{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# CS 237 Spring 2021, HW 03 \n",
"\n",
"#### Due date: Friday February 19th at Midnight (1 minute after 11:59pm on 2/11) via Gradescope (6 hour grace period)\n",
"\n",
" Late policy: You may submit the homework up to 24 hours late for a 10% penalty. Hence, the late deadline is Saturday 2/20 at Midnight (with the same 6 hour grace period). \n",
"\n",
"#### General Instructions\n",
"\n",
"Please complete this notebook by filling in solutions where indicated. Be sure to \"Restart and Run All\" from the Kernel menu before submitting to Gradescope. \n",
"\n",
"There are 10 analytical problems and one extended programming problem (worth as much as two problems). An introductory video will be posted on YT for\n",
"the analytical problems, and the programming problem will be covered Friday in lab. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"