index.json

[{"authors":["admin"],"categories":null,"content":"Professor Courtney Gibbons wants to change the world. From stumping for Dukakis-Bentsen \u0026lsquo;88 as a first-grader and mailing her first one-pager to the White House when President George H.W. Bush came out as anti-broccoli in the early \u0026rsquo;90s, she has never been afraid to speak up on something that matters to her. Though her early efforts to effect political (and vegetable) change were not successful, she\u0026rsquo;s gotten better with practice.\nA mathematician and policy worker with experience in the legislative and executive branches of the Federal government, Dr. Gibbons is currently an associate professor of mathematics, she joined the faculty at Hamilton College in July, 2013.\nIn the 2023-2024 academic year, Dr. Gibbons is a fellow hosted at the National Science Foundation in the Computer and Information Sciences and Engineering Directorate, Intelligent Systems Division, as an AI policy fellow through the AAAS Science and Technology Policy Fellow program. In the 2022-2023 academic year, she was a legislative branch fellow working for the majority staff of the Homeland Security and Governmental Affairs Committee of the U.S. Senate (Chairman Gary C. Peters) covering parts of the portfolio related to Federal data, artificial intelligence, and federal financial assistance.\nIn her life as a mathematician, Professor Gibbons studies commutative and homological algebra, and her primary research interest is the study of infinite free resolutions (often through the lens of Boij-Soderberg theory). Gibbons also has a secondary interest in algebraic statistics. Since coming to Hamilton College, Professor Gibbons has supervised several commutative algebra undergraduate research projects at Hamilton, the Willamette Valley Mathematics Consortium REU, and the COURAGE (virtual) REU. She is currently an elected member of the Executive Committee of the Association for Women in Mathematics.\nDaughter of a jazz musician and public school teacher, Professor Gibbons grew up near New Haven, CT; she attended public schools in West Haven, Woodbridge, and Bethany, CT and earned her diploma from Amity High School in 2000. In 2006, she graduated Summa Cum Laude with her B.A. in mathematics with distinction from the Colorado College in Colorado Springs, CO. Subsequently, she worked for CC\u0026rsquo;s Math and Computer Science Department for a year after graduation as a paraprofessional. In 2009 and 2013 respectively, she earned her M.S. and Ph.D. in mathematics from the University of Nebraska-Lincoln.\nIn addition to being a multiply-certified math nerd and a reformed college dropout, Professor Gibbons likes to rock climb, argue about notation, and snuggle with cats.\n","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"2525497d367e79493fd32b198b28f040","permalink":"https://crgibbons.github.io/author/courtney-r.-gibbons/","publishdate":"0001-01-01T00:00:00Z","relpermalink":"/author/courtney-r.-gibbons/","section":"authors","summary":"Professor Courtney Gibbons wants to change the world. From stumping for Dukakis-Bentsen \u0026lsquo;88 as a first-grader and mailing her first one-pager to the White House when President George H.W. Bush came out as anti-broccoli in the early \u0026rsquo;90s, she has never been afraid to speak up on something that matters to her.","tags":null,"title":"Courtney R. Gibbons","type":"authors"},{"authors":null,"categories":null,"content":"Revised Spring 2025\nThe Big Picture This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine several big themes:\n Belonging – what is “mathematical identity” and where does it come from? Civil Rights – can mathematical literacy be viewed as a tool for advancing equity? Policy – how does mathematics fit into the law and public policy? Algorithms – in what ways do algorithms contribute to or fight against social stratification?  Educational Goals In addition to satisfying the Social, Structural, and Institutional Hierarchies (SSIH) requirement for the concentration in Mathematics and Statistics, this course addresses the following Educational Goals.\n Intellectual Curiosity and Flexibility – examining fact, phenomena, and issues in-depth, and from a variety of perspectives, and having the courage to revise beliefs and outlooks in light of new evidence Understanding of Cultural Diversity – critically engaging with multiple cultural traditions and perspectives Ethical, Informed, and Engaged Citizenship – developing an awareness of the challenges and responsibilities of local, national, and global citizenship Communication and Expression – expressing oneself with clarity and eloquence, in both traditional and contemporary media, through writing and speaking  Expectations and Assignments To dig deeply into the main themes of the course, you will need to prepare in advance for each class, actively participate, and complete all of the assignments. This is reflected in the final grade composition:\n Blog Posts: 40% Participation: 30% Final Deliverable: 30%  Pre-Class Tasks (Reading, Watching, or Listening) Complete the relevant task (reading, watching, or listening) assigned for each class, think about it carefully, and outline some thoughts to share in our class discussion. The list of tasks can be found on the last page of this document and may be updated (in a timely manner!) as the semester progresses.\nAttendance Your attendance and active participation is really important to the stability and success of our learning community! If you need to miss more classes, please fill out the Absence Request Form in advance (link available on Blackboard). Every student may miss one class; if you need to miss more than that, we need to talk. Undiscussed absences (besides the first freebie) will lower your participation grade.\nBlog Posts Our course blog is a (class-only) space for you to engage critically with the course materials. Writing the blog posts will help you and your classmates initiate and inform class discussions. They will also give you the opportunity to practice skills directly related to effective writing, such as conciseness, clarity, and vividness. You will contribute an original blog post five (5) times throughout the semester according to the schedule posted on Blackboard.\nEach blog post should:\n identify a specific concept/idea/argument from the assigned task (with reference); either demonstrate understanding of the concept at issue and express agreement or disagreement, giving reasons, OR connect it to previous ideas/discussions, or to contemporary issues, OR introduce an example/counter-example not explored in the text; be more than be simply a summary or an unsupported opinion (“I liked this reading”); end with a potential question or topic for class discussion, related to your post.  Each blog post should be between 150 and 250 words. You must post your contribution by 7pm the day before our class meeting. I will grade each post according to the rubric posted on Blackboard.\nFinal Deliverable: Example - Poster As a capstone assignment, you will create a poster to explore a topic of your choice. This poster will be due after spring break, and we will convene for one more class session to present the class posters to the Math and Stats department. You must submit a brief outline (bullet points are fine) of the content of your poster by the last day of the course. A pdf of your final poster is the third Monday after spring break, and you should submit your request to print the poster to LITS on this date as well. The poster should be well organized with clear exposition and proper citations. Please see Hamilton Library Guides for more information about the technical aspects of creating a poster.\nRequired Books Robert P. Moses ‘56, Radical Equations: Civil Rights from Mississippi to the Algebra Project (Beacon Press, 2001) NOTE: ebook available with Hamilton College login Radical Equations\nHonor Code Your blog posts and final poster must consist primarily of your own individual work and include citations for works that you are responding to or works that informed your thinking (this includes formal works, websites, videos, or other sources). You and I are also bound by the Hamilton Honor Code to report instances of plagiarism or other academic dishonesty that we become aware of.\nAccessibility Students who require academic accommodations should contact the Dean of Students Office to coordinate services. Talk to me to ensure that your needs will be met this semester, too.\nReading and Discussion Schedule Week 1 - Belonging Wednesday, 1/22\n Introductions, Classroom Conversations, and Mathematics Identity  Weeks 2 and 3 - Civil Rights Monday, 1/27\n Read: Andrew Hacker, Is Algebra Really Necessary?  Wednesday, 1/29- California Math and Congressional Commentary\n Read: NYT: The Algebra Problem: How Middle School Math Became a National Flashpoint Read: July 2023, Extended Congressional Comments on Math Education Read: July 2022, Congressional Comments on Math Education  Monday, 2/3 - Radical Equations\n Read: Robert P. Moses ‘56, Radical Equations, Chapters 1 and 2  Wednesday, 2/5 - Radical Equations\n Read: Robert P. Moses ‘56, Radical Equations, Chapters 3 and 4  Weeks 4, 5, and 6 - Mathematics and Policy Monday, - College Score Card\n Do: Look up Hamilton College on the College Scorecard website. What kinds of information do you find? What kinds of comparisons can you make? Read: Better\tInformation\tfor\tBetter College Choice and Institutional Performance  Wednesday - College Rankings\n Read: TBD  Monday - Mathematics of Apportionment\n Read: It\u0026rsquo;s 1789. How do you divvy up the House of Representatives?  Wednesday - Mathematics of Apportionment\n Read: U.S. Census Bureau: Congressional Apportionment  Monday - Mathematics and Voting\n Read: TBD  Weeks 6 and 7 - Algorithms Wednesday - Weapons of Math Destruction\n Read: Cathy O’Neill, Weapons of Math Destruction, Intro \u0026amp; Chapters 1, 2  Monday - Ethical Applications?\n Watch: Youtube Playlist  Wednesday - Algorithmic Impact Assessment\n Read:  Group 1. Cathy O’Neil and Hanna Gunn, “The Ethical Matrix” [Introduction, Sections 8.4-8.7] Group 2. TBD    Week 8 - Belonging Revisited Monday - Belonging Revisited\n Read: \u0026ldquo;STEM Identity Development in Latinas: The Role of Self- and Outside Recognition\u0026rdquo;[Section - Literature Review (pp. 2-3); Section - Implications for Policy and Practice (pp. 16-17)] Listen: My Favorite Theorem podcast interview with Ranthony Edmonds  Wednesday- Course Conclusions\n","date":1735707600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1735707600,"objectID":"48432d39a4af58e7227a0c4055c0d9d4","permalink":"https://crgibbons.github.io/post/syllabi/2025-math498/","publishdate":"2025-01-01T00:00:00-05:00","relpermalink":"/post/syllabi/2025-math498/","section":"post","summary":"This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine the themes of Belonging, Civil Rights, Political Districting, and Algorithms.","tags":"syllabus","title":"Math 498 (Seminar): Mathematics in Social Context, Spring 2025","type":"post"},{"authors":null,"categories":null,"content":"Revised Spring 2025\nThe word \u0026ldquo;Algebra\u0026rdquo;\u0026hellip; \u0026hellip; and its mathematical connotation stem from a 9th century Arabic treatise entitled, The Concise Book on Calculation by Restoration and Compensation, by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c=0$ for nonzero $a$, by completing the square\u0026mdash;hence \u0026ldquo;restoration\u0026rdquo; and \u0026ldquo;compensation.\u0026rdquo; This is where our journey begins. By the end of the course, we\u0026rsquo;ll have an understanding of what tools and techniques \u0026ldquo;modern\u0026rdquo; (19th and 20th century) algebra brings to bear on polynomials and their roots. This course gets more abstract as the semester progresses, so set good habits early. (See Endotes 1)\nTexts  Abstract Algebra: A Concrete Introduction, by Robert Redfield (available from the Hamilton College Bookstore; see me if you have difficulty acquiring the book) The Princeton Companion to Mathematics, edited by Bowers-Green, Leader, and Gowers (access the ebook via the Hamilton College library with your Hamilton SSO)  Schedule of Topics See the list at the end of the page for the day-to-day topics coverage.