Math 308 P

Matrix Algebra with Applications

Winter, 2019

Professor: Robin Graham Teaching Assistant: Jacob Richey

Lectures: Bagley 154, MWF 12:30-1:20

TA Sections: Mary Gates Hall 271, Tuesdays at 1:30 (PA), 2:30 (PB), 3:30 (PC)


Course Content: Math 308 is an introductory course in linear algebra intended for students in engineering, mathematics, and the sciences. Topics will include systems of linear equations, vectors in Euclidean space, matrices, subspaces, determinants, eigenvalues, eigenvectors, and applications.

This course will probably be unlike other math courses you have had before. It involves some abstract reasoning and logical arguments to justify answers in addition to computational methods. It is particularly important to focus on learning the vocabulary and how to use it correctly. Many of the ideas can be interpreted geometrically which helps develop intuition. The subject has applications in many different areas which we will also explore.


Text: Linear Algebra with Applications, Second Edition, by Jeffrey Holt

Videos: These YouTube videos by 3Blue1Brown are an excellent resource for understanding the geometry behind many of the concepts we will learn in this class. Links to the relevant videos will be posted in the weekly assignments.

Homework: There will be two kinds of homework assignments:

Exams: There will be be two midterm exams and a final exam:

Grading: Your grade will be based on a total obtained as follows:

Webassign Homework 10%
Conceptual Problems Homework 10%
Midterm 1 20%
Midterm 2 20%
Final Exam 40%


Math 308 P Course Schedule: The schedule is being adjusted because of the Snow Days. See the weekly assignments below.

Department of Mathematics Math 308 webpage contains more Conceptual Problems and an archive of old exams.



Weekly Assignments


Week 1 (Jan 7-11)

Readings from the textbook:

  • Section 1.1: Lines and linear equations
  • Section 1.2: Linear systems and matrices

    Video:

  • Essence of linear algebra

    Homework:

  • Conceptual Problems #1 Due in lecture Wednesday, January 9.
  • WebAssign Homework Due Thursday, January 10, 11pm

    WebAssign support in the Math Study Center: WebAssign support staff will be present to help with access and code issues at these times.


    Week 2 (Jan 14-18)

    Readings from the textbook:

  • Section 2.1: Vectors
  • Section 2.2: Span
  • Section 2.3: Linear Independence

    Video:

  • Vectors
  • Linear combinations, span, bases

    Homework:

  • Conceptual Problems #2 Due in lecture Wednesday, January 16.
  • WebAssign Homework sections 1.2, 2.1, Due Thursday, January 17, 11pm


    Week 3 (Jan 21-25)

    Readings from the textbook:

  • Section 2.3: Linear Independence
  • Section 3.1: Linear Transformations

    Video:

  • Linear combinations, span, bases
  • Linear Transformations


    Homework:

  • Conceptual Problems #3 Due in lecture Wednesday, January 23.
  • WebAssign Homework Sections 2.2, 2.3 Due Thursday, January 24, 11pm


    Week 4 (Jan 28-Feb 1)

    Readings from the textbook:

  • Section 3.1: Linear Transformations
  • Section 3.2: Matrix Algebra (skip elementary matrices and partitioned matrices)

    Video:

  • Linear Transformations
  • Matrix Multiplication
  • Three-dimensional Linear Transformations


    Midterm 1: Wednesday, January 30 in class

    Includes everything we covered in Chapters 1 and 2

  • Exam Policy:

  • Make-Ups: There are no make-up exams. If you have a conflict with an exam because of religious holidays or participation in university sponsored activities (such as a class field trip or athletics), speak to Prof. Graham about it at least one week before the exam. You will be required to provide documentation for your absence.

  • Here is a collection of Midterm 1 Exams from recent quarters. Most of these exams include questions about Section 3.1: Linear Transformations. Our Midterm 1 will not cover Linear Transformations.

  • Jacob will conduct review sessions in the TA sections on Tuesday, January 29.

  • The Center for Learning and Undergraduate Enrichment (CLUE) will run a priority drop-in session for Math 308 on Tuesday evening, January 29. This can be a good resource for getting your questions answered in preparation for the exam.

    Homework:

  • No Conceptual Problems due this week
  • WebAssign Homework Section 3.1 Due Thursday, January 31, 11pm


    Week 5 Revised (Feb 4-8)

    Readings from the textbook:

  • Section 3.3: Inverses (skip partitioned matrices)

    Video:

  • Three-dimensional linear transformations
  • Linear transformations with non-square matrices


    Homework:

  • Conceptual Problems #4 Due date postponed until next week because of Snow Days
  • WebAssign Homework Sections 3.2, 3.3 Due Thursday, February 7, 11 pm


    Week 6 Re-Revised (Feb 11-16)

    Readings from the textbook:

  • Section 5.1: The Determinant Function
  • Section 5.2: Properties of the Determinant (skip Partitioned Matrices)
  • Section 4.1: Introduction to Subspaces
  • Begin Section 4.2: Basis and Dimension

    Video:

