The Timpson Lyceum · Linear Algebra (2026)
Syllabus
A one-year course · Lay, Lay & McDonald, Linear Algebra and Its Applications, 5th ed. · Chapters 1–8
Email: dt323259@gmail.com · Phone: 435-619-1784 · Course site: timpson-lyceum.vercel.app
Course Description
An introduction to linear algebra, from the concrete methods of solving linear systems to the abstract structures that unify them. Topics: systems of linear equations and row reduction; matrix algebra and invertibility; determinants; vector spaces, bases, dimension, and rank; eigenvalues, eigenvectors, and diagonalization; orthogonality, projections, and least squares; symmetric matrices, quadratic forms, and the singular value decomposition; and the geometry of vector spaces. The course balances computational fluency with conceptual understanding and short proofs, and draws applications throughout — from computer graphics and Markov chains to regression and image compression.
Text: Lay, Lay & McDonald, Linear Algebra and Its Applications, 5th edition. The course covers Chapters 1–8 in full.
Learning Objectives
By the end of the year, you will be able to:
- Solve and analyze linear systems by row reduction, and interpret solution sets geometrically.
- Perform matrix algebra fluently, determine invertibility, and apply the Invertible Matrix Theorem.
- Compute determinants and use their properties.
- Reason about vector spaces, subspaces, linear independence, bases, dimension, rank, and coordinates.
- Find eigenvalues and eigenvectors, diagonalize matrices, and apply them to dynamical systems.
- Use inner products, orthogonal projections, the Gram–Schmidt process, and least-squares methods.
- Diagonalize symmetric matrices, analyze quadratic forms, and compute the singular value decomposition.
- Read and write short proofs, and justify your reasoning precisely.
Materials
- Textbook: Lay, Lay & McDonald, Linear Algebra and Its Applications, 5th ed.
- Calculator: a scientific or graphing calculator.
- Course site: your Timpson Lyceum account at timpson-lyceum.vercel.app — lectures, weekly problem sets, posted solutions, and attendance all live here.
Grading
Your grade is submitted each semester. The same weighting applies within each semester, with that term's cumulative exam (midterm in the fall, final in the spring) as its big exam.
| Category | Weight |
|---|---|
| Attendance | 10% |
| Homework (weekly problem sets) | 20% |
| Quizzes (weekly) | 10% |
| Unit Tests (four) | 30% |
| Midterm & Final | 30% |
| Base total | 100% |
| Extra Credit | up to +5% |
Maximum possible grade: 105%.
Extra credit. Every problem set, every unit test, and both exams include an optional extra-credit problem. Do them and they lift your final grade — together they can add up to 5 percentage points (a 105% ceiling). There is no extra credit on quizzes or attendance.
Attendance — 10%. Honor system. Attend the weekly session, or — if you must miss it — watch the recorded lecture on the course site and mark it watched. Credit is per lecture. One 3-hour block is a full week of the course, so keep up.
Homework — 20%. A problem set for each section, due weekly. Solutions are posted the moment the set is due, so you get immediate feedback — and no late work is accepted. Each set carries an optional extra-credit problem.
Quizzes — 10%. A short quiz at the start of most classes on the previous week's material — quick retrieval practice to keep ideas fresh across the week between blocks.
Unit Tests — 30% (four across the year, ~15% each per semester). Each test has two parts: a unit portion on the newest material and a cumulative portion reaching back over everything so far — plus an optional extra-credit problem.
Midterm & Final — 30%. The midterm (end of fall) covers Chapters 1–4; the final (end of spring) covers Chapters 5–8 and leans cumulative. Each has a unit portion, a cumulative portion, and an extra-credit problem. Score replacement: your midterm replaces your lower Test 1 / Test 2 score when it is higher, and your final replaces your lower Test 3 / Test 4 score — so a strong exam can rescue one weak unit test.
Grade Scale
A 93–100 · A− 90–92 · B+ 87–89 · B 83–86 · B− 80–82 · C+ 77–79 · C 73–76 · C− 70–72 · D+ 67–69 · D 63–66 · D− 60–62 · F below 60
Extra credit can carry a final grade above 100%, to a maximum of 105%.