\nSkills and Practices If this course works as expected, you will become a better mathematician and a better person as a result of thinking long and hard about knotty problems; this is a skill that will serve you well in the complicated world we live in. You will, with support from your professor and your peers, develop new ways of thinking and a tolerance for being stumped.\nWriting Intensive: We will focus on writing during class, and you will have several revision opportunities on writing assignments and the writing portions of exams. The final paper in the course will allow you to tie together what you\u0026rsquo;ve learned (and what you\u0026rsquo;ve already written in earlier writing assignments) into a mathematical survey paper written for a mathematically literate audience.\nTo support your progress as a writer of mathematics, I can help you during open hours, and the QSR Center and the Writing Center both have a number of peer tutors who are familiar with mathematical proof writing and $\\LaTeX$.\nEducational Goals: This course supports several of Hamilton\u0026rsquo;s Educational Goals. Much of the Disciplinary Practice, Creativity, and Communication and Expression within mathematics comes through the process of solving a problem/proving a proposition and then writing it up. In this class, you will refine your proof writing skills and develop new mathematical prose writing skills.\nTypes of Assessments  Ready for Class (RC): Beginning of Class. We we are working toward answering one (huge!) mathematical problem; you will find it really helpful to review your notes and preview the book for these short quiz-like multiple choice assignments. I don’t reschedule these, but I do drop (at least) three low scores for everyone. For these assessments, you will need a Plickers card (distributed in class). If you lose yours, can you find a printable card here: Plickers Cards Homework (HW): Due Tuesdays at 4pm (rigid). The homework is graded by a Hamilton student and will be returned in 2-3 class periods. Because the written homework is graded by a student who is super-busy just like you, homework is due when it\u0026rsquo;s due! (Don\u0026rsquo;t @ me!) However, to help you out, I drop your lowest 2 homework scores. Midterm Exams (ME): Two 2-hour self-scheduled midterms. Before the first exam, I will post a preview that describes the kinds of questions, the point distributions, and other information that will help you study. Final Exam (FE): One 3-hour self-scheduled exam. The material on the final, though cumulative, will be weighted toward the material covered at the end of the course that was not tested on midterms. Writing Assignments (WA): Due Thursdays at 4pm (flexible). You will write up solutions to problems and responses to writing prompts roughly once a week using $\\LaTeX$ (via Overleaf with your Hamilton credentials) (sometimes solo, sometimes in partners). Each writing assignment is graded among the options E (exemplary), P (proficient), R (revisions necessary to meet expectations), and X (not enough to assess). You will have revision opportunities by invitation throughout the semester. Final Paper (FP): Due by beginning of our scheduled final exam period. This will be graded like a writing assignment; a lot of the content of this paper will come from writing assignments you\u0026rsquo;ve already completed, so think of it as a way to study for the final and get a chance to revise your writing one last time.  Grades Your base grade (A, B, C, D, or F) is calcullated by a combination of weighted average on some of your assignments (HW (25%); ME and FE (75%)) and minimum specifications on others (average RC score, scores out of $n$ total writing assignments, and score on the final paper). The following table lists minimum thresholds for each base grade. You must meet all the requirements in the row to earn that base grade. Ranges for $\\pm$ will be determined at the end of the semester at the professor’s discretion (typically $-$ will be assigned if you are close to a base grade but didn’t quite meet one of the criteria, and $+$ will be assigned for work consistently at the top of the base grade range).\n   Base Grade Ready for Class Weighted Avg of HW and Exams Writing Assignment scores Final Paper score     A 3 [90,100) $n-2$ scores of P or better and at least 3 E E   B 3 [80,90) $n-3$ scores of P or better and at least 2 E P   C 2 [70,80) $n-3$ scores of P or better P   D 1 [55,70) $n-4$ scores of P or better R   F 0 [0,55) $n$ scores of X or better X    The big picture is that, to do well in the course, you will need to demonstrate that you can do the computations well and write well at the 300-level.\nClassroom Environment The American Mathematical Society (the largest professional society for mathematicians) outlines its vision for a welcoming environment as follows:\n The AMS strives to ensure that participants in its activities enjoy a welcoming environment. In all its activities, the AMS seeks to foster an atmosphere that encourages the free expression and exchange of ideas. The AMS supports equality of opportunity and treatment for all participants, regardless of gender, gender identity or expression, race, color, national or ethnic origin, religion or religious belief, age, marital status, sexual orientation, disabilities, veteran status, or immigration status\u0026hellip;. A commitment to a welcoming environment is expected of all attendees at AMS activities, including mathematicians, students, guests, staff, contractors and exhibitors, and participants in scientific sessions and social events.\n I am committed to the same vision for our classroom environment, and I sincerely thank you for your contributions toward making our classroom (and office hours) a lively and respectful community of thinkers. Please let me know if you feel that we have strayed from this vision at any point during the semester. (See Endnotes 2)\nYour Responsibilities Accommodations, Conflicts, \u0026amp; Makeup Exams Please give me notice at least one week prior to an that you have an academic accommodation or a conflict. Since the exams in this course are self-scheduled, I hope this allows you the flexibility to plan around your other obligations, but I\u0026rsquo;m happy to work with you if you need additional flexibility.\nAttendance \u0026amp; Honor By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner\u0026rsquo;s attitude, and to encourage your fellow students to do the same. If you will miss a class, please fill out the Class Absence Request Form (link available on Blackboard). You are part of a community that believes in the power of the Honor Code to make Hamilton College a great place to be a student and a teacher. We are all bound by the responsibility to actively create and maintain a culture of learning, academic integrity, and personal honor. I do not take my responsibility lightly; nor should you! (See Endnotes 3)\nResponsible Generative AI Use You may use generative AI to help you debug $\\LaTeX$ errors or assist with tricky formatting (like diagrams or tables). The line you may not cross is this one: You may not use AI\u0026mdash;or any other resource, including calculators, people, solutions manuals, etc.\u0026mdash;to circumvent the thinking and problem-solving you are doing in order to learn the course material. Any resource that you do use should be cited (format is not terribly important in this class), and if you do use generative AI, you should (a) look for an opensource model and (b) digitally document and submit the prompts and responses from your session. Here\u0026rsquo;s an example of an open source AI assistant that\u0026rsquo;s fair game for LaTeX help: Natural Language to LaTeX.\nGetting Stuck Being stumped is part of learning mathematics, so please attempt to solve homework problems on your own before asking for help on them. Collaboration on the homework is encouraged as long as you are collaborating with your peers currently enrolled in any section of Math 325. However, make sure to write up your final drafts separately to ensure that you have each fully understood the answer(s). Similarly, even though you will be assigned a writing partner for the writing assignments, it is your responsibility to make sure you understand and approve of all the mathematics your team turns in. (See Endnotes 4)\nIMPORTANT! If in doubt, check with me before using resources other than your classmates, tutors at the QSR or Writing Centers, or online $\\LaTeX$ help. For example, check with me before asking other professors, students not currently enrolled in Math 325, the internet, a magic eight ball, the ghost of Gauss, etc! Mathematical plagiarism is a subtle business, and it\u0026rsquo;s easy to accidentally plagiarize by copying a solution you\u0026rsquo;ve read somewhere else. (See Endnotes 5)\nEndnotes  The Oxford English Dictionary, retrieved 01/30/2021. AMS Policy on a Welcoming Environment, retrieve 01/30/2021. If you wantonly skip class, aside from missing out on the learning community within the walls of our classroom, you\u0026rsquo;ll penalize yourself by getting lower homework and test scores than you otherwise would. And anyway, I do notice if you\u0026rsquo;re not in class. Honor Code issues aside, you\u0026rsquo;re doing your education a disservice if you turn in work you have not personally thought through carefully. Plus, some Writing Assignment problems will reappear on exams or on the final paper. Seriously, though: you can\u0026rsquo;t \u0026ldquo;unsee\u0026rdquo; someone else\u0026rsquo;s solution. There are deep and interesting ethical conundra lurking here; Googling unwisely (or at all) may lead you down a path you didn\u0026rsquo;t intend to low.  Spring 2025 Tentative Schedule of Topics (may be revised as we go) Spring Modern Topics Schedule 2025 Professor Gibbons will be out of town on days marked with * and will provide instructions for those class periods (some will be synchronous on Zoom, some will be asynchronous videos).\nMIDTERM EXAM 1 covers material from chapters 1-8. MIDTERM EXAM 2 coaver material from chapters 9-18. FINAL EXAM covers material from chapters 19-28.