Math 3593H: Honors Mathematics II

Vic Reiner
Spring 2017

Prerequisites: Single variable calculus, the willingness to think and learn, including how to prove things, along with the equivalent of Math 3592H.
Victor Reiner (You can call me "Vic")
Office: Vincent Hall 256
Telephone (with voice mail): (612) 625-6682

Recitation TA: Steven Collazos
Office: Vincent Hall 504
Telephone (with voice mail): (612) 624-1543
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.

Other useful resources
Category Title Author(s) Location
Past Math 3592-3H
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 )
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.
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.
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.
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
Midterm exam 1 15%
Midterm exam 2 15%
Final exam 25%

Homework, quiz,
or exam
Thursday recitation
due date
Problems from
Hubbard and Hubbard
Lecture notes,
recitation materials (if any)
HW 1 Jan. 26 Section 3.1: 2*,3,5,8*,11*,14,19
Section 3.2: 2,3*,6*,11
Lecture Jan. 18
Lecture Jan. 20
(missed lectures Jan. 23, 35)
Lecture Jan. 27 (Steven Collazos)
HW 2 + Quiz Feb. 2 Section 3.3: 1,2,6*,9
Section 3.4: 1,2*,6*
(Sections 3.5, 3.6 got moved to next homework)
Quiz, solutions
Lecture Jan. 30
Lecture Feb. 1
Recitation Feb. 2 (make-up lecture)
Lecture Feb. 3
HW 3 Feb. 9 Section 3.5: 4*,6,8*,9,13
Section 3.6: 2*,7
Section 3.7: 1*,3,10*,11,15
Lecture Feb. 6
Recitation Feb. 7 (make-up lecture)
Lecture Feb. 8
Recitation Feb. 9 (make-up lecture)
Lecture Feb. 10
Midterm exam 1 Feb. 16 Covering up through Section 3.7.
A good review is Section 3.9, Exercises 1-22, 25.
Exam 1, solutions
Lecture Feb. 13
Lecture Feb. 15
Lecture Feb. 17
HW 4 Feb. 23 Section 3.8: 1,2*,5,8*
Section 4.1: 3,6*,8,10,14*
Section 4.2: 4,5*,7*
Section 4.3: 1b*,4,5*
Lecture Feb. 20
Lecture Feb. 22
Lecture Feb. 24
HW 5 + Quiz Mar. 2 Section 4.4: 1,2*
Section 4.5: 4*,5,6,8*,10*
Section 4.6: 1, 4abc*, 5*
Quiz covers up through Section 4.3, a page of notes allowed;
A good review is Sec. 3.9, Exer. 23,26 and Sec. 4.12, Exer. 1,2,6,7.
Quiz, solutions
Lecture Feb. 27
Lecture Mar. 1
Recitation Mar. 2 (Steven Collazos)
Lecture Mar. 3
HW 6 Mar. 9 Section 4.7: 1*, 2a*
Section 4.8: 2*,8,11*,14,20
Section 4.9: 1*,3
Lecture Mar. 6
Lecture Mar. 8
Lecture Mar. 10
Spring break Mar. 16
HW 7 + Quiz Mar. 23 Section 4.10: 2*,5*,7,11,15*
Section 4.11: 1*,3*,9,11*
Section 5.1: 1*,3,4,5*
Quiz covers up through Section 4.9, a page of notes allowed;
A good review is Sec. 4.12, Exer. 1-20.
Quiz, solutions
Lecture Mar. 20
Lecture Mar. 21 (make-up lecture)
Lecture Mar. 22
Lecture Mar. 24
HW 8 Mar. 30 Section 5.2: 1,6*
Section 5.3: 1*,4*,8,11a*
Lecture Mar. 29
Lecture Mar. 31
Midterm exam 2 Apr. 6 Covering up through Section 5.3, a page of notes allowed;
A good review is the remainder of Sec. 4.12, and all of Sec. 5.6.
Exam 2, solutions
Lecture Apr 3
Lecture Apr 5
Lecture Apr 7
HW 9 Apr. 13 Section 6.1: 1*, 6, 8*, 10, 12
Section 6.2: 2*,3,7*
Section 6.3: 1,2*,3,4*,5,7,10,12*
Section 6.5: 1,2,6*,10*,12,18
Lecture Apr 10
Lecture Apr 12
Lecture Apr 14
HW 10 + Quiz Apr. 20 Section 6.4: 1*,2,4*,6
Section 6.6: 2*, 3, 6*
Section 6.7: 2*,5,6*,7,11*
Quiz covers up through Section 6.5 (including Sec. 6.4), a page of notes allowed;
A good review is Sec. 6.13, Exercises 1-14
Quiz, solutions
Lecture Apr 17
Lecture Apr 19
Lecture Apr 21
HW 11 Apr. 27 Section 6.8: 1,3*,6*,7,12*
Section 6.9: 1*,2,5*,6
Section 6.10: 1,4*,5*,7,8*,11
Lecture Apr 24
Lecture Apr 26
Lecture Apr 28
Last week of class May 4 (Not to hand in; just for practice)
Section 6.12: 2,4
Lecture May 1
Final exam Mon May 8
1:30-4:30pm in VinH301
Two pages of notes allowed!

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