University of Minnesota
CSCI2033: Linear Algebra
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Syllabus
CSci 2033, Spring 2025

Instructor

Carl Sturtivant, carl@umn.edu

Textbook

Lipschutz, “3000 Solved Problems in Linear Algebra”, 9780070380233.

Optional

Lipschutz & Lipton, “Linear Algebra”, 6th Edition, 9781260011449.

Read this document very carefully, as it defines what is required to perform effectively in this class. You will be assumed to have read and understood this syllabus: ignorance is not an excuse. If later in the semester you realize for example, that you can't attend the final exam, this will be your fault and no makeup exam will be supplied. Avoid attempting to make yourself an exception.

Warning Be sure to read and fully understand theorems and proofs and get sufficient practice to be able to survive the quizzes, and therefore the course.

This class assumes no previous experience with linear algebra. Linear algebra bridges the abstract and the concrete and its uses pervade both mathematics and science, including computer science. In this course you will be introduced to how the basic machinery of linear algebra works, putting you in a strong position to pursue applications in all areas of computer science.

It is essential for most students to carefully follow the class lectures and closely read any distributed documents, as well as attend office hours to learn about problem solving in parallel to understanding theory, and do exercises pertaining to those, for typically ten hours per week. This provides you with an opportunity to work in groups and get help of any kind. Attend your discussion section where you will be able to do this. Your job is to internalize the workings of linear algebra so that both technical matters and semantics are clear. Both will be examined on quizzes and the final examination.

On occasion you may want to use GNU Octave which is a free software implementation of the MATLAB programming language. Some hand computations may be very laborious. This is free software and you may download an installation for your computer, or use it on CSE machines. Nevertheless, this course covers how linear algebra actually works, and you will need to be able to establish your understanding of such by hand in a quiz or exam. You will not be examined on your use of these software tools.

Course content very approximately in temporal order is as follows. However some subjects may be approached non-linearly because of natural cross connections in the material. A detailed listing of scheduled topics kept updated as the course is taught is available on the class website: consider this to be a part of this syllabus.

  • The algebraic form of many linear equations in many variables

    • Column vectors, scaling, addition

    • Linear combination

    • The matrix-vector product

  • The Geometric interpretation of scaling, addition, linear combination

  • The algebra of linear combinations and matrix-vector multiplication

  • Exploring linear transformations

    • The range and its parametric representation

    • Coordinates, base vectors

    • Injectivity, surjectivity, the null space

  • Subspaces and Linearity

    • Closure under linear combination

    • Linear Independence

    • The matrix of a linear transformation

  • Elimination & matrix multiplication

    • Elementary row operations and matrix multiplication

    • Composition of linear transformations

    • Inverses of bijective linear transformations

  • Matrix algebra and operations on linear transformations

  • Solving homogeneous linear equations

    • Elimination and elementary matrices

    • Row Echelon Form, Row Canonical Form (reduced row echelon form)

    • Finding the range of a linear transformation

  • Solving inhomogeneous linear equations

    • Existence and uniqueness of solutions

    • Detecting invertibility of a matrix

    • Finding the inverse of a matrix

  • Dimension, Vector Spaces

  • Determinants, the formalities of the inverse

  • Lengths, angles, orthogonality

  • Change of scalars, the complex numbers

  • Inner product spaces

  • Eigenvalues and Eigenvectors

    • Invariant subspaces

    • Symmetric and hermitian transformations

    • Orthogonal and unitary transformations

    • Singular Value decomposition

Evaluation: The following rules will be strictly enforced.

Evaluation will consist of quizzes (12), and a final examination. You must pass the final examination by attaining at least 50% of the available points on it. Persons who fail to do so will receive an F for the course. All quizzes and examinations are open book and open notes, but NO ELECTRONIC DEVICES. Do not schedule any absences during the course –- there are no make-up quizzes. However, to account for unavoidable absences for any reason the two lowest quiz scores will be discarded. Thus your grade depends upon ten (10) quiz scores.

Warning: Quizzes are comprehensive –- they may have questions on any previously covered material, not just recently covered material. The final examination is also comprehensive.

Grading is absolute (i.e. not on a curve). The overall grade will be based upon: 6% for each quiz for a total of 60%, and 32% for the final. In addition 8% of the course will be recorded for scholastic conduct. Students who do not violate the scholastic conduct rules (see below) will receive the full 8%. A minimum of 60% is necessary for an S or C- grade.

Grading will be as follows: 95.0% or above yields an A, 90.0% an A-, 85% = B+, 80% = B, 75% = B-, 70% = C+, 65% = C, 60% = C-, 55% = D+, 50% = D, and less than 50% yields an F. Percentages are not rounded when using this scheme, because this would be tantamount to moving all of the grade boundaries down by 0.5%.

Quizzes and the final examination will be scanned into Gradescope and graded there. If you have a question about grading, address it to the TAs via Gradescope by making a regrade request. Only if something wholely unreasonable has occurred will the instructor intervene.

Furthermore, there is a limit of 7 days from when a quiz grade is posted online for grading problems to be dealt with. So check your grading online frequently.

Incompletes will in general not be given. An incomplete will be considered only when a provably serious family or personal emergency arises during the end part of the course, proof is presented, and the student has already completed all but a small portion of the work.

Make-up Exams will in general not be given. Verify at the start of the semester that you can attend all quizzes and exams at the stated dates and times, and if you cannot do so, then withdraw from the course. A make up final will be considered only when a provably serious family or personal emergency arises during the relevant part of the course, and proof is presented. There are no make up quizzes.

Scholastic conduct must be acceptable. Specifically, you must do your quizzes, and examinations yourself, on your own. Read these linked documents as a part of this syllabus. The minimum penalty for an egregious violation of these rules is an F for the course. A lesser penalty may be given at the instructor's sole discretion if he deems the violation is not egregious.