tag:blogger.com,1999:blog-8551680375687404762021-02-10T11:25:25.641-05:00Elbow GreaseThoughts, confessions, ideas, and advice from a working mathematician.Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-855168037568740476.post-53895741369376391322021-01-19T22:17:00.003-05:002021-01-19T22:18:00.613-05:00A day of work in honor of MLKjr's legacy<p>You know I’m an academic because my first instinct was block out space for an abstract for this blog post.</p><p><strong>Abstract:</strong> On MLK day, I, a white mathematics professor, consciously and intentionally dedicated myself to working <em>only</em> in honor of Martin Luther King Jr.'s legacy. That is, all of my professional activities were focused on social equity, especially along the axes of race, ethnicity, and socioeconomic status. I’m writing this post for accountability, transparency, invitations for collaboration on any of these ideas, and for constructive feedback for those feeling generous. The content? A break down of my day, starting at 9am.</p><span></span><span><a name='more'></a></span><h3 id="active-bystander-workshop-9am">Active Bystander Workshop (9am)</h3><p>Here are some highlights from this workshop (run by <a href="https://twitter.com/Rhodes_Perry">Rhodes Perry</a> and focused on interventions on a college campus).</p><ul><li><p>What an active bystander is.</p></li><li><p>Why we don’t intervene even when we know we should: we don’t know how (so we have to practice!), we’re afraid of repurcussions (so we have to understand the difference between being uncomfortable and being unsafe), we’re afraid of escalating the situation (so we have to learn to embrace mistakes, because we’re definitely going to make some mistakes).</p></li><li><p>A 4 Step Approach to being an Active Bystander (“microinterventions”)</p><ol><li>Assess your safety (<strong>comfort is not safety</strong>)</li><li>Make the invisible visible (raise consciousness of the commenter)</li><li>Educate the person commenting (what matters is the impact of their comment, not their intention – decenter their point of view)</li><li>Have patience and expect progress (redirect and educate about harm)</li></ol></li><li><p>What if I mess up?</p><ul><li>Embrace mistakes and don’t quit</li><li>Keep trying to build stamina and moral courage</li><li>If you’re exhausted, you’re probably on the right track</li><li>Super important to model this on campus where students are watching!</li><li>Lean into the “active” part of being an active bystander</li></ul></li></ul><p>Further actions for me following this workshop:</p><ul><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Fill out personal reflection worksheet</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Set up a place/time for colleagues to practice bystander intervention together. <ul><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Send some emails to follow up with interested parties</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Zoom with colleague who is interested in coordinating this effort to fill in the details <ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Determine a platform</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop some starter scenarios (“Your professional society just announced they will award a [sic] <em>Fellowship for a Black Mathematician</em> to the dismay of potential recipients imagining putting that on their CV…”)</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop process for sharing intervention ideas</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop process for giving feedback on intervention ideas</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop accountability system</li></ul></li></ul></li></ul><h3 id="syllabus-review-modern-algebra-10am">Syllabus Review, Modern Algebra (10am)</h3><p>I initially intended to grab my notes from a webinar on cultivating a liberatory classroom, but I ended up working with<a href="https://www.unco.edu/nhs/stem-inclusive-excellence-collective/pdf/syllabus-review-protocol.pdf">Syllabus Review for Equity-Minded Practice</a> (h/t @wrinkle_nancy on the bird app for this awesome resource!), put out by <a href="https://twitter.com/Center4UrbanEd">The Center for Urban Education in the School of Education at USC Rossier</a>. (I’m not abandoning the original plan, just triaging it for now.)</p><p>From the guide, here are a few introductory ideas.</p><blockquote><p><strong>What is syllabus review?</strong><br />Syllabus review is an inquiry tool for promoting racial/ethnic equity and equity-minded practice. To achieve this goal, the syllabus review process promotes faculty inquiry into teaching approaches and practices, especially how they affect African American, Latinx, Native American, Pacific Islander, and other racially/ ethnically minoritized students; facilitates a self-assessment of these teaching approaches and practices from a racial/ethnic equity lens; and allows faculty to consider changes that result in more equitable teaching approaches and practice.</p><p><strong>What is in the guide?</strong><br />The Syllabus Review Guide is comprised of six parts that provide the conceptual knowledge and practical know-how to conduct equity-minded self-reflection on an essential document in academic life: the syllabus. Throughout the Guide are examples that illustrate the ideas motivating syllabus review, as well opportunities to practice inquiry and to reflect on how to change your syllabi—and your teaching more generally—so are more equity-minded.</p></blockquote><p>What I learned from this resource so far:</p><ul><li>You can write stuff in your syllabus specifically to support and encourage students. It doesn’t have to be a boring contract; it can communicate a lot more about the class, including the environment (eg, “joyful exploration”), the support systems, your underlying assumptions (everything from “If you’re enrolled in this class, I assume you have taken these classes and feel comfortable with these topics. If any of those are a little hazy, let’s talk to solidify your foundation.” to things like <a href="http://math.sfsu.edu/federico/">Federico Ardila’s axioms</a>).</li><li>This kind of syllabus review seeks to make the hidden curricula of college visible to students. It’s about transparency as much as it’s about what’s going to be covered and how grades are going to be calculated.</li><li>There’s a lot of stuff in this guide that I think my syllabi already accomplish (or at least, that I have made an intentional effort to accomplish: welcoming students, describing the support structures, describing my role as a partner in their learning).</li><li><em>BUT!</em> I have not intentionally grappled with “affirm[ing] the belonging of racially/ethnically minoritized students in higher education by representing their experiences in the course materials and by deconstructing the presentation of white students and white experiences as the norm.” This is where my focus is going to be as I revamp my syllabus this time around.</li></ul><p>Further actions:</p><ul><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Complete the first worksheet (“Do I Know My Syllabus?”)</li><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Preliminary run through my syllabus to target areas that need work (before reading further); jot down ideas with the big <em>BUT!