\n   Dates Week Monday Tuesday Wednesday Thursday Friday     01/20/2025 1 MLK Jr. Day math autobio due Intro, Chapter 1 (Well-Ordering, Division Algorithm) WA 0 due Chapter 1 (GCD, FTA)   01/27/2025 2 Chapter 1 (Induction) HW 1 due Chapter 3 (Complex Numbers) WA 1 due Chapter 3 (Complex Numbers)   02/03/2025 3 Chapter 4 (Modular Arithmetic) HW 2 due LaTeX, catch-up WA 2 due Chapter 4 (Zero Divisors, Quats)   02/10/2025 4 Chapter 5 (Fields) HW 3 due Chapter 5 (Subfields) WA 3 due Chapter 6 (Solvability by Radicals)   02/17/2025 5 Chapter 6 (Solvability by Radicals) HW 4 due Chapter 7 (Rings) WA 4 due Chapter 7 (Rings)   02/24/2025 6 Chapter 7 (Rings)* HW 5 due Chapter 8 (Polynomial Rings) WA 5 due Chapter 8 (Polynomial Rings)   03/03/2025 7 Chapter 9 (PIDs)* HW 6 due Chapter 9 (PIDs)* EXAM 1 (Ch 1-8) Ring Homomorphisms   03/10/2025 8 Chapter 10 (Algebraic Elements) HW 7 due Chapter 10 (Algebraic Elements) Final Paper Early Draft due Chapter 11 (Irreducibility)   03/17/2025 — Spring Break — — — —   03/31/2025 9 Chapter 12 (Extension Fields as Vector Spaces) HW 7 due Chapter 13 (Auts of Fields) WA 6 due Chapter 14 (Counting Auts)   04/07/2025 10 Chapter 15 (Groups) WELLNESS DAY (no HW due) Chapter 15 (Groups) WA 7 due Chapter 16 (Permutation Groups)   04/14/2025 11 Chapter 17 (Group Homomorphisms) HW 8 due Chapter 18 (Subgroups)* WA 8 due Chapter 19 (Generators)*   04/21/2025 12 Chapter 20 (Cosets) HW 9 due Chapter 21 (Lagrange) EXAM 2 (Ch 9-18) Chapter 23 (Normal Subgroups)   04/28/2025 13 Chapter 23 (Quotient Groups) HW 10 due Chapter 25 (Galois Revisited) WA 9 due Chapter 26 (Solvable Groups)   05/05/2025 14 Chapter 26 (Solvable Groups) HW 11 due Chapter 27-28 WA 10 due Catch up/Review*   05/12/2025 15 Catch up/Review C\u0026amp;C Day — — FINAL EXAM (Ch 19-28) and Final Paper due    ","date":1735707600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1735707600,"objectID":"e9a2f06508a1d685e0bb665c8e37ad4b","permalink":"https://crgibbons.github.io/post/syllabi/2025s-math325/","publishdate":"2025-01-01T00:00:00-05:00","relpermalink":"/post/syllabi/2025s-math325/","section":"post","summary":"The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we'll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.","tags":"syllabus","title":"Math 325 (Writing Intensive): Modern Algebra, Spring 2025","type":"post"},{"authors":null,"categories":null,"content":"Revised Spring 2025\nPolls and Forms  Plickers: Get Plickers Do you like to include polls or quizzes in class? If you want to be able to poll students without requiring them to use a smart device, try Plickers (\u0026ldquo;Paper Clickers\u0026rdquo;). You can set it up so that students can use an app to take the poll/quiz, but the beauty is that each student can use a paper QR code to respond. No gadgets necessary! Google Forms:   Mathematical Autobiography: I use this to get to know students early in the semester. You can see one here to see the questions I use (and fill it out if you feel inspired!).    Course Materials   Linear Algebra: I teach linear algebra as an intro-to-proofs course, and over the years I\u0026rsquo;ve created some materials to use alongside different books.\n Logic textbooklet: Logic for Linear Algebraists: 150 minutes of logic for proof writing. This is the first \u0026ldquo;stable\u0026rdquo; version, but I will continue to add materials to it over time. You can also fork it on github: github.com/crgibbons/LogicForLinearAlgebra Standards: (coming soon!)    Modern Algebra: For the first semester of abstract algebra, I use Galois Theory (a very light touch version!) as a motivating story to introduce rings, fields, and groups (in roughly that order).\n Textbook (in progress): (link coming soon!) Animations: (links coming soon!) 2020-2022 Covid Era Videos, badly organized on YouTube: (links coming soon)    Math in Social Context:\n Syllabi: Materials: Lesson Plans:    Applied Math Sampler with a focus on Social, Structural, and Institutional Hierarchies\n Syllabus: Materials:    Mathematical Writing Guides Many of my courses are considered Writing Intensive, which means there is an emphasis on writing instruction.\n(links eventually)\n","date":1735707600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1735707600,"objectID":"f7371ad9522a701d7505e6d92a3dabcc","permalink":"https://crgibbons.github.io/post/syllabi/resources-for-instructors/","publishdate":"2025-01-01T00:00:00-05:00","relpermalink":"/post/syllabi/resources-for-instructors/","section":"post","summary":"These are resources I've created or used (and endorse), available for instructors.","tags":"resources","title":"Resources for Instructors","type":"post"},{"authors":null,"categories":null,"content":"","date":1731097800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1731097800,"objectID":"48aaf69010d81a95c23c03bc7fbcae9a","permalink":"https://crgibbons.github.io/talk/2024-su/","publishdate":"2024-11-08T15:30:00-05:00","relpermalink":"/talk/2024-su/","section":"talk","summary":"In this talk, I will present some results that the late Nick Baeth and I proved about tensor products of [your favorite adjective here] semigroups. I will also outline Nick's grand vision and our intended future directions for those interested in carrying on in Nick's footsteps. Our journey start with the results on tensor products due to Fulp, Grillet, and Head from the 1960s (groovy!) and maybe ends with... you?!","tags":null,"title":"Toward understanding semigroup properties under the tensor product(s)","type":"talk"},{"authors":null,"categories":null,"content":"Revised Fall 2024 (updates still coming)\nThe word \u0026ldquo;Algebra\u0026rdquo;\u0026hellip; \u0026hellip; and its mathematical connotation stem from a 9th century Arabic treatise entitled, The Concise Book on Calculation by Restoration and Compensation, by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c=0$ for nonzero $a$, by completing the square\u0026mdash;hence \u0026ldquo;restoration\u0026rdquo; and \u0026ldquo;compensation.\u0026rdquo; This is where our journey begins. By the end of the course, we\u0026rsquo;ll have an understanding of what tools and techniques \u0026ldquo;modern\u0026rdquo; (19th and 20th century) algebra brings to bear on polynomials and their roots. This course gets more abstract as the semester progresses, so set good habits early. (See Endotes 1)\nTexts  Abstract Algebra: A Concrete Introduction, by Robert Redfield (available from the Hamilton College Bookstore; see me if you have difficulty acquiring the book) The Princeton Companion to Mathematics, edited by Bowers-Green, Leader, and Gowers (access the ebook via the Hamilton College library with your Hamilton SSO)  Schedule of Topics See the Topics Schedule Table (tentative; still being updated!) or the list at the end of the page for the day-to-day topics coverage.\nSkills and Practices Writing Intensive: We will focus on writing during class, and you will have several revision opportunities on writing assignments and the writing portions of exams. The final paper in the course will allow you to tie together what you\u0026rsquo;ve learned (and what you\u0026rsquo;ve already written in earlier writing assignments) into a mathematical survey paper written for a mathematically literate audience.\nTo support your progress as a writer of mathematics, I can help you during open hours, and the QSR Center and the Writing Center both have a number of peer tutors who are familiar with mathematical proof writing and $\\LaTeX$.\nEducational Goals: This course supports several of Hamilton\u0026rsquo;s Educational Goals. Much of the Disciplinary Practice, Creativity, and Communication and Expression within mathematics comes through the process of solving a problem/proving a proposition and then writing it up. In this class, you will refine your proof writing skills and develop new mathematical prose writing skills.\nTypes of Assessments  Ready for Class (RC): Beginning of Class. We we are working toward answering one (huge!) mathematical problem; you will find it really helpful to review your notes and preview the book for these short quiz-like multiple choice assignments. I don’t reschedule these, but I do drop (at least) three low scores for everyone. For these assessments, you will need a Plickers card (distributed in class). If you lose yours, can you find a printable card here: Plickers Cards Homework (HW): Due Tuesdays at 4pm (rigid). The homework is graded by a Hamilton student and will be returned in 2-3 class periods. Because the written homework is graded by a student who is super-busy just like you, homework is due when it\u0026rsquo;s due! (Don\u0026rsquo;t @ me!) However, to help you out, I drop your lowest 2 homework scores. Midterm Exams (ME): Two 2-hour self-scheduled midterms. Before the first exam, I will post a preview that describes the kinds of questions, the point distributions, and other information that will help you study. Final Exam (FE): One 3-hour cumulative self-scheduled exam. The material on the final, though cumulative, will be weighted toward the material covered at the end of the course that was not tested on midterms. Writing Assignments (WA): Due Thursdays at 4pm (flexible). You will write up solutions to problems and responses to writing prompts roughly once a week using $\\LaTeX$ (via Overleaf with your Hamilton credentials) (sometimes solo, sometimes in partners). Each writing assignment is graded among the options E (exemplary), M (masterful), R (revisions necessary to meet expectations), and X (not enough to assess). You will have revision opportunities by invitation throughout the semester. Final Paper (FP): Due by beginning of our scheduled final exam period. This will be graded like a writing assignment; a lot of the content of this paper will come from writing assignments you\u0026rsquo;ve already completed, so think of it as a way to study for the final and get a chance to revise your writing one last time.  Grades Your base grade (A, B, C, D, or F) is calcullated by a combination of weighted average on some of your assignments (HW (25%); ME and FE (75%)) and minimum specifications on others (average RC score, scores out of $n$ total writing assignments, and score on the final paper). The following table lists minimum thresholds for each base grade. You must meet all the requirements in the row to earn that base grade. Ranges for $\\pm$ will be determined at the end of the semester at the professor’s discretion (typically $-$ will be assigned if you are close to a base grade but didn’t quite meet one of the criteria, and $+$ will be assigned for work consistently at the top of the base grade range).\n   Base Grade Ready for Class Weighted Avg of HW and Exams Writing Assignment scores Final Paper score     A 3 [90,100) $n-2$ scores of E E   B 3 [80,90) $n-3$ scores of E M   C 2 [70,80) $n-2$ scores of M or better M   D 1 [55,70) $n-4$ scores of M or better R   F 0 [0,55) $n$ scores of X or better X    The big picture is that, to do well in the course, you will need to demonstrate that you can do the computations well and write well at the 300-level. Throughout the semester you will have opportunities to revise your writing (and potentially receive a new score on an assignment) by responding to professor feedback.\nClassroom Environment The American Mathematical Society (the largest professional society for mathematicians) outlines its vision for a welcoming environment as follows:\n The AMS strives to ensure that participants in its activities enjoy a welcoming environment. In all its activities, the AMS seeks to foster an atmosphere that encourages the free expression and exchange of ideas. The AMS supports equality of opportunity and treatment for all participants, regardless of gender, gender identity or expression, race, color, national or ethnic origin, religion or religious belief, age, marital status, sexual orientation, disabilities, veteran status, or immigration status\u0026hellip;. A commitment to a welcoming environment is expected of all attendees at AMS activities, including mathematicians, students, guests, staff, contractors and exhibitors, and participants in scientific sessions and social events.\n I am committed to the same vision for our classroom environment, and I sincerely thank you for your contributions toward making our classroom (and office hours) a lively and respectful community of thinkers. Please let me know if you feel that we have strayed from this vision at any point during the semester. (See Endnotes 2)\nYour Responsibilities Accommodations, Conflicts, \u0026amp; Makeup Exams Please give me notice at least one week prior to an that you have an academic accommodation or a conflict. Since the exams in this course are self-scheduled, I hope this allows you the flexibility to plan around your other obligations, but I\u0026rsquo;m happy to work with you if you need additional flexibility.