# Math 341 Fall 2015

## Basic course information

Time: MTWF 2:00–2:50 p.m.
Place: 301 Deady Hall.
Textbook: Linear Algebra and Its Applications by David Lay, 5th edition.
Office hours: Tuesday 4:30 - 6:30 and Friday 3:00 - 4:00 in Fenton 303. Subject to change.
Final exam: 2:45 p.m. Tuesday, December 8, per the university Final Exam Schedule
Midterm exams: October 21 and November 13, in class.
There is also WebWork homework, a Canvas webpage for tracking grades and a blog about using computer software.

## Prerequisites

Math 253 or instructor's permission.

## Description and goals

At its heart, linear algebra is about the geometry of systems of linear equations. Linear algebra's importance to both mathematics and its applications rivals—and perhaps exceeds—that of calculus. Unlike calculus, linear algebra becomes clearer in a somewhat abstract setting of vector spaces andlinear transformations. This course is the first in a two-quarter introduction to both concrete and abstract linear algebra.

The main goals of this course are:

• To provide the first tools from linear algebra needed in mathematics, science and engineering. In this course, those tools include Gauss-Jordan elimination, matrix algebra, and determinants.
• To introduce abstract vector spaces and linear transformations and the first notions relating to them, including subspaces, bases, dimension, linear independence, and rank.

Specific "learning outcomes" include being able to find the solutions of a system of linear equations and understand the geometric meaning of the space of solutions; understanding the notions of a subspace, basis, and dimension, finding bases, and computing dimensions; understanding how to represent vectors with respect to different bases; understanding the definitions of linear transformations, some basic examples, and how to write linear transformations in terms of matrices; being able to find bases for the kernel and image of a linear transformation; and being able to compute determinants.

## Policies

 Written homework 20% Online homework 10% Midterm 1 20% Midterm 2 20% Final 30%

### Homework

The course will have both written and online homework. Written homework is due at the beginning of class on Wednesdays, except as noted. Online homework, via WebWorks, is due before class on Mondays, except as noted. (Due dates may change.) You may use any resources you like on the homework, but all resources except the textbook must be cited on your assignment. This includes help from your classmates, friends, or Google. Failure to cite sources constitutes plagiarism, a serious form of academic dishonesty, and will be punished.

You may work together on homework assignments, but you must write up the final version of your answers by yourself. Working on the final write-ups together constitutes cheating.

Late homeworks will not be accepted, but the lowest written homework score and lowest online homework score will be dropped.

The WebWork homework site, for online homework, is https://webwork2.uoregon.edu/webwork2/Math341-13832/ . Written homework assignments are posted below.

A small number of bonus points -- a maximum of 10% of the score on each homework assignment -- will be awarded for following the tutorial on using SageMathCloud alongside the class.

### Exams

All exams will be given in class, and there will typically not be makeup exams. If you know in advance that you will miss an exam, contact me immediately to make arrangements. If you miss an exam because of an emergency (medical, family, ...) you will be expected to provide documentation of that emergency.

All exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). Using any notes or electronic device or communicating with anyone except me during an exam constitutes cheating.

### Students with disabilities

I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.

## Written homework

Again, all written homework is due at the beginning of class on the due date.

## Schedule

This schedule is tentative, and may change during the quarter.

Week
Material
Textbook
Announcements
09/28 - 10/02 Systems of linear equations, row-reduced echelon form 1.1, 1.2, 1.3 Welcome!
10/05 - 10/09 Matrix-vector product, solution sets, applications 1.4, 1.5, 1.6
10/12 - 10/16 Linear independence, linear transformations 1.7, 1.8, 1.9, 1.10
10/19 - 10/23 Applications of linear transformations, review, midterm. Matrix multiplication. 1.10, 2.1 Midterm 1 on Wednesday, October 21
10/26 - 10/30 Inverses, matrix factorizations 2.2, 2.3, 2.4, 2.5
11/2 - 11/6 Subspaces of R^n. Determinants 2.8, 2.9, 3.1

11/9 - 11/13

More determinants. Review, midterm. 3.2, 3.3 Midterm 2 on Friday, November 13
11/16 - 11/20 Vector spaces, subspaces. Null space, column space. 4.1, 4.2
11/23 - 11/25
Linear independence, bases. Dimension. (3 lectures) 4.3, 4.4, 4.5 Happy Thanksgiving.
11/30 - 12/04 Rank, change of basis. Review. 4.6, 4.7

## Handouts

Handouts will be posted here, in case you lost the physical copy.