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# Course Information for Linear Algebra

PREREQUISITES : Math 12 or 17 or consent .

TEXT: Linear Algebra and its applications (3rd edition) by David Lay. Pearson-Addison-
Wesley.

COURSE DESCRIPTION: Math 46 is concerned with the study of systems of linear equations
and matrix properties . “Linear” means that unknowns appear multiplied by known
constants only, not as part of more complicated expressions — for instance, there are no
products , ratios, or transcendental functions of unknowns. (You will learn a better definition
of “linear” early in Math 46.) For example, 2x + 3y = 5 is a linear equation in the
unknowns x and y, whereas xy = 1 and ex = y are nonlinear. Systems of linear equations
arise everywhere in mathematics and its applications. Even when the main focus is on
nonlinear equations , as is often the case in real -world application, linear systems still play
a central role, since the most common methods for studying nonlinear systems use linear
approximations.

The study of systems of linear equations quickly leads to more abstract concepts —
vector spaces, dimension (you will learn about four-, five-, and even infinite-dimensional
spaces), linear transformations , eigenvalues, etc. These concepts prove central in understanding
systems of linear equations, as well as other, more sophisticated problems which
arise often in applications.

Mathematics majors and minors are required to take Math 46, and are urged to take
it as early as possible, as it is a prerequisite for most upper-level mathematics courses.
However, the course is also intended and useful for majors in computer science and engineering,
as well as those in the natural and social sciences.

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