\nAttendance \u0026amp; Honor By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner\u0026rsquo;s attitude, and to encourage your fellow students to do the same. If you need to miss a class, please fill out the Class Absence Request Form (link available on Blackboard). You are part of a community that believes in the power of the Honor Code to make Hamilton College a great place to be a student and a teacher. We are all bound by the responsibility to actively create and maintain a culture of learning, academic integrity, and personal honor. I do not take my responsibility lightly; nor should you! (See Endnotes 3)\nGetting Stuck Being stumped is part of learning mathematics, so please attempt to solve homework problems on your own before asking for help on them. Collaboration on the homework is encouraged as long as you are collaborating with your peers currently enrolled in any section of Math 325. However, make sure to write up your final drafts separately to ensure that you have each fully understood the answer(s). Similarly, even though you will be assigned a writing partner for the writing assignments, it is your responsibility to make sure you understand and approve of all the mathematics your team turns in. (See Endnotes 4)\nIMPORTANT! Please check with me before using resources other than your classmates, tutors at the QSR or Writing Centers, or online $\\LaTeX$ help. For example, check with me before asking other professors, students not currently enrolled in Math 325, the internet, a magic eight ball, the ghost of Gauss, etc! Mathematical plagiarism is a subtle business, and it\u0026rsquo;s easy to accidentally plagiarize by copying a solution you\u0026rsquo;ve read somewhere else. (See Endnotes 5)\nEndnotes  The Oxford English Dictionary, retrieved 01/30/2021. AMS Policy on a Welcoming Environment, retrieve 01/30/2021. If you wantonly skip class, aside from missing out on the learning community within the walls of our classroom, you\u0026rsquo;ll penalize yourself by getting lower homework and test scores than you otherwise would. And anyway, I do notice if you\u0026rsquo;re not in class. Honor Code issues aside, you\u0026rsquo;re doing your education a disservice if you turn in work you have not personally thought through carefully. Plus, some Writing Assignment problems will reappear on exams or on the final paper. Seriously, though: you can\u0026rsquo;t \u0026ldquo;unsee\u0026rdquo; someone else\u0026rsquo;s solution. There are deep and interesting ethical conundra lurking here; Googling unwisely (or at all) may lead you down a path you didn\u0026rsquo;t intend to low.  Fall 2024 Schedule of Topics (may be revised)    Monday Tuesday Wednesday Thursday Friday         8/30       Introductions The Quadratic Formula   9/2 9/3 9/4 9/5 9/6   Chapter 1 (Divisibility) HW 1 due Chapter 1 (FTa, Induction) WA 1 due Chapter 3 (Complex Nums)   9/9 9/10 9/11 9/12 9/13   Chapter 3 (Complex Nums) HW 2 due LaTeX Day WA 2 due Chapter 4 (Modulo N)   9/16 9/17 9/18 9/19 9/20   Chapter 4 (Zero Divs, Quats) HW 3 due Chapter 5 (Fields \u0026amp; Subfields) WA 3 due Chapter 5/6 (Solv by Rads)   9/23 9/24 9/25 9/26 9/27   Chapter 6 (Solvable by Rads) HW 4 due Chapter 7 (Rings) WA 4 due Chapter 7 (Rings)   9/30 10/1 10/2 10/3 10/4   Chapter 7/8 (Poly. Rings) HW 5 due Chapter 8 (Polynomial Rings) WA Rewrite due Chapter 9 (PIDs)   10/7 10/8 10/9 10/10 10/11   Chapter 9 (PIDs) HW 6 due Ring Homomorphisms Midterm 1 (self-scheduled) Chapter 11 (Irreducibility)   10/14 10/15 10/16 10/17 10/18   Chapter 10 (Algebraic Elts) HW 7 due Chapter 10 (Algebraic Elts) WA 5 due No Class   10/21 10/22 10/23 10/24 10/25   Chapter 12 (Fields as VS) HW 8 due Chapter 13 (Auts of Fields) WA 6 due Chapter 14 (Counting Auts)   10/28 10/29 10/30 10/31 11/1   Chapter 15 (Groups) HW 9 due Chapter 15 (Groups) WA 7 due Chapter 16 (Permutations)   11/4 11/5 11/6 11/7 11/8   Chapter 17 (Group Homoms) HW 10 due Chapter 18 (Subgroups) Midterm 2 (self-scheduled) Chapter 19 (Generators)   11/11 11/12 11/13 11/14 11/15   Chapter 20 (Cosets) HW 11 due Chapter 21 (Lagrange) WA 8 due Chapter 23 (Normal Sgps)   11/18 11/19 11/20 11/21 11/22   Chapter 23 (Quotient Gps) HW 12 due Chapter 25 (Galois again) WA 9 due No Class   11/25 11/26 11/27 11/28 11/29   No Class  No Class Thanksgiving No Class   12/2 12/3 12/4 12/5 12/6   Chapter 26 (Solvable Gps) HW 13 due Chapter 26 (Commutators) WA 10 due Chapter 26 (Commutators)   12/9 12/10 12/11 12/12 12/13   Chapters 27-28 (Putting it Together) HW 14 due Catch-up/Review WA 11 due Catch-up/Review    ","date":1722484800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1722484800,"objectID":"3fa0f0ee2d31a9c1cb95c2b11bad6456","permalink":"https://crgibbons.github.io/post/syllabi/2024f-math325/","publishdate":"2024-08-01T00:00:00-04:00","relpermalink":"/post/syllabi/2024f-math325/","section":"post","summary":"The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we'll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.","tags":"syllabus","title":"Math 325 (Writing Intensive): Modern Algebra","type":"post"},{"authors":null,"categories":null,"content":"Revised Fall 2024\n\u0026ldquo;Number Theorists are like lotus eaters - having tasted this food they can never give it up.\u0026rdquo; -Leopold Kronecker \u0026ldquo;What\u0026rsquo;s up with prime numbers?\u0026rdquo; is our motivating question for a lot of this course. \u0026ldquo;How can we use that cool property of prime numbers?\u0026rdquo; is our motivating question for most of the rest. Number theory begins with the integers and the relationships (and remainders) that come from trying to divide one integer into another or find integer solutions to polynomial equations (like $x^3 + y^3 + z^3 = 42$). Although some original numberphiles celebrated number theory\u0026rsquo;s purity (read: its lack of applications to the \u0026ldquo;real world\u0026rdquo;), they\u0026rsquo;d be annoyed to know that we now use their results to accomplish many practical ends, like sending information via secure webpages, listening to scratched CDs, and speed-testing computers. This course will focus on the fundamental results in the field and their applications (especially to cryptography and cryptanalysis). Expect distinguished visitors from different schools and sectors to give short guest presentations in class. (See Endnotes 1)\nTexts   Number Theory Through Inquiry, by David C. Marshall, Edward Odell, and Michael Starbird (available from the Hamilton College Bookstore; see me if you have difficulty acquiring the book) The Princeton Companion to Mathematics, edited by Bowers-Green, Leader, and Gowers (access the ebook via the Hamilton College library with your Hamilton SSO)  Schedule of Topics Students will be (collectively) responsible for preparing, presenting, and recording solutions to almost every problem in Chapters 1-6. This makes it difficult to predict exactly when each topic will be covered, but we\u0026rsquo;ll start by assuming the following breakdown (roughly) and adapting as necessary:\n First third of the semester: Chapters 1-3; Middle third of the semester: Chapters 4-6; Remaining third of the semester: Choose Your Own Adventure (see below) In defiance of linear time: We will also cover some basic principles of cryptography and cryptanalysis \u0026ldquo;between\u0026rdquo; the first and second thirds of the semester.  Skills and Practices Speaking Intensive: This class will help you develop your ability to communicate mathematics orally in both formal and informal settings, and you will have several assessments to help you keep track of your progress: two oral midterms of very different natures along with assessments of your class presentations. To support your progress as an oral communicator of mathematics, I can help you during open hours and the QSR Center and the Oral Communication Center both have peer tutors who are familiar with mathematical presentations.\nEducational Goals: This course supports several of Hamilton\u0026rsquo;s Educational Goals. Much of the Disciplinary Practice, Creativity, and Communication and Expression within mathematics comes through the process of solving a problem or proving a proposition and communicating it to others. In this class, you will put your proof writing skills to work and develop new mathematical speaking skills.\nActive Learning: At first, you might feel a little uncomfortable if you are used to lecture-based classes, but there\u0026rsquo;s good news! A Harvard study in the Proceedings of the National Academy of Sciences recently demonstrated that students learn more in active learning classes: \u0026ldquo;[T]hough students felt as if they learned more through traditional lectures, they actually learned more when taking part in classrooms that employed so-called active-learning strategies.\u0026rdquo;\nTypes of Assessments  Active Attendance and Participation (AAP): Every Class. (10%) Get ready to work like a mathematician in this class. No more lectures! This class is active learning all-the-way, which means your attendance is critical for its success. You and your classmates will work together and uncover the major results through activities, groupwork, and good, old-fashioned hard work. Class Participation (CP): Frequently. (10%) Everyone will present often. Your CP grade will include your presentations and also your active participation in the discussion following (and sometimes during) others\u0026rsquo; presentations. Want help? Visit the Oral Communication Center to practice presenting. Oral Midterm Exam (OME): 30 minutes. (20%) We will use a random number generator (like a 10-sided die) to select from a list of pre-selected midterm problems, and you will present the selected problem to me in my office at the blackboard. I will follow up with some questions. Oral Midterm Conversation (OMC): 30 minutes. (20%) You will explain an application of Number Theory to a non-specialist during this exam. Details will be posted on Blackboard. Midterm Skills Exam (MSE): 1 hour. (15%) This short problem set will test your computational skills. Provided the Honor Code is working for our class, you will be able to self-schedule this exam. Choose Your Own Adventure (CYOA): (25%) Team-based self-guided inquiry on a number theoretic topic of your choosing. A menu of options is available, but you can also pitch your own topic. As part of this assignment, you will write a short chapter on the topic in the collaborative course notes (including homework problems and solutions).  Grades    A+ A A- B+ B B- C+ C C- D+ D D-     98% 94% 90% 87% 84% 80% 77% 73% 70% 66% 62% 60%    Classroom Environment The American Mathematical Society (the largest professional society for mathematicians) outlines its vision for a welcoming environment as follows:\n The AMS strives to ensure that participants in its activities enjoy a welcoming environment. In all its activities, the AMS seeks to foster an atmosphere that encourages the free expression and exchange of ideas. The AMS supports equality of opportunity and treatment for all participants, regardless of gender, gender identity or expression, race, color, national or ethnic origin, religion or religious belief, age, marital status, sexual orientation, disabilities, veteran status, or immigration status\u0026hellip;. A commitment to a welcoming environment is expected of all attendees at AMS activities, including mathematicians, students, guests, staff, contractors and exhibitors, and participants in scientific sessions and social events.\n I am committed to the same vision for our classroom environment, and I sincerely thank you for your contributions toward making our classroom (and office hours) a lively and respectful community of thinkers. Please let me know if you feel that we have strayed from this vision at any point during the semester. (See Endnotes 2)\nYour Responsibilities Accommodations, Conflicts, \u0026amp; Makeup Exams. Please give me notice at least one week prior to an that you have an academic accommodation or a conflict. Since the exams in this course are self-scheduled, I hope this allows you the flexibility to plan around your other obligations, but I\u0026rsquo;m happy to work with you if you need additional flexibility.