Linear Algebra (2026)

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.

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)

Semester II — Chapters 5–8 (Weeks 15–29)