Introduction

Linear algebra has spectacular applications in disciplines as apparently diverse as computing, engineering and biology; moreover, it's at the core of much of pure mathematics. This course provides an introduction to linear algebra. As befits a 300-level course, it will involve a mixture of computation and proof, and of theory and application.

Logistics

Professor Jeff Achter
j.achter@colostate.edu
Weber 216, 491-6716
Lecture: MWF 12-12:50PM, Engrg E104
Office hours: TBA
The main textbook for this course is the free, on-line textbook A First Course in Linear Algebra, by Robert Beezer, sometimes supplemented with additional notes. More information about textbooks.

Requirements and other expectations

Homework and classwork -- 35% Homework will be assigned weekly, and is due at the beginning of class on Wednesdays. No late homework will ever be accepted. Your work must be neat, and the pages stapled, in order to be graded.
There will occasionally be short, in-class activities. These experiences cannot be made up. Grades from these will be used to help assess borderline grades at the end of semester.
Midterms -- 40% There will be in-class exams on Wednesday, October 1 and Wedesday, November 12.
Final -- 25% The final exam for this course will be held on Tuesday, December 16, 9:10-11:10AM.
No makeup exams will be given; you must take each exam as scheduled. You must pass the final in order to pass the course.

Help

This is challenging material, and you may need a little help every now and then.

Questions directed to j.achter@colostate.edu will be answered swiftly.
Professors Dan Bates and Kelly McArthur are also teaching sections of Math 369, and will make some of their office hours available to us.
Professor Dick Painter will also hold common office hours for 369 on Monday 2-4 and Tuesday 10-12. (Room to be announced.)
Keep an eye on the help section of the page for more resources.

Topics

Here is a rough estimate of the syllabus for the course.

Week	Topic	Ref
1	Systems of linear equations examples and applications; row reduction; echelon forms; associated(augmented) matrices	WILA What is Linear Algebra? SSLE Solving Systems of Linear Equations RREF Reduced Row-Echelon Form
2	Matrix equations Rⁿ; arithmetic of vectors; Ax=b structure of (in)homogeneous solutions	VO Vector Operations MO Matrix Operations MM Matrix Multiplication HSE Homogeneous Systems
3	Matrix operations matrix multiplication; row operations; inverse matrices; span.	MISLE Matrix Inverses and Systems of Linear Equations LC Linear Combinations SS Spanning Sets
3	Independence linear independence; column space; solvability; rank	LI Linear Independence LDS Linear Dependence and Spans CRS Column and Row Spaces DM Determinant of a Matrix PDM Properties of Determinants of Matrices
5	Determinants, applications
6	Backwards and forwards review; exam; abstract vector spaces	VS Vector Spaces
7	Vector spaces dimension; basis; coordinates	S Subspaces LISS Linear Independence and Spanning Sets B Bases D Dimension PD Properties of Dimension
8	Transformations linear transformations	LT Linear Transformations rank and nullity
9	Bases and matrices	VR Vector Representations MR Matrix Representations CB Change of Basis
10	Eigenvectors eigenvalues and eigenvectors; geometry;	EE Eigenvalues and Eigenvectors PEE Properties of Eigenvalues and Eigenvectors
11	Eigenvectors II characteristic polynomial; diagonalization; applications
12	Backwards and forwards review; exam; inner products
13	Inner products norm, orthogonality	Section O Orthogonality
14	Orthogonalization Gram-Schmidt, projection	function approximation least squares
15	Wrapping up applications; review