Policies
Late work. None accepted. Because solutions post exactly when an assignment is due, turning something in late isn't possible — the trade is that you always get fast feedback.
Missed tests & exams. There are no make-ups for a missed unit test, midterm, or final. A missed unit test is cushioned by the score-replacement rule above: your midterm or final can stand in for your lowest unit test in that semester.
Course Schedule
Twenty-seven weeks of instruction on a 3-hour weekly block, covering all of Chapters 1–8. Two flexible catch-up / review weeks in the spring absorb schedule disruptions; dates are approximate and may shift.
Semester I — Chapters 1–4 (Weeks 1–14)
| Wk | Topics | Assessment |
|---|---|---|
| 1 | 1.1 Systems of Linear Equations · 1.2 Row Reduction & Echelon Forms | Course intro |
| 2 | 1.3 Vector Equations · 1.4 The Matrix Equation Ax = b · 1.5 Solution Sets | |
| 3 | 1.6 Applications of Linear Systems · 1.7 Linear Independence | |
| 4 | 1.8 Introduction to Linear Transformations · 1.9 The Matrix of a Linear Transformation · 1.10 Linear Models | |
| 5 | 2.1 Matrix Operations | Test 1 · Ch 1 |
| 6 | 2.2 The Inverse of a Matrix · 2.3 Characterizations of Invertible Matrices | |
| 7 | 2.4 Partitioned Matrices · 2.5 Matrix Factorizations (LU) · 2.6 Leontief Input–Output | |
| 8 | 2.7 Computer Graphics · 2.8 Subspaces of ℝⁿ · 2.9 Dimension and Rank | |
| 9 | 3.1 Introduction to Determinants · 3.2 Properties of Determinants · 3.3 Cramer's Rule, Volume & Transformations | |
| 10 | 4.1 Vector Spaces and Subspaces | Test 2 · Ch 2–3 |
| 11 | 4.2 Null Spaces, Column Spaces & Linear Transformations · 4.3 Linearly Independent Sets; Bases | |
| 12 | 4.4 Coordinate Systems · 4.5 The Dimension of a Vector Space · 4.6 Rank · 4.7 Change of Basis | |
| 13 | 4.8 Applications to Difference Equations · 4.9 Applications to Markov Chains | Midterm review |
| 14 | Midterm Examination — Chapters 1–4 | Midterm |
Semester II — Chapters 5–8 (Weeks 15–29)
| Wk | Topics | Assessment |
|---|---|---|
| 15 | 5.1 Eigenvectors and Eigenvalues · 5.2 The Characteristic Equation | |
| 16 | 5.3 Diagonalization · 5.4 Eigenvectors and Linear Transformations | |
| 17 | 5.5 Complex Eigenvalues · 5.6 Discrete Dynamical Systems · 5.7 Differential Equations · 5.8 Iterative Estimates | |
| 18 | 6.1 Inner Product, Length, and Orthogonality | Test 3 · Ch 5 |
| 19 | 6.2 Orthogonal Sets · 6.3 Orthogonal Projections | |
| 20 | 6.4 The Gram–Schmidt Process · 6.5 Least-Squares Problems | |
| 21 | 6.6 Applications to Linear Models · 6.7 Inner Product Spaces · 6.8 Applications of Inner Product Spaces | |
| 22 | 7.1 Diagonalization of Symmetric Matrices | Test 4 · Ch 6 |
| 23 | 7.2 Quadratic Forms · 7.3 Constrained Optimization | |
| 24 | 7.4 The Singular Value Decomposition · 7.5 Image Processing & Statistics | |
| 25 | Catch-up & review | |
| 26 | 8.1 Affine Combinations · 8.2 Affine Independence · 8.3 Convex Combinations | |
| 27 | 8.4 Hyperplanes · 8.5 Polytopes · 8.6 Curves and Surfaces | |
| 28 | Catch-up & final review | |
| 29 | Final Examination — Chapters 5–8 | Final |