</em> in mind (this is kind of like a pre-assessment to see where I’m currently at in my equity-mindedness)</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Read on critically: “grade” my self-assessment as I work through the rest of the resource and, of course, improve upon my efforts. <ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Related: Finalize standards for SBG</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Revamp final paper assignment yet again</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Work out the blog/vlog/alog (audio log, is that a thing) structure for contributing to the course in a way that doesn’t add make-work, supports student learning, and doesn’t require writing necessarily</li></ul></li><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Call in some pals who will be receptive to meeting to work on this stuff</li><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Schedule the zoom for the pals</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Don’t forget the original plan: dig out notes from “the liberatory classroom” webinar and put them into place!</li></ul><p>Final thoughts – I admit that I skimmed the whole resource even though I really intended to give myself an honest self-assessment. Let me share my excitement about the section that helps you deconstruct your syllabus to help clarify who the syllabus serves:</p><ul><li>the institution – think student learning outcomes, specific institution-wide boxes the course checks, advertising institutional supports like relevant peer tutoring services;</li><li>the department – think “This class builds on… from [earlier courses] and will set you up to continue on in [later courses]”</li><li>the academic field – think “This course will expose you to some of the core ideas in modern algebra, like <em>primes</em>, <em>fields</em>, <em>rings</em>, <em>ideals</em>, and <em>groups</em>”;</li><li>the faculty – think “I’m your partner in learning in all of these ways” (the commitments you make to your students, like how you’ll assign grades, your deadline policies, how you’ll support student learning…</li></ul><h3 id="math-in-society-11am">Math in Society (11am)</h3><p><em>Context: we have a “Social, Structural, and Institutional Hierarchies” requirement at Hamilton that embeds questions about equity, access, fairness into each concentration (it’s really cool and afaik we’re the only place that does this).</em></p><p><em>So, in our math department, you can fulfill this requirement in a few ways (through a stats class with focused applications — eg, an age discrimination legal case and how stats can be used to determine there is age discrimination happening; through courses in the education program that deal directly with these issues — many of our students are interested in teaching). We also have the Math in Society Reading Seminar.</em></p><p>The Math in Society course brings in books like <em>The Algebra Project</em> by Bob Moses, <em>Weapons of Math Destruction</em> by Cathy O’Neil; it touches on the mathematics of fairness (gerrymandering, voting theory); and it generates discussions, blog posts, and a final paper. After a couple years of one steadfast colleague offering this course, we’re moving to sharing the teaching of this course in different modules. I’m taking responsibility for a 2-week ethics module to go along with WoMD. (<em>Hello, PredPol!</em>)</p><p>Here are some of my thoughts from my work session:</p><ol><li>Sharing the Ethics in Math AWM panel (or related video content depending on if this panel is publicly available) with students and discussing it <ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Find out if this session will be shared publicly</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop questions for discussion</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Decide on a platform for student discussion (Perusall?)</li><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Come up with some back-up options if the panel isn’t made available (currently, a playlist with short videos featuring each of the panelists: <a href="https://www.youtube.com/playlist?list=PLvQ06rWj7XfMBOaihDDFL7vGUWtLZwlY1">https://www.youtube.com/playlist?list=PLvQ06rWj7XfMBOaihDDFL7vGUWtLZwlY1</a>)</li></ul></li><li><em>Weapons of Math Destruction</em><ul><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop Jigsaw assignment for presenting the chapters after Ch 2 and before Conclusion</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Develop a short class component featuring ORCAA and the ethics matrix - what is it, examples (where can I find some of these? what’s the name of Cathy’s coauthor in philosophy/ethics, are there papers somewhere to see this work through an academic lens? maybe the philosophy collaborator? This is all follow-up work that I need to break down into actual tasks). <ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Read/vet: <a href="https://www.fastcompany.com/90172734/this-logo-is-like-an-organic-sticker-for-algorithms-that-arent-evil">Fast Company short piece on ORCAA</a></li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Read/vet: <a href="https://redtailmedia.org/2018/10/29/redtail-talks-about-flipping-the-script-on-how-we-value-algorithims-with-the-weapons-of-math-destruction-author/">Red Tail Media interview with Cathy O’Neil</a></li></ul></li></ul></li><li><em>Phi Beta Kappa visiting scholar</em><ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Coordinate PBK visit, including class visit (relates to the Ramanujan course content) <ul><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Determine date</li><li class="task-list-item"><input checked="true" class="task-list-item-checkbox" disabled="" type="checkbox" /> Determine topic preferences</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Set up pre-visit conference call to discuss stuff</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Organize venue stuff (with PBK chapter help)</li></ul></li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Determine how to advertise public event well on campus and to students in class <ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Identify opportunities for related events</li></ul></li></ul></li></ol><h3 id="lunch-and-a-break-to-go-outside-and-pet-cats-1215pm">Lunch and a break to go outside and pet cats (12:15pm)</h3><p><em>The cats were happy to be the center of attention.</em></p><h3 id="quarantine-support-introductory-meeting-130pm">Quarantine Support Introductory Meeting (1:30pm)</h3><p>I won’t go into too much detail here because this meeting is a little bit of a stretch from my purpose for the day, but I didn’t have control over its timing. I took the Johns Hopkins online contact-tracing course last fall so I could be part of the support group that checks in on students in isolation/quarantine in the spring. This meeting went into some details about all that stuff (logistics, tips, etc). I’m placing a mental flag to be conscious of how inequities manifest for students in isolation/quarantine when I start this work.</p><h3 id="prison-mathematics-project-correspondence-230pm">Prison Mathematics Project Correspondence (2:30pm)</h3><p>As of last fall, I correspond with two math enthusiasts through the <a href="https://www.prisonmathproject.org/">Prison Mathematics Project</a>, both of whom are on self-guided tours of number theory. I caught up on reading their letters and got a start (but not a finish, damn) on my next letters.</p><p>Further actions:</p><ul><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Look into getting books to my penpals (specifically <em>Number Theory Through Inquiry</em>)</li><li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox" /> Finish writing back</li></ul><h3 id="break-330pm">Break (3:30pm)</h3><p>More cats, screen-time break, and a very brief walk outside.</p><h3 id="bonus-zoom-4pm">Bonus Zoom (4pm)</h3><p>I clocked out of work for this one, but I want to mention it anyway. I chatted with twitter math friend @Maryamization about practical stuff (how to add a paper clip to a cloth mask to get it to stop fogging up your glasses) but, carried away with the zeitgeist, we talked about math and community, and she also explained Moonshine to me (monstrous, umbral, or other). This was a soul-restoring chat that, in the context of the day, gave me a lot to think about in terms of what I like about math and why that makes the other parts worth doing.