MqpmZmZmZmY2J7wRW0dvb+1QAWLFmzRp6e3ubVCMzMzMzM7Px4SCwimXLlo0o3czMzMzMbLJwEFjFnDlzRpRuZmZmZmY2WTgIrGLhwoV0dHQMSuvo6GDhwoVNqpGZmZmZmdn4aFgQKGkvSTdJWizpiCrLuyVdnaffSXpJvWXHW3d3N319fXR2diKJzs5O+vr6PCiMmZmZmZlNeg0ZHVTSdOA4YA9gOXCFpHMi4vpCttuA10TEfZL2BvqAnessO+66u7sd9JmZmZmZ2ZTTqDuBOwGLI+LWiFgLnAUsKGaIiN9FxH159nJgdr1lzczMzMzMrD6NCgK3BW4vzC/PabW8D/j5SMtK6pG0SNKilStXjqG6ZmZmZmZmU1OjgkBVSYuqGaXXkoLAT4y0bET0RcS8iJi35ZZbjqqiZmZmZmZmU1lDngkk3b3brjA/G7ijnEnSi4FTgL0jYtVIypqZmZmZmdnwGnUn8ApgrqTtJW0A7AecU8wgaQ7wE+DdEXHzSMqamZmZmZlZfRpyJzAiHpd0KHABMB04NSKuk3RwXn4i8GlgBnC8JIDHc9fOqmUbUW8zMzMzM7OpplHdQYmI84HzS2knFv5/P/D+esuamZmZmZnZyDXsx+LNzMzMzMys+RwEmpmZmZmZtREHgWZmZmZmZm3EQaCZmZmZmVkbcRBoZmZmZmbWRhwEmpmZmZmZtREHgWZmZmZmZm3EQaCZmZmZmVkbcRBoZmZmZmbWRhwEmpmZmZmZtREHgWZmZmZmZm3EQaCZmZmZmVkbGTIIlLShpAMl/VTSMkmr89+fSXqvpA0bVVEzMzMzMzMbu5pBoKSDgKXA+4A/A4cBb85/rwQOApZIeu9EV9LMzMzMzMzGx3pDLNsTeE1E3FRl2U+Az0l6PvAZ4NsTUTkzMzMzMzMbXzWDwIjYb7jCOUB817jWyMzMzMzMzCaMB4YxMzNrIkl7SbpJ0mJJR1RZLknfyMuvlvTyesuamZlVU1cQKGmWpJMkXSnp5uI00RU0MzNrJknbTeC6pwPHAXsDOwDvlLRDKdvewNw89QAnjKDsuOrv76erq4vXve51dHV10d/fP5Gbs0micl5MmzbN58UYtWJbjnedRrO+esrUylNv+iGHHPLU+9vMmTOZOXMm06ZNe+p/Say33nqD/k6bNg1JEz5NiIgYdgJ+AVwGHAIcUJzqKd+M6RWveEWYmdnUByyKCbyeAI8B55MGR5s+zut+NXBBYf6TwCdLeU4C3lmYvwnYpp6y1abRXh/PPPPM6OjoCOCpqaOjI84888xRra+V/OpXv2p2FcZVI/enEedFuxyfVnyN1VOnkRyf0exjPWVq5fngBz9Yd3qrT6NV6xpZ70XqAWDTevK2yuQg0MysPTQgCHwu8HlgOXAn8AXgueO07n2BUwrz7wa+VcpzLrBrYf4SYF49ZatNo70+dnZ2Vv1g0tnZOar1tZJ2CTImQiPOi3Y5Pq34GqunTiM5PqPZx3rK1Mozffr0EaW38jRata6RQ40OWrQcWL/OvGZmZlNGRNwCHCnpU8AbSD+RdJ2ky4CTgR9HxOOjXH21fj5RZ556yqYVSD2krqTMmjWLgYGBEVQxWbZsWc300ayvlaxevXrS70NRI/enEedFuxyfVnyN1VOnkRyf0exjPWVq5XniiSdGlN7KxvscqDcI/AJwuqSjgLuKCyLijnGtkZmZWQuKiCclXQRsDjwH2Cn//Yqk90fEBaNY7XKg+MzhbKB8Xa2VZ4M6ylbq3gf0AcybNy/mz58/4orOmTOHpUuXVk0fzfpaycDAwKTfh6JG7k8jzot2OT6t+Bqrp04jOT6j2cd6ytTKM3369KoBX630Vjbe50C9o4OeAbwRWATcnqfl+a+ZmdmUJukVkk4gdQf9MHA88OyIeA7pWbxTR7nqK4C5kraXtAGwH3BOKc85wHvyKKGvAh6IiDvrLDtuFi5cSEdHx6C0jo4OFi5cOFGbtEnA58X4acW2HO86jWZ99ZSplaenp6fu9LZTrY9oeQI6a031lG/G5GcCzczaAxP/TOBVwIOkrp/zauRZMYb17wPcDNwC9Oa0g4GD8/8ijQJ6C3BNsQ7Vyg43jeX6eOaZZ0ZnZ2dIis7OzikxKExE+zxzNlEm+rxop+PTiq+x4eo00uMzmn2sp0ytPPWmf/CDH3xqfsaMGTFjxoxB/1N4lrDyV1JLPw8YUfsaqbRs6pk3b14sWrSo2dUwM7MJJunKiJg3ges/GOiPiIcmahuNNB7Xx3bpnjdZeX9am/entU21/al1jazZHVTSezXMD1PkrinvHY8KmpmZtaKIOHGqBIBmZmYw9DOBewJ/ldQraSdJmwJI2jTPH0nqgrJHIypqZmZmZmZmY1czCIyIdwL7Ay8CLgIekPQE6TcDLwJ2BN4dEe9qREXNzMzMzMxs7IbqDnpFRFyeg7xvkoLBXfPfLSLiXRFxeb0bkrSXpJskLZZ0RJXlL5D0e0mPSvp4adkSSddIukqSH/QzMzMzMzMbpaF+J3CuJOVRZT4cEZ8a7UYkTSeNbLYH6aclrpB0TkRcX8h2L2nY7TfXWM1rI+Ke0dbBzMzMzMzMhg4C/wBcKukGYCNJfdUyRURPHdvZCVgcEbcCSDoLWAA8FQRGxApghaQ31Ft5MzMzMzMzG5mhBobZDzif9PtEAOvXmOqxLYN/WH55TqtXABdKulJSPUGnmZmZmZmZVVHzTmBE3Ad8AUDSrIgYy09BVPupiZH8QOEuEXGHpK2AiyTdGBGXrrORFCD2AMyZM2d0NTUzMzMzM5vChroT+JSIeNMYt7Mc2K4wPxu4o97CEXFH/rsCOJvUvbRavr6ImBcR87bccssxVNfMzMzMzGxqqisIHAdXkAaa2V7SBqSupufUU1DSJpKeUfmf9PuF105YTc3MzMzMzKawoQaGGTcR8bikQ4ELgOnAqRFxnaSD8/ITJW0NLAI2A56UdBiwAzATOFtSpb7fjYhfNKLeZmZmZmZmU01DgkCAiDifNNBMMe3Ewv93kbqJlj0IvGRia2dmZmZmZtYeGtUd1MzMzMzMzFqAg0AzMzMzM7M24iDQzMzMzMysjTgINDMzMzMzayMOAs3MzMzMzNqIg0AzMzMzM7M24iDQzMzMzMysjTgINDMzMzMzayMOAmvo7++nq6uLadOm0dXVRX9/f7OrZGZmZmZmNmbrNbsCrai/v5+enh7WrFkDwNKlS+np6QGgu7u7mVUzMzMzMzMbE98JrKK3t/epALBizZo19Pb2NqlGZmZmZmZm48NBYBXLli0bUbqZmZmZmdlk4SCwijlz5owo3czMzMzMbLJwEFjFwoUL6ejoGJTW0dHBwoULm1QjMzMzMzOz8eEgsIru7m76+vro7OxEEp2dnfT19XlQGDMzMzMzm/Q8OmgN3d3dDvrMzMzMzGzK8Z1AMzMzMzOzNuIg0MzMzMzMrI04CDQzMzMzM2sjDgLNzMzMzMzaiINAMzMzMzOzNuIg0MzMzMzMrI04CDQzMzMzM2sjDgLNzMzMzMzaiINAMzMzMzOzNuIg0MzMzMzMrI04CDQzMzMzM2sjDgLNzMzMzMzaSMOCQEl7SbpJ0mJJR1RZ/gJJv5f0qKSPj6SsmZmZmZmZ1achQaCk6cBxwN7ADsA7Je1QynYv8GHgK6Moa2ZmNqlI2kLSRZL+mv9uXiNf1S9CJR0j6UZJV0s6W9KzGlZ5MzOb1Bp1J3AnYHFE3BoRa4GzgAXFDBGxIiKuAB4baVkzM7NJ6AjgkoiYC1yS5wcZ5ovQi4AdI+LFwM3AJxtSazMzm/QaFQRuC9xemF+e0ya6rJmZWataAJye/z8deHOVPDW/CI2ICyPi8ZzvcmD2xFbXzMymivUatB1VSYvxLiupB+gBmDNnTp2rNzMza4pZEXEnQETcKWmrKnmqfRG6c5V8BwHfr7Wh4vVx1qxZDAwMjLbOAKxevXrM62gl3p/W5v1pbd6fyalRQeByYLvC/GzgjvEuGxF9QB/AvHnz6g0yzczMJoSki4GtqyzqrXcVVdIGXd8k9QKPA/21VlK+Ps6fP7/OzVc3MDDAWNfRSrw/rc3709q8P5NTo4LAK4C5krYH/gbsB7yrAWXNzMyaJiJeX2uZpLslbZPvAm4DrKiSbcgvQiUdALwR2D0i/OWnmZnVpSHPBOZnFg4FLgBuAH4QEddJOljSwQCStpa0HPgo8ClJyyVtVqtsI+ptZmY2gc4BDsj/HwD8rEqep74IlbQB6YvQcyCNGgp8AnhTRKxpQH3NzGyKaNSdQCLifOD8UtqJhf/vosZD7dXKmpmZTXJfBH4g6X3AMuBtAJKeDZwSEftExOOSKl+ETgdOLXwR+i1gQ+AiSQCXR8TBjd4JMzObfBoWBJqZmdnTImIVsHuV9DuAfQrzVb8IjYjnTWgFzcxsymrUT0SYmZmZmZlZC3AQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtxEGgmZmZmZlZG3EQaGZmZmZm1kYcBJqZmZmZmbURB4FmZmZmZmZtpGFBoKS9JN0kabGkI6osl6Rv5OVXS3p5YdkSSddIukrSokbV2czMzMzMbKpZrxEbkTQdOA7YA1gOXCHpnIi4vpBtb2BunnYGTsh/K14bEfc0or5mZmZmZmZTVaPuBO4ELI6IWyNiLXAWsKCUZwFwRiSXA8+StE2D6mdmZmZmZtYWGhUEbgvcXphfntPqzRPAhZKulNRTayOSeiQtkrRo5cqV41BtMzMzMzOzqaVRQaCqpMUI8uwSES8ndRn9kKTdqm0kIvoiYl5EzNtyyy1HX1szMzMzM7MpqlFB4HJgu8L8bOCOevNEROXvCuBsUvdSMzMzMzMzG6FGBYFXAHMlbS9pA2A/4JxSnnOA9+RRQl8FPBARd0raRNIzACRtAuwJXNugepuZmZmZmU0pDRkdNCIel3QocAEwHTg1Iq6TdHBefiJwPrAPsBhYA7w3F58FnC2pUt/vRsQvGlFvMzMzMzOzqaYhQSBARJxPCvSKaScW/g/gQ1XK3Qq8ZMIraGZmZmZm1gYa9mPxZmZmZmZm1nwOAs3MzMzMzNqIg0AzMzMzM7M24iDQzMysCSRtIekiSX/NfzevkW8vSTdJWizpiCrLPy4pJM2c+FqbmdlU4CDQzMysOY4ALomIucAleX4QSdOB44C9gR2Ad0raobB8O2APYFlDamxmZlOCg0AzM7PmWACcnv8/HXhzlTw7AYsj4taIWAuclctVHAscDsQE1tPMzKaYhv1EhJmZmQ0yKyLuBIiIOyVtVSXPtsDthfnlwM4Akt4E/C0i/pJ/S7cmST1AD8CsWbMYGBgYU8VXr1495nW0Eu9Pa/P+tDbvz+TkINDMzGyCSLoY2LrKot56V1ElLSR15HXsWc9KIqIP6AOYN29ezJ8/v87NVzcwMMBY19FKvD+tzfvT2rw/k5ODQDMzswkSEa+vtUzS3ZK2yXcBtwFWVMm2HNiuMD8buAN4LrA9ULkLOBv4k6SdIuKucdsBMzObkvxMoJmZWXOcAxyQ/z8A+FmVPFcAcyVtL2kDYD/gnIi4JiK2ioiuiOgiBYsvdwBoZmb1cBBoZmbWHF8E9pD0V9IIn18EkPRsSecDRMTjwKHABcANwA8i4rom1dfMzKYIdwc1MzNrgohYBexeJf0OYJ/C/PnA+cOsq2u862dmZlOX7wSamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGGhYEStpL0k2SFks6ospySfpGXn61pJfXW3a89ff309XVxbRp0+jq6qK/v3+iN2lmZmZmZtYQ6zViI5KmA8cBewDLgSsknRMR1xey7Q3MzdPOwAnAznWWHTf9/f309PSwZs0aAJYuXUpPTw8A3d3dE7FJMzMzMzOzhmnUncCdgMURcWtErAXOAhaU8iwAzojkcuBZkraps+y46e3tfSoArFizZg29vb0TtUkzMzMzM7OGaVQQuC1we2F+eU6rJ089ZQGQ1CNpkaRFK1euHFVFly1bNqJ0MzMzMzOzyaRRQaCqpEWdeeopmxIj+iJiXkTM23LLLUdYxWTOnDkjSjczMzMzM5tMGhUELge2K8zPBu6oM089ZcfNwoUL6ejoGJTW0dHBwoULJ2qTZmZmZmZmDdOoIPAKYK6k7SVtAOwHnFPKcw7wnjxK6KuAByLizjrLjpvu7m76+vro7OxEEp2dnfT19XlQGDMzMzMzmxIaMjpoRDwu6VDgAmA6cGpEXCfp4Lz8ROB8YB9gMbAGeO9QZSeyvt3d3Q76zMzMzMxsSmpIEAgQEeeTAr1i2omF/wP4UL1lzczMzMzMbOQa9mPxZmZmZmZm1nwOAs3MzMzMzNqIg0AzMzMzM7M24iDQzMzMzMysjTgINDMzMzMzayMOAs3MzMzMzNqI0i8zTD2SVgJLx7iamcA941CdqcRtsi63SXVul3W5TdY1Hm3SGRFbjkdl2oGvj1V5f1qb96e1eX9aW9Vr5JQNAseDpEURMa/Z9WglbpN1uU2qc7usy22yLrfJ5DTVjpv3p7V5f1qb92dycndQMzMzMzOzNuIg0MzMzMzMrI04CBxaX7Mr0ILcJutym1TndlmX22RdbpPJaaodN+9Pa/P+tDbvzyTkZwLNzMzMzMzaiO8EmpmZmZmZtREHgWZmZmZmZm3EQWAVkvaSdJOkxZKOaHZ9GknSqZJWSLq2kLaFpIsk/TX/3byw7JO5nW6S9C/NqfXEkrSdpF9JukHSdZI+ktPbtl0kbSTpj5L+ktvkszm9bdukQtJ0SX+WdG6ed5tISyRdI+kqSYtyWtu3S6sa7hqo5Bt5+dWSXl5v2WYY4/6sc+42Wx378wJJv5f0qKSPj6RsM4xxfybj8enO59nVkn4n6SX1lm2GMe7PZDw+C/K+XCVpkaRd6y076USEp8IETAduAZ4DbAD8Bdih2fVq4P7vBrwcuLaQ9mXgiPz/EcCX8v875PbZENg+t9v0Zu/DBLTJNsDL8//PAG7O+9627QII2DT/vz7wB+BV7dwmhbb5KPBd4Nw87zaBJcDMUlrbt0srTvVcA4F9gJ/n94FXAX+ot+xk2p+8bJ1zdxLsz1bAK4GFwMdHUnYy7c8kPj7/BGye/997Crx+qu7PJD4+m/L0mCkvBm5s1eMz1sl3Ate1E7A4Im6NiLXAWcCCJtepYSLiUuDeUvIC4PT8/+nAmwvpZ0XEoxFxG7CY1H5TSkTcGRF/yv8/BNwAbEsbt0skq/Ps+nkK2rhNACTNBt4AnFJIbus2GYLbpTXVcw1cAJyR3wcuB54laZs6yzbaWPanFQ27PxGxIiKuAB4badkmGMv+tKJ69ud3EXFfnr0cmF1v2SYYy/60onr2Z3XkqA/YhPTZpq6yk42DwHVtC9xemF+e09rZrIi4E1JARPpWDtqwrSR1AS8j3flq63bJ3R6vAlYAF0VE27cJ8DXgcODJQlq7twmki+iFkq6U1JPT3C6tqZ72r5WnFY/dWPYHqp+7zTSWNp6sx2cok/34vI90F3o0ZRthLPsDk/T4SHqLpBuB84CDRlJ2Mlmv2RVoQaqS5t/RqK6t2krSpsCPgcMi4kGp2u6nrFXSply7RMQTwEslPQs4W9KOQ2Sf8m0i6Y3Aioi4UtL8eopUSZtSbVKwS0TcIWkr4KJ8ca2lndqlFdXT/rXytOKxG8v+QJVzN/eYaZaxtPFkPT5DmbTHR9JrSUFT5ZmzSX18quwPTNLjExFnkz7X7AYcDby+3rKTie8Erms5sF1hfjZwR5Pq0irurnSNyX9X5PS2aStJ65MCwP6I+ElObvt2AYiI+4EBYC/au012Ad4kaQmpm8jrJJ1Je7cJABFxR/67Ajib1K2m7dulRdXT/rXytOKxG8v+1Dp3m2ksbTxZj09Nk/X4SHox6bGBBRGxaiRlG2ws+zNpj09FDlifK2nmSMtOBg4C13UFMFfS9pI2APYDzmlynZrtHOCA/P8BwM8K6ftJ2lDS9sBc4I9NqN+EUrrl97/ADRHx1cKitm0XSVvmO4BI2pj0LdmNtHGbRMQnI2J2RHSR3jd+GRH708ZtAiBpE0nPqPwP7AlcS5u3Swur5xp4DvAeJa8CHshdelvx+jnq/Rni3G2msbTxZD0+VU3W4yNpDvAT4N0RcfNIyjbBqPdnEh+f5+XPfSiNFLwBsKqespPOeI0wM5Um0khhN5NGAeptdn0avO/fA+4kPYC9nHRrfwZwCfDX/HeLQv7e3E43AXs3u/4T1Ca7km75Xw1clad92rldSCNm/Tm3ybXAp3N627ZJqX3m8/TooG3dJqSR1P6Sp+sq76nt3i6tPFW7BgIHAwfn/wUcl5dfA8wbqmyzp9HuT61zt9lTHfuzNen6/SBwf/5/s0l8fKruzyQ+PqcA9/H054lFQ5Vt9jTa/ZnEx+cTub5XAb8Hdm3l4zOWqTIEqpmZmZmZmbUBdwc1MzMzMzNrIw4CzczMzMzM2oiDQDMzMzMzszbiINDMzMzMzKyNOAg0MzMzMzNrIw4CzczMzGxSkrSFpAskPSDpypx2lqT3jWAd3x9JfrOpwD8RYWZmZmaTkqQjgTcAr4mIxyW9CvguMDcinqhzHS8Afg10RcQjE1dbs9bhO4FmZmZmNlk9B7ghIh7P8x8Bvl1vAAgQETcCi4F3TkD9zFqSg0CzSU7SEklHSrpE0mpJ10r6p2bXy8zMbCJJ+j/gAOCAfP1bSLoreFEhT5ekkPRuSddLekjShZK2Ka3uIuDNDau8WZM5CDSbGg4CPgw8k3QhO7251TEzM5tYEfGvQD9wekRsCpwJPAO4vkr2dwC7AdsCmwCfKy2/Bnj5xNXWrLU4CDSbGk6KiOty95dTgOdJemazK2VmZtZAm+e/D1VZ9tmIuCciHiQ9MzivtPxBYIuJrJxZK3EQaDY13Fn4/+H89xnNqIiZmVmT3Jf/Vrv+la+T5TybAfdORKXMWpGDQDMzMzObCv4KrAZ2GEXZHYE/j291zFqXg0AzsyHkAQWGm+ZLOjD/v2mz6zwaeYChr4zTunaR9CdJf5cU473+qUTSnpIOq5J+mqRFTahSy8qvr0ObXQ9rXXmE0POA14+i+B7AT8e1QmYtbL1mV8DMrMW9uvD/xsAvgf8mfdCouB7oamCdJsJbgFXjtK6TgBXAvwCPTsD6p5I9gX2Br5XSjyadb2Y2Ml8HviPpCyP4ncDnA3NJzwqatQUHgWaTXER0leaXAGpKZaagiLi88n/hLt8txfS8rKH1Gm8RMZ7doF4A9EXErydo/UNSOhgbRsTfG7XN8RYRtzS7Du1E0sb+kfDJKSIOLM3/Pt9FPxD432rXxIg4DTitkHQU0OtzwNqJu4OamY2v7SVdJOlhSTdKems5g6QFkhbl7pJ3SfqypPWHWqmkAUk/kvReSbfl38T6jqQNJe0k6Y85bUDSnFLZL0q6Ji9fLqlf0talPIO6a1a6I0raQ9LVeX8uk/SiIeo4P3f/nA58PXffO63a+nPaoZJuz+v+qaTdK91r8/LK73u9sVRuUFdJSUdJukfSrpKuAP4OvC0v21XSryWtkbRK0smShh00SdJukn6V2+yB3K4vy8u2kXSqpFslPSLpZkn/LWmDQvlK3d+Vj9NDklZI+kyx3sDHgM5C1+JKe63THVTSS5V+D3SNpPvycZxVZZtvl3RSrvdySZ+VNOT1XsnRuY4P5v3bL6+vq5BvpqTTc1uuye1SHmURSe+XdJ2kRyUtlXR4afmLJP1C0r35+N8g6UPDHRdguqTPS1qZ63qcpA1L654j6ay87jWSLlC601Nup25JZ0i6H/i/vGyL3HZ3K70+fydp5zrqZS0kIvaLiP8dQf53RsQpE1kns1bjINDMbHx9FziH1P3xr8BZkmZXFkp6O/AT4I/Am4DPAj3AF+pY96tIP4z8H8DhwNuBbwInk7pA7Q88B+grldsK+DzpR5QPy3l+KWn6MNubAxwDLATemdfzA6nmbc8/8XT32f/J/x9dLaOkt+S6V9rqaqDuD21VdJB+H/MUYC/gj5J2AS4B7iJ1uTwM2Af49lArykHoJcBjpPZ+B/Ab0u+LAcwkjSL40bytY4D35v0pOwZYk7d/MvCZQrBzCul8uYvUVkO115bAQN7Pd5HOgdcAFxWDz+zLpMEx9iX9btqn8/9DOQw4Ejgx530kr6fsp6Ruvh8ntcs04FeSnleo638CJ+S8b8z/H63Bz/OdAzxBOmffRGq7ekY0/hjw7FzuGOADwEcK294CuAx4PnAw6TWyCXCxpHL32q+QfkrgbcDnczB5MenZsP8k/XD4ylx2a8zMppKI8OTJkydPdUzApkAAB1ZZdmBedlAhbQbwOHBwnhewFPh2qexBpA/dM4bY9gBwP/DMQtoP8jZ3K6QdktM6aqxnOimYKZdbAnylMH9arvvcQtqbc7kXDNNOARxaSiuv/wrgvFKe43PZ+Xm+K8+/sZTvNGBRYf6onG9BKd9vgF+V0l6X8+44RP1/DywCVOd5sR4pMPs7sEGp7heW8p4M/A2Ylue/Aiypss7yPn4xH//NCmk75W28s7TNM0rrugo4a4j6TycNn39cKf38vL6uPL9Xnn9NIc8mpEDppDy/GSkA/UxpXZ8jBbvTSUF0AP84wtdfAJeW0n4KXF6YP5r07OkWhbTNgQeAD5Xa6ezSut4HrGXwOb8ecAtwzEjq6smTJ0+tPvlOoJnZ+Lqw8k9ErCINkFK5E/gPpLtrP5C0XmUiDTazEWmI8qEsiogHCvOLSR9aLyulQbpbAoCkvXO3tgdIgd3yQn2GsiQi/lqYvz7/nV0tc73yHciXku4GFZXnRyKAnxe20UG6s1Zu68tId/heUaNumwA7A6dHRNTII0mHSbpe0iN5ff3AhqTjW3R2af4npGMz0jbciRRQPlhJiIg/koLrXUt5LyzNXz/M9rYDtmb447ETsDIGP+v5MHBuoQ6vJgWGP6xyjs/K9bgXuB04UdI7JG01RN3Khtu31wMXAQ8Wtv0QcCXr/jj4eaX51+d8txXKAvy6Slkzs0nNQaCZ2fi6vzS/lhTgQboDAukOy2OF6bacvt0o1v1QRDxZSqOyTUmvJH2YXw68m/Qh/VXFPCPcXj3lhrMl6Q7LylJ6eX4k7ouItYX5zUl3nY5ncFs/CqxP7bbenHTH9s4ayyF1nfwfUoC3gBQcVbp4lttmRY35bYZYfzXbAHdXSb8b2KKUdn9pvngOVlPp6jjc8ainDpVz/DoGt/uvcvp2+Xzdk3Rn8FTgLkm/UX7mchj3l+bL+zaT1E31sdL0WtY95uV9mUl6bZTLvrdKWTOzSc2jg5qZNc69+W8P1X+U+LYqaWP1FtKH+XdU7mxJ6pyA7YzEStIdyS1L6eX5yuie5WfeykEPpDuBRffntKNIQXfZHTXqdh/wJEMHaW8DfhgRvZUESbV+nLp8l6syP1SQWc2dVdYF6e7alSNcV9ld+e9wx2OoOlTO7crfN1I9YLwJICJuBP5NaUCkfwa+BJwnaXbpS42Rupf0pUe1ZysfKs2Xz5l7Sd2AP1il7KNV0szMJi0HgWZmjXMT6Xmwrog4uUHb3Bh4rNS1sbtB264qIp6QdBXpLtpJhUVvKmVdQboT88JKgtLPdLya9GzlUNt4WNLlwPMj4nMjqNvDkv4AvEfSt2p0Cd2YdYOCWm36FtLAKBVvJQVTlS65w92lq/gD8EFJz4iIh+Cpu7xdDO4OPBq3kwLBBcAFhfTy8fgD8FlJu0XEpbkOHaQBhyrdXn9Per712RFR7m65joh4jDRI0VdJg+Q8i6cDydG4hDQYzHUx8uH+LyHdoVwWEeU7uGZmU4qDQDOzBomIJyV9jPRDxpuRnmFbSxqt883AvhGxZpw3exFwmKSvkYbB/yfSyIrN9nngJ5K+RbpzswspmIB0J67SXj8D/p+kpaS7ex8jBRn1OBy4RNKTwI9Id4Lm5O30RsTNNcodQRol8ueS+oCHSYHnoog4l9SmH87B4i2kAPB5Ndb1IkknAT8GdiMNPvKRwt2uG4FZkg4ErgXuifS7ZmVfJd2hukDSl0iDFH0RuCave9RyUH4McIyklcBvSQHgP+YsleNxgaTfAt+XdARpAJaPk4LiY3Ke+5V++uLr+Y7zpaRHT/4BeG1EvEXSi0kD4nwfuJXUBfcTwF8iYiwBIKR22p8UWH6T9KXLLNJIqpdFxPeGKHsGaUTRAaWfM7mVNLjTTsBdEXHsGOtmZtYy/EygmVkDRcT3SXdcXgr8kDRQyCGkn1dYW7vkqLd3PukD9r+Rgq3XkLrqNVVEnA18mBT8/hR4JSmgAHiwkPVQUlByPHAc8D3SICP1bOMyUuC1JfAdUhB8OOnOV7WuipVyl5J+JqCD9BML3ye1W+Xu3edyPf47/12b96Waw0kjZv6Y9HMGRwPfKiz/AWkk0C+TRkw9qkadVpKea/t73uZxpNFP9yg9Czlax5IC80NyXTfP8zD4eLyFFAR/jXT+CnhdRFQGJCIivkzq8rw38LNc3+5cX0h3He8GeklfhBwP3MC6dx5HLCLuIT3Xd2PepwtJbftM0s+QDFX276Q2voj00y0Xkn56ZS7pJ13MzKYM1Rj8zMzMrKEkfYoUGGwxiq58LUXpB9ZvA/413z2cdCSdQgoym/0MqZmZjTN3BzUzs4bLP37+SdKokWtIg4N8AvjfyR4ATkaSdiSNqvk7UvfPvUmjYn6imfUyM7OJ4SDQzMyaYS3wAuA9pK56d5K63v1XMyvVxh4m/dbfoaTf+VtKCgD/p5mVMjOzieHuoGZmZmZmZm3EA8OYmZmZmZm1EQeBZmZmZmZmbcRBoJmZmZmZWRtxEGhmZmZmZtZGHASamZmZmZm1EQeBZmZmZmZmbeT/Ayi+MP6kI0OyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import useful libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# create the function that you need to calculate its limit\n",
    "def f(n):\n",
    "    return (n**3-2*n**2+1)/(3*n**3-4*n+9)\n",
    "     \n",
    "# create a list that contains the values of the function for n= 0: 1000\n",
    "# first initiate an empty list\n",
