Math 341: Elementary Linear Algebra I, Syllabus, Fall 2021

Instructor: Prof. Boris Botvinnik : e-mail botvinn[at]uoregon.edu

Office: Fenton 304

Lectures: Monday, Tuesday, Wednesday, and Friday at 1:00-1:50 pm, 307 University

Office hours: Monday, Tuesday 3:00-3:50 pm, or by appointment.

Textbook: Linear Algebra and Its Applications, 5th Edition, by David C. Lay, Steven R Lay, Judith McDonald, Judi J McDonald.

You are expected to read the textbook carefully, and will be responsible for all the material in those sections that are covered in class. The text contains solutions or hints for odd numbered problems. The homework assignments will consist mostly of even numbered problems, although I strongly recommend that you try some of the odd numbered problems on your own. The accompanying study guide contains a great deal of additional information that you should find helpful.

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.

Math 341 covers systems of linear equations, vector and matrix algebra, determinants, and eigenvectors and eigenvalues, along with various applications. These topics correspond to chapters 1, 2, 3, and 5 of the textbook. The homework page gives a tentative week-by-week breakdown of the sections that will be covered in class. This course will continue next semester with Math 342, which will cover the remainder of the text, including vector spaces, linear independence, bases, dimension, linear transformations, rank and nullity, and inner product spaces. Students will be expected not only to learn to perform vector and matrix computations, but also to understand the abstract theory of linear algebra, including the fundamental definitions and theorems.

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.

Homework

Homework is due in class on Wednesdays, beginning October 6. Late homework will not be accepted. There will be 9 homework assignments, the last of which will not be graded. Your lowest homework score will be dropped. You may collaborate with other class members on your homework, although you must each write up your solutions independently and in your own words. To avoid falling behind, you should do the reading and homework as the material is presented in class, rather than leaving it all until the last minute.

The homework should be uploaded to Canvas by the deadline. You can solve the homework by:

Exams

There will be two in-class midterm exams and a the final exam. It is allowed to have one index card with anything you would like to during the exam.

I would like to collect the exams electronically, similar to the homework, so that they could be returned to you graded with my notes electronically as well.

Homework:	20%
First Midterm Exam:	20%
Second Midterm Exam:	20%
Final Exam:	40%

Week	Material	Textbook	Announcements
09/27 - 10/01	Systems of linear equations, row-reduced echelon form	1.1, 1.2, 1.3	Welcome!
10/04 - 10/08	Matrix-vector product, solution sets, applications	1.4, 1.5, 1.6
10/11 - 10/15	Linear independence, linear transformations	1.7, 1.8, 1.9, 1.10
10/18 - 10/22	Applications of linear transformations, review, midterm. Matrix multiplication.	1.10, 2.1	Midterm 1 on Friday, October 22
10/25 - 10/29	Inverses, matrix factorizations	2.2, 2.3, 2.4, 2.5
11/1 - 11/5	Subspaces of R^n. Determinants	2.8, 2.9, 3.1
11/8 - 11/12	More determinants. Review, midterm.	3.2, 3.3	Midterm 2 on Friday, November 12
11/16 - 11/20	Vector spaces, subspaces. Null space, column space.	4.1, 4.2
11/22 - 11/24	Linear independence, bases. Dimension. (3 lectures)	4.3, 4.4, 4.5	Happy Thanksgiving.
11/29 - 12/03	Rank, change of basis. Review.	4.6, 4.7