Math 434
Spring 2021

The syllabus for Math 434 is linked as well as our current class schedule.  Much of that information is repeated bellow (but not all of it, so read the syllabus!)

Instructor
Rebecca E. Field
fieldre@math.jmu.edu
(540) 568-4962
Office: zoom
Office Hours: MW 11:30am-12:30pm, F 2:00-3:00pm
Also by appointment
(I can make appointments for Tuesdays, but am not available on Thursday afternoons)
Weekly Problem Session: evening TBD

Textbook:
A Second Course In Linear Algebra, by Stephan Ramon Garcia and Rodger A. Horn (Ⓒ 2017 Cambridge University Press)
(hopefully) available at the campus bookstore.
Please refer to the class canvas page for a scan of some early sections (this will give you time to legally acquire the book).

Course summary:
The goal of Math 434 is to solidify and expand your understanding of a fundamental topic in mathematics, Linear Algebra.  This class will be significantly harder than your first course in linear algebra (Math 300/Math 238/Introduction to Linear Algebra somewhere other than JMU), so take that `Advanced' from the title seriously.  The idea with this class is that Linear Algebra is probably our most widely used topic, both inside and outside mathematics.  It is both more interesting and more intricate than you've ever imagined and any introduction to the subject must prioritize computation due to its ubiquity.  The main topics covered in a first course in linear algebra are Systems of Equations, Vector Spaces, Linear Transformations, and Diagionalization and each of them is absolutely necessary in a wide variety of fields (Math, Physics, Engineering, etc.) and super useful in a wider variety of fields (Chemistry, Biology, Computer Science, etc.).  Because of that, none of them can be skipped, which leaves room no room for interesting digressions.  Things you may have wondered about, like how the standard basis is more than just a nice basis, its vectors are also unit length and perpendicular, and the consequences of trying to measure things like angles between vectors are truly interesting aspects of the subject and will occupy the first part of the course.

This is not so much a secrets-of-the-universe class like Math 410 (Intro to Real Analysis), or an introduction to true abstraction like Math 430 (Intro to Algebra), but given our increasing dependence on technology, it is a secrets-of-our-universe class, and consequently, it can change the way you think about the world, but only if you give it the time it deserves!

Here is my most important piece of advise about this course:   DO NOT FALL BEHIND!!  This includes things like DO NOT MISS CLASS!!  (If you must miss a class, get notes from one of your classmates and read them before the next class.)  It also includes things like DO YOUR HOMEWORK!!  It is not possible to actually learn this material without doing problems.  You might be able to convince yourself you understand, but if you can't do problems, you aren't at the level of understanding required to pass the class.  In fact, if the class seems too easy at any point, do extra problems!

Exams:
Big Quiz 1: Friday February 19, during class time
Midterm: week of March 22, individually scheduled oral exams
Big Quiz 2: Monday, April 19, during class time
Final: week of May 3, individually scheduled oral exams

Supplemental Texts:
• Your Introduction to Linear Algebra (Math 300/Math 238) text whatever that was
Other recommended options are
• Strang either Introduction to Linear Algebra or Linear Algebra and Its Applications by Gilbert Strang (old editions can be quite cheap).  These are both good books with a level of abstraction that is somewhere between your Math 300/238 text and our Math 434 text.
• Linear Algebra Done Wrong by Sergei Treil
This is a Creative Commons text (free for non-commercial use) and covers more or less the same material with a similar level of sophistication as our official text, think of it as a third opinion.  If you are interested in using this text, please take a look at the book's webpage as well.

Homework:
Problems will be divided into Easy, Medium, Hard and Extra Credit.  Easy problems are handed in but not graded.  The Medium and Hard problems are to be written down neatly (e.g. not your scrap work but a final draft) handed in weekly, some selection of them will be graded.  Easy problems will show up on your weekly quizzes so be absolutely sure you can do all of them!  Medium ones may show up on your big quizzes (definitions/notation are are mostly covered by daily vocab quizzes, but may appear as well).  Hard homework problems are fair game for your Midterm or your Final Exam.  There will sometimes be Extra Credit problems.

Homework 1:
Easy:   0.5, 0.8, 0.23, 1.1, 1.2, 1.6, 2.5, 2.9, 2.11, 3.3, 3.4, 3.5
Medium:   0.15, 0.24, 1.5, 1.7, 1.8, 2.6, 2.12, 2.17, 3.6
Hard:  1.15
Extra Credit:   2.18

LaTeX:
I am not requiring that students type set their assignments using LaTeX, but if you wish to, that is certainly an option.  Here is a link to a LaTeX Setup and Tutorial along with a sample document and its source code.

Extra Help:
Please zoom by my office hours or make an appointment if you need extra help!  I can also give you a recommended list of possible tutors (students who did well in MATH 434 Spring 2020) for hire.

Topics we will cover are roughly as follows:

Inner Product Spaces/Orthogonality/Graham Schmidt/Unitary Matrices
Eigenvalues/Eigenvectors/Caley-Hamilton/Canonical Forms
Connections between the two previous topics (Normal Matrices/Matrix Factorizations/Quadratic Forms)