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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