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Linear algebra is the branch of mathematics concerned with vectors. You may have encountered vectors in calculus or physics, where they are often used to represent forces or velocities, and are viewed as "living" in Euclidean space. But this setting is only one example of an algebraic structure called a vector space. We will study properties of vector spaces and the special maps between them called linear transformations. In particular, we will emphasize the relationship between linear transformations and matrices.
Linear algebra is fundamental to the development of abstract mathematics, and plays important roles in abstract algebra and functional analysis. Some of its more concrete applications are methods for solving systems of linear equations, which are used widely in the natural and social sciences. Many dynamical systems such as population growth or chemical processes can be approximated by linear models.
Because this course focuses on the theoretical framework of linear algebra, reading and understanding mathematical theorems and proofs will be a large part of what we do. You will also get lots of opportunity to learn how to write proofs yourselves. These are critical skills to master if you wish to continue in abstract mathematics.
Last updated August 28, 2006 11:07:14 EDT