Welcome to MATH 332

Fall 2026

Linear Algebra: Theory and Applications

This is the course website for MATH 332 — Fall 2026 Section 002 at Illinois Institute of Technology.

Course Description

This course develops the theory and applications of linear algebra through systems of equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, and inner product spaces. Python will support visualization, numerical computation, symbolic computation, and experimentation.

Instructor: Fred J. Hickernell

Fred J. Hickernell

Brief bio: Fred J. Hickernell is professor of applied mathematics. His research focuses on improving the efficiency of computer simulations and developing justifiable stopping criteria. He has spent most of his career at Hong Kong Baptist University and Illinois Institute of Technology, often in academic administrative roles. He has served on the editorial boards of the Journal of Complexity, Mathematics of Computation, and the SIAM Journal on Numerical Analysis. He is a Fellow of the Institute of Mathematical Statistics and the recipient of the 2016 Joseph F. Traub Prize for Achievement in Information-Based Complexity.

Hickernell speaks Cantonese and enjoys Chinese food. He is married with adult children. He enjoys discussing matters of substance. His most important identity is a disciple of Jesus.

Required course materials

  • WileyPLUS access: WileyPLUS is required for this course. All homework will be assigned, completed individually, and automatically graded through WileyPLUS. Launch each homework assignment from Canvas.
  • Textbook: Howard Anton, Elementary Linear Algebra: Applications Version, 12th edition. Single-term WileyPLUS access includes the online textbook for the duration of the course, so a separate printed copy is optional. See Resources for details.

To read the online textbook without opening a homework assignment, open Wiley Course Resources in Canvas, select Course Resources, and click Launch beside WileyPLUS eTextbook. Use the Practice tab for additional practice. See Wiley’s illustrated access instructions. If Wiley Course Resources is missing from your course menu, let the instructor know.

Recommended resources
Prerequisites

The prerequisite is MATH 251. It will help to be familiar with:

  • A bit of vectors and matrices (but not required)
  • Jupyter notebooks
Where to find it

Class meetings combine whiteboard explanation with linked lecture slides, live polls, and computational activities. Use the course website as the starting point for each meeting, and come prepared to open the slides, Canvas, and Jupyter notebooks during class.

The course website is the authoritative source for course information, schedules, lecture notes, and assignment details. Use Canvas for announcements, launching WileyPLUS homework, completing the diagnostic survey, and checking grades.

This course website Canvas
Course information Grades
Schedule and lecture slides Announcements
Jupyter notebooks WileyPLUS homework launches
Assignment rules, details, and due dates Diagnostic survey
Quizzes and tests
Required resources
Course policies
Repository access instructions
Course repository

Course Outline

Why Linear Algebra?

Lecture slides. Course motivation and roadmap.

Systems of Linear Equations and Matrices

Lecture slides. Anton, Chapter 1. Detailed pacing is TBD.

Inverses and Invertibility

Lecture slides. Anton, Chapter 1. Detailed pacing is TBD.

Matrix Structure and Transformations

Lecture slides. Anton, Chapter 1. Detailed pacing is TBD.

Determinants

Lecture slides. Anton, Chapter 2. Detailed pacing is TBD.

Euclidean Vector Spaces

Lecture slides. Anton, Chapter 3. Detailed pacing is TBD.

Vector Spaces, Subspaces, and Span — 3 hours

Lecture slides. Anton §§4.1–4.3: real vector spaces, subspaces, and spanning sets. Completed October 8; approximately three 50-minute classroom hours, excluding quiz time and the transition to Bases, Dimension, and Coordinates.

Bases, Dimension, and Coordinates

Lecture slides. Anton §§4.4–4.7: linear independence, coordinates and basis, dimension, and change of basis. Extracting a basis by elimination also connects to §4.8. Frames and infinite algebraic bases are enrichment; complex dimension and coordinate isomorphisms preview §§5.3 and 8.3. Detailed pacing is TBD.

Matrix Spaces and Rank

Lecture slides. Anton §§4.8–4.9: row, column, and null spaces; rank, nullity, and the fundamental matrix spaces. The closing examples of abstract linear transformations and their matrices preview §§8.1 and 8.4. Detailed pacing is TBD.

Eigenvalues and Eigenvectors

Lecture slides. Anton, Chapter 5. Detailed pacing is TBD.

Inner Product Spaces

Lecture slides. Anton, Chapter 6: inner products, orthogonal projection, Gram–Schmidt and QR, least squares and regression, and function approximation with Fourier coordinates. Detailed pacing is TBD.

Special Topics

Lecture slides. A draft capstone: SVD and regression, quadratic forms, FFT, tensor products, and network applications. Selected Anton Chapters 7–10 plus supplementary Fourier and tensor material. Topics and pacing will be selected as time permits.

Assessment

  • Homework assignments: 20%; all homework assignments are completed individually through WileyPLUS

  • Quizzes: 15%; see the linked quiz and test schedule for dates and coverage

  • Tests: 25%; see the linked quiz and test schedule for dates and coverage

  • Final Exam: 40%; on the date assigned by the registrar

  • Extra Credit: From August 24 through December 6, you may earn extra credit by being the first student to report a previously unreported error in

    • my lecture slides, Jupyter notebooks, or assignments at least 24 hours after the material was presented or posted; or
    • the textbook.

    Report each error by creating an issue in the course repository. Each confirmed error earns 0.5 or 1 percentage point, depending on the severity of the error, up to 10 percentage points total.

    Extra credit is added to your final weighted course total. Canvas may not display the weighted total correctly until grades have been recorded in every assessment category.