# Information on Linear Algebra

#### January 22, 2003

 TIME OF MEETING: Mon, Wed, & Fri 2:30 - 3:25 PLACE: Earth Science 143 INSTRUCTOR: W. F. Hammond, ES 137A, phone 442-4625. Office hours: Mon. & Thurs. 3:30 - 4:30 Email: hammond@math.albany.edu World Wide Web: http://www.albany.edu/~hammond/ TEXT: Fraleigh & Beauregard, Linear Algebra, 3rd edition, Addison-Wesley PRE-REQUISITE: Math 113 or Math 119

#### BULLETIN DESCRIPTION:

Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations, Euclidean spaces.

#### COURSE OBJECTIVE:

Linear algebra lies at the core of mathematics where algebra, geometry, and analysis come together. Knowledge of linear algebra is fundamental for further work in most branches of mathematics and in most other areas of knowledge where mathematics beyond K-6 arithmetic is used.

This course is consciously about both algebra and geometry. Analysis, which begins with the calculus, is not part of the discussion in this course. Nonetheless much of analysis, including both differentiation and integration in all contexts, concrete and abstract, involves the process of discerning linearity in complicated processes and situations. If the undergraduate curriculum were governed solely by mathematical content at the expense of pedagogical considerations, then it would be sensible to make this course a pre-requisite for third semester calculus.

Vectors, as objects with a list of coordinates, and matrices are the algebraic grist in this course. The theory of vector spaces and linear transformations endows the subject with a coordinate-free geometric context. Knowledge of both viewpoints is important, and the ability to move between them is essential.

A student's objective in taking this course will be to acquire a broad overview of linear algebra including an understanding of how the theory of vectors and matrices is essentially the same as the theory of coordinatized vector spaces and linear transformations and to acquire minimum competence in manipulating the basic objects in either of these two theories including the study of bases, determinants, characteristic polynomials, eigenvalues, inner products, and orthogonality.

#### TEST SCHEDULE:

 Event Weight Date Final examination 100 Wed., May 14, 3:30-5:30 Midterm test 50 Wed., Mar. 12, in class Weekly tests (10 @ 5 each) 50 often by surprise Total weight 200

#### ATTENDANCE:

Attendance at class meetings is a requirement for passing the course unless the student has been granted a special exception in advance. Unexcused absence may result in failure or grade reduction. There will be no retrospective excused absences from tests except for compelling emergencies and religious holidays.