Math 3592H: Honors Mathematics I

Vic Reiner
Fall 2016

Prerequisites: Single variable calculus, and willingness to think and learn, including how to prove things.
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 Smith Hall 121
Recitation section, Tues-Thur 10:10-11:00am Vincent Hall 207

Office hours: Reiner: Tues 2:30-3:20pm, Wed 9:05-9:55am, Mon and Wed 4:10-5:00pm; also by appointment.
Collazos: Tues and Wed at 9:05-10:05am.
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:
This is the first semester of the 2-semester Honors Math sequence. Our goal in the fall semester is Chapters 1-3 of Hubbard and Hubbard's book; the second semester is Chapters 4-6.

What is this course about? Linear algebra helps us to understand very thoroughly vectors, linear transformations, and matrices. This then helps us to handle nonlinear objects, like curves, surfaces, and maps between them. Much of the first semester (Math 3592H) in this sequence works toward generalizing how tangent lines give useful linear approximations to curves in the plane and single-variable functions. Toward the end of the semester we discuss 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.

Other useful resources
Category Title Author(s) Location
Past Math 3592H
Fall 2015 Brubaker course page
Fall 2012 Webb teaching materials
Linear algebra Linear algebra Hefferon free book
Linear algebra done wrong Treil free book
Linear algebra Hoffman and Kunze On reserve in math library
Vector calculus Math Insight Calculus Threads Nykamp list of topics
Vector Calculus Corral free book
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 Thanksgiving holiday). 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-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 Sept. 15 Section 1.1: 4, 6abe, 9*
Section 1.2: 2*aef,3,8*,10,11,13*,14,16,17,23*
Section 1.3: 2ad,4*,10,12*,13,16*,20
Recitation Sept. 6
Lecture Sept. 7
Lecture Sept. 9
Lecture Sept. 12
Lecture Sept. 14
HW 2 + Quiz Sept. 22 Section 1.4: (3ab)*, 6ab, (7ab)*, 9c, 10*, 15, 16*, 24, 28*
Quiz, solutions
Lecture Sept. 16
Lecture Sept. 19
Lecture Sept. 21
HW 3 Sept. 29 Section 1.5: 2,3,6*,8,10*,(14ac)*,16,18*,19,20* Lecture Sept. 23 (T. Douvropoulos)
Lecture Sept. 26
Lecture Sept. 28
Lecture Sept. 30
Midterm exam 1 Oct. 6 Covering Sections 1.1, 1.2, 1.3, 1.4, 1.5
A good review is Section 1.10, Exercises 1-22
Midterm 1, solutions
HW 4 Oct. 13 Section 0.5: 4
Section 0.7: 6, 13*
Section 1.6: 2*,3,6*,11
Section 1.7: 2*,4a,(6b,7b)*,9*,(11bd)
Lecture Oct. 3
Lecture Oct. 5
Lecture Oct. 7
Lecture Oct. 10
HW 5 + Quiz Oct. 20 Section 1.7: 13,15*,17,20*,21
Section 1.8: 2*,3*,6,8*,13
Section 1.10: 23
Quiz, solutions
Lecture Oct. 12
Lecture Oct. 14
Lecture Oct. 17
HW 6 Oct. 27 Section 1.8: (10a)*,12
Section 1.9: 3
Section 1.10: 24*,26,31,33*,36*
Lecture Oct. 19
Lecture Oct. 21
Lecture Oct. 24
Lecture Oct. 26
HW 7 + Quiz Nov. 3 Section 2.1: 2b, 4*, 6, 8*
Section 2.2: 2c, 4, 6*,7,10*
Section 2.3: (2bc)*,3b,6*,8, 13
Quiz, solutions
Lecture Oct. 28
Lecture Oct. 31
Lecture Nov. 2
Lecture Nov. 4
Midterm exam 2 Nov. 10 Covered up through Section 2.4.
A good review is next week's Section 2.4 homework, plus Section 2.11 Exercises 1-12.
Midterm 2, solutions
Lecture Nov. 7
Lecture Nov. 9
Lecture Nov. 12
Steven Collazos's solution to Sec. 10, Exer. 1.24
HW 8 Nov. 17 Section 2.4: 2, 3, 4, 6, 7, 8, 12*, 13*
Section 2.5: 2*, 3, 4, (6a)*, 7, 9*, 12, 13, 15*, 16
Lecture Nov. 14
Lecture Nov. 16
Lecture Nov. 18
Thanskgiving break Nov. 24 Lecture Nov. 21
Lecture Nov. 23
HW 9 + Quiz Dec. 1 Section 2.6: 4, 5*,7*,8,9,11
Section 2.7: 1,2*,3,4*,(5ab)*,(6a)*
Quiz, solutions (this quiz was later discarded from the grades)
Lecture Nov. 28
Lecture Nov. 30
Lecture Dec. 2
Proof of Inverse Function Thm following Spivak's "Calculus on manifolds", expanded by N. Wallach
HW 10 Dec. 8 Section 2.8: 4*, (5a)*,10,(12a)*
Section 2.10: 1,5*,8*,11,13*,15
Lecture Dec. 5
Lecture Dec. 7 (B. Brubaker)
Lecture Dec. 9 (S. Collazos)
Study day Dec. 15 Lecture Dec. 12
Recitation Dec. 13
Final exam Fri Dec. 16
1:30-4:30pm in VinH 207
Cumulative for whole course, up through end of Chapter 2.
Good review are problems from Sections 1.10 and 2.11,
along with Webb's review, Brubaker's review.
Final, solutions

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