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Math 590 - Linear Algebra

Spring 2019

TuTh 09:30 - 10:45 AM SNOW 302

Terry Soo, Snow 507

Office hours: Tuesdays 2-3. Wednesdays 2-3.

email: tsoo@ku.edu

tel: 785-864-4360

Course description.

One of Descartes many accomplishments was that he gave geometry coordinates so that we may describe a unit circle as the set of all points (x,y) on the Cartesian plane such that the sum of their squares is equal to one. You may recall that if we use polar coordinates, then this circle is simply the set of points (r, theta) such that r=1. One of the objectives of those exercises you did in calculus was to illustrate the importance of using coordinates and using a suitable coordinate system. Try describing a square using polar coordinates. Did you ever see the equation for a rotated ellipse?

In this course, we will study an important class of transformations that are linear. You may recall from calculus that differentiable functions are locally linear, that is, they can be approximated by a line with slope given by the derivative. In many mathematical and practical circumstances, it is necessary to understand the linear approximation to a difficult problem in order to comprehend its complex behavior. Thus linear algebra is an important and fundamental subject in mathematics. In order to do computations we will need to give linear transformations coordinates; these coordinates turn out to be matrices, which you might remember were introduced as a compact way of writing a system of linear equations.

A highlight of this course will be determining when a matrix is diagonalizable; that is, when we can find an suitable change of coordinates so that matrix mulitplication is simple mulitplication!

In this course, not only will you be required to be able to carry out routine computations in the sense of Math 290, you will be required to read and write proofs. Proofs will be an important part of the course and we will spend some time introducing how to read and write proofs. Computers are able to carry out all the computations done in Math 290 and Math 590, so it is more important than ever that we understand the mathematics behind why and how your calculator works, and in order to this, we must begin to understand the concept of a proof in mathematics.

We will aim to cover the following topics, as time permits.

1.) Reading and writing proofs

2.) Vector spaces

3.) Matrices

4.) Linear Transformations

5.) Determinants

6.) Eigenvalues

7.) Diagonalization

8.) Inner-product spaces

As Morpheus says, unfortunately, no one can be told what linear algebra is; you have take the course for yourself: Neo meets Morpheus

Prerequisites.

MATH 127 or MATH 147 or MATH 223 or MATH 243, and MATH 290 or MATH 291. Not open to students with credit in MATH 792.

Grading

Subject to revision

Best of Scheme A and B.

Scheme A

Homework 20%

Quizzes 20%

Midterm 20% (March 5)

Final 40%

Scheme B

Final 100%

Note, do not be rely on Scheme B; my experience tells me that rarely do the grades differ by more than a third of a letter grade under the two schemes.

KU final exam schedule

There are no possibilities for make-up quizzes or midterms; if you have a legitimate excuse for missing an exam (for example, medical reasons), then the absense will be excused without penalty; in the case of quizzes, your other quizzes will simply be worth more, and in the case of a midterm, your final exam will be worth more.

No textbook is required.

Lecture notes will be provided.

Suitable secondary references:

Linear Algebra, Friedberg, Insel, and Spence.

Linear Alegbra, Hoffman and Kunze.

Quizzes.

Quizzes can cover material from grade 1 up to and including the previous day.

Quiz 1: Tuesday February 12. Sample Quiz Q1.

Quiz 2: Tuesday February 26.

Homework:

HW0: Due Tuesday January 29.

Solutions

HW1: Due Thursday February 7.

Solutions

HW2: Due Thursday February 21.

Solutions.

HW3: Due Thursday February 28.

Notes:

Sets, relations, and functions

Writing Proofs

Induction and well-ordering

Introduction to vector spaces

Linear Independence

Linear transformations and isomorphisms