Honors Linear Algebra — Fall 2026

MATH-UA 148-001 · 4 points
New York University · Courant Institute of Mathematical Sciences

Course information

Course description

Honors Linear Algebra is a rigorous first course for students who want to move faster and explore the core material of an ordinary linear algebra course in greater depth. The course begins concretely with vectors, systems of linear equations, and matrices; moves quickly to vector spaces, bases, dimension, and linear maps; and then returns repeatedly to geometry, computation, and applications.

Prerequisites and readiness

Students must satisfy one of the official prerequisites listed on the MATH-UA 148 course page. MATH-UA 140 Linear Algebra is an anti-requisite; students cannot receive credit for both courses.

This course is intended for students who are ready to develop their mathematical reasoning and proof-writing skills. Comfort with algebra, functions, precise definitions, and multi-step reasoning will be helpful, but prior linear algebra and extensive proof experience are not required. We will practice reading and constructing proofs throughout the semester.

Learning objectives

By the end of the course, students should be able to:

1. solve linear systems and use matrices effectively;
2. reason with vector spaces, bases, dimension, linear transformations, and coordinates;
3. write clear proofs and connect abstract results with computation and geometry;
4. use determinants, orthogonality, eigenvalues, the spectral theorem, and the singular value decomposition; and
5. apply linear algebra to problems such as least squares, dynamical systems, and low-rank approximation.

Texts and course materials

Primary text

Sergei Treil, Linear Algebra Done Wrong, April 30, 2026 version. The book is legally available without charge from the author’s webpage.

Treil is the main reference for the course sequence, definitions, results, and many exercises. Assigned readings will be posted with each homework set.

Recommended companions

Gilbert Strang, Introduction to Linear Algebra, 6th edition, 2023. This classic reference is not freely available, but Strang’s YouTube lectures are highly recommended.

Sheldon Axler, Linear Algebra Done Right, 4th edition, 2024. The current electronic edition is legally available without charge from the author’s webpage. Axler offers especially useful alternative explanations and proofs. Selected companion readings may be recommended, but the course will not follow Axler’s order.

Dan Margalit and Joseph Rabinoff, Interactive Linear Algebra, 2019. This free online text uses interactive visualizations and geometric explanations to build intuition for systems of equations, linear transformations, determinants, eigenvectors, orthogonality, and related topics.

Class format and expectations

Lectures will combine definitions and theorems, proofs, examples, and computations. Recitation is an essential problem-solving component of the course: it will be used to discuss difficult homework ideas, practice proof writing and calculation, prepare for examinations, and administer the four quizzes.

Students should:

• attend lecture and recitation consistently;
• read the assigned material before or soon after the corresponding lecture;
• attempt problems before seeking help;
• write complete arguments, not merely answers or unexplained calculations;
• ask questions in lecture, recitation, and office hours; and
• take responsibility for understanding every line of submitted work.

Attendance is not a separate graded component, but missed quizzes, examinations, explanations, and course announcements remain the student’s responsibility.

Grading

Numerical cutoffs for final course letter grades will be determined at the end of the semester. To help students understand their progress, each midterm and the final examination will receive both a numerical score and a corresponding letter-grade assessment.

Homework

Homework will be assigned approximately weekly; due dates will be posted on the course site, and the lowest score will be dropped. Because generative AI makes unproctored work difficult to authenticate, homework constitutes only 10% of the course grade. Nevertheless, quiz and examination questions will be very similar to homework problems, so working seriously and independently on every assignment is essential for success in the course.

Solutions must show adequate reasoning. Discussion of general ideas is encouraged, but each student must write their own solutions and list collaborators and substantial outside sources. Copying or comparing written solutions is prohibited. Work submitted after solutions are released cannot receive credit.

Quizzes

There will be four 15–20 minute in-person quizzes during Friday recitation. Quizzes will be unannounced. The lowest quiz score will be dropped; each of the three remaining quizzes contributes equally. There is therefore no makeup for one missed quiz, regardless of reason. If a student misses more than one quiz because of approved accommodations or documented emergencies, the instructor will arrange an appropriate proctored alternative.

Examinations

Midterm I will be held during the regular lecture period on October 7. Midterm II will be held during the regular lecture period on Wednesday, November 11. The cumulative final will be held during the university final-examination period, December 16–22, at the date and time assigned by the registrar.

If a recognized religious observance, university-sanctioned activity, approved accommodation, or other known conflict affects an examination, notify the instructor as early as possible and before the examination. In an emergency, contact the instructor as soon as reasonably possible. Makeup assessments require approval and may be written, oral, or a combination; they may differ in format and content from the original assessment.

Permitted aids and zero-tolerance examination policy

All quizzes and examinations are closed-book and closed-note unless the instructor explicitly states otherwise in writing. Phones, computers, tablets, smartwatches, headphones, calculators, AI systems, written notes, solution materials, communication with another person, and every other unauthorized aid may not be used or kept within reach during an assessment.

Any violation of this rule will result, at minimum, in a score of zero for the entire quiz or examination, whether or not the unauthorized aid was actually used. Academic-misconduct incidents will also be reported through the applicable university procedures.

Oral verification of examination work

The instructor may require a brief oral follow-up after any quiz or examination to verify sole authorship and understanding of submitted work. The oral follow-up is part of that assessment and therefore part of its grade. A student may be asked to explain definitions, justify steps, reproduce an argument, or solve a closely related problem. An unsatisfactory explanation of submitted work will result in a score of zero on that quiz or examination.

Generative AI, computational tools, and outside resources

Homework must reflect the student’s own reasoning. Discussion of general ideas and use of assigned course materials are allowed. Unless an assignment states otherwise, computational or generative-AI tools may be used only to check work that the student has already completed independently. Discussion with your classmates, TA and the instructor is highly encouraged!

Students may not use another person, an AI system, or an online source to generate, outline, rewrite, or supply key arguments for a solution. Submitting generated or copied work, using unauthorized solutions, or sharing written solutions for others to copy is prohibited. Substantial assistance must be acknowledged, and every student must be able to explain all submitted work.

These course rules supplement the Courant Mathematics academic-integrity policy and the honor code of the student’s school.

Regrade requests

Requests to review the grading of a homework, quiz, or midterm must be submitted in writing within seven calendar days after the graded work is returned. The request must identify the specific issue and explain why the original grading may not match the posted solution or rubric. A regrade may involve review of the entire problem or assessment, and the score may increase, remain unchanged, or decrease. Clerical errors should be reported promptly.

Accessibility and student support

Students who may need academic accommodations should contact the Moses Center for Student Accessibility and provide the instructor with the official accommodation notice as early as possible. Accommodations are implemented prospectively and in coordination with the relevant university office.

Tentative course calendar