Prerequisite: Math 2130 (Calculus III), Math 2240 (Linear Algebra), & Math 2110 (Intro. to Proofs)
Texts: We will begin by looking at the final chapter of Susan Colley's Vector Calculus. Then we will move to our main text.
Web Page: My webpage is located here:
https://BillCookMath.com
and
our course webpage is located here: https://BillCookMath.com/courses/math3510-fall2018.
Meeting times: Monday, Wednesday, & Friday from 9:00am – 9:50am in Walker Hall room 304.
Final Exam: We will have final project presentations on during our final exam time on Monday, December 10th from 8:00am – 10:30am.
Lecturer:
| Name: | Dr. William (Bill) Cook | |
| Office: | Walker Hall 347 | |
| Office Hours: |
Monday, Tuesday, Wednesday, & Friday 10-11am Monday, Tuesday, & Friday 12-12:30pm Tuesday 3-4:30pm Other times by appointment. |
|
| Phone: | (828) 262-2367 | |
| Email: | cookwj@appstate.edu | |
| Webpage: | https://BillCookMath.com |
Technology: You are welcome to use any technology at your disposal to complete out of class assignments. We will periodically use Maple in class (Maple is a “computer algebra system”) and have Maple based homework sets. Maple should be available on all campus lab computers. If you would like a personal copy, I will provide an activation code so you can obtain a personal copy for free. Calculators and other computer technology will not be allowed on exams or quizzes. This includes cell phones. Your cell phone should never be out during an exam or quiz.
Course topics:
In this course, I plan on looking at a few topics just beyond the
end of intro. to linear algebra and calculus 3. I plan to explore:
quotient spaces, dual spaces, tensor products, and exterior algebras.
Following this intermediate linear algebra, I plan to delve into a
mini-course in topology. Specifically we will be studying the concept
of a "manifold" (1-dimensional manifolds are curves, 2-dimensional
manifolds are surfaces).
Then we look at vector fields, differential forms, and exterior
derivatives (exterior derivatives generalize gradient, curl, and
divergence). Our first big punchline will be the generalized Stokes'
theorem (this theorem includes the fundamental theorem of calculus,
the fundamental theorem of line integrals, Green's theorem, Stokes'
theorem, and the divergence theorem all as special cases).
After covering linear algebra and basic manifold theory, we can turn
our attention to topics that interest the class. These could include
bits of differential geometry (like curvature tensors, Riemannian
geometry, and the math of general relativity). Or we could explore
deRham cohomology and get a taste of algebraic topology. Or ....
the possibilities are endless.
A tentative course schedule can be found at:
https://BillCookMath.com/courses/math3510-fall2018/schedule.html.
Your term grade will be based on the results of your tests, homework, term project/presentation, and class participation. Here is more information about the individual components of your grade:
Tests: There will be two tests. Each test will make up 20% of your final grade. Dates of the tests listed in the tentative course schedule may change. The actual dates will be announced in class.
Homework & Quizzes: I will post homework problems (some suggested and some to be turned in) in class and on our course webpage. We might have a few short quizzes as well. I encourage you to work on your homework with your classmates. However, you must write up your solutions yourself. Do NOT copy your collaborators work and turn it in as your own. The quizzes and homeworks will make up 40% of your term grade.
Participation & Final Project:
Instead of having a final exam we will have final presentations. Everyone will pick a topic
to present (this topic will have to be approved and should be something related to what we
covered in class). I will require that you create a nice handout to go with your presentation.
We will have presentations during the final exam period.
Also, I except you to come to class and participate in discussions. I may periodically
ask you to present a homework problem.
Participation as well as your final presentation and handout will make up 20% of your term grade.
Here are the components of the term grade with their weights:
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Attendance: Don't miss class.
Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my posted office hours.
Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/resources/syllabi-policy-and-statement-information.