MATH-UA 140 Linear Algebra

4 points. Fall and Spring terms.

Course Description

Linear algebra is an area of mathematics devoted to the study of structure-preserving operators on special sets (linear operators on vector spaces). Linear algebra is a cornerstone of any mathematics curriculum for two very important (and related) reasons:

  1. The theory of linear algebra is well understood and so a first step in many areas of applied mathematics is to reduce the problem into one in linear algebra.
  2. The spaces and operations studied in the subject are commonplace in many different areas of mathematics, science, and engineering.

Over the semester we will study many topics that form a central part of the language of modern science. The successful student will be able to:

  • Formulate, solve, apply, and interpret systems of linear equations in several variables;
  • Compute with and classify matrices;
  • Master the fundamental concepts of abstract vector spaces;
  • Decompose linear transformations and analyze their spectra (eigenvectors and eigenvalues);
  • Utilize length and orthogonality in each of the above contexts;
  • Apply orthogonal projection to optimization (least-squares) problems;
  • Explore other topics (as time permits).

The material we take up in this course has applications in physics, chemistry, biology, environmental science, astronomy, economics, statistics, and just about everything else. We want you to leave the course not only with computational ability, but with the ability to use these notions in their natural scientific contexts, and with an appreciation of their mathematical beauty and power.


ACT and SAT scores must be submitted to NYU and posted in your academic records in order to satisfy the prerequisite. We do not accept screenshots of ACT or SAT scores.

To register for this course, students must satisfy only one (1) of the following prerequisites:

  1. SAT score of 670 or higher on mathematics portion
  2. ACT/ACTE Math score of 30 or higher
  3. Valid AP Score:
    • AP Precalculus score of 4 or higher
    • AP Calculus AB score of 3 or higher
    • AP Calculus BC score of 3 or higher
  4. A Level Maths score of C or higher 
    • Students who took A Level Further Maths should contact the Math Department
  5. AS Level Maths score of B or higher
  6. IB Exam Result from 2021 - 2027 
    • IB Analysis and Approaches HL score of 5 or higher
    • IB Applications and Interpretations HL score of 5 or higher
    • IB Analysis and Approaches SL score of 7
  7. IB Exam Result from 2014 - 2020
    • IB Mathematics HL score of 5 or higher
    • IB Mathematics SL score of 6 or higher
    • IB Mathematical Studies SL score of 7
  8. Completion of MATH-UA 009 Algebra, Trigonometry and Functions with a grade of C or higher
    • Grades of Incompete do NOT satisfy the prerequisite
  9. Passing Calculus/MFE I placement exam

Sample Syllabi

Linear Algebra is not coordinated in the same sense as other multi-section courses with a common final exam (e.g., calculus). As such, the instructor has final discretion in topics chosen and course policies. Below are syllabi from recent implementations.