</p><h3 id="personal-consciousness-raising-and-commitment-to-actions-630pm">Personal Consciousness Raising and Commitment to Actions (6:30pm)</h3><p>I’m going to write a separate blog post about this because there’s just too much to say here.</p><h3 id="clocking-out-for-real-830pm">Clocking Out For Real! (8:30pm)</h3> Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-70501996831696541072020-05-16T20:42:00.000-04:002020-05-16T20:42:25.095-04:00Book Club!I have lots of thoughts to jot down about the end of the semester, but first: would anyone like to join a virtual book club?Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-53752209918832010872020-05-11T18:06:00.000-04:002020-05-11T18:08:11.824-04:00Wrapping up the remote semester - a scratchpad of thoughts<b>Phew</b><div>Last day of classes! Finals, and then we're finished up.<div><br /></div><div><b>A couple links to helpful things that I didn't get a chance to share earlier</b><br />Questions for an exam: <a href="https://www.francissu.com/post/7-exam-questions-for-a-pandemic-or-any-other-time">https://www.francissu.com/post/7-exam-questions-for-a-pandemic-or-any-other-time</a></div><div>Scanning documents with your phone and Google Drive: <a href="https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ea65ca76-8d92-4fe5-8e9b-ab7c00e40ccc">https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ea65ca76-8d92-4fe5-8e9b-ab7c00e40ccc</a></div><div><br /></div><div><b>Tools that have been invaluable for teaching remotely</b></div><div>Gradescope (for grading)</div><div>Slack (for project-based learning)</div><div>Piazza (for asynchronous class discussions that support LaTeX)</div><div>Overleaf (for collaborative document editing, especially with the track changes panel!)</div><div>Explain Everything (for explainer videos)</div><div>Zoom (yeah yeah, privacy stuff aside: can't imagine teaching without some face-to-face)</div><div>Google Apps Suite (for all sorts of things but especially forms)</div><div>Google Calendar with Zoom integration</div><div>Boomerang for Gmail for the "Pause Inbox" function (helpful for focus)</div><div><br /></div><div>To be continued, I'm sure!</div></div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-80333946316695026862020-04-28T13:10:00.002-04:002020-04-28T13:10:24.444-04:00Mentoring Undergraduate ResearchI wrote a short piece for the Early Career section of the Notices of the American Mathematical Society, and you can read it online: <a href="https://www.ams.org/journals/notices/202005/rnoti-p663.pdf">https://www.ams.org/journals/notices/202005/rnoti-p663.pdf</a><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-_lbflBnfS6o/Xqhjb9az9KI/AAAAAAAABaY/6vnrSPvyY106VfTYVeqRUpopSsmRbfFfwCLcBGAsYHQ/s1600/Screenshot%2B2020-04-28%2B12.17.47.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="386" data-original-width="688" height="179" src="https://1.bp.blogspot.com/-_lbflBnfS6o/Xqhjb9az9KI/AAAAAAAABaY/6vnrSPvyY106VfTYVeqRUpopSsmRbfFfwCLcBGAsYHQ/s320/Screenshot%2B2020-04-28%2B12.17.47.png" width="320" /></a></div><br />Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-39457728515487462592020-04-23T02:17:00.001-04:002020-04-23T02:17:52.309-04:00Working at odd hoursDue to a combination of too much screen-time and an out-of-date glasses prescription, I get really bad headaches if I work for too long in front of the computer. (I know, right?) <div><br></div><div>To compensate for the breaks I take during the day, I've been finding myself up at 1 or 2 am trying to catch up. I used to do this before This Happened, but not as often: I intentionally left work physically at work so I would break the habit.</div><div><br></div><div>Anyway, a few weeks into this habit confirms for me that it's not actually worth the tiredness the next day even if I do get caught up. But I can't seem to shake the feeling that I am falling behind. Maybe a better way to say it is that I can't seem to make peace with falling behind.</div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com1tag:blogger.com,1999:blog-855168037568740476.post-56854753610600450052020-04-09T16:43:00.002-04:002020-04-09T16:43:05.525-04:00Hamilton's Spring 2020 Grading Policies<h3 id="last-night-faculty-voted-to-make-hamiltons-spring-2020-grade-policy-universal-creditno-creditincomplete-crnc.">Last night, faculty voted to make Hamilton's Spring 2020 grade policy universal Credit/No Credit/Incomplete (Cr/NC).</h3><p>The faculty's formal process for making decisions is (surprise!) complicated, so the purpose of this blog post is to give a little more information: how it worked and some things I considered while voting on policies.</p><h2 id="process">Process</h2><p>The process began with a proposed policy that a committee created based on faculty and student input. The committee's proposal was opt-in Cr/NC, and grades earned would be included on the transcript but no semester GPA would be calculated.</p><p>The process for moving from this policy to others we considered required proposing changes to the policy, voting on those changes, or substituting in a new policy and voting on which one we wanted to move forward. There were several rounds, and it took an extra long time because we were also adapting to the technical challenges of conducting what is supposed to be an in-person meeting online.</p><h2 id="my-thoughts">My Thoughts</h2><p>For students trying to understand some of the things faculty were weighing, here are some of the elements of my own decision-making. It's not exhaustive; I'm listing only those things that I think might not already be evident to students.</p><ul><li><p><strong>What happens to students if their professor(s) get sick?</strong> <br>The <a href="https://www.desmos.com/calculator/3oh34wdh3x">numbers and projections</a> for Oneida County scare me. <br>Writing with my own grade book in mind, if I were incapacitated by COVID19, my students would probably be forced to take their courses Cr/NC. Because I teach one section of a multi section class, it seems extra unfair that the other section might be able to elect grades because of something that happened to <em>me</em>. My own back-of-the-envelope estimate for faculty with elevated risk factors and comorbidities reinforced this point.</p></li><li><p><strong>Hamilton's faculty had only 2 weeks to figure out how to adapt courses to remote instruction.</strong><br>I had to revise how I'm going to assess my students' progress using new types of assignments (including plenty of Professor-introduced-error!), and each of the policies we considered have consequences not just at Hamilton, but for employment and post-bac degree programs.</p></li><li><p><strong>Many schools have already elected Cr/NC.</strong> <br>Employers, graduate programs, and med schools are already figuring out how to make that Cr/NC work. Some graduate and medical schools will accept Cr/NC grades <em>only if it is a universal policy</em>, which means that any policy intended to provide students with flexibility ironically left many students <em>without</em> choice. <br>There were nuanced and unique proposals that came up during the meeting that weren't as simple as "grades with optional Cr/NC" or "universal Cr/NC." By last night, I thought that if we enacted something unique among colleges, it would come back to bite us. The work that grad schools and employers are doing to adapt to college grading policies is based on what the most prevalent policies are. This is one time we don't want to stand out from the pack.