18.06-PS1.ipynb

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     "text": [
      "INFO: Removing Homework (unregistered)\n",
      "INFO: Cloning Homework from git://github.com/shashi/Homework.jl.git\n",
      "INFO: Computing changes...\n"
     ]
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       "<script charset=\"utf-8\">(function ($, undefined) {\n",
       "\n",
       "    function createElem(tag, attr, content) {\n",
       "\t// TODO: remove jQuery dependency\n",
       "\tvar el = $(\"<\" + tag + \"/>\").attr(attr);\n",
       "\tif (content) {\n",
       "\t    el.append(content);\n",
       "\t}\n",
       "\treturn el[0];\n",
       "    }\n",
       "\n",
       "    // A widget must expose an id field which identifies it to the backend,\n",
       "    // an elem attribute which is will be added to the DOM, and\n",
       "    // a getState() method which returns the value to be sent to the backend\n",
       "    // a sendUpdate() method which sends its current value to the backend\n",
       "    var Widget = {\n",
       "\tid: undefined,\n",
       "\telem: undefined,\n",
       "\tlabel: undefined,\n",
       "\tgetState: function () {\n",
       "\t    return this.elem.value;\n",
       "\t},\n",
       "\tsendUpdate: undefined\n",
       "    };\n",
       "\n",
       "    var Slider = function (typ, id, init) {\n",
       "\tvar attr = { type:  \"range\",\n",
       "\t\t     value: init.value,\n",
       "\t\t     min:   init.min,\n",
       "\t\t     max:   init.max,\n",
       "\t\t     step:  init.step },\n",
       "\t    elem = createElem(\"input\", attr),\n",
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       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this); // Initialize communication\n",
       "    }\n",
       "    Slider.prototype = Widget;\n",
       "\n",
       "    var Checkbox = function (typ, id, init) {\n",
       "\tvar attr = { type: \"checkbox\",\n",
       "\t\t     checked: init.value },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.checked;\n",
       "\t}\n",
       "\telem.onchange = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Checkbox.prototype = Widget;\n",
       "\n",
       "    var Button = function (typ, id, init) {\n",
       "\tvar attr = { type:    \"button\",\n",
       "\t\t     value:   init.label },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return null;\n",
       "\t}\n",
       "\telem.onclick = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Button.prototype = Widget;\n",
       "\n",
       "    var Text = function (typ, id, init) {\n",
       "\tvar attr = { type:  \"text\",\n",
       "\t\t     placeholder: init.label,\n",
       "\t\t     value: init.value },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.value;\n",
       "\t}\n",
       "\telem.onkeyup = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Text.prototype = Widget;\n",
       "\n",
       "    var Textarea = function (typ, id, init) {\n",
       "\tvar attr = { placeholder: init.label },\n",
       "\t    elem = createElem(\"textarea\", attr, init.value),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.value;\n",
       "\t}\n",
       "\telem.onchange = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Textarea.prototype = Widget;\n",
       "\n",
       "    // RadioButtons\n",
       "    // Dropdown\n",
       "    // HTML\n",
       "    // Latex\n",
       "\n",
       "    var InputWidgets = {\n",
       "\tSlider: Slider,\n",
       "\tCheckbox: Checkbox,\n",
       "\tButton: Button,\n",
       "\tText: Text,\n",
       "\tTextarea: Textarea,\n",
       "\tdebug: false,\n",
       "\tlog: function () {\n",
       "\t    if (InputWidgets.debug) {\n",
       "\t\tconsole.log.apply(console, arguments);\n",
       "\t    }\n",
       "\t},\n",
       "\t// a central way to initalize communication\n",
       "\t// for widgets.\n",
       "\tcommInitializer: function (widget) {\n",
       "\t    widget.sendUpdate = function () {};\n",
       "\t}\n",
       "    };\n",
       "\n",
       "    window.InputWidgets = InputWidgets;\n",
       "\n",
       "})(jQuery, undefined);\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: No packages to install, update or remove\n",
      "WARNING: Interact requires IJulia >= v0.1.3 to work properly.\n"
     ]
    },
    {
     "data": {
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       "<script charset=\"utf-8\">(function (IPython, $, _, MathJax, Widgets) {\n",
       "    $.event.special.destroyed = {\n",
       "\tremove: function(o) {\n",
       "\t    if (o.handler) {\n",
       "\t\to.handler.apply(this, arguments)\n",
       "\t    }\n",
       "\t}\n",
       "    }\n",
       "\n",
       "    var redrawValue = function (container, type, val) {\n",
