Math 20F, Linear Algebra, Syllabus

Paul Horn
Email: phorn (at) math dot ucsd dot edu
Office: AP& M 6436
Office Hours: Tuesday, Thursday 2-4, Friday 12:30-1:30

Classes: MWF, 2-4 in CSB 001
Sections:

A01: T10-12, Solis 109; Matlab Section: R10-12, CLICS
A02: T12-2, Solis 109; Matlab Section: R12-2, CLICS

Textbook: Linear Algebra 3rd Edition, by David Lay
Website: http://www.math.ucsd.edu/~phorn/20f

Section A01:

Eric Tressler
Email: etressle (at) math dot ucsd dot edu
Office: AP& M 6436

Section A02:

Raul Gomez
Email: r1gomez (at) math dot ucsd dot edu
Office: AP& M 6446

Linear Algebra is a collection of ideas related to the solution of linear equations. With the advent of computers, linear algebra has become one of the most widely used forms of mathematics. It is used more than calculus. There are applications to all the sciences as well as economics, and statistics. For example, engineers will need to understand the ideas of linear transformations and orthogonality to begin to use Fourier series. Biologists and economists will benefit from diagonalizing matrices to consider iterated powers of matrices which can be used to study and predict survival rates of living organisms. Economists use Markov processes to predict future behavior. All scientists gather data and the questions around correlation and error analysis are best studied using methods of linear algebra. Time permitting, we will show some of the basic applications.

To have such wide application, the methods will need to be introduced in rather abstract forms. This may be the first time the student will be asked to actually prove an abstract theorem and then use it to draw conclusions about a practical problem. There will be many more theorems and ideas to be used than what the student used in previous math courses. Each idea by itself is fairly easy, but to keep track of many ideas can be challenging. This requires the student to be able to consider abstract concepts and be conversant in a new language of mathematics.

When the student enters the work world, the theoretical concepts of linear algebra are used together with the computer to produce solutions. For this reason, this course has a MATLAB computer component. Our goal in introducing MATLAB is not to provide a complete course, but to give a sampling of applications so that when the student enters upper division courses, the transition to computer applications will be less painful. Engineering students should take the Matlab component very seriously as it is often a prerequisite to getting a job in industry.

A warning! This course moves at a faster pace than the other Math 20 courses. This is even more true since this is a summer session course! This course, more than any of the other 20 series courses requires thinking about things in a different way, and becoming comfortable with the concepts takes time.

There will be one midterm exam and one final exam for the course. The midterm will be held on Friday August 22nd, during lecture. The final will be cumulative and will be held Saturday, September 6th, 3-6pm. There will be NO MAKEUP EXAMS.

Doing homework in any mathematics course is vital to build an understanding of the topic. Though homework will not be collected, weekly homework quizzes will be held during the Matlab section, and exams will be partially based on homework questions. There will be NO MAKEUP QUIZZES, however the lowest quiz will be dropped. Homework assignments are available here.

Matlab assignments are designed to allow one to explore some of the important concepts of the course with a computer, allowing the student to examine concepts where the computations involved are too tedious to do by hand. Each week during matlab sections, labs will be done. Matlab labs are due in section the next week. There will be no matlab final. Matlab lab information is available here.

Grades will be assigned based on the following rubric:

15% - Matlab assignments
20% - Homeworks
25% - Midterm
40% - Final

Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction that may include suspension or expulsion from the university.