  • 3Blue1Brown: Determinants
  • 3Blue1Brown: Inverses, column space, rank and nullspace
  • MIT Professor Strang Lecture 18: Properties of Determinants
  • MIT Professor Strang Lecture 19: Determinant formulas and cofactors


    Homework:

  • Conceptual Problems #4 Due in lecture Wednesday, February 13
  • WebAssign Homework Section 5.1, Due Thursday, February 14, 11 pm
  • WebAssign Homework Section 5.2, Due Saturday, February 16, 11 pm


    Week 7 (Feb 18-22)

    Readings from the textbook:

  • Section 4.2: Basis and Dimension
  • Section 4.3: Row and Column Spaces

    Video:

  • 3Blue1Brown: Inverses, column space, rank and nullspace
  • MIT Professor Strang Lecture 6 : Column Space and Nullspace
  • MIT Professor Strang Lecture 9 : Independence, Basis, and Dimension
  • MIT Professor Strang Lecture 10 : The Four Fundamental Subspaces


    Homework:

  • Conceptual Problems #5 Due in lecture Friday, February 22
  • WebAssign Homework Sections 4.1, 4.2 Due Thursday, February 21, 11 pm


    Week 8 (Feb 25-March 1)

    Readings from the textbook:

  • Section 4.3: Row and Column Spaces
  • Section 4.4: Change of Basis (only through the end of p. 201)
  • begin Section 6.1: Eigenvalues and Eigenvectors

    Video:

  • 3Blue1Brown: Inverses, column space, rank and nullspace
  • 3Blue1Brown: Change of bases
  • MIT Professor Strang Lecture 6: Column Space and Nullspace
  • MIT Professor Strang Lecture 9: Independence, Basis, and Dimension
  • MIT Professor Strang Lecture 10: The Four Fundamental Subspaces
  • MIT Professor Strang Lecture 31: Change of Basis; Image Compression


    Homework:

  • Conceptual Problems #6 Due in lecture Wednesday, February 27
  • WebAssign Homework Sections 4.3, 4.4 Due Thursday, February 28, 11 pm


    Week 9 (March 4-8)

    Readings from the textbook:

  • Section 6.1: Eigenvalues and Eigenvectors
  • begin Section 6.2: Diagonalization

    Video:

  • 3Blue1Brown: Eigenvectors and eigenvalues
  • MIT Professor Strang Lecture 21: Eigenvalues and Eigenvectors
  • MIT Professor Strang Lecture 22: Diagonalization and Powers of A


    Midterm 2: Wednesday, March 6 in class

    Includes everything we covered in Chapters 3,4,5

  • Exam Policy:

  • Make-Ups: There are no make-up exams. If you have a conflict with an exam because of religious holidays or participation in university sponsored activities (such as a class field trip or athletics), speak to Prof. Graham about it at least one week before the exam. You will be required to provide documentation for your absence.

  • Here is a collection of Midterm 2 Exams from recent quarters. Some of these exams may include material that we did not cover or are have not gotten to yet, like eigenvalues and eigenvectors. Eigenvalues and eigenvectors will not be included on our exam.

  • Jacob will conduct review sessions in the TA sections on Tuesday, March 5.

  • The Center for Learning and Undergraduate Enrichment (CLUE) will run priority drop-in sessions for Math 308 on Thursday evening, February 28 and Monday evening March 4, from 7-9 pm in the Mary Gates Hall Commons. This can be a good resource for getting your questions answered in preparation for the exam.

    Homework:

  • No Conceptual Problems due this week
  • WebAssign Homework Section 6.1, Due Thursday, March 7, 11 pm


    Week 10 (March 11-15)

    Readings from the textbook:

  • Section 6.2: Diagonalization
  • Section 6.3: Complex Eigenvalues and Eigenvectors

    Video:

  • 3Blue1Brown: Eigenvectors and eigenvalues
  • MIT Professor Strang Lecture 21: Eigenvalues and Eigenvectors
  • MIT Professor Strang Lecture 22: Diagonalization and Powers of A

    Homework:

  • Conceptual Problems #7 Due in lecture Friday, March 15
  • WebAssign Homework Sections 6.2, 6.3 Due Thursday, March 14, 11 pm



    Final Exam Information

    The final exam is Thursday, March 21, from 8:30-10:20 am, in our usual classroom BAG 154

    It will cover the entire course.

    Class on Friday, March 15 will consist of a review.

  • Exam Policy:
  • Make-Ups: There are no make-up exams. If you anticipate a problem making the exam, speak to Prof. Graham about it in advance.

  • Seating Chart: We will use a seating chart for the final exam. Before the exam I will send you a chart of the seats in the room with an assigned seat for each student. Jacob and I will be checking that each student is the assigned seat.

  • Here is a collection of Final Exams from recent quarters. All classes do not necessarily cover the same material, so there may be some problems on these exams on material that we did not cover and you are not responsible for.



    UW Resources:

    Disability Resources for Students

    Counseling Center

    Center for Learning and Undergraduate Enrichment (CLUE)

    UW Math Home Page