       "\tvar selector = $(\"<div/>\");\n",
       "\tvar oa = new IPython.OutputArea(_.extend(selector, {\n",
       "\t    selector: selector,\n",
       "\t    prompt_area: true,\n",
       "\t    events: IPython.events,\n",
       "\t    keyboard_manager: IPython.keyboard_manager\n",
       "\t})); // Hack to work with IPython 2.1.0\n",
       "\n",
       "\tswitch (type) {\n",
       "\tcase \"image/png\":\n",
       "            var _src = 'data:' + type + ';base64,' + val;\n",
       "\t    $(container).find(\"img\").attr('src', _src);\n",
       "\t    break;\n",
       "\tdefault:\n",
       "\t    var toinsert = IPython.OutputArea.append_map[type].apply(\n",
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       "\t    );\n",
       "\t    $(container).empty().append(toinsert.contents());\n",
       "\t    selector.remove();\n",
       "\t}\n",
       "\tif (type === \"text/latex\" && MathJax) {\n",
       "\t    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub, toinsert.get(0)]);\n",
       "\t}\n",
       "    }\n",
       "\n",
       "\n",
       "    $(document).ready(function() {\n",
       "\tWidgets.debug = false; // log messages etc in console.\n",
       "\tfunction initComm(evt, data) {\n",
       "\t    var comm_manager = data.kernel.comm_manager;\n",
       "        //_.extend(comm_manager.targets, require(\"widgets/js/widget\"))\n",
       "\t    comm_manager.register_target(\"Signal\", function (comm) {\n",
       "            comm.on_msg(function (msg) {\n",
       "                //Widgets.log(\"message received\", msg);\n",
       "                var val = msg.content.data.value;\n",
       "                $(\".signal-\" + comm.comm_id).each(function() {\n",
       "                var type = $(this).data(\"type\");\n",
       "                if (val[type]) {\n",
       "                    redrawValue(this, type, val[type], type);\n",
       "                }\n",
       "                });\n",
       "                delete val;\n",
       "                delete msg.content.data.value;\n",
       "            });\n",
       "\t    });\n",
       "\n",
       "\t    // coordingate with Comm and redraw Signals\n",
       "\t    // XXX: Test using Reactive here to improve performance\n",
       "\t    $([IPython.events]).on(\n",
       "\t\t'output_appended.OutputArea', function (event, type, value, md, toinsert) {\n",
       "\t\t    if (md && md.reactive) {\n",
       "                // console.log(md.comm_id);\n",
       "                toinsert.addClass(\"signal-\" + md.comm_id);\n",
       "                toinsert.data(\"type\", type);\n",
       "                // Signal back indicating the mimetype required\n",
       "                var comm_manager = IPython.notebook.kernel.comm_manager;\n",
       "                var comm = comm_manager.comms[md.comm_id];\n",
       "                comm.then(function (c) {\n",
       "                    c.send({action: \"subscribe_mime\",\n",
       "                       mime: type});\n",
       "                    toinsert.bind(\"destroyed\", function() {\n",
       "                        c.send({action: \"unsubscribe_mime\",\n",
       "                               mime: type});\n",
       "                    });\n",
       "                })\n",
       "\t\t    }\n",
       "\t    });\n",
       "\t}\n",
       "\n",
       "\ttry {\n",
       "\t    // try to initialize right away. otherwise, wait on the status_started event.\n",
       "\t    initComm(undefined, IPython.notebook);\n",
       "\t} catch (e) {\n",
       "\t    $([IPython.events]).on('status_started.Kernel', initComm);\n",
       "\t}\n",
       "    });\n",
       "})(IPython, jQuery, _, MathJax, InputWidgets);\n",
       "</script>"
      ]
     },
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: This version of the GnuTLS library (3.2.11) is deprecated\n",
      "and contains known security vulnerabilities. Please upgrade to a\n",
      "more recent version.\n"
     ]
    },
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       "<script>(function ($) {\n",
       "        // hijack IPython's methods of all CodeCells with the required metadata\n",
       "    if (!window.Homework) {\n",
       "        var get_text = IPython.CodeCell.prototype.get_text\n",
       "        IPython.CodeCell.prototype.get_text = function () {\n",
       "            if (this.metadata && typeof(this.metadata.question) !== \"undefined\") {\n",
       "                var fn = (Homework.mode() == \"create\") ? \"new_question\" : \"attempt_prompt\";\n",
       "                return 'Homework.' + fn + '(' + [\n",
       "                                         JSON.stringify(JSON.stringify(this.metadata)),\n",