    "list=[]\n",
    "for n in np.arange(1,1000,2):\n",
    "   list.append(f(n))\n",
    "\n",
    "# plot your sequence and check if it converged \n",
    "#plt.plot(list,'ko')\n",
    "#plt.xlabel('n',fontsize=13)\n",
    "#plt.ylabel('f(n)',fontsize=13)\n",
    "\n",
    "# Make two subplots: One plots the sequence against its index and the other plots the sequence \n",
    "# on the number line\n",
    "\n",
    "fig,subs=plt.subplots(1,2,figsize=(15,5))\n",
    "subs[0].plot(list,'ko')\n",
    "subs[0].set_xlabel('n', fontsize=13)\n",
    "subs[0].set_ylabel('f(n)', fontsize=13)\n",
    "subs[0].set_title('Sequence plotted against its index',fontsize=13)\n",
    "\n",
    "subs[1].plot(list,np.zeros(len(list),),'ko')\n",
    "subs[1].set_xlabel('f(n)', fontsize=13)\n",
    "subs[1].set_ylabel('y', fontsize=13)\n",
    "subs[1].set_title('Sequence plotted on the number line',fontsize=13)\n",
    "subs[1].grid()\n",
    "\n",
    "# Title and caption the main figure\n",
    "fig.suptitle('Two different visualizations for the same sequence of numbers',fontsize=15)\n",
    "fig.text(.5, .01, 'The main figure caption goes here', ha='center',fontsize=15)\n",
    "\n",
    "plt.savefig('Fig_m248_conv_seq.png')\n",
    "\n",
    "print('The length of the list containing the members of the sequence is:',len(list))\n",
    "print('The numerical (not the analytical) limit is:',list[len(list)-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program C: Convergence of a sequence to its limit. Aproaching the limit to within an $\\epsilon$ distance. \n",
    "\n",
    "Write a program that tells you the least $n$ so that the\n",
    "        sequence $a_n=\\frac{n^2}{2n^2-1}$ is within distance $0.000001$\n",
    "        of its limit. Is this sequence fast to converge or slow?\n",
    "        Compare to the above problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first n that makes the sequence enter the vicinity \n",
      "      of its limit to within 1e-06 is: 501\n",
      "\n",
      " a(501)= 0.5000009960139522\n",
      "\n",
      " |a(501)-L|= 9.960139522036116e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Plotting the sequence against its index')"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import plotting library and numpy for using zeros function in the last plot\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# write a function for the formula\n",
    "def a(n):\n",
    "    return n**2/(2*n**2-1)\n",
    "\n",
    "# define the limit if you know it (analytically)\n",
    "L=0.5\n",
    "n=1\n",
    "eps=0.000001\n",
    "\n",
    "# Let's save the sequence members in a list so we can plot it later\n",
    "list=[]\n",
    "while (abs(a(n)-L)>eps):\n",
    "    list.append(a(n))\n",
    "    n =n+1\n",
    "    \n",
    "print(f'''The first n that makes the sequence enter the vicinity \n",
    "      of its limit to within {eps} is:''',n)\n",
    "print(f'\\n a({n})=',a(n))\n",
    "print(f'\\n |a({n})-L|=',a(n)-0.5)\n",
    "\n",
    "# Let's plot this covergence\n",
    "plt.plot(list,'k.')\n",
    "plt.xlabel('n',fontsize=13)\n",
    "plt.ylabel('a(n)',fontsize=13)\n",
    "plt.title('Plotting the sequence against its index',fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program D: Finite Sum\n",
    "Write a program that calculates the following sum\n",
    "        $\\sum_{k=6}^{50}k^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finite sum (this is not series of numbers)= 42870\n"
     ]
    }
   ],
   "source": [
    "sum=0\n",
    "for k in range(6,51,1):\n",
    " sum=sum+k**2\n",
    "print('Finite sum (this is not series of numbers)=',sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program E: Random number generators. Uniform Distribution.\n",
    "Write a program that generates a random number between $0$ and $1$ sampled from the uniform distribution $U[0,1]$, meaning each of the numbers between 0 and 1 is equally likely to be chosen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7605188783296494\n",
      "<class 'float'>\n",
      "[[0.81087146 0.62276948 0.34847188]\n",
      " [0.12161246 0.44157302 0.8595859 ]]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "# This will generate one random number between 0 and 1 sampled from the uniform distribution .\n",
    "z=np.random.rand()\n",
    "print(z)\n",
    "print(type(z))\n",
    "\n",
    "# this will generate a 2 by 3 matrix containing random numbers\n",
    "# between zero and 1 sampled from the uniform distribution.\n",
    "x=np.random.rand(2,3)\n",
    "print(x)\n",
    "print(type(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program F: Random number in any interval $[a,b]$\n",
    "Write a program that generates a random number between $11$ and\n",
    "        $24$ uniformly sampled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[13.26263972 16.95785085 17.55672806 22.10139034]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's generate a four random numbers between 11 and 24\n",
    "y=11+13*np.random.rand(4) # y=a+(b-a)*np.random.rand()\n",
    "print(y)\n",
    "type(y)\n",
    "\n",
    "# If we want our work to be reproducible by other people, \n",
    "# then we can set a specific random seed before we generate our random numbers, for example:\n",
    "# np.random.seed(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program G: Generate a random *integer* in an interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  7  -5   9   0  -3]\n",
      " [ 10 -13   6  13   2]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use randint from numpy.random to generate random integers instead of floats\n",
    "z=np.random.randint(-20,21,(2,5)) # randint(lowest value inclusive, highest value not inclusive, how many you want: could be a matrix)\n",
    "print(z)\n",
    "type(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program F: Generate a random number sampled from the Normal Gaussian Distribution (has mean $0$ and variance $1$) not the uniform distribution. Then make a histogram to make sure your samples were generated from the normal gaussian distribution.\n",
    "\n",
    "Probability density function for the normal distribution:\n",
    "\n",
    "$$g(x;\\mu,\\sigma)=\\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.26405266  1.52790535 -0.97071094  0.47055962 -0.10069672  0.30379318\n",
      " -1.72596243  1.58509537  0.13429659 -1.10685547  1.57822555  0.10749794\n",
      " -0.76404783 -0.77518851  1.38384717  0.76038508 -0.28564551  0.53836748\n",
      " -2.08389663  0.93778171 -0.005778   -0.46747897 -0.4230153   1.06448209\n",
