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Linear Algebra UAF MATH 314

Dr. Latrice Bowman

Section Course Information

Math 314 Linear Algebra Summer 2026 Course Syllabus.

This is a 3-credit asynchronous course. This means that this course is offered through Canvas and there are no set meeting times. For this course, you will be asked to work through the material by watching videos, practicing problems, and completing quizzes and assessments. While this is a self-paced course, there are due dates and completion deadlines that need to be met.
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In this course, I will use a standards-based assessment format instead of the traditional percentage-based system you’ve seen before. This style of assessment will give you a clearer picture of the expectations in our course, how well you have mastered the course material, and how you can improve your understanding (and your grade!). Throughout the course, you will be given opportunities to further develop your skills, assess these skills, and relearn material to improve your understanding. We will have weekly quizzes, weekly activities, and an assessment about every two weeks. Every problem that you see on a quiz or assessment will be mapped to one of the course standards. In addition to these assignments, you will also be asked to complete reflective assignments and course surveys.
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The key ideas of mastery-based learning are:
  • You will either receive credit or need to reassess; There are no 0 grades unless you do not try;
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  • You will be given many opportunities to improve your understanding and your score;
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  • Non-mastery items are based on completion;
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  • Once you have attained a minimum grade you can only improve.
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Instructor and Section Information.

Instructor: Dr. Latrice Bowman
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Office: Chapman 301B
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phone: 907-474-5427 (you will find it easier to reach me through email)
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Student Help Hours.

Hours are by appointment through Zoom. You can use Dr. Bowman’s Appointment Scheduler to set up an appointment.
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Class Meetings.

This is an asynchronous online course so there are no class meeting times, however, you will need to set up times with your proctor to take assessments.
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Course Description.

The goal of linear algebra is to study systems of linear equations. It is difficult to describe the content informally, but there are many algebraic computations that we will extend to arrays of numbers like vectors and matrices. Many applications of linear algebra outside of the textbook are solved using computers however we will be looking at the math behind these so many of the computations will be done by hand and with the use of a calculator. This means that students will:
  • Ability to use matrices to solve equations
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  • Ability to obtain linear combinations of vectors
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  • Ability to solve applications related to vector equations
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  • Ability to demonstrate understanding of linear independence
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  • Ability to find images of and geometrically describe linear transformations
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  • Ability to perform basic and advanced operations on matrices
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  • Ability to prove theorems and demonstrate concept knowledge about invertibility
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  • Ability to compute determinants using multiple methods
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  • Ability to use determinants to solve applications
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  • Ability to prove whether a set is a vector space or a subspace
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  • Ability to demonstrate understanding of spanning sets and bases
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  • Ability to use dimension and rank to demonstrate understanding of vector spaces
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  • Ability to find eigenvalues and eigenvectors in order to diagonalize matrices
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  • Ability to find inner products to demonstrate understanding of orthogonality, normality, and factorizations
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To meet these course outcomes students will be specifically assessed on the following standards:
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Student Learning Outcomes.

Habit Standards assessed throughout the entire semester
  • LA-1 GP (written practice)
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  • LA-2 Communication
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  • LA-3 Reflections
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  • LA-4 Participation
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Content Outcomes assessed within specific content modules (complete descriptions can be found in Canvas)
  • LSAI-1 Linear Equations
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  • LSAI-2 Linear Independence
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  • LSAI-3 Linear Transformations
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  • LSAI-4 Applications of Linear Systems
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  • MD-1 Matrix Operations
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  • MD-2 Matrix Inverses
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  • MD-3 Determinants and Cramer’s Rule
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  • VS-1 Vector Spaces and Subspaces
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  • VS-2 Linearly Independent Set and Coordinate Systems
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  • VS-3 Bases, Dimension and Rank
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  • VS-4 Change of Basis
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  • EIPO-1 Eigenvalues and Eigenvectors
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  • EIPO-2 Diagonalization
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  • EIPO-3 Inner Products
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  • EIPO-4 Orthogonality
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  • EIPO-5 Gram-Schmidt Process
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  • EIPO-6 Least Squares
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