I will state key lemmas and theorems and summarize the main points. Thus more emphasis is placed on self-learning and lemmas and theorems will not typically be worked out in detail in lectures. This course is intended to be a precursor to graduate courses in differential geometry and topology. Time does not permit us to rigorously develop all these foundations, which are treated in Math 425/515 (not a pre-requisite). In order to do this, we will introduce the concept of Lebesgue measure and Lebesgue integrals and revisit multivariable calculus from this perspective (chapter 5). We will follow the modern point of view on differential geometry by emphasizing global aspects of the subject whenever possible. One of the main results in this direction which we will prove near the end of the course is the Gauss-Bonnet theorem (chapter 8). A central theme of this course will be to study different kinds of curvature - defined locally on a curve (in chapter 1 of the book) or surface (in chapter 3) - and how curvature relates to global properties of the curve or surface (in chapters 4, 6, 7, and 9). We will also study the ``intrinsic" geometry of surfaces: that is, geometric notions which are described just in terms of the surface and not in terms of an embedding into higher dimensional euclidean space. This course is about the geometry of curves and surfaces in three-dimensional space. You can use Canvas to post questions about the course, including questions about topics covered in class or regarding the homework. I will be available to answer questions during my office hoursĪs will Leo. If you find yourself confused, please seek help sooner rather than In the event of illness or family emergency I must be notified ideally at least 24 hours in advance and documentation from your magister (or a doctor's note) must be provided to me in order to receive accommodations for the midterm or final project. You may use outside resources with my permission. Collaboration with classmates during the proposal stage is encouraged. It is in the nonstandard format of Choose your own Differential Adventure! It is due Tuesday May 3 at 5pm. The final project will count for 30% of your course grade. You are allowed to refer to canvas materials, the course textbook, and Folland's Advanced Calculus, but no other books. You are not permitted to work with other students and you are not permitted to consult the internet.
It will be made available TBA and due one week later. There will be one pledged take home midterm, worth 25% of yourĬourse grade, which you should spend no more than 6 hours actively Two extensions per student will be given (with 3 days advance notice and my approval) and your lowest or nonexistent homework score will be dropped. Please indicate the students that you worked with. Students are encouraged to work with classmates on homework, but the solutions must be written by you in your own words. Homework will count for 30% of your final grade, and you must upload your homework to gradescope on Mondays by 11pm CST. Homework Students should expect to spend 3-6 hours a week on homework in this course, and there will be approximately 10 homework sets in total. Comportment not meeting these standards will result in a reduction from your attendance and participation grade.
This means abiding by the department's policy on Collegiality, Respect, and Sensitivity. Students are expected to be kind to each other and foster a friendly atmosphere both inside and outside of the classroom. He will hold office hours, grade homework and the midterm.Īttendance and participation will count for 15% of your final grade. The teaching assistant for this course is Leo DiGiosia. 69 (The first chapter is available for free)Īn informal blog post explaining the Gauss-Bonnet Theorem, which will give you a flavor of what topics we will study rigorously in this course.
Ros, Curves and Surfaces Second Edition, GSM, Vol. Math 401: Curves and Surfaces, Spring 2022
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