Overview

Linear algebra is a branch of mathematics devoted to the theory of linear equations and transformations. A solid understanding of linear algebra allows you to (among other things):

• solve systems of linear equations;

• determine the geometry of the set of solutions to such a system;

• analyze the geometry of an arbitrary linear transformation.

These skills will no doubt be used in your future mathematics and STEM courses.

Math 0520 is a first course in linear algebra that will focus on the development of the standard algorithms in the subject, as well as the underlying geometry. Along the way, you will also develop your ability to understand proofs---the logical arguments that form the foundation of mathematical reasoning---and get the opportunity to write some of your own.

By the end of this course, you will be able to:

1. use your knowledge of algorithms in linear algebra to solve systems of linear equations and to calculate optimal coordinate systems for linear transformations.

2. explain phenomena surrounding the nature of systems of linear equations, and properties of transformations, in both geometric and algebraic terms.

3. apply your linear algebra skills to solve problems from a variety of other disciplines.

4. use introspective methods to help you monitor the development of your mathematical maturity.

5. produce logical arguments grounded in axiomatic principles that explain properties of vector spaces and linear transformations.

6. classify a proof in terms of its global argument structure and identify for yourself the largest gaps in your understanding of the argument.

7. use the critical and abstract thinking skills developed in this course as a foundation for future courses in geometry and algebra.

Here are some of the topics that we will cover in Math 0520:

• vectors and vector operations;

• systems of linear equations;

• matrix operations;

• linear transformations;

• vector spaces;

• inner-products.

Additional topics will be covered depending on time and class interests.

In addition to Math 0520, Brown also offers Math 0540: Honors Linear Algebra. Math 0540 is a higher-level introduction to linear algebra with a greater emphasis on the development of foundational principles and proof-writing skills. Come talk to us if you need help deciding on your course placement.

Am i ready for math 0520?

There are no prerequisites for Math 0520, although it is generally recommended that students have taken at least one previous mathematics course at the college level. Please reach out if you have questions about your preparation.