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   "source": [
    "## Homework 1"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "This is due on Thurs, 6/1"
   ]
  },
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   "metadata": {},
   "source": [
    "1. Consider the polynomial $p(x) = (x-2)^9 = x^9 - 18x^8 + 144x^7 - 672x^6 + 2016x^5 - 4032x^4 + 5376x^3 - 4608x^2 + 2304x - 512$\n",
    "\n",
    "  a. Plot $p(x)$ for $x=1.920,\\,1.921,\\,1.922,\\ldots,2.080$ evaluating $p$ via its coefficients $1,\\,,-18,\\,144,\\ldots$\n",
    "\n",
    "  b. Plot the same plot again, now evaluating $p$ via the expression $(x-2)^9$.\n",
    "\n",
    "  c. Explain the difference.\n",
    "  \n",
    "  *(The numpy method linspace will be useful for this)*"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2\\. How many different double-precision numbers are there?  Express your answer using powers of 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3\\. Using the updated [Numbers Every Programmer Should Know](https://people.eecs.berkeley.edu/~rcs/research/interactive_latency.html), how much longer does a main memory reference take than an L1 cache look-up?  How much longer does a disk seek take than a main memory reference?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4\\. From the Halide Video, what are 4 ways to traverse a 2d array?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5\\. Using the animations below ([source](https://www.youtube.com/watch?v=3uiEyEKji0M)), explain what the benefits and pitfalls of each approach. Green squares indicate that a value is being read; red indicates a value is being written. Your answers should be longer in length (give more detail) than just two words.\n",
    "\n",
    "  a. <img src=\"images/Halide1.gif\" alt=\"Halide\" style=\"width: 70%\"/>\n",
    "  \n",
    "  b. <img src=\"images/Halide2.gif\" alt=\"Halide\" style=\"width: 70%\"/>\n",
    "  \n",
    "  c. <img src=\"images/Halide3.gif\" alt=\"Halide\" style=\"width: 70%\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6\\. Prove that if $A = Q B Q^T$ for some orthnogonal matrix $Q$, the $A$ and $B$ have the same singular values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7\\. What is the *stochastic* part of *stochastic gradient descent*?"
   ]
  }
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