<br>Here's an incomplete list of colleges with universal Cr/NC policies:</p><ul><li>Harvard</li><li>Yale</li><li>Columbia</li><li>Dartmouth</li><li>Stanford</li><li>Johns Hopkins</li><li>Duke</li><li>MIT</li><li>Williams</li><li>Smith</li><li>Wellesley</li></ul></li><li><p><strong>Hamilton needs a policy now that's <em>still</em> a good policy at the end of the semester when the true toll of COVID19 on our community is more evident.</strong>That's not an unambiguous point in favor of Cr/NC, but it was compelling to me combined with the points above and with the perspectives of students who were initially in favor of opt-in policies and changed their minds as they faced unexpected challenges.</p></li></ul> Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-14326962587227102492020-04-06T11:24:00.002-04:002020-04-09T16:57:06.621-04:00Workflows: "live" Office HoursAs I’m figuring this out, here’s what works for me.<br /><ol><li>Have course materials (weekly assignments, textbook with bookmarked pages, a blank Overleaf document) to hand.<br /><em>I have the luxury of a second monitor at home, so I pull up the assignments, etc. and tile that monitor with them so I can more easily share them on Zoom.</em></li><li>Have a way of sharing a view of what I’m writing with students.<br /><em>I have the luxury of an iPad that I can use with a stylus to create a digital document while sharing its screen on Zoom.</em></li><li>Post a summary of questions and answers to our online course space.<br /><em>Piazza is what I’m using – I was already using it before the online adventure to allow for asynchronous office hours, which I really like. Definitely going to use the iPad in regular office hours and keep this part of the workflow going.</em></li><li>Record and (selectively) share the recordings with students.<br /><em>I feel weird about this part, so I have been editing the recordings down to just me to share with them. I need to get better at rephrasing their questions if I I plan to continue doing this.</em><br />At times, I stop the recording to do a more personal check-in with students if there are only a few of us there. And then I forget to record again. A nice hack: put a post-it on your computer screen/keyboard/mouse to remind you to start recording again when it’s business time.</li></ol><blockquote>Written with <a href="https://stackedit.io/">StackEdit</a>.</blockquote>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-35996335859467837822020-04-02T11:20:00.002-04:002020-04-02T11:20:40.551-04:00Adaptations<p>So far, the technologies I’m using for the remote semester are working pretty well (relative to expectations). Now I’m looking at pedagogy and (a) trying to abandon principles that are noble but irrelevant in the face of a global pandemic while (b) trying to maximize the joyful opportunities to engage with mathematics.</p><p>A few ideas so far at various stages of implementation:</p><ul><li><em>Mathematics for Human Flourishing</em>: an invitation to read, reflect, and write about the value of mathematics independent of its applications. This seems to be a particularly timely opportunity for students, especially math majors, to reconnect with the joy of mathematics. The only hurdle right now is finding a way for students to access Francis Su’s book remotely. I’m honestly tempted to just buy and ship this book to students interested in this option.</li><li>Student designed exam (thanks to @katemath on Twitter!): <ul><li>Choose/create 4 problems whose complete and correct solutions show mastery of the big ideas in the course</li><li>Justify your choices</li><li>Submit complete and correct solutions</li></ul></li><li>Choose Your Own Adventure: <ul><li>Select from a series of predefined Adventures</li><li>Adventure materials include YouTube playlists, books that can be accessed online through Hamilton’s library, and additional content created or curated by me for the students</li><li>For the interested: topics include… <ul><li><strong>Applied Cryptography</strong>. Extra stuff comes from a very nice Udacity course, <a href="https://www.udacity.com/course/applied-cryptography--cs387">https://www.udacity.com/course/applied-cryptography--cs387</a>.</li><li><strong>Elliptic Curves and Lenstra’s Algorithm</strong>. Additional content created by me that gives a very, very brief introduction to elliptic curves over finite fields and projective space.</li><li><strong>Continued Fractions and Convergence</strong>. Additional content from a fair-use selection from one of my favorite texts, Hardy and Wright’s <em>Introduction to Number Theory</em>. I’ve also selected a portion of an MIT open courseware Number Theory course for undergraduates.</li><li><strong>Quadratic Reciprocity and Polynomial Congruences</strong>. Content follows <em>Number Theory through Inquiry</em>. Still curating fun resources on the internet – send me your suggestions?</li><li><strong>Pythagorean Triples to Pell Equations</strong>. Ditto the previous.</li></ul></li><li>Students are also free to pitch me their own adventure and I will help as much as possible.</li></ul></li></ul><blockquote><p>Written with <a href="https://stackedit.io/">StackEdit</a>.</p></blockquote> Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-58626611663360140532020-03-31T15:32:00.000-04:002020-03-31T15:32:04.289-04:00Doing a bad job and being okay with itThe whole "lower your expectations" thing is really hard to do.<div><br /></div><div>First day of remote instruction: done. It was weird. I don't know if it was good or bad or just weird. I'm not used to being bad at my job, and I feel really bad at my job right now. I'm sure this is a universal feeling among faculty and students, but it's also very personal for each of us. I want to help students find the joyful parts of math, and it seems extra impossible right now.</div><div><br /></div><div>On the "life" front, I've got a lot happening that's also making it hard to focus on doing the job.</div><div><br /></div><div>The question I keep coming back to is, "How long can I sustain 'all hands on deck' without getting sick?"</div><div><br /></div><div>Sorry -- no cheerful updates here. Just wishing things could go back to normal. I miss the feeling of community and I didn't realize how hard it would be to do class remotely without it.</div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-80404880648808558352020-03-26T15:44:00.000-04:002020-03-26T16:58:10.396-04:00Exponential Growth - activity for kiddosDo you have a bag of dried beans and a watch/phone that can time seconds? Then you can talk to your kids about exponential growth as you talk about why COVID-19 is so frightening.<br /><br />Materials:<br />128 (at least) dried beans in a pile, bowl, stash, or whatever.<br />1 plate or bowl.<br />Timing device<br /><br />One player is the shouter (keeps track of time) and one player is the doubler (counts beans).<br />Discuss in advance how often your beans will double (I recommend 5 seconds to start).<br /><br />The doubler puts one bean from the stash on the plate. The shouter starts keeping track of time; when time has elapsed, shouter shouts, "Double!"<br /><br />For the doubler:<br />Round 0.<br />Put one bean from the stash on the plate. (Plate: 1 bean)<br /><br />Round 1.<br />Put another bean from the stash on the plate, count the beans. (Plate: 2 beans)<br /><br />Round 2.<br />Put 2 more beans from the stash on the plate. (Plate: 4 beans)<br /><br />Round 3.<br />Put 4 more beans from the stash on the plate. (Plate: 8 beans)<br />[this should have been pretty leisurely so far]<br /><br />Round 4.<br />Put 8 more beans from the stash on the plate. (Plate: 16 beans)<br /><br />Round 5.<br />Put 16 more beans from the stash on the plate. (Plate: 32 beans)<br /><br />Round 6.<br />Put 32 more beans from the stash on the plate. (Plate: 64 beans)<br /><br />...<br /><br />Round \(n\).