MA 113: Linear Algebra


Back to my homepage


Syllabus [PS] [PDF]

Exam materials: sample papers, actual papers, solutions

Course materials on this webpage are in two different formats: PDF and PS (Postscript). PDF files are handled, for example, by Adobe Acrobat Reader. It makes sense to learn how to handle PS files as well. I suggest some public-domain software that opens these files: Ghostview, a user-friendly interface to Ghostscript (so you need both of these).
A sample Michaelmas term paper [PS] [PDF]
Solutions to the sample Michaelmas Term paper [PS] [PDF]
The Michaelmas Term paper [PS] [PDF]
Solutions to the Michaelmas Term paper [PS] [PDF]
A sample Hilary term paper [PS] [PDF]
Solutions to the sample Hilary Term paper [PS] [PDF]
The Hilary term paper [PS] [PDF]
Solutions to the Hilary Term paper [PS] [PDF]
A sample Trinity Term paper (warning: it is more time-consuming than the actual exam paper; I just tried to squeeze in enough things for you to practice!) [PS] [PDF]
Solutions to the sample Trinity Term paper [PS] [PDF]
The Trinity Term paper [PS] [PDF]
Solutions to the Trinity Term paper [PS] [PDF]


Reading suggestions

There will be no lecture notes for this course, so you are encouraged to take notes during the lectures — it takes effort but is really helpful. There are many books which you might find helpful, though they do not correspond exactly to the course content and the order of presentation of topics. For the first part of the course (Linear Algebra in 2d and 3d, systems of linear equations, operations with matrices), have a glance at Anton/Rorres' Elementary Linear Algebra (applications version). For the second part of the course (abstract vector spaces, linear operators, quadratic forms etc.) the exposition will be mostly close to the one from Gelfand's Lectures on Linear Algebra (there should be several copies in the College Library, also some 20 copies belonging to the School of Maths are in my office, and you may borrow them as well). You are also encouraged to attempt problems from Linear Algebra Problem Book by Paul Halmos (some of these problems are quite difficult!).

Online textbooks

Elementary Linear Algebra, lecture notes by Keith Matthews (this link is just for your information, you should not expect it to be much related to what happens in class!)
MIT Linear Algebra Course, you can find several useful essays on Linear Algebra there, as well as lots of problems with solutions. (Again, this course is different from what we have in class, so do not rely on these materials too much!)


These handouts will be used during the second and the third term; they will be distributed in class, so you do not need to download them.

Linear operators on a finite-dimensional vector space: a brief HOWTO [PS] [PDF]
Jordan normal form theorem [PS] [PDF]
Examples on computations with Jordan normal forms [PS] [PDF]
Orthonormal bases, orthogonal complements, and orthgonal direct sums [PS] [PDF]
Some standard types of linear algebra questions [PS] [PDF]
Several problems in Linear Algebra (bonus questions for those who feel confident with the course) [PS] [PDF]

Assessment etc.

You will get home assignments each week. There will be two half-exams (90 minutes each) on the weeks after the end of Michaelmas and Hilary terms, and a 3-hour exam in the end of the year. Your final grade will be maximal of 100% final exam, and 70% of final exam plus 15% of home assignments grade plus 15% of the arithmetic mean of two half-exam results.