\nAttendance \u0026amp; Honor. By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner\u0026rsquo;s attitude, and to encourage your fellow students to do the same. If you need to miss a class, please fill out the Class Absence Request Form (link available on Blackboard). You are part of a community that believes in the power of the Honor Code to make Hamilton College a great place to be a student and a teacher. We are all bound by the responsibility to actively create and maintain a culture of learning, academic integrity, and personal honor. I do not take my responsibility lightly; nor should you! (See Endnotes 3)\nGetting Stuck. Being stumped is part of learning mathematics, so please attempt to solve problems on your own before asking for help on them. Collaboration on problem sets is encouraged as long as you are collaborating with your peers currently enrolled in any section of Math 512. However, make sure to write up your final drafts separately to ensure that you have each fully understood the answer(s). Similarly, even though you may submit joint assignments, it is your responsibility to make sure you understand and approve of all the mathematics your team turns in. (See Endnotes 4)\nIMPORTANT! Please check with me before using resources other than your classmates, tutors at the Academic Resource Centers, or online $\\LaTeX$ help. For example, check with me before asking other professors, students not currently enrolled in Math 325, the internet, a magic eight ball, the ghost of Gauss, etc! Mathematical plagiarism is a subtle business, and it\u0026rsquo;s easy to accidentally plagiarize by copying a solution you\u0026rsquo;ve read somewhere else. If you use external resources on an assignment that allows them, you must use an open source resource (no Chegg, Math Stack Exchange, or ChatGPT!), you must disclose that you used it, and in the case of generative AI you must share your prompt or sequence of prompts. (See Endnotes 5)\nEndnotes  The Oxford English Dictionary, retrieved 08/19/2024. AMS Policy on a Welcoming Environment, retrieved 08/19/2024. If you wantonly skip class, aside from missing out on the learning community within the walls of our classroom, you\u0026rsquo;ll penalize yourself by getting lower homework and test scores than you otherwise would. And anyway, I do notice if you\u0026rsquo;re not in class. Honor Code issues aside, you\u0026rsquo;re doing your education a disservice if you turn in work you have not personally thought through carefully. Plus, some problems will reappear on exams. Seriously, though: you can\u0026rsquo;t \u0026ldquo;unsee\u0026rdquo; someone else\u0026rsquo;s solution. There are deep and interesting ethical conundra lurking here; Googling or GPTing unwisely (or at all) may lead you down a path you didn\u0026rsquo;t intend to follow.  ","date":1722484800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1722484800,"objectID":"f61fb0fa2067732e27ea84130f789a60","permalink":"https://crgibbons.github.io/post/syllabi/2024-math512/","publishdate":"2024-08-01T00:00:00-04:00","relpermalink":"/post/syllabi/2024-math512/","section":"post","summary":"Number Theory is the study of the properties of the positive integers. Topics include divisibility, congruences, quadratic reciprocity, numerical functions, Diophantine equations, continued fractions, distribution of primes. Applications will include cryptography - the practice of encrypting and decrypting message, and cryptanalysis - the practice of developing secure encryption and decryption protocols and probing them for possible flaws. Students will also explore topics of interest independently.","tags":"syllabus","title":"Math 512: Number Theory, Fall 2024","type":"post"},{"authors":null,"categories":null,"content":"","date":1680377400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1680377400,"objectID":"498bdfbe3375384c053ae387c96dc799","permalink":"https://crgibbons.github.io/talk/2023-gmu/","publishdate":"2023-04-01T15:30:00-04:00","relpermalink":"/talk/2023-gmu/","section":"talk","summary":"In this talk, we take a problem in commutative algebra (identifying an object called a nearly complete intersection ideal) and build on the well-established theory of edge ideals to come up with a graph theoretic condition to solve the problem. This sounds dry, but the talk will be full of pictures and intuition (and maybe even a short proof!) to introduce the audience to the big new idea and how it works. Please bring scratch paper, a sense of mathematical adventure, and a willingness to ask lots of questions. These results were obtained by my team of then-undergraduates (Chiara Bondi, Yuye Ke, Spencer Martin, Shrunal Pothagoni, and Ada Stelzer) during Clemson's COURAGE REU in the summer of 2020. Interested parties can find the [paper on the arXiv](https://arxiv.org/abs/2101.08401) and in Springer's Association for Women in Mathematics Series, vol 29.","tags":null,"title":"Hypergraphs Applied to Commutative Algebra, or, why prove theorems when you can draw pictures?","type":"talk"},{"authors":null,"categories":null,"content":"From the brief description:\n Woodbridge native and Hamilton College math professor Courtney Gibbons was recently selected as a Science and Technology Policy Fellow serving the U.S. Congress. Read more\n ","date":1669266000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1669266000,"objectID":"03e829cbaa04c578bc3590279c48247b","permalink":"https://crgibbons.github.io/post/inthemedia/newhavenregister/","publishdate":"2022-11-24T00:00:00-05:00","relpermalink":"/post/inthemedia/newhavenregister/","section":"post","summary":"Woodbridge native and Hamilton College math professor Courtney Gibbons was recently selected as a Science and Technology Policy Fellow serving the U.S. Congress. [Read more](https://www.nhregister.com/news/article/Woodbridge-native-math-professor-policy-congress-17604180.php).","tags":"in the media","title":"Woodbridge native, math prof brings policy passion to Congress","type":"post"},{"authors":["Chiara Bondi","Courtney Gibbons","Yuye Ke","Spencer Martin","Shrunal Pothagoni","Ada Stelzer"],"categories":null,"content":"","date":1647230400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1647230400,"objectID":"27cb8da7cc3ecf56cea73bc46a2eee92","permalink":"https://crgibbons.github.io/publication/g-reu-2020/g-reu-2020/","publishdate":"2022-03-14T00:00:00-04:00","relpermalink":"/publication/g-reu-2020/g-reu-2020/","section":"publication","summary":"Recently, nearly complete intersection ideals were defined by Boocher and Seiner to establish lower bounds on Betti numbers for monomial ideals (arXiv:1706.09866). Stone and Miller then characterized nearly complete intersections using the theory of edge ideals (arXiv:2101.07901). We extend their work to fully characterize nearly complete intersections of arbitrary generating degrees and use this characterization to compute minimal free resolutions of nearly complete intersections from their degree 2 part.","tags":["Nearly Complete Intersections"],"title":"A hypergraph characterization of nearly complete intersections","type":"publication"},{"authors":null,"categories":null,"content":"From the episode description:\n On this episode of My Favorite Theorem, we were delighted to talk with Courtney Gibbons, a mathematician at Hamilton College, about Emmy Noether\u0026rsquo;s isomorphism theorems. Episode 73\n ","date":1642050000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1642050000,"objectID":"fbd48f21cd36f8f9080b320d0e84534d","permalink":"https://crgibbons.github.io/post/inthemedia/myfavthmep73/","publishdate":"2022-01-13T00:00:00-05:00","relpermalink":"/post/inthemedia/myfavthmep73/","section":"post","summary":"On this episode of My Favorite Theorem, we were delighted to talk with Courtney Gibbons, a mathematician at Hamilton College, about Emmy Noether's isomorphism theorems. Listen to [Episode 73](https://kpknudson.com/my-favorite-theorem/2022/1/13/episode-73-courtney-gibbons)!","tags":"in the media","title":"My Favorite Theorem: Episode 73","type":"post"},{"authors":null,"categories":null,"content":"Revised Spring 2022\nThe Big Picture This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine several big themes:\n Belonging – what is “mathematical identity” and where does it come from? Civil Rights – can mathematical literacy be viewed as a tool for advancing equity? Political Districting – how does mathematics help us understand gerrymandering? Algorithms – in what ways do algorithms contribute to or fight against social stratification?  Educational Goals In addition to satisfying the Social, Structural, and Institutional Hierarchies (SSIH) requirement for the concentration in Mathematics and Statistics, this course addresses the following Educational Goals.\n Intellectual Curiosity and Flexibility – examining fact, phenomena, and issues in-depth, and from a variety of perspectives, and having the courage to revise beliefs and outlooks in light of new evidence Understanding of Cultural Diversity – critically engaging with multiple cultural traditions and perspectives Ethical, Informed, and Engaged Citizenship – developing an awareness of the challenges and responsibilities of local, national, and global citizenship Communication and Expression – expressing oneself with clarity and eloquence, in both traditional and contemporary media, through writing and speaking  Expectations and Assignments To dig deeply into the main themes of the course, you will need to prepare in advance for each class, actively participate, and complete all of the assignments. This is reflected in the final grade composition:\n Blog Posts: 40% Participation: 30% Final Poster: 30%  Pre-Class Tasks (Reading, Watching, or Listening) Complete the relevant task (reading, watching, or listening) assigned for each class, think about it carefully, and outline some thoughts to share in our class discussion. The list of tasks can be found on the last page of this document and may be updated (in a timely manner!) as the semester progresses.\nAttendance Your attendance and active participation is really important to the stability and success of our learning community! If you need to miss more classes, please fill out the Absence Request Form in advance (link available on Blackboard). Every student may miss one class; if you need to miss more than that, we need to talk. Undiscussed absences (besides the first freebie) will lower your participation grade.\nBlog Posts Our course blog is a (class-only) space for you to engage critically with the course materials. Writing the blog posts will help you and your classmates initiate and inform class discussions. They will also give you the opportunity to practice skills directly related to effective writing, such as conciseness, clarity, and vividness. You will contribute an original blog post five (5) times throughout the semester according to the schedule posted on Blackboard.\nEach blog post should:\n identify a specific concept/idea/argument from the assigned task (with reference); either demonstrate understanding of the concept at issue and express agreement or disagreement, giving reasons, OR connect it to previous ideas/discussions, or to contemporary issues, OR introduce an example/counter-example not explored in the text; be more than be simply a summary or an unsupported opinion (“I liked this reading”); end with a potential question or topic for class discussion, related to your post.  Each blog post should be between 150 and 250 words. You must post your contribution by 7pm the day before our class meeting. I will grade each post according to the rubric posted on Blackboard.\nFinal Poster As a capstone assignment, you will create a poster to explore a topic of your choice. This poster will be due after spring break, and we will convene for one more class session to present the class posters to the Math and Stats department. You must submit a brief outline (bullet points are fine) of the content of your poster by the last day of the course. A pdf of your final poster is the third Tuesday after spring break, and you should submit your request to print the poster to LITS on this date as well. The poster should be well organized with clear exposition and proper citations. Please see https://libguides.hamilton.edu/c.php?g=749942\u0026amp;p=5370642 for more information about the technical aspects of creating a poster.