Prerequisites: 
Single variable calculus, the willingness to think and learn,
including how to prove things, along with the equivalent
of Math 3592H.

Instructor:  Victor Reiner (You can call me "Vic") Office: Vincent Hall 256 Telephone (with voice mail): (612) 6256682 Email: reiner@math.umn.edu 
Recitation TA: 
Steven Collazos Office: Vincent Hall 504 Telephone (with voice mail): (612) 6241543 Email: colla054@math.umn.edu 
Classes: 
Lectures, MonWedFri 10:1011:00am in Vincent Hall 301 Recitation section, TuesThur 10:1011:00am Vincent Hall 301 
Office hours:  Reiner: Mon and Wed 9:059:55am, Tues 1:252:15pm, and also by appointment. Collazos: Tues 3:003:50pm, Wed 12:301:20pm 
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 oddnumbered exercises. 
Course content: 
What is this course about? This is the second semester of the 2semester 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.

Category  Title  Author(s)  Location 

Past Math 35923H materials 
201516  Brubaker  fall course page spring course page 
20122013  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 20minute quizzes at the beginning of roughly every other Thursday recitation section, on the material from that week's homework, including the nonstarred problems. They are intended to be very straightforward. The lowest quiz score will be dropped. 

Exams: 
There will be two 50 minute midterm exams inclass during Thursday recitations, one 3hour 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. Makeup policy: If you must miss an exam, you may arrange to take a makeup exam in advance by emailing me. Otherwise, makeup exams will only be granted with valid medical excuses. 

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. 

Grading scheme 


Schedule 