<br />Put \(2^{n-1}\) beans from the stash on the plate. (Plate: \(2^n\) beans)<br /><br />You get the idea. This game gets frantic pretty quickly, and that is the kind of overwhelmed state exponential growth should invoke: "this is getting really big really fast!"<br /><br />To compare to other modes of growth, you can do growth rates like Round \(n\): put \(n\) [or \(n^2\) if you have a fast counting doubler] beans on the plate -- see how much longer it takes for this type of growth to get frantic.<br /><br />Enjoy!<br /><br /><span style="font-size: x-small;">(This is an activity I developed as part of my Project FULCRUM fellowship at the University of Nebraska-Lincoln when I was a graduate student.)</span><br /><br /><br /><br /><br />Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-67461614369991302572020-03-26T10:55:00.000-04:002020-03-26T16:57:30.981-04:00Remote Semester Orientation<span style="font-size: x-small;">Advice from Abbi Jutkowitz, Film Editor, who has worked from home on and off for 5+ years, and worked from home exclusively for the past 8 months (<a href="https://www.imdb.com/name/nm1631659/">https://www.imdb.com/name/nm1631659/</a>), in collaboration with Courtney Gibbons, Math Professor, who has worked from home for the last week (<a href="https://people.hamilton.edu/cgibbons">https://people.hamilton.edu/cgibbons</a>). To download this advice: <a href="https://people.hamilton.edu/cgibbons/files/RemoteSemesterOrientation.pdf">RemoteSemesterOrientation.pdf</a></span><br /><h2></h2><a name='more'></a><br /><h3>Guiding Principles </h3>Lower your expectations. Then: <br /><br /><ol><li>Develop a plan to satisfy your expectations!</li><li>Put the plan into action–do the ideas.</li><li>Evaluate which actions worked and which did not; tweak the plan.</li><li>Repeat steps 1-3 until you are able to raise expectations. Then:</li></ol><br />Repeat steps 1-4 until you feel comfortable.<br />(The goal is to have a plan that is “good enough” without further tweaking, not to be endlessly tweaking.)<br /><br /><h3>Plan Elements</h3>✮✮✮<br /><h4>Distractions / Focus</h4><br /><ul><li>Block out times with specific objectives, and find ways to support your schedule.</li><ul><li>Use a napkin, a planner, a web calendar, or whatever works for you to have a reference for your time management.</li></ul><li>Some specific objectives might be... </li><ul><li>email time - clear out your inbox; </li><li>class time - complete homework problems / write a draft of a paper; </li><li>social time - have Zoom breakfast with your breakfast crew / update your insta story</li></ul><li>Some tech options include</li><ul><li>Google Apps suite - Google Calendar, Google Tasks for organizing deadlines and specific tasks</li><li>Gmail extensions like Boomerang or Pause Inbox to catch up on existing email without being distracted by new email</li></ul></ul><br /><br />✮✮✮<br /><h4>Work Space</h4><br /><ul><li>Adopt the mindset that wherever you work is your workspace and therefore should not be used for anything else while you are working.</li><ul><li>For example, if you want to work in bed, do so, but only if you are able to focus and not sleep or do anything else you’d normally do in a bed</li></ul><li>When you are in your workspace, designate to yourself and family members/housemates that you are working and therefore not to be disturbed. Be creative.</li><ul><li>Hang a sock or tie or Hamilton swag on your door</li><li>If in a shared room, put a noticeable item on your desk</li><li>If not using a desk, put a binder clip or something similar clipped to your book or screen</li></ul><li>Create the soundscape you need</li><ul><li>If you desire silence, use noise-canceling headphones (if possible)</li><li>For working with some background noise which is not music, try https://coffitivity.com/</li></ul></ul><br /><br />✮✮✮<br /><h4>Routines</h4><br /><ul><li>One of the benefits of taking classes at Hamilton is that its residential setting comes with lots of routines: classes, meals, sports, clubs, office hours, etc. To the extent possible, identify your Hamilton daily/weekly routine and imagine recreating it at home.</li><ul><li>Breakfast with pals → breakfast with the family?</li><li>Class time → class time / engage with asynchronous course materials/office hours if that is what your professor has scheduled</li><li>Sports time → do people still have ShakeWeights?</li></ul></ul><div>(Remember that this is your first draft of your plan!)</div><br /><br />✮✮✮<br /><h4>Managing Conflict</h4><ul><li>Family / Roommates</li><ul><li>Set your expectations with your cohabitants and come up with a plan in advance for resolving difficulties. </li><li>“Do not disturb me when the binder clip is on my laptop; it means I’m ‘at college’ -- when there’s no binder clip, I can help you around the house if you need me.”</li></ul><li>Classmates / Instructors</li><ul><li>This is new territory for your classmates and your instructors, too. Adopt an attitude of compromise, compassion, and positivity before addressing issues with your campus colleagues. Your constructive criticism will be extremely helpful to your instructors (and collaborator classmates), but the circumstances of the semester may make it difficult for anyone to respond rapidly to even the simplest and best advice.</li><li>Remember too that your instructors are invested in your success, even though it may be harder to “see” that investment without in-person meetings.</li><li>With all that in mind: Express your needs, frustrations, and concerns clearly, openly, and kindly. </li><ul><li>Professor Gibbons says: I would always rather know what’s going on for you, my students, than try to guess or anticipate.</li></ul></ul></ul><br /><br />✮✮✮<br /><h4>Health & Wellness</h4><br /><ul><li>We’re in a global pandemic! Take care of yourself and your loved ones first and foremost.</li></ul><br /><br />✮✮✮<br /><i>Be well!</i>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-22752073506678718192020-03-25T08:19:00.001-04:002020-03-26T16:57:50.681-04:00Womp womp!I managed to put a sad trombone sound effect (royalty-free) into a video.<div><br></div><div>That's it, that's the whole news.</div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-30759325735187331672020-03-21T13:06:00.001-04:002020-03-26T16:57:50.779-04:00Principles in conflict?Last summer, I taught in a correctional facility. There were no iPads, no smart boards or projectors or computers. No internet at all and no smart devices. If I wanted a box of chalk with a few colors, I had to get permission to bring it in and was required to bring it out.<div><br></div><div>The students in my class didn't have computers. They had a textbook (it had to be approved by the facility), access to a small library of books contingent on a bunch of circumstances, one or two pencils, and paper they mostly had to purchase for themselves unless I got permission to bring some in.</div><div><br></div><div>That summer made me rethink my reliance on the bells and whistles: online videos, fancy animations, etc. I made a pledge in my teaching log (yep, still have a paper and pencil teaching log!) to make sure that whatever class stuff I develop is doable with pencil, paper, and discussion. I also pledged to keep my courses as self-contained as possible: between the class and the textbook, students would have the necessary tools (physical, like pencil and paper, and intellectual, like strategies, outlines, examples, and suggested steps for starting problems) to complete assignments -- or at least make progress until the next class meeting.</div><div><br></div><div>I have been <i>just okay</i> at keeping those pledges (better than if I hadn't made them), and I find that it's hard to keep them with the shift to remote instruction. My litmus test is, "Could I teach this course at a correctional facility with minimal changes?" and suddenly the answer has shifted from "kinda" to "not even close."