      " -2.9033676   1.61689037  1.42550989 -0.66475512  0.98501786 -1.70046527\n",
      " -1.10014381 -1.31564409  0.81050091 -1.04477837 -0.68922937 -0.85275686\n",
      "  1.11347211 -1.92116972 -0.70140242  0.84908785  1.05069979 -0.53687446\n",
      " -0.02919272  1.39405598 -0.39786744  1.01912738  1.8988813  -0.35484964\n",
      " -0.38701647 -1.92730539  0.55075659  0.95435581  0.7827765  -1.7932379\n",
      "  1.2418555   1.70774688  0.3231534  -0.99183439 -1.16328237 -0.0213351\n",
      " -1.58199529 -1.24311418 -0.41016902 -1.05507534 -1.05731214 -1.28411722\n",
      "  0.91312604 -1.38774534  0.03002776 -0.45000776  0.20563314 -0.46002618\n",
      " -0.17341299 -0.21665484 -0.25993484  0.56629343  0.99052247 -0.5947633\n",
      "  0.34346298 -2.58932253 -0.01650232 -0.06609069 -0.1283657  -0.89557729\n",
      "  0.57509771 -0.49844671 -1.15530009  0.90083869  0.87896131 -1.49493601\n",
      " -0.30249371 -1.06379773  1.70472385  0.8774262   1.00256029 -1.04376454\n",
      "  1.26802778 -0.28202225  0.33168039  0.43706141]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Count'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use randn or normal from numpy.random to generate n random numbers sampled from the normal Gaussian distribution\n",
    "n=100\n",
    "mu=0\n",
    "sigma=1\n",
    "# Let's fix the seed to generate the same exact random numbers every time I or someone else runs this. \n",
    "# This allows my work to be reproducible.\n",
    "np.random.seed(30)\n",
    "s=np.random.normal(loc=mu, scale=sigma, size=n)\n",
    "print(s)\n",
    "\n",
    "# Let's use seaborn library to make a nice histogram. The function displot (distribution plot) makes a histogram.\n",
    "import seaborn # version 0.11.1\n",
    "seaborn.set_theme(style=\"darkgrid\") #cosmetics\n",
    "seaborn.displot(data=s,bins=20,color=\"pink\")\n",
    "# kernel density estimation plot: graphs the probability density function this data was probably sampled from\n",
    "seaborn.kdeplot(data=s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> # A note about using the uniform distribution to generate a random number from any other distribution\n",
    "> The [Universality Theorem](https://en.wikipedia.org/wiki/Probability_integral_transform) for the Uniform distribution allows us to use the uniform distribution to generate a random number from any other continuous distribution, by inverting the cummulative distribution function of that distribution. [This link](https://en.wikipedia.org/wiki/Inverse_transform_sampling) specifies this sampling method. However, this is inefficient if we don't know the inverse of the cummulative distribution function of our desired distribution, so other methods like [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling) or Gibbs Sampler based on Markov Chain Monte Carlo methods are employed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program G: Let's sample some noisy data whose underlying generating function is a linear function (a straightline $y=b+ax$ controlled by $2$ parameters $a$ for its slope and $b$ for its $y$-intercept). \n",
    "In reality, we get our data points but we don't know their underlying generating function. We make assumptions about this true function and try to estimate its parameters by fitting the data points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f87e4022d60>]"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate a hundred random x points between zero and 2\n",
    "x=2*np.random.rand(100,1)\n",
    "# y=2-3x+noise. We add noise otherwise all data points will lie perfectly on y=2-3x \n",
    "y=2-3*x+np.random.rand(100,1)\n",
    "# plot the data points\n",
    "plt.plot(x,y,'b.')\n",
    "\n",
    "# Plot the line y=1-2x. This will not be a good fit.\n",
    "plt.plot(x,1-2*x,'r')\n",
    "\n",
    "# Plot the line y=2-3x in green. This is a better but not best fit.\n",
    "plt.plot(x,2-3*x,'g')\n",
    "\n",
    "# Plot the line y=2.5-3x in magenta. This is a better fit.\n",
    "plt.plot(x,2.5-3*x,'m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program H: Let's sample some noisy data whose underlying generating function is a nonlinear function, in particular a Gaussian function with mean $\\mu$ and standard deviation $\\sigma$:\n",
    "$$y=\\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
    "The parameter $\\mu$ controls the location of the center of the bell curve and the parameter $\\sigma$ controls the spread of the bell curve. The *normalization constant* $\\frac{1}{\\sigma\\sqrt{2\\pi}}$ ensures that the total area under the bell curve is $1$, making it a probability density function.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f87d343e730>]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gaussian function plus noise. \n",
    "mu=3\n",
    "sigma=2\n",
    "x=-3+12*np.random.rand(100,1)\n",
    "y=np.exp(-0.5*(x-mu)**2/sigma**2)/(sigma*np.sqrt(2*np.pi))+0.05*np.random.rand(100,1)\n",
    "# plot the data points\n",
    "plt.plot(x,y,'b.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Note that even though we know the generating function, if we only had partial view of the data, it is very hard to guess what non-linear function it was generated from. Here's a parial view of the above data, with reduced noise level:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb8975f5490>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=7+3*np.random.rand(50,1)\n",
    "# Gaussian function plus noise, over x in [4,7]. \n",
    "mu=3\n",
    "sigma=2\n",
    "y=np.exp(-0.5*(x-mu)**2/sigma**2)/(sigma*np.sqrt(2*np.pi))+0.02*np.random.rand(50,1)\n",
    "# plot the data points\n",
    "plt.plot(x,y,'b.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look at the picture above. It's not clear this is a part of a Gaussian function. We can try to fit it to a gaussian, and see if it generalizes well to the test data. But for each data set are we going to just sit there are try to fit it to every nonlinear function out there? \n",
    "This is where we need to make assumptions about the underlying generating function (some form with a bunch of parameters), and try to estimate the best parameters that make the function fit both seen and unseen data. Functions constructed using neural networks in machine learning perform well on wide sets of data with wide range of applications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "># *Note*:  Specifying the *seed* for your random number generator would produce the same random number everytime. This helps make your work reproducible. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's make three dimensional surface plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this enables three dimensional axes\n",
