Mathematics 2270-03: Linear Algebra

Schedule: Monday, Wednesday, Friday at 4:35-5:50 PM (in LCB 308)

Text: Serge Lang, Linear Algebra, Third Edition, Springer


Office: LCB 104

Phone: (801)581-5272


Office hours: After classes or by arrangement.

Course Content: This is a Honors section of Math-2270. We use a different, considerably more difficult, textbook than the regular sections. Moreover, the exams are more difficult.
We plan to cover chapters 1 to 8 of the textbook.
Goals and Objectives: The main objective of this course is to learn rigorous foundation of linear algebra, to learn how to do proofs and write them in mathematically precise form.
We will assume that students are familiar with routine calculations done in regular calculus courses, so these will be deemphasized in the course.
We shall start by studying general vector spaces and linear maps between them. We shall discuss the notions of linear independence of vectors, bases of vector spaces and their dimension. For finite dimensional vector spaces, we shall discuss their relationship with spaces of column vectors and matrices introduced in calculus.
Then we shall introduce the notion of inner product spaces and study their geometric properties. We shall define special classes of linear maps: orthogonal, unitary, symmetric and hermitian, and study their properties.
Then we shall introduce the notions of eigenvalues and eigenvectors of linear maps, and study spectral theorem for various classes of linear maps.
We plan to cover first eight chapter of the textbook. Time permitting, we shall also discuss the Jordan normal form of linear maps.
Tests and Grading:
Homeworks will be assigned on regular basis, but not collected or graded. Some interesting homework problems will be discussed in class after students worked on them.
There will be three take-home midterm tests. They will be posted here on regular intervals.
The problems on these tests will be of different degree of difficulty. They will require from students to write up detailed proofs of various statements related to the material covered in class. The students will have about two weeks to work on each take-home exam.
The final grade will be based on the score on these three exams.
Practice problems:
Gauss elimination
First Midterm Test
Second Midterm Test
Third Midterm Test

Notes on determinants (an appendix to Ch. VI)

Last edit by dm, October 15, 2018.