{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "45469f87",
   "metadata": {},
   "source": [
    "# Welcome to Math 124!\n",
    "\n",
    "## Lewis Pan - math.berkeley.edu/~yllpan\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fef93b86",
   "metadata": {},
   "source": [
    "### Office hour poll\n",
    "\n",
    "Plan: Your homework is due on Wednesdays 8am, projects due on Friday midnight so\n",
    "1. One OH on Monday/Tuesday, before hw due\n",
    "2. One OH on Thursday/Friday before project is due\n",
    "\n",
    "My time constraints:\n",
    "* Cannot do 12-1 any day\n",
    "* Cannot do Tuesday/Thursday 8-9:30, 2-3:30\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e39811cc",
   "metadata": {},
   "source": [
    "Office hours will be:\n",
    "\n",
    "* 9-10:30 Monday\n",
    "* 2-3 Friday\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d0d0833",
   "metadata": {},
   "source": [
    "### Logistics for Section"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a5f47e",
   "metadata": {},
   "source": [
    "I am flexible on this - I am happy to go over any material people are confused by, give summaries of material, or even give you a headstart on material to come if you feel comfortable with the stuff already covered.\n",
    "\n",
    "On quizzes, I plan to do this at the end of each section. There will be 6 quizzes, each 15 minutes. Your lowest score will be dropped. If you have DSP arrangements please come and talk to me. The quizzes will be in person but I will upload them after on gradescope.\n",
    "\n",
    "Unfortunately section is on Wednesday **AFTER** your homework is due. If you have hw questions office hours is probably a better idea, although I would be happy to go over homework solutions in section also. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "069f1722",
   "metadata": {},
   "source": [
    "### Julia installation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7297511b",
   "metadata": {},
   "source": [
    "Julia website: https://julialang.org/downloads/\n",
    "\n",
    "IJulia: https://julialang.github.io/IJulia.jl/stable/manual/installation/\n",
    "\n",
    "0. Download julia\n",
    "1. Open julia in terminal, or whatever environment is native to your OS\n",
    "2. type in `using Pkg`\n",
    "3. type in `Pkg.add(\"IJulia\")`\n",
    "\n",
    "This should install IJulia (only needs to be done once). To open a notebook:\n",
    "\n",
    "1. `using IJulia`\n",
    "2. `notebook()`\n",
    "\n",
    "Alternatively you can just stick to using datahub. The official version the class is using is 1.6.3 - although if you use an older version try to stick to one after 1.2 as the functionality before that is slightly different. I'm on 1.6.2 and everything works fine."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6064daac",
   "metadata": {},
   "source": [
    "### Demo time - LaTeX (pronounced latech)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e837ac7",
   "metadata": {},
   "source": [
    "There are two ways to write an equation,\n",
    "\n",
    "``\n",
    "\\begin{equation}\n",
    "    ...\n",
    "\\end{equation}\n",
    "``\n",
    "\n",
    "``\n",
    "$$\n",
    "    ...\n",
    "$$\n",
    "``"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93814d4e",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "    1+1 = 2\n",
    "\\end{equation}\n",
    "\n",
    "$$\n",
    "    1+1 = 2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24f21650",
   "metadata": {},
   "source": [
    "Here is a list of common things:\n",
    "\n",
    "1. Commands predicated w/ backslash \\\n",
    "2. Subscript, superscript is done with _ ^\n",
    "3. For example integral sign is \\int\n",
    "4. Summation sign is given by \\sum\n",
    "5. Infinity is \\infty\n",
    "6. Fraction \\frac{}{}\n",
    "7. Power is also ^\n",
    "8. Greek letters, backslash + spell it out e.g. \\pi\n",
    "9. https://www.overleaf.com/learn/latex/Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea7bfbf",
   "metadata": {},
   "source": [
    "For example:\n",
    "$$ \n",
    "    \\int_0^1 x dx = \\frac{1}{2} \\\\\n",
    "    \\sum_{n=1}^\\infty \\frac{1}{n^2} = \\frac{\\pi^2}{6} \\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bab6115c",
   "metadata": {},
   "source": [
    "For more latex things, google is your best friend - I forget what the commands are all the time. Any questions?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1174048",
   "metadata": {},
   "source": [
    "### Markdown things:\n",
    "\n",
    "1. Headers is #\n",
    "2. Bolding stuff **bold stuff**\n",
    "3. Italics is *italic stuff*\n",
    "4. Both **_both_**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea150e9",