    "fig=plt.figure() # you can pass figsize=(,) to control the size of the figure\n",
    "fig=plt.axes(projection='3d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.92, '3-dimensional contour plot')"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# formula for the function of two variables that we want to plot\n",
    "def f(x,y):\n",
    "    return x**2+y**2\n",
    "# create the x and y grid points using numpy.linspace\n",
    "x=np.linspace(-6,6,30)\n",
    "y=np.linspace(-6,6,30)\n",
    "# create the two dimensional grid\n",
    "X,Y=np.meshgrid(x,y)\n",
    "# Z=f(each point in the mesh grid)\n",
    "Z=f(X,Y)\n",
    "\n",
    "# Now plot Z \n",
    "picture=plt.figure(figsize=(8,8))\n",
    "picture=plt.axes(projection='3d')\n",
    "picture.contour3D(X,Y,Z,30) #you can specify the color map using the argument cmap=\n",
    "# set labels for axes\n",
    "picture.set_xlabel('x')\n",
    "picture.set_ylabel('y')\n",
    "picture.set_zlabel('z=f(x,y)')\n",
    "# set image title\n",
    "picture.set_title('3-dimensional contour plot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program I: Classes and new instances within your classes\n",
    "Check this [link](https://medium.com/@DakshHub/object-oriented-python-class-es-and-object-s-f9f016674e40) on classes, methods and dictionaries in Python.\n",
    "\n",
    "Write a Python class that defines instances with your name, your\n",
    "        jmu eid, your phone number, then introduce a bunch of instances in your class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hala\n",
      "12345\n",
      "123 444 8181\n",
      "Zed\n",
      "Nada 467582\n",
      "<__main__.student object at 0x7f87d3f6da90>\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'student' object has no attribute 'grade'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-115-fd14946d0168>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0;31m# doe not have that attribute:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstudent_1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrade\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'student' object has no attribute 'grade'"
     ]
    }
   ],
   "source": [
    "# Define a class named student, takes instances (individual students) with attributes name, eid, and phone\n",
    "class student:\n",
    "    def __init__(instance,name,eid,phone):\n",
    "        instance.name=name\n",
    "        instance.eid=eid\n",
    "        instance.phone=phone\n",
    "\n",
    "# now define instances in the student class\n",
    "student_1=student('Hala',12345,'347 111 3535')\n",
    "student_2=student('Maya', 55212, '123 444 8181')\n",
    "student_3=student('Zed',1102,'112 456 7654')\n",
    "student_4=student('Sam', 64732, '345 277 2222')\n",
    "student_5=student('Nada', 467582,'223 445 5555')\n",
    "\n",
    "# now check that your instances are saved the way they are supposed to\n",
    "print(student_1.name)\n",
    "print(student_1.eid)\n",
    "print(student_2.phone)\n",
    "print(student_3.name)\n",
    "print(student_5.name,student_5.eid)\n",
    "# if you print the instance without specifying its attribute, you will \n",
    "# get its type and memory location\n",
    "print(student_1)\n",
    "\n",
    "# If you call an attribute for an instance in the class that you did not define\n",
    "# within the class you will get an error that the instance object in the class \n",
    "# does not have that attribute:\n",
    "\n",
    "print(student_1.grade)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program H: Dictionaries and Data Frames\n",
    "Write a dictionary containing your name, jmu eid, major, phone number, then create a data frame for your dictionary. Dictionaries in python are indexed by keys. You can use the library pandas and the method DataFrame to create a data frame for your dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " My dictionary = {'name': ['Hala'], 'eid': ['12345'], 'major': ['Math'], 'phone': ['222 134 5555']}\n",
      "\n",
      " Type of the variable me is:\n",
      " <class 'dict'>\n",
      "\n",
      " Value stored under the key name is:\n",
      " ['Hala']\n",
      "\n",
      " Value stored under the key eid is:\n",
      " ['12345']\n",
      "\n",
      "This is my first data frame:\n",
      "    name    eid major         phone\n",
      "0  Hala  12345  Math  222 134 5555\n",
      "\n",
      "\n",
      "\n",
      "This is a new data frame:\n",
      "    x  y  z\n",
      "0  1  3  0\n",
      "1  2  4  0\n",
      "2  3  5  5\n",
      "3  8  1  4\n",
      "4  9  1  5\n",
      "5  2  1  6\n",
      "6  1  1  1\n",
      "\n",
      "This is only the head of my data frame:\n",
      "   x  y  z\n",
      "0  1  3  0\n",
      "1  2  4  0\n",
      "2  3  5  5\n",
      "3  8  1  4\n",
      "4  9  1  5\n",
      "              x         y         z\n",
      "count  7.000000  7.000000  7.000000\n",
      "mean   3.714286  2.285714  3.000000\n",
      "std    3.352327  1.704336  2.581989\n",
      "min    1.000000  1.000000  0.000000\n",
      "25%    1.500000  1.000000  0.500000\n",
      "50%    2.000000  1.000000  4.000000\n",
      "75%    5.500000  3.500000  5.000000\n",
      "max    9.000000  5.000000  6.000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'x'}>,\n",
       "        <AxesSubplot:title={'center':'y'}>],\n",
       "       [<AxesSubplot:title={'center':'z'}>, <AxesSubplot:>]], dtype=object)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ba4Hzh7MhngPcW1V3jTiTJE2N0Q5BVNWhJBcBnwKOAy6vqjuSXDCs3wHsAl4M7AMeAF411jwc4yGMRqtx7tU4Mzj3SlqNM8Myzz3aN+EkSUfmlXCS1MQAS1KTNR/gpS6HnlZJLk9yd5KvdM8yqSRbklyfZG+SO5K8rnumpSR5RJIvJbltmPnt3TM9FEmOS/Lvwzn1q0KSbyb5cpJbk+xe+h39khyf5CNJ7hz+fJ+xLJ+7lo8BD5dD/wfwIuZOebsZeHlVfbV1sAkkeR5wP3NXCj69e55JDFcxnlhVe5I8BrgF+I1p/v1OEuBRVXV/ko3ADcDrhiszp16SNwAzwGOr6pzueSaR5JvATFWtmgsxkrwf+EJVXTqc1fXTVfW9Y/3ctb4HPMnl0FOpqj4PfLd7joeiqu6qqj3D8+8De4HNvVMd2XAZ/P3Dy43DY1XslSQ5CfhV4NLuWdayJI8FngdcBlBVP1yO+MLaD/BmYP+817NMeRDWiiQnA6cCNzWPsqThv/G3AncDn66qqZ958E7gT4D/bZ7joSrgn5PcMtxmYNo9GTgI/O1wuOfSJI9ajg9e6wGe6FJnLa8kjwauAl5fVfd1z7OUqvpRVT2TuSsxT08y9Yd8kpwD3F1Vt3TPchTOrKrTmLsb4oXD4bZptgE4Dbikqk4F/htYlu8nrfUAe6nzChuOo14FXFlVV3fP81AM/638LPCgm6ZMoTOBXx+Op34QeH6Sv+8daTJVdWD49W7gGuYOFU6zWWB23v+MPsJckI/ZWg/wJJdDa5kM39C6DNhbVe/onmcSSTYlOX54/kjghcCdrUNNoKr+rKpOqqqTmftz/Zmq+t3msZaU5FHDN2gZ/hv/K8BUn+lTVf8J7E/ylGHRC4Bl+cbymHdDa3e4y6Gbx5pIkg8AZwEnJJkF3lZVl/VOtaQzgVcAXx6OqQK8pap29Y20pBOB9w9nzDwM+HBVrZpTulahxwPXzP1bzQbgH6rqut6RJvJa4MphR+7rLNNtE9b0aWiSNM3W+iEISZpaBliSmhhgSWpigCWpiQGWpCYGWJKaGGBJamKAte4luWC4N+2tSb6R5PrumbQ+eCGGNBjuY/EZ4K+q6mPd82jtcw9Y+om/Ye6eCsZXK2JN3wtCmlSSVwJPBC5qHkXriIcgtO4l+QXg/cAvVdV/dc+j9cNDENLcXu/jgOuHb8T5I360ItwDlqQm7gFLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1+T/2Jmb+uFqpbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This is my dictionary\n",
