| Prerequisites: |
Single variable calculus, the willingness to think and learn,
including how to prove things, along with the equivalent
of Math 3592H.
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| Instructor: | Victor Reiner (You can call me "Vic") Office: Vincent Hall 256 Telephone (with voice mail): (612) 625-6682 E-mail: reiner@math.umn.edu |
| Recitation TA: |
Steven Collazos Office: Vincent Hall 504 Telephone (with voice mail): (612) 624-1543 E-mail: colla054@math.umn.edu |
| Classes: |
Lectures, Mon-Wed-Fri 10:10-11:00am in Vincent Hall 301 Recitation section, Tues-Thur 10:10-11:00am Vincent Hall 301 |
| Office hours: | Reiner: Mon and Wed 9:05-9:55am, Tues 1:25-2:15pm, and also by appointment. Collazos: Tues 3:00-3:50pm, Wed 12:30-1:20pm |
| Required text: |
Vector calculus, linear algebra, and differential forms: a unified approach, 4th edition, by Hubbard and Hubbard. (Matrix Editions, 2009) Warning: There is a 5th edition, but we are not using it. Get the 4th edition, for example, from our University bookstore, or from the publisher's website. Note that they also have an errata page, and they sell a student solution manual for the odd-numbered exercises. |
| Course content: |
What is this course about? This is the second semester of the 2-semester Honors Math sequence. In the fall semester we got through Section 3.1 of Hubbard and Hubbard's book, dealing with linear algebra (vectors, linear transformations, matrices), with the goal of handling nonlinear objects (curves, surfaces, and maps between them). At the end of the semester we discussed how curves and surfaces generalize in higher dimensions to objects called manifolds. The second semester (Math 3593H) is more about the accompanying integration theory, culminating in differential forms and Stokes's Theorem, including the classical theorems of vector calculus and physics, such as the Divergence Theorem and Green's Theorem. We will skip Sections 5.4 on curvature proofs, 5.5 on fractals, 6.11 on electromagnetism, as well as some of the more technical and long proofs in the Appendix, occasionally settling for sketches or plausibility arguments.
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| Category | Title | Author(s) | Location |
|---|---|---|---|
| Past Math 3592-3H materials |
2015-16 | Brubaker | fall course page spring course page |
| 2012-2013 | Webb | teaching materials | |
| Vector calculus | Math Insight Calculus Threads | Nykamp | list of topics |
| Vector Calculus | Corral | free book | |
| Differential forms: theory and practice | Weintraub | our library link | |
| Calculus on manifolds | Spivak | On reserve in math library | |
| MIT's OpenCourseWare Calculus | Strang | MIT link | |
| Div, Grad, Curl and all that | Schey | On reserve in math library | |
| Proof writing and reading |
How to read and do proofs | Solow | In Math Library (QA9.54.S65 2014) or on reserve there |
| How to prove it | Velleman | In Wilson Library (QA9.V38 1994 ) | |
| How to solve it | Polya | In Math Library (QA11 .P6 1971 ) |
| Homework: |
There is homework due each week (with no midterm exam or spring break). You should write down solutions for all of the homework problems listed in the table below, but only hand in solutions for the starred problems in Thursday recitation or in Steven Collazos's mailbox (in the mailroom on the first floor of Vincent Hall) by 5pm. Lowest homework score will be dropped. NO late homework accepted, since solutions and graded work will be given out shortly after the due dates. I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates their collaborators on the homework paper. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Quizzes: |
There will be small (closed book, no notes) 15 or 20-minute quizzes at the beginning of roughly every other Thursday recitation section, on the material from that week's homework, including the non-starred problems. They are intended to be very straightforward. The lowest quiz score will be dropped. |
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| Exams: |
There will be two 50 minute midterm exams in-class during Thursday recitations, one 3-hour final exam; see table of assignments below for dates and times. Exams will also be closed book, no notes allowed. We will have a course Moodle page that will be used as an ongoing gradebook to check your exam, quiz, and homework scores, but not for any other purposes. Make-up policy: If you must miss an exam, you may arrange to take a make-up exam in advance by emailing me. Otherwise, make-up exams will only be granted with valid medical excuses. |
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| Incompletes: |
The grade I ("incomplete") shall be assigned at the lecturer's discretion when, due to extraordinary circumstances, the student was prevented from completing the entire course. It is my policy to assign incompletes only rarely, and only when almost all of the course has already been completed in a satisfactory fashion prior to the extraordinary circumstances. See me (Vic) if something occurs which makes you think you should receive an incomplete. |
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| Grading scheme |
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| Schedule |
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