   "metadata": {},
   "source": [
    "### More demo - Coding!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55856a69",
   "metadata": {},
   "source": [
    "Basic Types:\n",
    "1. Integers\n",
    "2. Float64/Double - Floating point numbers, i.e. decimals (3.14159)\n",
    "3. Strings - This is basically text (\"This is a string.\")\n",
    "4. Arrays - Lists of things"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48186a31",
   "metadata": {},
   "source": [
    "Printing is one of the most important tools - it is extremely helpful for debugging. \n",
    "\n",
    "``\n",
    "println(\"This stuff here will be printed.\")\n",
    "println(480)\n",
    "``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5f3ec580",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This stuff here will be printed.\n",
      "480\n"
     ]
    }
   ],
   "source": [
    "### Printing a string, if you are inputting the string it needs to be surrounded by \"\"\n",
    "println(\"This stuff here will be printed.\")\n",
    "\n",
    "### Printing an integer\n",
    "println(480)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "534eb6bd",
   "metadata": {},
   "source": [
    "The basic arithmetic operations are given by +,-,*,/ \n",
    "\n",
    "```\n",
    "1+1\n",
    "2-1\n",
    "8/3\n",
    "1.23*3\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "86e4454b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.69"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1+1\n",
    "2-1\n",
    "8/3\n",
    "1.23*3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55d3473b",
   "metadata": {},
   "source": [
    "Why did they not all show up? In jupyter only the last thing evaluated will show up unless you print it explicitly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7b65c84",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "1\n",
      "2.6666666666666665\n",
      "3.69\n"
     ]
    }
   ],
   "source": [
    "println(1+1)\n",
    "println(2-1)\n",
    "println(8/3)\n",
    "println(1.23*3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feca7611",
   "metadata": {},
   "source": [
    "Even though you supply integers, the result will not necessarily stay the same type unlike in some other languages. In this case 8/3 automatically is cast into a float in Julia."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc5f704",
   "metadata": {},
   "source": [
    "Setting variables is done with `=`:\n",
    "\n",
    "``\n",
    "var1 = 1;\n",
    "var2 = 100;\n",
    "var3 = 1000;\n",
    "var1 + var2\n",
    "``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5a4c47d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var1 = 1;\n",
    "var2 = 100;\n",
    "var3 = 1000;\n",
    "var1 + var2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e558e2",
   "metadata": {},
   "source": [
    "It is **VERY** good practice to name your variables something descriptive. What I just did is actually terrible practice. If you are working on a long project keeping track of what var1... means is not only tedious, but say you leave it for a while and then pick it up again later, you will forget what it means. I have done this before and have had to deal with a very upset supervisor as a result."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aca0657",
   "metadata": {},
   "source": [
    "Let's try and define a function now for this mathematical expressions:\n",
    "\n",
    "$$ \n",
    "    f(x) = 1 - \\frac{x^2}{2!} + \\frac{x^4}{4!}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca64e22",
   "metadata": {},
   "source": [
    "Function definition is done like so:\n",
    "\n",
    "``\n",
    "function cosApprox( x )\n",
    "    ...\n",
    "    return ...\n",
    "end\n",
    "``\n",
    "\n",
    "A function will take in an argument and return another value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6bb0915f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cosApprox (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function cosApprox( x )\n",
    "    sum = 1;\n",
    "    sum -= x^2 / 2;\n",
    "    sum += x^4 / ( 1*2*3*4 );\n",
    "    return sum\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "289265fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9950041666666667"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosApprox(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0060756d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9800666666666666"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosApprox(0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c769f3c0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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