# 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:

- 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.
- 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.

## Prerequisites

ACT and SAT scores must be submitted to NYU and posted in your academic records in order to satisfy the prerequisite.

One of the following:

- SAT score of 670 or higher on mathematics portionĀ
**March 2016 and later** - SAT score of 650 or higher on mathematics portionĀ
**before March 2016** - ACT/ACTE Math score of 30 or higher
- AB score of 3 or higher
- BC score of 3 or higher
- A level Maths score of C or higher (anyone who took Further Maths should contact the math department as it varies depending on the exam board)
- AS level Maths score of B or higher
- IB HL score of 5 or higher
- IB SL score of 6 or higher
- Completion of Algebra and Calculus (MATH-UA 009) with a grade of C or higher
- Passing 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.