       "                                         \"begin \\n\" + get_text.call(this) +\"\\n end\"\n",
       "                                       ].join(\", \") + \")\"\n",
       "            } else {\n",
       "                console.log(\"vs\", get_text.call(this))\n",
       "                return get_text.call(this)\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var cell_to_json = IPython.CodeCell.prototype.toJSON\n",
       "        IPython.CodeCell.prototype.toJSON = function () {\n",
       "            if (this.metadata && typeof(this.metadata.question) !== \"undefined\") {\n",
       "                data = cell_to_json.call(this)\n",
       "                data.source = get_text.call(this)\n",
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       "                return cell_to_json.call(this)\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var rename_keys = IPython.OutputArea.prototype.rename_keys;\n",
       "        IPython.OutputArea.prototype.rename_keys = function (data, key_map) {\n",
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       "\n",
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       "            }\n",
       "            return data\n",
       "        }\n",
       "\n",
       "        var delete_cell = IPython.Notebook.prototype.delete_cell\n",
       "        IPython.Notebook.prototype.delete_cell = function (index) {\n",
       "            var i = this.index_or_selected(index);\n",
       "            var cell = this.get_selected_cell();\n",
       "            if (cell.metadata && typeof(cell.metadata.question) !== \"undefined\") {\n",
       "                alert(\"Cannot delete this cell. You need to code the answer to Question \" + \n",
       "                        cell.metadata.question + \" here.\")\n",
       "            } else {\n",
       "                // go on and delete\n",
       "                delete_cell.call(this, i)\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "\n",
       "\n",
       "    function get_question(q) {\n",
       "        var i = 0\n",
       "        var cell = IPython.notebook.get_cell(i)\n",
       "        while(cell !== null) {\n",
       "            if (cell.metadata && cell.metadata.question === q) {\n",
       "                return cell\n",
       "            }\n",
       "            cell = IPython.notebook.get_cell(i)\n",
       "            i+=1\n",
       "        }\n",
       "        return null\n",
       "    }\n",
       "\n",
       "    function mount_message(cell) {\n",
       "        if (!cell) { return }\n",
       "        var meta = cell.metadata,\n",
       "            msg = meta.msg || \"<span class='icon-terminal'></span> &nbsp; Code your answer above, hit &lt;Shift+Enter&gt;, then Submit. <span style='float: right'>\",\n",
       "            score = meta.score || 0,\n",
       "            max_score = meta.max_score || 0,\n",
       "            attempts = meta.attempts || 0,\n",
       "            max_attempts = meta.max_attempts || 0\n",
       "\n",
       "        msg += \"<span style='position:absolute; top: 0.5em; right:0.5em' class='label label-info'> Score: \"\n",
       "        if (Homework.mode() === \"answering\") {\n",
       "            msg += \"<b>\" + score + \"</b> / <b>\" + max_score + \"</b>\"\n",
       "        } else if (Homework.mode() === \"create\") {\n",
       "            msg += \"<b>\" + max_score + \"</b>\"\n",
       "        }\n",
       "\n",
       "        msg += \" &middot; Attempts: \"\n",
       "        if (Homework.mode() === \"answering\") {\n",
       "            msg += \"<b>\" + attempts + \"</b>\"\n",
       "            if (max_attempts != 0) {\n",
       "                msg += \" / <b>\" + max_attempts + \"</b>\"\n",
       "            }\n",
       "        } else if (Homework.mode() === \"create\") {\n",
       "            msg += \"<b>\" + max_attempts + \"</b>\"\n",
       "        }\n",
       "        msg += \"</span>\"\n",
       "\n",
       "        var level = meta.alert || \"info\"\n",
       "\n",
       "        msg = \"<div class='hw-msg alert alert-\" + level + \"' id='hw-msg-\" + meta.question +\n",
       "               \"' style='padding: 0.5em; margin: 0; position:relative; border-radius: 0'>\" +\n",
       "               msg + \"</div>\"\n",
       "\n",
       "        $(cell.element).find(\".hw-msg\").remove()\n",
       "        $(cell.element).find(\".input_area\").eq(0).append(msg)\n",
       "        if (cell.metadata.finished) { $(cell.element).find(\".widget-area\").hide() }\n",
       "    }\n",
       "\n",
       "    function set_meta(question, extension) {\n",
       "        console.log(\"set meta\", question, extension)\n",
       "        var cell = get_question(question)\n",
