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 e^{x} = 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.