\nRequired Books Robert P. Moses ‘56, Radical Equations: Civil Rights from Mississippi to the Algebra Project (Beacon Press, 2001) NOTE: ebook available with Hamilton College login https://hamilton.primo.exlibrisgroup.com/permalink/01HAMILTON_INST/15ojthq/alma9917657883304131\nHonor Code Your blog posts and final poster must consist primarily of your own individual work and include citations for works that you are responding to or works that informed your thinking (this includes formal works, websites, videos, or other sources). You and I are also bound by the Hamilton Honor Code to report instances of plagiarism or other academic dishonesty that we become aware of.\nAccessibility Students who require academic accommodations should contact the Dean of Students Office to coordinate services. Talk to me to ensure that your needs will be met this semester, too.\nReading and Discussion Schedule Week 1 - Belonging Thursday\n Introductions, Classroom Conversations, and Mathematics Identity  Weeks 2 and 3 - Civil Rights Tuesday\n Read: Andrew Hacker, Is Algebra Really Necessary?  Thursday - Radical Equations\n Read: Robert P. Moses ‘56, Radical Equations, Chapters 1 and 2  Tuesday - Radical Equations\n Read: Robert P. Moses ‘56, Radical Equations, Chapters 3 and 4  Thursday - College Rankings\n Read: TBD  Weeks 4, 5, and 6 - Political Districting Tuesday - Gerrymandering Overview\n Read: David Wasserman, “Hating Gerrymandering is Easy: Fixing it is Harder” FiveThirtyEight, The Gerrymandering Project Read: Nick Corasanti et al., “How Maps Reshape American Politics”  Thursday - Efficiency Gap\n Read: Mira Bernstein and Moon Duchin, A Formula Goes to Court: Partisan Gerrymandering and the Efficiency Gap  Tuesday - Monte Carlo Markov Chains\n Read: TBD  Thursday- Supreme Court\n Read: Chief Justice John Roberts and Justice Elena Kagan, Opinion and Dissent in Gerrymandering Case, June 27, 2019 This document is 72 pages long; allow 2 - 3 hours reading time.  Tuesday, Trial by Mathematics\n Read: Laurence Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process  Weeks 6 and 7 - Algorithms Thursday - Weapons of Math Destruction\n Read: Cathy O’Neill, Weapons of Math Destruction, Intro \u0026amp; Chapters 1, 2  Tuesday - Ethical Applications?\n Watch: Youtube Playlist  Thursday - The Ethics Matrix\n Read: Cathy O’Neil and Hanna Gunn, “The Ethical Matrix” [Introduction, Sections 8.4-8.7]  Week 8 - Belonging Revisited Tuesday - Belonging Revisited\n Read: “STEM Identity Development in Latinas: The Role of Self- and Outside Recognition” [Section - Literature Review (pp. 2-3); Section - Implications for Policy and Practice (pp. 16-17)] Listen: My Favorite Theorem podcast interview with Ranthony Edmonds  Thursday- Course Conclusions\n","date":1641013200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1641013200,"objectID":"c7c6b3d801725a9e443200cc165ef917","permalink":"https://crgibbons.github.io/post/syllabi/2022-math498/","publishdate":"2022-01-01T00:00:00-05:00","relpermalink":"/post/syllabi/2022-math498/","section":"post","summary":"This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine the themes of Belonging, Civil Rights, Political Districting, and Algorithms.","tags":"syllabus","title":"Math 498 (Seminar): Mathematics in Social Context, Spring 2022","type":"post"},{"authors":null,"categories":null,"content":"Revised Spring 2022\nThe word \u0026ldquo;Algebra\u0026rdquo;\u0026hellip; \u0026hellip; and its mathematical connotation stem from a 9th century Arabic treatise entitled, The Concise Book on Calculation by Restoration and Compensation, by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c=0$ for nonzero $a$, by completing the square\u0026mdash;hence \u0026ldquo;restoration\u0026rdquo; and \u0026ldquo;compensation.\u0026rdquo;\u0026rdquo; This is where our journey begins. By the end of the course, we\u0026rsquo;ll have an understanding of what tools and techniques \u0026ldquo;modern\u0026rdquo; (19th and 20th century) algebra brings to bear on polynomials and their roots. This course gets more abstract as the semester progresses, so set good habits early. (See Endotes 1)\nTexts  Abstract Algebra: A Concrete Introduction, by Robert Redfield (available from the Hamilton College Bookstore; see me if you have difficulty acquiring the book) The Princeton Companion to Mathematics, edited by Bowers-Green, Leader, and Gowers (access the ebook via the Hamilton College library with your Hamilton SSO)  Schedule of Topics See the Topics Schedule Table (tentative) or the list at the end of the page for the day-to-day topics coverage.\nSkills and Practices Writing Intensive: We will focus on writing during class, and you will have several revision opportunities on writing assignments and the writing portions of exams. The final paper in the course will allow you to tie together what you\u0026rsquo;ve learned (and what you\u0026rsquo;ve already written in earlier writing assignments) into a mathematical survey paper written for a mathematically literate audience.\nTo support your progress as a writer of mathematics, I can help you during open hours or on Piazza, and the QSR Center and the Writing Center both have a number of peer tutors who are familiar with mathematical proof writing and $\\LaTeX$.\nEducational Goals: This course supports several of Hamilton\u0026rsquo;s Educational Goals. Much of the Disciplinary Practice, Creativity, and Communication and Expression within mathematics comes through the process of solving a problem/proving a proposition and then writing it up. In this class, you will refine your proof writing skills and develop new mathematical prose writing skills.\nTypes of Assessments  Ready for Class (RC): Beginning of Class. We we are working toward answering one (huge!) mathematical problem; you will find it really helpful to review your notes and preview the book for these short quiz-like multiple choice assignments. I don’t reschedule these, but I do drop (at least) three low scores for everyone. (We can work out COVID contingencies as necessary!) Homework (HW): Due Tuesdays at 4pm (rigid). The homework is graded by a Hamilton student and will be returned in 2-3 class periods. Because the written homework is graded by a student who is super-busy just like you, homework is due when it\u0026rsquo;s due! (Don\u0026rsquo;t @ me!) However, to help you out, I drop your lowest 2 homework scores. Midterm Exams (ME): Two 2-hour self-scheduled midterms. Before the first exam, I will post a preview that describes the kinds of questions, the point distributions, and other information that will help you study. Final Exam (FE): One 3-hour cumulative self-scheduled exam. The material on the final, though cumulative, will be weighted toward the material covered at the end of the course that was not tested on midterms. Writing Assignments (WA): Due Thursdays at 4pm (flexible). You will write up solutions to problems and responses to writing prompts roughly once a week using $\\LaTeX$ (via Overleaf with your Hamilton SSO) (sometimes solo, sometimes in partners). Each writing assignment is graded among the options E (exemplary), M (masterful), R (consider revising), and X (not enough to assess). Final Paper (FP): Due by beginning of our scheduled final exam period. This will be graded like a writing assignment; a lot of the content of this paper will come from writing assignments you\u0026rsquo;ve already completed, so think of it as a way to study for the final and get a chance to revise your writing one last time.  Classroom Environment The American Mathematical Society (the largest professional society for mathematicians) outlines its vision for a welcoming environment as follows:\n The AMS strives to ensure that participants in its activities enjoy a welcoming environment. In all its activities, the AMS seeks to foster an atmosphere that encourages the free expression and exchange of ideas. The AMS supports equality of opportunity and treatment for all participants, regardless of gender, gender identity or expression, race, color, national or ethnic origin, religion or religious belief, age, marital status, sexual orientation, disabilities, veteran status, or immigration status\u0026hellip;. A commitment to a welcoming environment is expected of all attendees at AMS activities, including mathematicians, students, guests, staff, contractors and exhibitors, and participants in scientific sessions and social events.\n I am committed to the same vision for our classroom environment, and I sincerely thank you for your contributions toward making our classroom (and office hours) a lively and respectful community of thinkers. Please let me know if you feel that we have strayed from this vision at any point during the semester. (See Endnotes 2)\nYour Responsibilities Accommodations, Conflicts, \u0026amp; Makeup Exams Please give me notice at least one week prior to an that you have an academic accommodation or a conflict. Since the exams in this course are self-scheduled, I hope this allows you the flexibility to plan around your other obligations, but I\u0026rsquo;m happy to work with you if you need additional flexibility.\nAttendance \u0026amp; Honor By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner\u0026rsquo;s attitude, and to encourage your fellow students to do the same. If you need to miss a class, please fill out the Class Absence Request Form (link available on Blackboard). You are part of a community that believes in the power of the Honor Code to make Hamilton College a great place to be a student and a teacher. We are all bound by the responsibility to actively create and maintain a culture of learning, academic integrity, and personal honor. I do not take my responsibility lightly; nor should you! (See Endnotes 3)\nGetting Stuck Being stumped is part of learning mathematics, so please attempt to solve homework problems on your own before asking for help on them. Collaboration on the homework is encouraged as long as you are collaborating with your peers currently enrolled in any section of Math 325. However, make sure to write up your final drafts separately to ensure that you have each fully understood the answer(s). Similarly, even though you will be assigned a writing partner for the writing assignments, it is your responsibility to make sure you understand and approve of all the mathematics your team turns in. (See Endnotes 4)\nIMPORTANT! Please check with me before using resources other than your classmates, tutors at the QSR or Writing Centers, or online $\\LaTeX$ help. For example, check with me before asking other professors, students not currently enrolled in Math 325, the internet, a magic eight ball, the ghost of Gauss, etc! Mathematical plagiarism is a subtle business, and it\u0026rsquo;s easy to accidentally plagiarize by copying a solution you\u0026rsquo;ve read somewhere else. (See Endnotes 5)\nEndnotes  The Oxford English Dictionary, retrieved 01/30/2021. AMS Policy on a Welcoming Environment, retrieve 01/30/2021. If you wantonly skip class, aside from missing out on the learning community within the walls of our classroom, you\u0026rsquo;ll penalize yourself by getting lower homework and test scores than you otherwise would. And anyway, I do notice if you\u0026rsquo;re not in class. Honor Code issues aside, you\u0026rsquo;re doing your education a disservice if you turn in work you have not personally thought through carefully. Plus, some Writing Assignment problems will reappear on exams or on the final paper. Seriously, though: you can\u0026rsquo;t \u0026ldquo;unsee\u0026rdquo; someone else\u0026rsquo;s solution. There are deep and interesting ethical conundra lurking here; Googling unwisely (or at all) may lead you down a path you didn\u0026rsquo;t intend to low.  