       "        for (var key in extension) {\n",
       "            if (extension.hasOwnProperty(key)) {\n",
       "                cell.metadata[key] = extension[key]\n",
       "            }\n",
       "        }\n",
       "        mount_message(cell)\n",
       "    }\n",
       "\n",
       "    function get_question_cells() {\n",
       "        var cell = IPython.notebook.get_cell(0),\n",
       "            i = 0,\n",
       "            cells = []\n",
       "        while(cell !== null) {\n",
       "            if (cell.metadata && typeof(cell.metadata.question) !== \"undefined\") {\n",
       "                var q = cell.metadata.question\n",
       "                cells.push(cell)\n",
       "            }\n",
       "            i+=1\n",
       "            cell = IPython.notebook.get_cell(i)\n",
       "        }\n",
       "        return cells\n",
       "    }\n",
       "\n",
       "    function hw_create(host, course, s, f) {\n",
       "        if(!s) {\n",
       "            s = function(result){\n",
       "                if(result.code == 0) {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Problemset created',\n",
       "                        body: \"The problem set was created. Now run <code>Homework.clear_answers()</code> to get the notebook ready for distribution.\"\n",
       "                    })\n",
       "                }\n",
       "                else {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Problemset NOT created',\n",
       "                        body: \"Non-zero result code. There was a problem saving the problem set!\"\n",
       "                    })\n",
       "                }\n",
       "            };\n",
       "        };\n",
       "        if(!f) {\n",
       "            f = function() {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Failure',\n",
       "                        body: \"Failed to create problem set. Are you sure you have permission to edit the course? Unexpected server error.\"\n",
       "                    })\n",
       "            };\n",
       "        };\n",
       "        console.log({\n",
       "            'mode': 'create',\n",
       "            'params': JSON.stringify(course)\n",
       "        })\n",
       "        $.ajax({\n",
       "            url: host + '/jboxplugin/hw/',\n",
       "            method: 'POST',\n",
       "            data: {\n",
       "                'mode': 'create',\n",
       "                'params': JSON.stringify(course)\n",
       "            },\n",
       "            success: s,\n",
       "            failure: f\n",
       "        })\n",
       "    }\n",
       "\n",
       "    function create_problemset(config) {\n",
       "        config = config || IPython.notebook.metadata.homework\n",
       "\n",
       "        var cells = get_question_cells()\n",
       "\n",
       "        if (!config.host) { config.host == \"\" }\n",
       "        var questions = []\n",
       "        for (var i=0, l=cells.length; i < l; i++) {\n",
       "            questions.push({\n",
       "                id:    String(cells[i].metadata.question),\n",
       "                score: cells[i].metadata.max_score,\n",
       "                attempts: cells[i].metadata.max_attempts,\n",
       "                ans:   cells[i].metadata.answer,\n",
       "                explanation: cells[i].metadata.explanation || \"\"\n",
       "            })\n",
       "        }\n",
       "\n",
       "        var course = {\n",
       "             admins: config.admins || [],\n",
       "             id: config.course,\n",
       "             problemsets: [{\n",
       "                 id: config.problemset,\n",
       "                 questions: questions\n",
       "             }]\n",
       "        }\n",
       "\n",
       "        console.log(course)\n",
       "\n",
       "        try {\n",
       "            hw_create(config.host || \"\", course)\n",
       "        } catch (e) {\n",
       "            alert(\"An error occured. Problem set not saved!\")\n",
       "        }\n",
       "   }\n",
       "\n",
       "   function clear_admin_metadata() {\n",
       "       var cells = get_question_cells()\n",
       "       for (var i=0, l=cells.length; i < l; i++) {\n",
       "           var cell = cells[i]\n",
       "           delete cell.metadata.answer\n",
       "           delete cell.metadata.msg\n",
       "           cell.metadata.finished && delete cell.metadata.finished\n",
       "           delete cell.metadata.alert\n",
       "       }\n",
       "       IPython.notebook.metadata.homework.mode = \"answering\"\n",
       "       Homework.refresh_messages()\n",
       "   }\n",
       "\n",