</div><div><br></div><div>I'm trying to figure out how to bring my principles into alignment. Suggestions welcome.</div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-2623796739433885872020-03-19T13:20:00.001-04:002020-03-26T16:57:50.754-04:00Learning curvesThere's nothing like looking at a finished video and thinking: "Wow. What a piece of sh*t."<div><br></div><div>Between driving 8 hours in the past two days (with another 4-5 tomorrow), trying to work with a delightful baby demanding more dancing around and being held upside down, telling my parents to take COVID-19 seriously (Mom, that's you: 6 feet from other people, no handing over your phone or taking someone else's, no matter how cute the baby pictures are), etc etc -- not exactly a highly productive time.</div><div><br></div><div>But! Some small victories: our campus has a license for Adobe Premiere Rush and I worked through the quick tutorial. I made another few minutes of content. I'm ready for a remote meeting later today. We made french fries for breakfast. I scripted a few really awful math jokes to intersperse in my course video playlists. When I say really bad, I mean: "Why couldn't the base field have puppies? Because it was fixed." (A little Galois humor! Like gallows humor, but French.)</div><div><br></div><div>Unfinished business: I've written about 5 drafts of an email to my advisees. I hope to finish it and send it soon. Probably a faux pas to start with, "What the actual eff?!" but it's the most honest opener I've got at the moment.</div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-26213913021568843602020-03-16T08:36:00.000-04:002020-03-26T16:57:50.730-04:00Challenges and silver liningsWe're all facing challenges as we adapt to CDC guidelines and their implications for our work and social lives. As I put together my plans for my courses, I'm reminding myself this applies to my students and me.<br /><br />The Twitter math scene is a really supportive place. I've found some video lectures appropriate for my modern algebra classes and I'll make some to fill gaps. Best practices, ideas, remote workshops -- all of these and more are happening as people come together. I'm glad my social media use has led me to this wonderful community. I'll add some folks to follow in my next post!<br /><br />Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-6128070754540789292020-03-15T19:34:00.000-04:002020-03-26T16:57:50.902-04:00Setting up a home workspaceIt seems unlikely that we'll be allowed to work in our offices for the rest of the semester (which is good, as far as the CDC recommendations go). But that means carting home a bunch of stuff and setting up a comfortable (and cat-proof, and mostly partner-proof) workspace.<br /><br />It will take some time to figure out how to rig up all the things I will be using -- microphone, webcam, iPad, dual monitors, possibly a really old pen-tablet, chalk board. And then it will take time to fix up a few issues in my office (I need to hang up curtains so I can see my screens midday).<br /><br />Meanwhile, in another reality, I would have been on a flight to Turkey right now, heading off to a vacation with a goal of flying back to the US with my sister and my niece. With everything going on, I'm obviously not on a plane right now, but my sister and niece will be back in the US on Wednesday. I'll head back to my hometown on Tuesday and help get her house ready for her, then pick her up Wednesday and help her get settled back in, and then Friday I'll head back to Clinton to keep prepping for remote classes.Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-67703739637525795622020-03-13T12:16:00.001-04:002020-03-13T12:16:33.469-04:00Class PreferencesToday in our in-person Modern Algebra class, my students and I talked about our concerns moving forward and I solicited some student preferences that I found useful to rethink my delivery of course material in the coming weeks.<br /><br />First, my students expressed a preference for lecture-length [50 minute] videos. Color me surprised! I (naively) thought the TikTok generation would prefer short videos. I predict I will get overwhelmed with the creation and editing of 50 minute videos, so I'll do short edits. But I will probably use the YouTube playlist feature to put together 50 minutes of content that will autoplay for students.<br /><br />The apps I'm most familiar with for pencasting (creating digital whiteboard lecture that you speak on top of, either as you create it or as you play back the penstrokes or both) are Doceri (<a href="https://apps.apple.com/us/app/doceri-interactive-whiteboard/id412443803">https://apps.apple.com/us/app/doceri-interactive-whiteboard/id412443803</a>, fairly simple to learn, direct post-to-YouTube option that's easy to use) and ExplainEverything (<a href="https://apps.apple.com/us/app/explain-everything-whiteboard/id1020339980">https://apps.apple.com/us/app/explain-everything-whiteboard/id1020339980</a>, more [maybe too many?] features, a steeper for me learning curve, but it has an infinite canvas!) on an iPad.<br /><br />I've also dug out my 2013 Wacom Intuos tablet, which still works with the latest Mac OS, for the Zoom whiteboard feature. I know you can theoretically connect yourself and your iPad to Zoom, but I think the old-skool approach -- a specific pen-tablet that you plug into your computer as an additional input device -- will be easier to manage as I get used to Zoom. I'm already familiar with how to use a pen-tablet from my math cartoonist days (ha!), so I'm feeling better about online office hours via Zoom than I was when I imagined figuring out how to manage multiple connections, etc.<br /><br />I'm also cooking up a low-tech solution (h/t to <a href="https://twitter.com/benblumsmith" target="_blank">@benblumsmith</a> on Twitter, who seems to have a similar low-tech problem-solving strategy) of mounting a (physical) blackboard to my office bookshelves using pulleys so I can raise and lower it and still be in my "recording zone" with the current configuration of the old mic and webcams I dug out for better quality recording.<br /><br />Okay -- time to draft out a first attempt at a plan for Modern Algebra done online!Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-75279723525051520292020-03-13T09:43:00.001-04:002020-03-26T16:57:50.952-04:00Nothing ever happens on Mars<iframe allowfullscreen="" frameborder="0" height="344" src="https://www.youtube.com/embed/RxxmLuVF4MM" width="459"></iframe><br /><br /><br /><br />I woke up with the weird earworm "Nothing Every Happens on Mars" from the equally weird (and charming) <i>Waiting for Guffman</i>.<br /><br /><br /><br />Why? I don't know, but in the cold light of day (literally -- it's cold and rainy here) it seems relevant. Both for its contrast to the state of things: everything is happening all at once! and for its looming, stark relevance: social distancing is going to be, well, boring.* I'm kind of a master of boredom that comes from not having a whole lot going on (as are many residents of more rural areas).** But I feel for those of you in (or about to be in) big cities who are (a) way more likely to be dealing with COVID-19 firsthand (a topic that's heavy on my mind but that I have no capacity to write about yet) and (b) further frustrated by the lack of normalcy. No sports. No concerts. No museums. Yikes. At least here in Clinton I have a hill I can walk to, alone and without seeing anyone else, and from its top I can see the beautiful sunrise and sunset.<br /><br /><br /><br />More thoughts more closely related to the challenge of changing to online courses with a widely dispersed audience later. In the meantime, I'll be thinking about that poor Martian looking for a little excitement. Right now, we have a little extra to share.