Spring 2022 Schedule of Topics  W 01/19/2022: Ch 1, Well-Ordering and Division F 01/21/2022: Ch 1, Primes and GCDs M 01/24/2022: Ch 1, Induction, FT of arithmetic W 01/26/2022: Ch 3, Complex Numbers F 01/28/2022: Ch 3, Complex Numbers M 01/31/2022: Ch 4, Modular Arithmetic W 02/02/2022: LaTeX Day F 02/04/2022: Ch 4, Zero Divisors M 02/07/2022: Ch 5, Fields W 02/09/2022: Ch 5, Subfields F 02/11/2022: Ch 6, Solvability by Radicals M 02/14/2022: Ch 6, Solvability by Radicals W 02/16/2022: Ch 7, Rings F 02/18/2022: Ch 7, Rings M 02/21/2022: Ch 7, Rings W 02/23/2022: Ch 8, Polynomial Rings F 02/25/2022: Ch 8, Polynomial Rings NOTE: Midterm 1 covers Chs 1 through 8 M 02/28/2022: Ch 9, Ideals W 03/02/2022: Ch 9, Principal Ideals and PIDs F 03/04/2022: Ring Homomorphisms M 03/07/2022: Ch 10, Algebraic Elements W 03/09/2022: Ch 10, Algebraic Elements F 03/11/2022: Ch 11, Irreducible polynomials NOTE: Spring Break! Final Paper first look due M 03/28/2022: Ch 12, Extension Fields as Vector Spaces W 03/30/2022: Ch 13, Automorphism that Fix a Field F 04/01/2022: Ch 14, Counting Automorphisms M 04/04/2022: Ch 15, Groups W 04/06/2022: Ch 15, Groups F 04/08/2022: Ch 16, Permutation Groups M 04/11/2022: Ch 17, Group Homomorphisms W 04/13/2022: Ch 18, Subgroups NOTE: Midterm 2 covers Chs 9 through 18 F 04/15/2022: Ch 19, Generators of (Sub)Groups M 04/18/2022: Ch 20, Cosets W 04/20/2022: Ch 20-21, Cosets and Lagrange\u0026rsquo;s Theorem F 04/22/2022: Ch 23, Normal Subgroups M 04/25/2022: Ch 23, Quotient Groups W 04/27/2022: Ch 25, Galois Theory Revisited F 04/29/2022: Ch 26, Solvable Groups M 05/02/2022: Ch 26, Solvable Groups W 05/04/2022: Ch 27-28, Putting it All Together F 05/06/2022: Ch 27-28, Putting it All Together M 05/09/2022: Workshop on Final Papers NOTE: Final Exam emphasizes Chs 19-28  ","date":1641013200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1641013200,"objectID":"8a31f5899016e9b84ed5e50ba3e5691b","permalink":"https://crgibbons.github.io/post/syllabi/2022-math325/","publishdate":"2022-01-01T00:00:00-05:00","relpermalink":"/post/syllabi/2022-math325/","section":"post","summary":"The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we'll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.","tags":"syllabus","title":"Math 325 (Writing Intensive): Modern Algebra","type":"post"},{"authors":["Courtney Gibbons","David Jorgensen","Janet Striuli"],"categories":null,"content":"","date":1640754000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1640754000,"objectID":"96ebdb66f5bb95ada0b0e30c8a7744ff","permalink":"https://crgibbons.github.io/publication/gjs-2021/gjs-2021/","publishdate":"2021-12-29T00:00:00-05:00","relpermalink":"/publication/gjs-2021/gjs-2021/","section":"publication","summary":"We introduce a new homological dimension for finitely generated modules over a commutative local ring $R$, which is based on a complex derived from a free resolution $L$ of the residue field of $R$, and called $L$-dimension. We prove several properties of $L$-dimension, give some applications, and compare $L$-dimension to complete intersection dimension.","tags":["Nearly Complete Intersections"],"title":"L-dimension for modules over a local ring.","type":"publication"},{"authors":["Courtney Gibbons"],"categories":null,"content":"","date":1636606800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1636606800,"objectID":"57fccc9827146c6768da1f89cbdb2e64","permalink":"https://crgibbons.github.io/publication/amsfeaturescolumn/featuresnov2021/","publishdate":"2021-11-11T00:00:00-05:00","relpermalink":"/publication/amsfeaturescolumn/featuresnov2021/","section":"publication","summary":"","tags":[""],"title":"What is a prime, and who decides?","type":"publication"},{"authors":null,"categories":null,"content":"","date":1619989200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1619989200,"objectID":"84c785c0c9207040e3c3dc988868be93","permalink":"https://crgibbons.github.io/talk/2021-amswesternsectional/","publishdate":"2021-05-02T17:00:00-04:00","relpermalink":"/talk/2021-amswesternsectional/","section":"talk","summary":"Recently, nearly complete intersection ideals were defined by Boocher and Seiner to establish lower bounds on Betti numbers for monomial ideals (arXiv:1706.09866). Stone and Miller then characterized nearly complete intersections using the theory of edge ideals (arXiv:2101.07901). The authors extend their work to fully characterize nearly complete intersections of arbitrary generating degrees and use this characterization to compute minimal free resolutions of nearly complete intersections from their degree 2 part. This work was initiated as part of the virtual COURAGE REU in Summer 2020, supported by Clemson University’s School of Mathematical and Statistical Science.","tags":null,"title":"A Hypergraph Characterization of Nearly Complete Intersections","type":"talk"},{"authors":null,"categories":null,"content":"","date":1618428600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1618428600,"objectID":"3645e1024d2507bb5869fb996262cf2d","permalink":"https://crgibbons.github.io/talk/2021-theotherside/","publishdate":"2021-04-14T15:30:00-04:00","relpermalink":"/talk/2021-theotherside/","section":"talk","summary":"Whether you’re buying shoes from Zappos or voting on a networked ballot box, you want to be confident that your information is verified (it really came from you!) and secure (only you and the approved second parties can see it!). Professor Gibbons will talk about the math behind encrypting and authenticating messages online.","tags":null,"title":"The Math of Online Privacy","type":"talk"},{"authors":null,"categories":null,"content":"I\u0026rsquo;ve had a lot of conversations with students lately that start with disclaimers like \u0026ldquo;I\u0026rsquo;m sorry, I\u0026rsquo;m not really good at math, so\u0026hellip;\u0026rdquo; and since it\u0026rsquo;s not so easy to give a pep talk in-person with the whole pandemic and everything, I thought I\u0026rsquo;d give the pep talk here. Watch the Pep Talk!\n","date":1612760400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1612760400,"objectID":"471812772921460159bfc876e60b262a","permalink":"https://crgibbons.github.io/post/inthemedia/youtubepeptalk/","publishdate":"2021-02-08T00:00:00-05:00","relpermalink":"/post/inthemedia/youtubepeptalk/","section":"post","summary":"I've had a lot of conversations with students lately that start with disclaimers like, I'm sorry, I'm not really good at math, so..., and since it's not so easy to give a pep talk in-person with the whole pandemic and everything, I thought I'd give the pep talk here. Watch the [Pep Talk](https://www.youtube.com/watch?v=kenf8E1RuoA)!","tags":"in the media","title":"So You Think You're Bad at Math (video pep talk)","type":"post"},{"authors":null,"categories":null,"content":"","date":1602185400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1602185400,"objectID":"ed33f05b6669c41b317da08da5615628","permalink":"https://crgibbons.github.io/talk/2020-tmwyf/","publishdate":"2020-10-08T15:30:00-04:00","relpermalink":"/talk/2020-tmwyf/","section":"talk","summary":"Ever wondered what your life might have been like if you chose differently in the past? This talk is about how I nearly became a geometric group theorist -- until I saw homological algebra used to prove theorems about modules. My emphasis will be on what Betti numbers are, a few ways to think about them, some lovely borrowed ideas from calculus, and a few of my favorite theorems and conjectures.","tags":null,"title":"The Real Friends are the Betti Numbers We Calculated Along the Way","type":"talk"},{"authors":["Courtney Gibbons"],"categories":null,"content":"","date":1587441600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1587441600,"objectID":"515d901cef554b6b16ff696b89038270","permalink":"https://crgibbons.github.io/publication/notices2020/notices2020/","publishdate":"2020-04-21T00:00:00-04:00","relpermalink":"/publication/notices2020/notices2020/","section":"publication","summary":"Complete these exercises several months in advance of your anticipated research project with undergraduates. For example, if you are thinking of working with students over a summer, consider working on them between the fall and spring semesters.","tags":["Boij-Soederberg"],"title":"Mentoring Undergraduate Research: Advanced Planning Tools and Tips","type":"publication"},{"authors":null,"categories":null,"content":"","date":1564844400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1564844400,"objectID":"bd4365c1568f88bf004f024edc2d0138","permalink":"https://crgibbons.github.io/talk/2019-mathfest/","publishdate":"2019-08-03T11:00:00-04:00","relpermalink":"/talk/2019-mathfest/","section":"talk","summary":"In astronomy, a syzygy is an alignment of celestial bodies. In mathematics, a syzygy is an alignment of a kernel of one homomorphism with the image of another! In this talk I'll introduce free resolutions, syzygies, and a few applications thereof.","tags":null,"title":"Syzygy: When Submodules Align","type":"talk"},{"authors":null,"categories":null,"content":"","date":1547960400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1547960400,"objectID":"9abaece3068269367573a62ef33b7153","permalink":"https://crgibbons.github.io/talk/2019-jmm/","publishdate":"2019-01-20T00:00:00-05:00","relpermalink":"/talk/2019-jmm/","section":"talk","summary":"Commutative algebra is ripe with topics for undergraduate research, and I will discuss one such topic: Boij-Soederberg theory. I will focus on specific results from two undergraduate research projects I mentored in this context, including how I developed the projects to dovetail with my own research agenda. I will also (briefly!) describe my experience as a mentor to undergraduates and a few things I wish I’d known ahead of time.","tags":null,"title":"Boij-Soederberg Theory as an Introduction to Research in Commutative Algebra","type":"talk"},{"authors":null,"categories":null,"content":"","date":1532028600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1532028600,"objectID":"797be3f4a167f477650314f892a6fe97","permalink":"https://crgibbons.github.io/talk/2018-pcmi/","publishdate":"2018-07-19T15:30:00-04:00","relpermalink":"/talk/2018-pcmi/","section":"talk","summary":"From 0 to syzygy in 5 minutes!","tags":null,"title":"Syzygy: a mysterious mathematical object","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529553600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529553600,"objectID":"2728c3ae896b721980b753c466d5aebf","permalink":"https://crgibbons.github.io/talk/2018-pcmi-ignite/","publishdate":"2018-06-21T00:00:00-04:00","relpermalink":"/talk/2018-pcmi-ignite/","section":"talk","summary":"Syzygies are among the most important, useful, and beautiful objects in algebra. After this talk, you'll have a feel for what they are and what they can do.  _Ignite talks are fast-paced: 20 slides at 15 seconds each_","tags":null,"title":"From 0 to Syzygy in 5 minutes","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529553600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529553600,"objectID":"946c8f9481572cab0c91aba17bfa6252","permalink":"https://crgibbons.github.io/talk/2017-googlingit/","publishdate":"2018-06-21T00:00:00-04:00","relpermalink":"/talk/2017-googlingit/","section":"talk","summary":"Have you ever wondered how Google decides which search results are most relevant to your search query?  The secret to Google's early success was PageRank, an algorithm for scoring the relevance and popularity of websites, and the math that makes the algorithm possible is linear algebra.  We'll take a look under the hood and see how the algorithm works.  