       "   function clear_answers() {\n",
       "       var cells = get_question_cells()\n",
       "       for (var i=0, l=cells.length; i < l; i++) {\n",
       "           var cell = cells[i]\n",
       "           cell.clear_input()\n",
       "           cell.clear_output()\n",
       "       }\n",
       "       IPython.notebook.metadata.homework.mode = \"answering\"\n",
       "       Homework.refresh_messages()\n",
       "   }\n",
       "\n",
       "    function refresh_messages(q) {\n",
       "        _.map(q ? [get_question(q)] : get_question_cells(), mount_message)\n",
       "    }\n",
       "\n",
       "    $([IPython.events]).on('notebook_loaded.Notebook', refresh_messages)\n",
       "    $([IPython.events]).on('select.Cell', refresh_messages)\n",
       "\n",
       "    setTimeout(refresh_messages, 100)\n",
       "    setTimeout(refresh_messages, 200)\n",
       "    setTimeout(refresh_messages, 400)\n",
       "    setTimeout(refresh_messages, 500)\n",
       "    setTimeout(refresh_messages, 1000)\n",
       "    setTimeout(refresh_messages, 2000)\n",
       "    setTimeout(refresh_messages, 4000)\n",
       "\n",
       "    $([IPython.events]).on('status_started.Kernel', function (data) {\n",
       "        var k = data.kernel || IPython.notebook.kernel\n",
       "        k.comm_manager.register_target(\"HomeworkData\", function (comm) {})\n",
       "    })\n",
       "    IPython.notebook && IPython.notebook.kernel &&\n",
       "        IPython.notebook.kernel.comm_manager.register_target(\"HomeworkData\", function (comm) {})\n",
       "\n",
       "    window.Homework = {\n",
       "        config: {},\n",
       "        metadata: function (field) {\n",
       "            return IPython.notebook.metadata.homework[field]\n",
       "        },\n",
       "        mode: function () {\n",
       "            return Homework.metadata(\"mode\") || \"answering\"\n",
       "        },\n",
       "        set_meta: set_meta,\n",
       "        mount_message: mount_message,\n",
       "        clear_answers: clear_answers,\n",
       "        clear_admin_metadata: clear_admin_metadata,\n",
       "        get_question: get_question,\n",
       "        get_question_cells: get_question_cells,\n",
       "        refresh_messages: refresh_messages,\n",
       "        create_problemset: create_problemset\n",
       "    }\n",
       "\n",
       "})(jQuery)\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<script>IPython.notebook.kernel.comm_manager.comms[\"b5f82849-8130-4c4e-865b-53040dcdc1e1\"].then(\n",
       "    function (comm) {\n",
       "        comm.send({\n",
       "            cookie: document.cookie,\n",
       "            host: IPython.notebook.metadata.homework.host,\n",
       "            course: IPython.notebook.metadata.homework.course,\n",
       "            mode: IPython.notebook.metadata.homework.mode,\n",
       "            problemset: IPython.notebook.metadata.homework.problemset\n",
       "        })\n",
       "    }\n",
       ")</script>"
      ],
      "text/plain": [
       "Html(\"<script>IPython.notebook.kernel.comm_manager.comms[\\\"b5f82849-8130-4c4e-865b-53040dcdc1e1\\\"].then(\\n    function (comm) {\\n        comm.send({\\n            cookie: document.cookie,\\n            host: IPython.notebook.metadata.homework.host,\\n            course: IPython.notebook.metadata.homework.course,\\n            mode: IPython.notebook.metadata.homework.mode,\\n            problemset: IPython.notebook.metadata.homework.problemset\\n        })\\n    }\\n)</script>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning: Method definition writemime(IO,MIME{symbol(\"text/html\")},AbstractDataFrame) in module DataFrames at /opt/julia_packages/.julia/v0.3/DataFrames/src/abstractdataframe/io.jl:135 overwritten in module Homework at /home/juser/.julia/v0.3/Homework/src/coloredtable.jl:10.\n"
     ]
    }
   ],
   "source": [
    "# Run this (ugly, sorry) cell by hitting <Shift+Enter>. Ignore the warnings, they are harmless.\n",
    "\n",
    "display(MIME(\"text/html\"), \"\"\"<script> var cell = \\$(\".container .cell\").eq(0), ia = cell.find(\".input_area\"); if (cell.find(\".toggle-cell\").length == 0) { ia.after(\\$('<div class=\"toggle-cell\">Run this cell to set up the Homework. Please fill in the form below. You only need to fill it once. <strong>Ignore any INFO or WARNING messages. They are harmless</strong> </div>').dblclick(function (){ ia.toggle(); }));};ia.hide();</script>\n",
    "<iframe src=\"https://docs.google.com/forms/d/1uPqGeJChe0FFOsuUkdeLVbgPo9LzQEbRnS0xIzE-VGo/viewform?embedded=true\" width=\"720\" height=\"570\" frameborder=\"0\" marginheight=\"0\" marginwidth=\"0\">Loading...</iframe>\"\"\")\n",
    "\n",
    "# Run this cell. Ignore the warning messages, they are harmless\n",
