Lecture: MWF 12:20-1:10, Malott 253
Instructor: Dan
Collins (Office hours: Tuesday 2:45-3:45, Friday 1:30-2:30, Malott 583)
(Note my Tuesday office hours have changed for the last few weeks of
the semester).
TA: TaoRan
Chen (Office hours: Sunday 2:00-4:00, Malott 218)
TA: Thomas
Bååth (Office hours: Monday 9:00-10:00, Malott 218)
Math 4310 is an upper-level course on linear algebra, a subject that underlies many areas of mathematics and its applications to sciences and engineering. The biggest difference between Math 4310 and earlier linear algebra courses such as Math 2210 is that this course is more focused on abstraction and mathematical rigor. For instance, we will focus on studying abstract vector spaces (which are defined in terms of a list of axioms) and how to prove theorems about them based on precise, abstract definitions.
The primary focus of this course (both in class and in homework) will be on writing and constructing proofs, as opposed to computations with matrices. You do not need to have prior experience with writing proofs to enroll in this course; we will start out with an introduction to proofs. However, since this is a 4000-level course we will move through the introduction fairly quickly (as opposed to 3000-level courses which are more focused on teaching how to work rigorously and write proofs).
Prerequisites: The only official prerequisite is one of the 2000-level linear algebra courses (Math 2210, Math 2230, Math 2310, or Math 2940). A prior proof-based course is not required, but may be helpful.
Math 4310 vs. Math 4330: Math 4310 has an "honors" counterpart, Math 4330, which is offered in the fall. The courses cover roughly the same list of material, but Math 4330 proceeds at a deeper and more thorough level. If you are considering going to grad school in mathematics, you are strongly encouraged to take Math 4330 instead.
Textbook: The textbook is Linear Algebra by Larry Smith (ISBN 978-1-4612-7238-0), published in the Springer "Undergraduate Texts in Mathematics" series. An E-Book version is available to students for free through the Cornell library (You can download it from here on the campus network, or log in from off campus here).
The course will cover most of the chapters from the textbook; generally I will spend two or three lectures on a chapter, going through the details of the definitions and proofs. You should read the relevant chapter before class to help you follow along what we're doing in the lecture! We'll also discuss some material not in the book (most importantly, working with arbitrary fields); I will provide supplementary notes on these things. The chapters and supplementary material listed on the schedule page will be what are covered on the exams.
Other Resources: It can be helpful to look at other textbooks, to see multiple presentations of the same material and to have somewhere else to look if the main textbook is confusing. In the past this course has used Linear Algebra by Charles Curtis as a textbook; another popular one is Linear Algebra Done Right by Sheldon Axler. There are many, many others as well. (These links should all let you download the corresponding E-Book if you're on campus; if you're off-campus you can log in through the library website).