Prerequisites: 
Single variable calculus, and willingness to think and learn,
including how to prove things.

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 Smith Hall 121 Recitation section, TuesThur 10:1011:00am Vincent Hall 207 
Office hours:  Reiner: Tues 2:303:20pm,
Wed 9:059:55am,
Mon and Wed 4:105:00pm;
also by appointment. Collazos: Tues and Wed at 9:0510:05am. 
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 oddnumbered exercises. 
Course content: 
This is the first semester of the 2semester Honors Math sequence. Our goal in the fall semester is Chapters 13 of Hubbard and Hubbard's book; the second semester is Chapters 46.
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 singlevariable 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.

Category  Title  Author(s)  Location 

Past Math 3592H materials 
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 ) 
Homework: 
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.  
Quizzes: 
There will be small (closed book, no notes) 15minute 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 