Then we'll talk about the ramifications of a smart card catalog, aka Google, that decides what users see first.","tags":null,"title":"Googling It: How Google Ranks Search Results","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529553600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529553600,"objectID":"ffb23ec6920ee0c5472c3156bac11db3","permalink":"https://crgibbons.github.io/talk/siamaag17/","publishdate":"2018-06-21T00:00:00-04:00","relpermalink":"/talk/siamaag17/","section":"talk","summary":"The goal of this talk is to highlight a theorem proved during the Mathematical Research Community: Algebraic Statistics summer program by the Likelihood Geometry group. This group was led by Serkan Hosten and Jose Israel Rodriguez. In the talk, I will focus on the application of the theorem to graphical models.","tags":null,"title":"Maximum Likelihood Degrees for Discrete Random Models","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529553600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529553600,"objectID":"f9e081b1f152721a51794160cbfec4fe","permalink":"https://crgibbons.github.io/talk/2018-rte81/","publishdate":"2018-06-21T00:00:00-04:00","relpermalink":"/talk/2018-rte81/","section":"talk","summary":"In this talk we introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators.  This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition.","tags":null,"title":"Recursive Decompositions of Betti diagrams of complete intersections","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529553600,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529553600,"objectID":"500d1efd122e9322429ceba578ac12a0","permalink":"https://crgibbons.github.io/talk/shidoku/","publishdate":"2018-06-21T00:00:00-04:00","relpermalink":"/talk/shidoku/","section":"talk","summary":"It turns out that algebra is more than just x's and torturing high school students.  Algebra has been used to solve problems from biology, physics, and economics.  In this talk, I'll walk through an example of using algebra to solve a slightly less ambitious problem: a 4 by 4 sudoku puzzle.  We'll develop all the tools used to solve the big problems, too.","tags":null,"title":"Shidoku: A Crash Course on Ideals and Varieties","type":"talk"},{"authors":null,"categories":null,"content":"","date":1529467200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1529467200,"objectID":"8b9284098c70a8cd8df94e8d135f6f47","permalink":"https://crgibbons.github.io/talk/2018-levitt/","publishdate":"2018-06-20T00:00:00-04:00","relpermalink":"/talk/2018-levitt/","section":"talk","summary":"Just about everyone agrees that partisan gerrymandering is unfair; arguments center around how to detect it and whether there are other gerrymanders (racial, ethnic, socioeconomic) that we should be looking for, too. We will examine several mathematical criteria and metrics for fair districting that have been, are being, and will be discussed in legislatures and courts across the country.","tags":null,"title":"Gerrymandering: The Math Behind the Madness.","type":"talk"},{"authors":["Nick Baeth","Terri Bell","Courtney Gibbons","Janet Striuli"],"categories":null,"content":"","date":1502942400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1502942400,"objectID":"245e9a6ea564761a170a352a7ce5786a","permalink":"https://crgibbons.github.io/publication/bbgspaper2020/bbgspaper2020/","publishdate":"2017-08-17T00:00:00-04:00","relpermalink":"/publication/bbgspaper2020/bbgspaper2020/","section":"publication","summary":"The divisor sequence of an irreducible element (_atom_) $a$ of a reduced monoid $H$ is the sequence $(s_n)_{n \\in \\mathbb{N}}$ where, for each positive integer $n$, $s_n$ denotes the number of distinct irreducible divisors of $a^n$. In this work we investigate which sequences of positive integers can be realized as divisor sequences of irreducible elements in Krull monoids. In particular, this gives a means for studying non-unique direct-sum decompositions of modules over local Noetherian rings for which the Krull-Remak-Schmidt property fails. [This paper is dedicated to Roger and Sylvia Wiegand -- mentors, role models, and friends -- on the occasion of their combined 151st birthday]","tags":["Boij-Soederberg"],"title":"Recursive strategy for decomposing Betti tables of complete intersections","type":"publication"},{"authors":["Courtney Gibbons","Robert Huben","Branden Stone"],"categories":null,"content":"","date":1502942400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1502942400,"objectID":"1415a56997641661d2ba17e9c44aef84","permalink":"https://crgibbons.github.io/publication/ghspaper2018/ghspaper2018/","publishdate":"2017-08-17T00:00:00-04:00","relpermalink":"/publication/ghspaper2018/ghspaper2018/","section":"publication","summary":"We introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition. We also provide a detailed analysis of the Boij-Soederberg decomposition for Betti diagrams of codimension four complete intersections where the largest generating degree satisfies the size condition.","tags":["Boij-Soederberg"],"title":"Recursive strategy for decomposing Betti tables of complete intersections","type":"publication"},{"authors":["Mike Annunziata","Courtney Gibbons","Cole Hawkins","Alex Sutherland"],"categories":null,"content":"","date":1491883200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1491883200,"objectID":"e3717c93006a887342b42bc31f069b95","permalink":"https://crgibbons.github.io/publication/g-reu-2014/reupaper/","publishdate":"2017-04-11T00:00:00-04:00","relpermalink":"/publication/g-reu-2014/reupaper/","section":"publication","summary":"We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-Soederberg theory. That is, given a Betti diagram, we determine if it is possible to decompose it into the Betti diagrams of complete intersections. To do so, we determine the extremal rays of the cone generated by the diagrams of complete intersections and provide a factorial time algorithm for decomposition.","tags":[],"title":"Rational combinations of Betti diagrams of complete intersections","type":"publication"},{"authors":["Carlos Am\u0026#233;ndola","Nathan Bliss","Isaac Burke","Courtney R Gibbons","Martin Helmer","Serkan Ho\u0026#351;ten","Evan D Nash","Jose Israel Rodriguez","Daniel Smolkin"],"categories":null,"content":"","date":1489723200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1489723200,"objectID":"ecf45146e62b8c64a163eae8de3ebb7d","permalink":"https://crgibbons.github.io/publication/algstatmrcpaper/maximumlikelihood/","publishdate":"2017-03-17T00:00:00-04:00","relpermalink":"/publication/algstatmrcpaper/maximumlikelihood/","section":"publication","summary":"We study the maximum likelihood degree (ML degree) of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML degree. We show that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal $A$-determinant. We also illustrate how to compute the ML estimate of a toric variety numerically via homotopy continuation from a scaled toric variety with low ML degree. Throughout, we include examples motivated by algebraic geometry and statistics. We compute the ML degree of rational normal scrolls and a large class of Veronese-type varieties. In addition, we investigate the ML degree of scaled Segre varieties, hierarchical loglinear models, and graphical models.","tags":[],"title":"The Maximum Likelihood Degree of Toric Varieties","type":"publication"},{"authors":["Courtney Gibbons","Josh Laison","Eric J. Paul"],"categories":null,"content":"","date":1420606800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1420606800,"objectID":"93676bc71613234376dcbd5528e2e3fe","permalink":"https://crgibbons.github.io/publication/glaisonpaul/glaisonpaul/","publishdate":"2015-01-07T00:00:00-05:00","relpermalink":"/publication/glaisonpaul/glaisonpaul/","section":"publication","summary":"We define three new pebbling parameters of a connected graph $ G $, the $ r $-, $ g $-, and $ u $-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $ n $ and the diameter $ d $ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $ r $-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $ r $-critical pebbling number is $2^ d $.","tags":["Graph Theory"],"title":"Critical pebbling numbers of graphs","type":"publication"},{"authors":["Richard Bedient","Courtney Gibbons"],"categories":null,"content":"","date":1420088400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1420088400,"objectID":"d5881e540aefb972e77d1d682453b91e","permalink":"https://crgibbons.github.io/publication/bedientg/granola/","publishdate":"2015-01-01T00:00:00-05:00","relpermalink":"/publication/bedientg/granola/","section":"publication","summary":"In introductory calculus, most optimization problems begin with a continuous function. Departing from this trend, we describe a plausible micro-economic scenario with a discontinuous cost function. The case of multiple workers requires a more refined analysis than simply taking a derivative.","tags":["Teaching","Calculus"],"title":"Grandma makes Granola","type":"publication"},{"authors":["Courtney Gibbons","Jack Jeffries","Sarah Mayes","Claudiu Raicu","Branden Stone","Bryan White"],"categories":null,"content":"","date":1420088400,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1420088400,"objectID":"47acb31aa067b73ce312a1692d15da53","permalink":"https://crgibbons.github.io/publication/g-et-al-msri-2012/msripaper/","publishdate":"2015-01-01T00:00:00-05:00","relpermalink":"/publication/g-et-al-msri-2012/msripaper/","section":"publication","summary":"We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-Soederberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a simple expression of the decomposition of the Betti diagram of any complete intersection in terms of the degrees of its minimal generators. In the more traditional sense, the decomposition of complete intersections of codimension at most 3 are also computed as given by the totally ordered decomposition algorithm obtained from (ES1). In higher codimension, obstructions arise that inspire our work on an alternative algorithm.","tags":["Boij-Soederberg"],"title":"Non-simplicial decompositions of Betti diagrams of complete intersections","type":"publication"},{"authors":["Courtney Gibbons","Josh Laison"],"categories":null,"content":"","date":1349064000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1349064000,"objectID":"e67c08dd91817054ad2f85b6894de205","permalink":"https://crgibbons.github.io/publication/glaison1/glaison1/","publishdate":"2012-10-01T00:00:00-04:00","relpermalink":"/publication/glaison1/glaison1/","section":"publication","summary":"The fixing number of a graph $G$ is the smallest cardinality of a set of vertices $S$ such that only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing set of a group $\\Gamma$ is the set of  all fixing numbers of finite graphs with automorphism group $\\Gamma$. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label $G$ so that the automorphism group of the labeled graph is trivial. The fixing number can be thought of as a variation of the distinguishing number in which every label may be used only once, and not every vertex need be labeled. We characterize the fixing sets of finite abelian groups, and investigate the fixing sets of symmetric groups.","tags":["Graph Theory"],"title":"Fixing numbers of graphs and groups","type":"publication"},{"authors":["Christine Berkesch","Jesse Burke","Daniel Erman","Courtney Gibbons"],"categories":null,"content":"","date":1349064000,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1349064000,"objectID":"272cea889a721518acd3d18127e7107b","permalink":"https://crgibbons.github.io/publication/bbegpaper2011/mrcpaper/","publishdate":"2012-10-01T00:00:00-04:00","relpermalink":"/publication/bbegpaper2011/mrcpaper/","section":"publication","summary":"We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form $k [x, y]/\\langle q \\rangle$, where $q$ is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including diagrams of infinite projective dimension, into pure diagrams. Boij–Söderberg theory completely describes the cone of Betti diagrams over a standard graded polynomial ring; our result provides the first example of another graded ring for which the cone of Betti diagrams is entirely understood.","tags":["Boij-Soederberg"],"title":"The cone of Betti diagrams over a hypersurface ring of low embedding dimension","type":"publication"}]