MATH 2210Q-004/008

Course Syllabus

Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications. Although the course is computational, we will try to mix in a fair amount of true and false questions to get ourselves used to reasoning and coming up with counterexamples.

Book:You will need to obtain a copy of the textbook, which is David C. Lay: Linear Algebra and Its Applications. Any edition you can find from the 3rd on should be fine for this class, so feel free to find a used copy. Homework will consist of problems from the book, I don't care which edition you use, but solutions that I post will be from the 5th edition.

Location: Monteith 112
Time: MWF, 9:05 (sec008), 10:10 (sec004)
Instructor: Bobby McDonald
Instructor Website: https://mathrjsm.com/
Office: Monteith 120 (it's across the hall!)
Office Hours: Mon 11:15-1:15, Fri 11:15-12:15
email: robert.j.mcdonald@uconn.edu (use this for logistical questions)

Piazza: piazza.com/uconn/fall2018/math2210q004008/home (use this for every other question)
HuskyCT: All course announcements, grades, solutions to quizzes and homework, practice exams, and filled out versions of the lecture notes will be posted to our course webpage at HuskyCT.

Tentative Outline

The outline below is tentative. Our plan is to cover an average of two sections per week, and use Friday to take a quiz (sometimes in groups), catch up on material, and have a discussion/review. Try to come with Friday's class with questions, so we have plenty of examples to do. Homework is always due the Monday after we finish a section, and you can click on the assignments to see solutions after they're due. I'll always hand out the slides when we begin a section, but if you miss a class, you can click on the links in the table below to get a digital copy. Use the book to fill them out, come to my office hours, find a friend who is willing to share, or wait until Saturday when I post them to HuskyCT!

Week Day What we expect to do in class Homework
1 Mon 8/27 1.1 Systems of Linear Equations
Wed 8/29 1.2 Row Reduction and Echelon Forms
Fri 8/31 1.3 Vector Equations 6, 9, 11, 15, 21, 23, 25
2 Mon 9/3 Labor Day (start reading 1.4 and 1.5)
Wed 9/5 1.4 Matrix Equations, 1.5 Solution Sets 5, 11, 15, 19, 23, 30, 32
Fri 9/7 Quiz (1.1-1.3) 5, 11, 15, 23, 30, 32
3 Mon 9/10 1.7 Linear Independence 1, 5, 7, 15, 16, 20, 21
Wed 9/12 1.8 Introduction to Linear Transformations 2, 8, 9, 21, 31
Fri 9/14 Quiz (1.4-1.5)
4 Mon 9/17 1.9 The Matrix of a Linear Transformation 1, 5, 13, 19, 23, 26, 34
Wed 9/19 2.1 Matrix Operations 2, 5, 7, 10, 15
Fri 9/21 Quiz (1.7-1.8)
5 Mon 9/24 2.2 The Inverse of a Matrix 3, 6, 7, 9, 13, 29
Wed 9/26 2.3 Characterizations of Invertible Matrices 1, 3, 11, 13, 15, 28
Fri 9/28 Quiz (1.9-2.1)
6 Mon 10/1 2.5 Matrix Factorizations
Wed 10/3 mock quiz (2.2-2.5), review for exam
Fri 10/5 EXAM 1 (chapters 1 and 2) Practice Exam
7 Mon 10/8 3.1 Introduction to Determinants 4, 8, 13, 20, 21, 37, 39
Wed 10/10 3.2 Properties of Det, 8, 10, 16, 17, 20, 27, 34
Fri 10/12 Quiz (3.1), 3.3 Cramer’s Rule 4, 5, 6, 22, 23
8 Mon 10/15 4.1 Vector Spaces and Subspaces 1, 3, 8, 13, 23, 31
Wed 10/17 4.2 Null Spaces, Column Spaces 3, 11, 17, 25, 33, 34
Fri 10/19 Quiz (3.1-3.3)
9 Mon 10/22 4.3 Linearly Independent Sets; Bases
Wed 10/24 4.4 Coordinate Systems
Fri 10/26 Quiz (4.1,4.2)
10 Mon 10/29 5.1 EigenVectorss
Wed 10/31 5.2 The Characteristic Equation
Fri 11/2 Quiz (4.3,4.4)
11 Mon 11/5
Wed 11/7 mock quiz (5.1,5.2), review for exam
Fri 11/9 EXAM 2 (chapters 3 and 4, 5.1 and 5.2)
12 Mon 11/12 5.3 Diagonalization
Wed 11/14 5.4 Eigenvectors and Linear Transformations
Fri 11/16 Quiz (5.1-5.2)
13 Mon 11/19 Thanksgiving Break
Wed 11/21 Thanksgiving Break
Fri 11/23 Thanksgiving Break
14 Mon 11/26 6.1 Inner Product, Length, and Orthogonality
Wed 11/28 6.2 Orthogonal Sets
Fri 11/30 Quiz (5.1-5.4)
15 Mon 12/3 6.3 Orthogonal Projections
Wed 12/5 6.4 The Gram–Schmidt Process
Fri 12/7 Review