Linear Algebra Honors (Post-AP)
Course Description
Linear Algebra Honors is an introductory post-AP mathematics course for students ready to move beyond Precalculus into more advanced
abstract and applied mathematical thinking. The course develops core ideas such as systems of linear equations, matrices, vector spaces,
eigenvalues, eigenvectors, and linear transformations, while also strengthening proof-based reasoning. It provides an important foundation
for future study in engineering, physics, computer science, data science, and higher-level mathematics.
| Credits | 5 (one semester) |
| UC A–G Area | G — College-Preparatory Elective (confirm on UCOP A–G list) |
| Level & GPA Weight | Post-AP (Honors) — weighted per UCOP |
| Recommended Grades | By placement (typically upper high school students ready for post-AP math) |
| Prerequisites | Precalculus (required). Background in computer science is preferred, including Introduction to Computer Science, AP Precalculus, Precalculus Honors with Computer Science, AP CSA, or AP CSP. |
| Textbook / Materials | Introduction to Linear Algebra for Science and Engineering, 3rd Edition, Wolczuk & Norman, ISBN-13: 9780134682631; MATLAB Academy: Introduction to Linear Algebra with MATLAB; access to MATLAB Student License included. :contentReference[oaicite:2]{index=2} |
What You’ll Learn
- Solve systems of linear equations using algebraic and matrix methods.
- Interpret vectors, subspaces, and linear mappings geometrically and algebraically.
- Work with determinants, eigenvalues, eigenvectors, and diagonalization.
- Apply linear algebra concepts to engineering, physics, computing, and data-oriented problems.
- Strengthen mathematical communication through proofs, justification, and structured problem solving.
Course Outline
1. Euclidean Vector Spaces — vectors, geometry, and algebraic structure.
2. Systems of Linear Equations and Applications — solving systems and modeling applications.
3. Matrices, Linear Mapping, and LU Decomposition — matrix operations and computational methods.
4. General Vector Spaces — span, basis, dimension, and subspaces.
5. Determinants and Properties — determinants as algebraic and geometric tools.
6. Eigenvalues, Eigenvectors, and Diagonalization — core theory with applications.
7. Inner Product and Projections — orthogonality, least squares, and geometric interpretation.
8. Symmetric Matrices and Quadratic Forms — optional extension topics.
Practical Work
- Problem Sets — algebraic proofs, matrix computations, and applications.
- MATLAB Applications — selected problem sets and computational explorations using MATLAB.
- Optional Project — applications in science, engineering, computer science, or related fields, as time permits.
Technology & Platforms
- MATLAB Student License included for course use.
- MATLAB Academy modules may be used to reinforce concepts and applications.
- Online submission/feedback tools as assigned by the instructor.
Delivery Options & Tuition
| Model | What’s Included | Typical Live Hours | Tuition |
|---|---|---|---|
| Mini-One-on-One | Targeted coaching with the asynchronous curriculum, guided problem solving, and personalized pacing support | Typically 12 hours | $1,428.00 |
| One-on-One | Fully personalized instruction, deeper coaching, and flexible pacing | Typically 22 hours | $2,618.00 |
Time & Workload Expectations
- Assessment at the beginning: students complete an initial assessment to help determine readiness and support needs; it does not count toward the course grade.
- Mini-One-on-One: plan for approximately 12 hours of live sessions, plus additional independent work between meetings.
- One-on-One: plan for approximately 22 hours of live instruction, plus independent work between sessions.
- Independent work: regular assignments, problem sets, review, and MATLAB-based applications are expected throughout the course.
- Communication: email-based questions and periodic progress updates may be used to support pacing and success.
- Weekly load scales with your chosen course window. Example:
(live hours + independent hours) ÷ weeks ≈ weekly time
Grading & Course Policies
| Category | Weight |
|---|---|
| Classwork | 10% |
| Tests/Quizzes | 20% |
| Homework | 30% |
| Midterm | 20% |
| Final Test | 20% |
- Assignments: unless otherwise noted, assignments are due by the next session and must include both work and answers for full credit. One-session late submissions may receive reduced credit.
- Quizzes: generally begin at the start of class and last about 30–40 minutes.
- Major exams: one midterm and one final for the semester.
Additional Notes
- Placement guidance: If the initial readiness assessment shows that additional support is needed, students may be assigned supplementary work or advised to pursue tutoring or a different class placement.
- Pacing Guide: Course pacing may be personalized based on the selected start/end dates.
- Office Hours: Available by arrangement.