    "\n",
    "Pkg.rm(\"Homework\")\n",
    "Pkg.clone(\"git://github.com/shashi/Homework.jl.git\")\n",
    "\n",
    "using Homework\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Run this cell to see your scores, your score will appear once you have answered at least one of the problems\n",
    "# Please try again if it does not work the first time\n",
    "Homework.progress(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 1. Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(a) (1 pt) SUM OF VECTORS:** What is the sum V of the twelve unit vectors that go from the center of a clock to the hours 1:00, 2:00, ..., 12:00? Write down your answer as a pair of coordinates, correct up to .01."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 2,
    "max_score": 1,
    "precision": 2,
    "question": "1a"
   },
   "outputs": [],
   "source": [
    "V=[ ? ,  ? ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://2.bp.blogspot.com/-Y5mnXTd33z0/VDGXB-3qE3I/AAAAAAAASl0/mD1sb0gaLtU/s1600/clock-face-time4.jpg\" height=100>\n",
    "**(b) (1 pt) (SUBTRACTING VECTORS)** In the sum of vectors above, if the 2:00 vector is removed, you can show that the remaining vectors add to 8:00. This is because subtracting a vector is the same as adding \n",
    "<span style=\"border-bottom: 1px solid black; padding-left: 200px\">&nbsp;</span> ? <br>\n",
    "Write your answer as a number from 1 through 4 below:<br>\n",
    "1. An Opposite Vector\n",
    "2. An Orthogonal Vector\n",
    "3. A Parallel Vector\n",
    "4. Zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 2,
    "max_score": 1,
    "question": "1b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c) (2 pts) (COMPONENTS)** What are the components of the 2:00 vector, v=cos θ,sin θ? (write the answer correct to 2 decimal places)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "1c"
   },
   "outputs": [],
   "source": [
    "v=[  ? , ?  ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2.  Elimination sometimes breaks down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts)** We would like you to use elimination to solve the following linear system of two equations:\n",
    "\n",
    "$ax + 3y = −3$\n",
    "\n",
    "$4x + 6y = 6$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For which number $a$ does elimination break down permanently?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "2a"
   },
   "outputs": [],
   "source": [
    "a = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For which number $a$ does elimination break down temporarily?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "2b"
   },
   "outputs": [],
   "source": [
    "a = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts) SOLVING THE NON-SINGULAR SYSTEM**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fix the temporary breakdown above by a row exchange and then solve.\n",
    "\n",
    "Enter the value of $x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "2c"
   },
   "outputs": [],
   "source": [
    "x = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the value of $y$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "2d"
   },
   "outputs": [],
   "source": [
    "y = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 3.  Linear Combinations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts)** The column vectors\n",
    "$u=(1,1,2)^T,v=(1,2,3)^T,w=(3,5,8)^T$\n",
    "are in a plane because w is a linear combination of u and v. <br> If w=au+bv:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $a$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 3,
    "max_score": 1,
    "question": "3a"
   },
   "outputs": [],
   "source": [
    "a = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 2,
    "max_score": 1,
    "question": "3b"
   },
   "outputs": [],
   "source": [
    "b = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts) LINEAR COMBINATIONS 2**\n",
    "\n",
    "The combination above is unique. However, there is more than one combination of u,v,w that produces z=(0,0,0)<sup>T</sup>. <br> Let us find two of them. First, if $2u+cv+dw=(0,0,0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 2,
    "max_score": 1,
    "question": "3c"
   },
   "outputs": [],
   "source": [
    "c = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $d$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 2,
    "max_score": 1,
    "question": "3d"
   },
   "outputs": [],
   "source": [
    "d = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt) LINEAR COMBINATIONS 3**\n",
    "Second, $u+cv+dw=(0,0,0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 0.5,
    "question": "3e"
   },
   "outputs": [],
   "source": [