    "me={'name': ['Hala'], 'eid': ['12345'], 'major': ['Math'], 'phone': ['222 134 5555']}\n",
    "print(\"\\n My dictionary =\",me)\n",
    "\n",
    "# check that the type of your new object is a dictionary\n",
    "print(\"\\n Type of the variable me is:\\n\",type(me))\n",
    "\n",
    "# access values in my dictionary\n",
    "print(\"\\n Value stored under the key name is:\\n\",me['name'])\n",
    "print(\"\\n Value stored under the key eid is:\\n\",me['eid'])\n",
    "\n",
    "# To create data frames using dictionaries you need to import pandas\n",
    "import pandas\n",
    "\n",
    "# put your dictionary in a data frame\n",
    "df1=pandas.DataFrame(me)\n",
    "# print the data frame\n",
    "print(\"\\nThis is my first data frame:\\n\",df1)\n",
    " \n",
    "# let's skip couple lines in the output to make it look prettier\n",
    "print('\\n\\n')\n",
    "\n",
    "# Create a new dictionary and frame it in a data frame\n",
    "df = pandas.DataFrame({'x': [1, 2, 3, 8, 9, 2, 1], 'y': [3, 4, 5, 1, 1, 1, 1], \n",
    "                       'z':[0, 0, 5, 4, 5, 6,1]})\n",
    "\n",
    "# print the data frame\n",
    "print(\"This is a new data frame:\\n\",df)\n",
    "\n",
    "# print only the head of your data frame (first five rows)\n",
    "print(\"\\nThis is only the head of my data frame:\")\n",
    "print(df.head())\n",
    "\n",
    "print(df.describe())\n",
    "\n",
    "# let's visualize the data in my new data frame\n",
    "import seaborn\n",
    "# each alone\n",
    "seaborn.displot(df.iloc[:,0])\n",
    "seaborn.displot(df.iloc[:,1])\n",
    "seaborn.displot(df.iloc[:,2])\n",
    "\n",
    "# or you can use the .hist attribute for pandas data frames. It plots a histogram for each feature of the data \n",
    "df.hist(bins=3, figsize=(10,10), color='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Program J: We can change instances in our classes into dictionaries using the .dict method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'name': 'Hala', 'eid': 12345, 'phone': '347 111 3535'}\n",
      "{'name': 'Maya', 'eid': 55212, 'phone': '123 444 8181'}\n",
      "{'name': 'Zed', 'eid': 1102, 'phone': '112 456 7654'}\n",
      "{'name': 'Sam', 'eid': 64732, 'phone': '345 277 2222'}\n",
      "{'name': 'Nada', 'eid': 467582, 'phone': '223 445 5555'}\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>eid</th>\n",
       "      <th>phone</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Hala</td>\n",
       "      <td>12345</td>\n",
       "      <td>347 111 3535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Maya</td>\n",
       "      <td>55212</td>\n",
       "      <td>123 444 8181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Zed</td>\n",
       "      <td>1102</td>\n",
       "      <td>112 456 7654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sam</td>\n",
       "      <td>64732</td>\n",
       "      <td>345 277 2222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Nada</td>\n",
       "      <td>467582</td>\n",
       "      <td>223 445 5555</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   name     eid         phone\n",
       "0  Hala   12345  347 111 3535\n",
       "1  Maya   55212  123 444 8181\n",
       "2   Zed    1102  112 456 7654\n",
       "3   Sam   64732  345 277 2222\n",
       "4  Nada  467582  223 445 5555"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's take our student class example above\n",
    "# Define a class named student, takes instances as students with name, eid, and phone\n",
    "class student:\n",
    "    def __init__(instance,name,eid,phone):\n",
    "        instance.name=name\n",
    "        instance.eid=eid\n",
    "        instance.phone=phone\n",
    "\n",
    "# now define instances in the student class\n",
    "student_1=student('Hala',12345,'347 111 3535')\n",
    "student_2=student('Maya', 55212, '123 444 8181')\n",
    "student_3=student('Zed',1102,'112 456 7654')\n",
    "student_4=student('Sam', 64732, '345 277 2222')\n",
    "student_5=student('Nada', 467582,'223 445 5555')\n",
    "\n",
    "# Now create dictionaries for these instances:\n",
    "s1=student_1.__dict__\n",
    "s2=student_2.__dict__\n",
    "s3=student_3.__dict__\n",
    "s4=student_4.__dict__\n",
    "s5=student_5.__dict__\n",
    "\n",
    "# Now print these and see if they are dictionaries:\n",
    "print(s1)\n",
    "print(s2)\n",
    "print(s3)\n",
    "print(s4)\n",
    "print(s5)\n",
    "\n",
    "# Let's change this to a pandas Data Frame using DataFrame.from_records method\n",
    "data=[s1,s2,s3,s4,s5]\n",
    "pandas.DataFrame.from_records(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Consider the following image of a data table showing the generic information of participants in a certain study.\n",
    "![image](DataTable.png)\n",
    "Image source: https://www.researchgate.net/publication/325550404_Busuu_how_do_users_rate_this_app_for_language_learning\n",
    "\n",
    "1. Use pandas data frames to recreate the table above.\n",
    "2. Use seaborn to construct a histogram of the age distribution of the participants.\n",
    "3. Contruct a histogram for the gender distribution of the participants.\n",
    "4. Construct a histogram for the nationality ditribution of the paticipants. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            number gender  age nationality      education spanish_level\n",
      "0    participant 1      F   49     British       Graduate            B2\n",
      "1    participant 2      F   20     British  Undergraduate            A2\n",
      "2    participant 3      F   54     British       Graduate            A1\n",
      "3    participant 4      F   51     British       Graduate            A2\n",
      "4    participant 5      F   23     British  Undergraduate            A2\n",
      "5    participant 6      M   24     British  Undergraduate            A1\n",
      "6    participant 7      M   47     British       Graduate            B1\n",
      "7    participant 8      M   23     British  Undergraduate            A2\n",
      "8    participant 9      M   33  Belarusian       Graduate            A1\n",