<br /><br /><br /><br />*And at the same time, absolutely necessary to save lives. The latest UCSF report forecasts 1 to 1.5 million COVID-19 deaths. Take all of this seriously, okay? Even if you will be okay, you inevitably know lots of people who might not be.<br /><br /><br /><br />*That's not totally fair to Clinton, NY, and the Utica area: there is a bunch happening, but it's not the same as living in a big city where there's a lot of stuff happening and you can just step outside and find it.Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-53221903358951149512020-03-13T07:01:00.000-04:002020-03-26T16:57:50.876-04:00LaTeX in Blogger? Q.E.Done! \(\square\)I think, my dudes, that I properly configured MathJax. Let's see: \(\displaystyle \sum_{n=1}^\infty 2^{-n}\)Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-52118973678472936222020-03-12T18:36:00.001-04:002020-03-26T16:57:50.851-04:00And Now for Something Completely Different!There's no time like a global pandemic to (re)start a blog, right?<br /><br />Hi! I'm Courtney Gibbons. I'm an Associate Professor of Mathematics at Hamilton College, and I'm writing from within my own personal cloud of panic about the shift from traditional classes to remotely delivered content to students spread across multiple time zones. When I glimpse a view of the horizon through the panic, though, I have to admit I'm a little bit excited by the challenge.<br /><br />This blog, whatever it becomes, will be a place for me to record what I'm trying, how it's going, and -- inevitably -- some of the math we're doing along the way.<br /><br /><br /><a name='more'></a><br /><br /><br />Tonight I'm testing out some Zoom features with mathematics educators that I know from the Twitter math world. I'm excited to see some friends I haven't seen in a long time and meet some new people through mutual connections.<br /><br />What can you expect as far as the math for the next few weeks? Currently: I'm eight weeks into Modern Algebra (we're discovering why there's no algebraic quintic formula) and Number Theory and Applications (we cracked Enigma with group theory, just worked through the implementation of RSA and read about some of the flaws of its implementation, and started talking about primality tests and pseudoprimes). Modern Algebra is a Writing Intensive course, so my students complete weekly writing assignments (with partners) and a final paper (individually). Number Theory is a Speaking Intensive course, so my students had oral midterms earlier in the semester and... well, we were going to do a conversation midterm (a future blog post on that, I promise) but now -- who knows?<br /><br />Students (past and future, but especially present!), if you're following this grand adventure and would like to contribute to the blog, I'm absolutely thrilled with that prospect!<br /><br />Wishing you health, safety, and just enough excitement. -CRG<br /><br />PS: just because I think I finally got MathJax working... \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2}\)<br /><br /><br />Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-74710364131025447462019-12-01T20:33:00.000-05:002020-03-26T16:58:05.239-04:00How to use Office Hours<div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;">My office hours, and generally those of the faculty in the math department, are drop-in. That means that you can show up and expect me to be there during my posted office hours (plus or minus five minutes if I’m running a little bit late). You don’t need to schedule an appointment to see me; I usually operate on a first-come, first-served basis.</span></span></div><div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;"></span></span></div><a name='more'></a><br /><div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;">I try to keep the waiting short by limiting an office hours visit to 5-10 minutes if there’s a long line, which means you might not get all of your questions answered at once. That’s okay, though! One of the benefits of coming to office hours is that you’ll almost inevitably find someone working on the same problems you are, and you can team up to ask me more questions or figure out a solution together.</span></span></div><div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;">You might discover that I’m more likely to answer questions like, “Why should I use integration by parts on this problem instead of partial fractions?” than questions like, “How do I do this problem?” My role is to stoke your intellectual curiosity and give you opportunities to learn how to apply what we’re doing in class to new problems. But you might find that a classmate is willing to walk you through a problem if you’re really stumped. Take this as a reminder to identify the resources you have (me, your book, a tutor, other students, … ) and find out how to use them most effectively.</span></span></div><div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;">The very last thing you should know about office hours is that I really like math, and I really like talking to you about math, so it’s hard to imagine a better way to spend a couple hours in the afternoon. If you can make the regularly scheduled office hours, that’s ideal: I’ve set that time aside for students, not for other parts of my job. When I’m not holding office hours, I’m working on those other tasks: research, class preparation or grading, or the kind of stuff that keeps the college chugging along (like serving on committees). Please don’t take it personally if you drop in outside of office hours and I have to turn you away! I’d much rather talk to you about math, but I can’t neglect my other duties, either.</span></span></div><div style="background-color: white; margin-bottom: 0.875em;"><span style="color: #383838; font-family: Times, Times New Roman, serif;"><span style="font-size: 19px;">Hope to see you in office hours soon!</span></span></div><div style="background-color: white; color: #383838; font-size: 19px; margin-bottom: 0.875em;"><span style="font-family: Times, Times New Roman, serif;"><span id="more-57"></span></span></div>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-71048206860338810162018-06-20T20:00:00.003-04:002020-03-26T17:21:07.235-04:00How to Study for ExamsFor math exams in general, it can be useful to form a study group to talk over problems and solutions before the exams. It’s also useful to retry problems you’ve seen on homeworks, quizzes, and writing assignments (without looking at your previous attempt or the graders’ comments) to figure out what you need to focus on studying.<br /><hr />Prof. Gibbons’ Linear Algebra exams should take you about 90 minutes to complete. The format:<br /><ul><li><strong>First Page:</strong> “Example or impossible” and True False problems.</li><li><strong>Middle 2-3 Pages:</strong> Homework-like problems (~5 of them).</li><li><strong>Last Page:</strong> Writing Assignment-like problems (~2 of them).</li></ul><hr /><strong>Studying for the First Page</strong><br /><ul><li>At the end of each chapter, the book has True of False questions and discussion questions. These are great problems to make sure that you have a handle on the theory in the class (meaning, literally, the theorems and other results that we have proved throughout the semester). If you are studying these and would like solutions, contact Prof. Gibbons.</li><li>Try to read my mind! Make up questions for this page by looking at the theorems and examples in the notes and book and seeing if you can find good questions that seem to be like the quiz questions. Often the reason that something is impossible is that a theorem says it can’t happen.