    "c = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enter the numerical value of $d$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 0.5,
    "question": "3f"
   },
   "outputs": [],
   "source": [
    "d = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point you should note that there are infinite ways to write any vector on that plane as a linear combination of $u,v,w$.<br>\n",
    "However, there is no way to do that for any vector outside the plane."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts) LINEAR COMBINATIONS 4**\n",
    "\n",
    "Think about the vector $b=(1,−1,e)^T$. What is the only possible number e that gives a vector on the plane? <br>\n",
    "Enter the numercal value of $e$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "3g"
   },
   "outputs": [],
   "source": [
    "e = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 4. ORTHOGONAL VECTORS "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts)** Find two vectors $v$ and $w$ that are perpendicular to $(1,0,1)$ and to each other. <br> Enter your answer in the form $[a,b,c]$ (note the square brackets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "4a"
   },
   "outputs": [],
   "source": [
    "v=[?, ? , ?]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "4b"
   },
   "outputs": [],
   "source": [
    "w=[?, ?, ?]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)A TASTE OF PROJECTION **\n",
    "With $v=\\begin{pmatrix} 1, 1\\end{pmatrix}$ and $w=(1,5)$, choose a number $c$ so that $w−cv$ is perpendicular to $v$.\n",
    "\n",
    "Enter the numerical value of $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 1,
    "question": "4c"
   },
   "outputs": [],
   "source": [
    "c = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 5: (Julia) Defining a Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)** In Julia you simply assign a variable to x by simply typing the letter x and specifying what it is equal to.  Ending the assignment with a semicolon suppresses printing.  In the IJulia notebook, you execute a Julia command by typing shift + enter.<br>\n",
    "\n",
    "Write Julia code that assigns 1234 to the variable x. See what happens if you follow with and without a semicolon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "5"
   },
   "outputs": [],
   "source": [
    "x = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 6: (Julia) Define a Row Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)** Julia, somewhat like python, and unlike MATLAB has \n",
    "one dimensional vectors, 1xn matrices, and nx1 matrices\n",
    "which are three different things.  If one needs a row vector\n",
    "in Julia, create a 1xn matrix. \n",
    "\n",
    "Why do Python and  Julia do it this way? Answer: There are many data science applications where one dimensional structures are extremely important. (see next problem to create a one dimensional structure)\n",
    "\n",
    "A 1xn matrix  is created by placing elements between square brackets, e.g. [1 1 2 4 6 3]\n",
    "\n",
    "Write Julia code that creates the vector y with values 3, 5, 2 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "6"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 7: (Julia) Define a One Column Matrix (there are no column vectors!) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)** To create a one dimensional vector in Julia\n",
    "one uses commas as in\n",
    " [1, 1, 2].\n",
    "The result is one dimensional and often prints in column format.\n",
    "Write Julia code that creates the 5 vector\n",
    "\n",
    "<table>\n",
    "<tr> <th> 1 </th>  </tr>\n",
    "<tr> <th> 2 </th> </tr>\n",
    "<tr> <th> -1  </th> </tr>\n",
    "<tr> <th> 0 </th> </tr>\n",
    "<tr> <th> 0 </th></tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "7"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 8: (Julia) Define a Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(1 pt) In Julia a matrix can be written <br>\n",
    "```\n",
    "    [1 2 3\n",
    "     4 5 6\n",
    "     7 8 9] \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write Julia code that creates the 2x2 matrix A= \n",
    "     <table>\n",
    "     <tr> <th> 8 </th> <th> 4 </th> </tr>\n",
    "     <tr> <th> 2 </th> <th> 3 </th> </tr>\n",
    "     </table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 5,
    "question": "8"
   },
   "outputs": [],
   "source": [
    "A = ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 9: (Julia) Solve a Linear System"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)** Solve  Ax=b, where\n",
    "\n",
    "```\n",
    "A=\n",
    " [ 2  1 -1\n",
    "  -1  2 -1\n",
    "   0 -1  1]\n",
    "``` \n",
    "  and\n",
    "```\n",
    "  b=[1,2,1]\n",
    "```\n",