      "9   participant 10      F   18     British  Undergraduate            A2\n",
      "10  participant 11      F   23     British  Undergraduate            A2\n",
      "11  participant 12      F   33     Italian       Graduate            B2\n",
      "12  participant 13      M   44     British       Graduate            B1\n",
      "13  participant 14      F   21       Greek  Undergraduate            A2\n",
      "\n",
      " [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]\n",
      "            number gender  age nationality      education  spanish_level\n",
      "0    participant 1      F   49     British       Graduate              2\n",
      "1    participant 2      F   20     British  Undergraduate              4\n",
      "2    participant 3      F   54     British       Graduate              3\n",
      "3    participant 4      F   51     British       Graduate              4\n",
      "4    participant 5      F   23     British  Undergraduate              4\n",
      "5    participant 6      M   24     British  Undergraduate              3\n",
      "6    participant 7      M   47     British       Graduate              1\n",
      "7    participant 8      M   23     British  Undergraduate              4\n",
      "8    participant 9      M   33  Belarusian       Graduate              3\n",
      "9   participant 10      F   18     British  Undergraduate              4\n",
      "10  participant 11      F   23     British  Undergraduate              4\n",
      "11  participant 12      F   33     Italian       Graduate              2\n",
      "12  participant 13      M   44     British       Graduate              1\n",
      "13  participant 14      F   21       Greek  Undergraduate              4\n",
      "            number  gender  age nationality  education  spanish_level\n",
      "0    participant 1       1   49     British          2              2\n",
      "1    participant 2       1   20     British          1              4\n",
      "2    participant 3       1   54     British          2              3\n",
      "3    participant 4       1   51     British          2              4\n",
      "4    participant 5       1   23     British          1              4\n",
      "5    participant 6       0   24     British          1              3\n",
      "6    participant 7       0   47     British          2              1\n",
      "7    participant 8       0   23     British          1              4\n",
      "8    participant 9       0   33  Belarusian          2              3\n",
      "9   participant 10       1   18     British          1              4\n",
      "10  participant 11       1   23     British          1              4\n",
      "11  participant 12       1   33     Italian          2              2\n",
      "12  participant 13       0   44     British          2              1\n",
      "13  participant 14       1   21       Greek          1              4\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAFgCAYAAACFYaNMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAQ+ElEQVR4nO3df7DldV3H8eeLXQjlh2KtDAO7g5aR5kzgXCmhsUSz9cdYmopMmjbU0hQK2Wha/+A00ziOOTT9MFYlSVFBAVMqFAfQQRRZEJGfZYaJELtEBmQTA7z74x7qzro/7q587vuce56PmTN7z7lnz+c9n9l58uV7z/neVBWSpJW3T/cAkjSvDLAkNTHAktTEAEtSEwMsSU3Wdg+w1MaNG+uSSy7pHkOSHkvZ2Tem6gj4nnvu6R5BklbMVAVYkuaJAZakJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpiQGWpCbDApzkqCTXL7ndl+T0UetJ0qwZdjGeqroNOBogyRrgO8BFo9aTpFmzUqcgng/8c1V9a4XWk6Spt1IBfg3w0R19I8mmJFuSbNm2bdtevfjh6zeQZNXeDl+/4QfZe0lTKqN/K3KS/YA7gZ+sqrt39dyFhYXasmXL3qzBiWddtZcTTr/zTjkOf3u1NLNarwf8IuC63cVXkubNSgT4JHZy+kGS5tnQACd5PPALwIUj15GkWTT0d8JV1feAHx65hiTNKj8JJ0lNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTYYGOMkTk3wiya1JbknynJHrSdIsWTv49f8UuKSqXplkP+Dxg9eTpJkxLMBJDgaeC7wBoKoeBB4ctZ4kzZqRpyCeCmwD/jrJV5O8P8kB2z8pyaYkW5Js2bZt28BxJGm6jAzwWuBZwHur6hjgv4C3bf+kqtpcVQtVtbBu3bqB40jSdBkZ4DuAO6rq6sn9T7AYZEkSAwNcVf8GfDvJUZOHng/cPGo9SZo1o98F8Ubg3Mk7IL4J/Prg9SRpZgwNcFVdDyyMXEOSZpWfhJOkJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaGGBJamKAJamJAZakJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaGGBJamKAJamJAZakJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpydqRL57kduB+4GHgoapaGLmeJM2SoQGeeF5V3bMC60jSTPEUhCQ1GR3gAj6b5NokmwavJUkzZfQpiOOr6s4kTwYuTXJrVX1h6RMmYd4EsGHDhsHjSNL0GHoEXFV3Tv7cClwEHLuD52yuqoWqWli3bt3IcSRpqgwLcJIDkhz06NfAC4EbR60nSbNm5CmIQ4GLkjy6zkeq6pKB60nSTBkW4Kr6JvBTo15fkmadb0OTpCYGWJKaGGBJamKAJamJAZakJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaGGBJamKAJamJAZakJgZYkpoYYElqYoAlqYkBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaGGBJamKAJamJAZakJgZYkpoYYElqYoAlqYkBlqQmwwOcZE2Srya5ePRakjRLVuII+DTglhVYR5JmytAAJzkCeAnw/pHrSNIsGn0EfCbwVuCRwetI0swZFuAkLwW2VtW1u3nepiRbkmzZtm3bqHEkDXb4+g0kWbW3w9dveMz3bO1ynpTk+Kr64u4e287xwMuSvBjYHzg4yYer6rVLn1RVm4HNAAsLC7VH00uaGnfe8W1OPOuq7jGGOe+U4x7z11zuEfCfLfOx/1NVb6+qI6rqSOA1wGXbx1eS5tkuj4CTPAc4DliX5M1LvnUwsGbkYJK02u3uFMR+wIGT5x205PH7gFcud5GqugK4Yg9nk6RVbZcBrqrPA59P8sGq+tYKzSRJc2FZP4QDfijJZuDIpX+nqk4YMZQkzYPlBvjjwF+x+IGKh8eNI0nzY7kBfqiq3jt0EkmaM8t9G9qnk/x2ksOSPOnR29DJJGmVW+4R8Osnf75lyWMFPPWxHUeS5seyAlxVTxk9iCTNm+V+FPnXdvR4Vf3NYzuOJM2P5Z6CePaSr/cHng9cBxhgSdpLyz0F8cal95M8AfjQkIkkaU7s7eUovwc87bEcRJLmzXLPAX+axXc9wOJFeJ4OnD9qKEmaB8s9B/zuJV8/BHyrqu4YMI8kzY1lnYKYXJTnVhaviHYI8ODIoSRpHiwrwEleDXwFeBXwauDqJMu+HKUk6fst9xTEHwLPrqqtAEnWAZ8DPjFqMEla7Zb7Loh9Ho3vxL/vwd+VJO3Aco+AL0nyGeCjk/snAn8/ZiRJmg+7+51wPwYcWlVvSfIK4GeBAF8Czl2B+SRp1drdaYQzgfsBqurCqnpzVf0ui0e/Z44dTZJWt90F+MiqumH7B6tqC4u/nkiStJd2F+D9d/G9xz2Wg0jSvNldgK9J8pvbP5jkZODaMSNJ0nzY3bsgTgcuSvKr/H9wF4D9gJcPnEuSVr1dBriq7gaOS/I84JmTh/+uqi4bPpkkrXLLvR7w5cDlg2eRpLnip9kkqYkBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaDAtwkv2TfCXJ15LclOQdo9aSpFm03Auy743/AU6oqgeS7AtcmeQfqurLA9eUpJkxLMBVVcADk7v7Tm41aj1JmjVDzwEnWZPkemArcGlVXb2D52xKsiXJlm3bto0cR5KmytAAV9XDVXU0cARwbJJn7uA5m6tqoaoW1q1bN3IcSZoqK/IuiKr6LnAFsHEl1pOkWTDyXRDrkjxx8vXjgBcAt45aT5Jmzch3QRwGnJNkDYuhP7+qLh64niTNlJHvgrgBOGbU60vSrPOTcJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1GRYgJOsT3J5kluS3JTktFFrSdIsWjvwtR8Cfq+qrktyEHBtkkur6uaBa0rSzBh2BFxVd1XVdZOv7wduAQ4ftZ4kzZoVOQec5EjgGODqHXxvU5ItSbZs27ZtJcbRFDp8/QaSrNrb4es3dG+xptDIUxAAJDkQuAA4varu2/77VbUZ2AywsLBQo+fRdLrzjm9z4llXdY8xzHmnHNc9gqbQ0CPgJPuyGN9zq+rCkWtJ0qwZ+S6IAB8Abqmq94xaR5Jm1cgj4OOB1wEnJLl+cnvxwPUkaaYMOwdcVVcCGfX6kjTr/CScJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1GRbgJGcn2ZrkxlFrSNIsG3kE/EFg48DXl6SZNizAVfUF4N5Rry9Js25t9wBJNgGbADZs2NA8jTTIPmtJ0j2Fpkx7gKtqM7AZYGFhoZrHkcZ45CFOPOuq7imGOu+U47pHmDm+C0KSmhhgSWoy8m1oHwW+BByV5I4kJ49aS5Jm0bBzwFV10qjXlqTVwFMQktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUxABLUhMDLElNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1ITAyxJTQywJDUxwJLUZGiAk2xMcluSbyR528i1JGnWDAtwkjXAXwAvAp4BnJTkGaPWk6RZM/II+FjgG1X1zap6EPgY8EsD15OkmZKqGvPCySuBjVX1G5P7rwN+uqpO3e55m4BNk7tHAbcNGWjnfgS4Z4XX3BPTPJ+z7Z1png2me75ZnO2eqtq4o7+wduAw2cFj31f7qtoMbB44xy4l2VJVC13r7840z+dse2eaZ4Ppnm+1zTbyFMQdwPol948A7hy4niTNlJEBvgZ4WpKnJNkPeA3wqYHrSdJMGXYKoqoeSnIq8BlgDXB2Vd00ar0fQNvpj2Wa5vmcbe9M82ww3fOtqtmG/RBOkrRrfhJOkpoYYElqMlcBTrI+yeVJbklyU5LTJo8/KcmlSf5p8uchUzTbGUm+k+T6ye3FDbPtn+QrSb42me0dk8fb920387Xv3WSONUm+muTiyf2p2LddzDct+3Z7kq9PZtgyeWxq9m4n8+3R3s3VOeAkhwGHVdV1SQ4CrgV+GXgDcG9VvXNyzYpDqur3p2S2VwMPVNW7V3Ke7WYLcEBVPZBkX+BK4DTgFTTv227m20jz3k3mezOwABxcVS9N8i6mYN92Md8ZTMe+3Q4sVNU9Sx6bmr3byXxnsAd7N1dHwFV1V1VdN/n6fuAW4HAWPyJ9zuRp57AYvmmZrV0temByd9/JrZiCfYNdztcuyRHAS4D3L3l4KvYNdjrfNJuavXsszFWAl0pyJHAMcDVwaFXdBYshBJ7cONr2swGcmuSGJGc3/m/+miTXA1uBS6tqqvZtJ/NB/96dCbwVeGTJY1Ozb+x4PujfN1j8j+hnk1ybxUsWwHTt3Y7mgz3Yu7kMcJIDgQuA06vqvu55ltrBbO8FfhQ4GrgL+JOOuarq4ao6msVPNB6b5Jkdc+zMTuZr3bskLwW2VtW1K7nucu1ivqn4NwccX1XPYvGKir+T5LlNc+zMjubbo72buwBPzhFeAJxbVRdOHr57cg720XOxW6dltqq6exKXR4D3sXiVuTZV9V3gChbPr07Fvi21dL4p2LvjgZdNzhV+DDghyYeZnn3b4XxTsG8AVNWdkz+3AhdN5piWvdvhfHu6d3MV4MkPaz4A3FJV71nyrU8Br598/Xrgb6dltkf/sU28HLixYbZ1SZ44+fpxwAuAW5mCfdvVfN17V1Vvr6ojqupIFj+Kf1lVvZYp2bedzde9bwBJDpj8MJokBwAvnMwxFXu3s/n2dO9GXg1tGh0PvA74+uR8IcAfAO8Ezk9yMvCvwKumaLaTkhzN4vmm24FTGmY7DDgnixfZ3wc4v6ouTvIl+vdtV/N9aAr2bkem4d/brrxrCvbtUOCixeMS1gIfqapLklzDdOzdzubbo39zc/U2NEmaJnN1CkKSpokBlqQmBliSmhhgSWpigCWpiQGWpCYGWJKaGGCtSkk+OblIyk2PXiglyclJ/jHJFUnel+TPJ4+vS3JBkmsmt+N7p9e88IMYWpWSPKmq7p18NPka4BeBLwLPAu4HLgO+VlWnJvkI8JdVdWWSDcBnqurpbcNrbszbR5E1P96U5OWTr9ez+DHvz1fVvQBJPg78+OT7LwCeMflYKcDBSQ6aXJdZGsYAa9VJ8vMsRvU5VfW9JFcAtwE7O6rdZ/Lc/16RAaUJzwFrNXoC8B+T+P4E8DPA44GfS3JIkrXAryx5/meBUx+9M7mYijScAdZqdAmwNskNwB8BXwa+A/wxi79l5HPAzcB/Tp7/JmBh8lsMbgZ+a+VH1jzyh3CaG0kOnPzizrUsXkD77Kq6qHsuzS+PgDVPzphca/lG4F+AT7ZOo7nnEbAkNfEIWJKaGGBJamKAJamJAZakJgZYkpr8L6NxxofyAZxZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's create the blueprint for our participant's data using a class\n",
    "class participant:\n",
    "    def __init__(instance,number,gender,age,nationality,education,spanish_level):\n",
    "        instance.number=number\n",
    "        instance.gender=gender\n",
    "        instance.age=age\n",
    "        instance.nationality=nationality\n",
    "        instance.education=education\n",
    "        instance.spanish_level=spanish_level\n",
    "# let's define partcipants as instances in our new class\n",
    "p1=participant('participant 1','F', 49, 'British', 'Graduate', 'B2')\n",
    "p2=participant('participant 2','F', 20, 'British', 'Undergraduate', 'A2')\n",
    "p3=participant('participant 3','F', 54, 'British', 'Graduate', 'A1')\n",
    "p4=participant('participant 4','F', 51, 'British', 'Graduate', 'A2')\n",
    "p5=participant('participant 5','F', 23, 'British', 'Undergraduate', 'A2')\n",
    "p6=participant('participant 6','M', 24, 'British', 'Undergraduate', 'A1')\n",
    "p7=participant('participant 7','M', 47, 'British', 'Graduate', 'B1')\n",
    "p8=participant('participant 8','M', 23, 'British', 'Undergraduate', 'A2')\n",
    "p9=participant('participant 9','M', 33, 'Belarusian', 'Graduate', 'A1')\n",
    "p10=participant('participant 10','F', 18, 'British', 'Undergraduate', 'A2')\n",
    "p11=participant('participant 11','F', 23, 'British', 'Undergraduate', 'A2')\n",
    "p12=participant('participant 12','F', 33, 'Italian', 'Graduate', 'B2')\n",
    "p13=participant('participant 13','M', 44, 'British', 'Graduate', 'B1')\n",
    "p14=participant('participant 14','F', 21, 'Greek', 'Undergraduate', 'A2')\n",
    "\n",
    "# let's put all my instances in a list (so I can convert them to dictionaries all at once)\n",
    "p=[p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14]\n",
    "\n",
    "# Now let's put them in a data frame all at once\n",
    "df=pandas.DataFrame([i.__dict__ for i in p])\n",
    "print(df)\n",
    "\n",
    "# Let's visualize using seaborn\n",
    "# This allows us to explore the data\n",
    "seaborn.displot(df.iloc[:,1]) # gender histogram\n",
    "seaborn.displot(df.iloc[:,2]) # age histogram\n",
    "seaborn.displot(df.loc[:,'nationality']) # nationality histogram, using the name of the column and loc instead of iloc\n",
    "seaborn.displot(df.loc[:,'education']) # education histogram\n",
    "seaborn.displot(df.loc[:,'spanish_level']) # spanish level histogram\n",
    "\n",
    "# Let's convert the gender columns to numbers: 0: Male and 1: Female. This is not 1-hot coding\n",
    "integer_gender=[]\n",
    "for a in df.loc[:,'gender']:\n",
    "    if a=='F':\n",
    "     integer_gender.append(1)\n",
    "    else: \n",
    "     integer_gender.append(0)\n",
    "print(\"\\n\",integer_gender)        \n",
    "\n",
    "# Let's convert spanish proficiency column into ordered numbers: B1:1, B2: 2, A1: 3, A2:4\n",
    "# this is important because there is an inherent order in this categorical data, and this\n",
    "# order should be reflected in how the data gets stored.\n",
    "# using a different method than looping through the whole column\n",
    "numerical={'spanish_level':{'B1':1, 'B2': 2, 'A1': 3, 'A2':4}}\n",
    "num_df = df.replace(numerical)\n",
    "print(num_df)\n",
    "\n",
    "# we can do the same for the gender column. In fact, you can change many attributes at the same time\n",
    "numerical={'gender':{'F': 1, 'M':0} ,'spanish_level':{'B1':1, 'B2': 2, 'A1': 3, 'A2':4},'education':{'Undergraduate':1,'Graduate':2}}\n",
    "num_df = df.replace(numerical)\n",
    "print(num_df)\n",
    "\n",
    "# To change the 'nationality' attribute from categorical to numerical you need one-hot coding. \n",
    "# Create four new attributes, one for each category, then each participant will get a 1 for their nationality\n",
    "# and zeros for the other three nationalities. The downside here is that if we have many nationalities (categories)\n",
    "# then the number of attributes will increase dramatically and that becomes computationally more expensive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A final note on Python classes\n",
    "A class is used to define a collection of instances of data that have certain attributes, like age, gender, height, education level, etc. \n",
    "Inside a class, you can define methods to make these instances do stuff: like talk, sing, stop (if it is a car), move backwards, move left, *etc*. Think how this will be useful if you are designing a robot. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".py",
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