</li><li>Come up with some examples that show lots of things. For example, the identity matrix and the zero matrix are great examples to keep in mind as you work these problems. The zero matrix works for all of the following statements:</li><li>A matrix that is singular</li><li>A matrix for which \(A\mathbf{x} = \mathbf{0}\) has infinitely many solutions</li><li>A matrix row equivalent to a matrix with a row of zeros<br />and others. The matrix \(\begin{bmatrix} 2& 6 \\ 3 & 1 \end{bmatrix}\) has already come up in class a few times as an example of: a singular matrix, a singular matrix without a zero row, a matrix that is not row equivalent to \(I_2\), a matrix that has a number other than one or zero in reduced row eschelon form, and so on.</li></ul><strong>Studying for the Middle Pages</strong><br /><ul><li>There are additional problems at the end of the chapter if you want a source of more problems. If you are studying these and would like solutions, contact Prof. Gibbons.</li><li>There are no caluclators on exams, so practice to be sure that you can do a few simple steps (like row reduce or substitute) by hand. (Prof. Gibbons doesn’t want to check your arithmetic, so she might try to help you out with some row reduction, etc., already completed.)</li></ul><strong>Studying for the Last Page</strong><br /><ul><li>These questions will require you to form a Proposition (that is, a <em>universally quantified implication</em>:</li><li><strong>Proposition.</strong> For all …, if …, then … .<br />and then to write a proof that starts with “Proof” and ends with an end-of-proof symbol like \(\square\) or QED. Your first and last sentences should conform to good style (state your assumptions in the first sentences, do the math, and then conclude what the proof technique you’re using requires you to conclude).</li><li>One problem will come from a writing assignment or class groupwork, so you will have seen it before. Another problem will be new, but it will use the same techniques as in class and on writing assignments (like letting \(r\) and \(s\) be real numbers where \(r+s = 1\) in order to come up something new from two existing things, or using the logical equivalence \[p \implies (q \lor r) \equiv (p \land \lnot q) \implies r).\]</li></ul>Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0tag:blogger.com,1999:blog-855168037568740476.post-33104637700143920102014-05-31T20:00:00.005-04:002020-03-26T18:29:56.843-04:00A Golden (Formal) Power SeriesAs you probably know, I wear my heart on my sleeve:<br />Well, I took the <em>golden opportunity</em> (ha!) to bring the golden ratio $\Phi = \frac{1+\sqrt{5}}{2}$ into Calc 2 this week, using it (and its little pal $\Psi = \frac{1-\sqrt{5}}{2}$) to find a closed formula for the $n$-th term of the Fibonacci sequence.<br />The ubiquitous Fibonacci sequence! It’s something you may have encountered out in the wild. You know, it goes a little like this:<br />$$F_0 = 1, F_1 = 1, F_n = F_{n-1} + F_{n-2},$$<br />so that $$F_2 = 2, F_3 = 3, F_4 = 5, F_5 = 8, F_6 = 13, F_7 = 21, \ldots $$<br />And let’s say for some reason, you need to cook up $F_{108}$. I hope you have some time on your hands if you’re planning to add all the way up to that. Instead, wouldn’t it be nice if we had a simple formula that we could use — i.e., a formula that was not recursive — to figure out the $n$-th Fibonacci number?<br />Luckily, such a formula exists, and there are lots of ways to find it. In this post, we’ll find it using power series. Read on, brave blogosphere traveler.<br /><a name='more'></a>First thing we’re going to do is build a power series:<br />$$\begin{array}{r c l} F(x) &=& \sum_{n=0}^\infty F_n x^n \\<br />&=& 1+ x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + 13x^6 + 21x^7 + \cdots.<br />\end{array}$$<br />Remember that $F_n = F_{n-1} + F_{n-2}$ as long as $n \geq 2$. This means that we can rewrite our power series:<br />$$\begin{array}{r c l} F(x) &=& \displaystyle\sum_{n=0}^\infty F_n x^n \\<br />&=& 1 + x + \displaystyle\sum_{n=2}^\infty(F_{n-1} + F_{n-2})x^n \\<br />&=& 1 + x + \displaystyle \sum_{n=2}^infty(F_{n-1}x^n + F_{n-2}x^n) \\<br />&=& 1 + x + \displaystyle \sum_{n=2}^\infty F_{n-1}x^n + \displaystyle \sum_{n=2}^\infty F_{n-1}x^n.<br />\end{array}$$<br />So far so good? We’re not done yet, though. We can do a little reindexing. In particular, note that by tweaking the index $n$ a little bit, we have equalities:<br />$$\begin{array}{r c l}<br />\displaystyle \sum_{n=2}^\infty F_{n-1}x^n &=& \displaystyle \sum_{n=1}^\infty F_n x^{n+1} \quad =\quad x(F(x) - 1),\\<br />\displaystyle \sum_{n=2}^\infty F_{n-2}x^n &=& \displaystyle \sum_{n=0}^\infty F_n x^{n+2} \quad = \quad x^2 F(x).<br />\end{array}<br />$$<br />You might want to grab a coffee and some scratch paper to make sure you believe all those equalities up there. No worries; the rest of the post will be here when you’re ready.<br />Okay — agree with me? Good! Remember what we figured out above, and substitute in to obtain<br />$$\begin{array}{r c l} F(x) &=& 1 + x + \displaystyle \sum_{n=2}^\infty F_{n-1}x^n + \displaystyle \sum_{n=2}^\infty F_{n-1}x^n \\<br />&=& 1 + x + x(F(x) - 1) + x^2 F(x) \\<br />&=& 1 + x F(x) + x^2 F(x).<br />\end{array}$$<br />Finally, if we solve all of that for $F(x)$, we get the marvelous rational function $F(x) = \frac{-1}{x^2 + x - 1}$.<br />All right, kids. Now the question becomes: (a) do you remember Partial Fraction Decomposition from earlier in the semester? and (b) do you remember the quadratic formula? We’re going to need both of those things. Let me google that for you… <a href="http://lmgtfy.com/?q=partial+fraction+decomposition" target="_blank" title="Partial Fraction Decomposition">Partial Fraction Decomposition</a> and <a href="http://lmgtfy.com/?q=quadratic+formula" target="_blank" title="Quadratic Formula">Quadratic Formula</a>.<br />Now that you’ve had a chance to review, you can double check that $x^2 + x - 1 = (x + \Phi)(x + \Psi)$ where $\Phi = \frac{1+\sqrt{5}}{2}$ (the Golden Ratio!) and $\Psi = \frac{1-\sqrt{5}}{2}$ (the, uh, Aluminum Ratio? Or something?). And this means that<br />$$\frac{-1}{x^2 + x - 1} = \frac{A}{x + \Phi} + \frac{B}{x + \Psi}.$$<br />I’ll let you check my math here, but I’d wager a cat that $A = \frac{-1}{\sqrt{5}} \Phi$ and $B = \frac{1}{\sqrt{5}}\Psi$.<br />First, let’s work with $\frac{A}{x+\Phi}$:<br />$$\begin{array}{r c l}<br />\frac{A}{x+\Phi} &=& \frac{-1}{\sqrt{5}}\cdot \frac{\Phi}{x+\Phi} \\<br />&=& \frac{-1}{\sqrt{5}}\cdot \frac{1}{(1 + \frac{x}{\Phi})} \\<br />&=& \frac{-1}{\sqrt{5}} \displaystyle \sum_{n=0}^\infty \left(\frac{x}{\Phi}\right)^n\\<br />&=& \frac{-1}{\sqrt{5}} x^n \Phi^{-n} \\<br />&=& \frac{1}{\sqrt{5}} x^n \Psi^n,\\<br />\end{array}$$<br />where that last equality comes from the fact that $\Phi \Psi = -1$, so $-\Phi^{-1} = \Psi^1$ (and vice versa). Similar trickery gives $$\frac{B}{x+\Psi} = \frac{-1}{\sqrt{5}} \displaystyle \sum_{n=0}^\infty x^n \Phi^n.$$<br />Putting all of this together, we have $$F(x) = \frac{1}{\sqrt{5}} \displaystyle \sum_{n=0}^\infty (\Phi_n - \Psi_n)x^n.$$ Remember that the coefficient of $x^n$ in $F(x)$ is actually $F_n$, and therefore — drumroll, please! —<br />$$F_n = \frac{1}{\sqrt{5}}(\Phi^n - \Psi^n).$$<br />And so, to calculate $F_{108}$, just pop $\frac{1}{\sqrt{5}} \left( \left(\frac{1+\sqrt{5}}{2} \right)^{108} - \left(\frac{1-\sqrt{5}}{2}\right)^{108}\right)$ into your into your favorite calculator. For instance, <a href="http://www.wolframalpha.com/input/?i=1%2Fsqrt%285%29+*%28+%28%281%2Bsqrt%285%29%29%2F2%29%5E%28108%29+-+%28%281-sqrt%285%29%29%2F2%29%5E%28108%29%29" target="_blank" title="F108">wolfram alpha</a> calculates that this Fibonacci number is merely sixteen sextillion, six hundred forty-one quintillion, twenty-seven quadrillion, seven hundred fifty trillion, six hundred twenty billion, five hundred sixty-three million, six hundred sixty-two thousand, and ninety-six. $\square$Courtney R Gibbonshttp://www.blogger.com/profile/04661173090248877692noreply@blogger.com0