    "  To solve for x, use the backlash command `x=A\\b`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# You need to run this cell to create variables A and b before answering\n",
    "A=\n",
    " [ 2  1 -1\n",
    "  -1  2 -1\n",
    "   0 -1  1]\n",
    "\n",
    "b=[1,2,1];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 5,
    "question": "9"
   },
   "outputs": [],
   "source": [
    "# Write the solution here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 10: (Julia) Plot a Line and Interact with it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(1 pt)** Plot the linear function $u(x) = 5 + 3x on 0 ≤ x ≤ 8$\n",
    "\n",
    "Julia has a number of packages for plotting because different people enjoy plotting in different ways.  We will use the *PyPlot* package from python for plotting, and the julia *Interact* package for interacting.  Some of these commands may not make complete sense yet, but you\n",
    "can use these \"magic incantations\" for many purposes without needing to understand how they work.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Loading help data...\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell\n",
    "using PyPlot    # takes a little time but only needs to be executed once\n",
    "using Interact  # adds the fun interactive feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 4.0,\"x\",4.0,0.0:0.5:8.0)"
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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7fe0c248cd10>)"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "comm_id": "ff21fc96-7c08-4cd8-ae1b-cab5f1c6a9e3",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Execute this cell as well\n",
    "u(x) = 5 + 3x\n",
    "range=0:.01:8\n",
    "f=figure()\n",
    "\n",
    "@manipulate for x=0:.5:8; withfig(f) do\n",
    "        plot(range,u(range))\n",
    "        plot(x,u(x),\"o\")\n",
    "        title(\"x=$x u(x)=$(round(u(x),2))\")\n",
    "   end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slide $x$ to $6.5$ and observe u(6.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There should be a plot that highlights $x=6.5$.  What is $u(6.5)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 5,
    "question": "10"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 11: (Julia) Plot Solutions of Linear Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(1 pt) Consider the linear system for various values of p and q that you can manipulate\n",
    "\n",
    "\n",
    "$x + y = p$\n",
    "\n",
    "$-x + 3y = q$\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where is the solution when $p=7$ and $q=1$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 7.0,\"p\",7.0,0.0:0.5:14.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 7.0,\"q\",7.0,0.0:0.5:14.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7fe0ff312bd0>)"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "comm_id": "0cd19799-d950-432f-963b-9f23f1f53383",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Execute the code below\n",
    "f=figure()\n",
    "x=-3:7:20\n",
    "@manipulate for p=0:.5:14,q=0:.5:14; withfig(f) do\n",
    "        plot(x,p-x)\n",
    "        plot(x,(q+x)/3)\n",
    "        plot((3*p-q)/4,  (p+q)/4, \"o\")\n",
    "        title(\"p=$p q=$q\")\n",
    "   end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 5,
    "question": "11"
   },
   "outputs": [],
   "source": [
    "# Obtain the solution when p=7 and q=1 and show the plot\n",
    "(  ?, ?  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 12: (Julia) Singular Matrices with no zeros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(2 pts)**\n",
    "Use the Julia [ones](http://julia.readthedocs.org/en/latest/stdlib/arrays/?highlight=ones#Base.ones) command to create a 10x10 matrix A all of whose entries are the number 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "12a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this matrix 1. singular or 2. nonsingular.  (Type 1 or 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "max_attempts": 5,
    "max_score": 2,
    "question": "12b"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script></script>"
      ],
      "text/plain": [
       "Html(\"<script></script>\")"
      ]
     },
     "metadata": {
      "comm_id": "480e4516-c862-4090-8ba7-c733640e42db",
      "reactive": true
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Button{Nothing}([Input{Nothing}] nothing,\"Submit \\ubb\",nothing)"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Run this cell to see your scores.\n",
    "Homework.progress()"
   ]
  }
 ],
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  "homework": {
   "course": "MIT-1806-Spring2015",
   "mode": "answering",
   "problemset": "set1"
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