Text(s)/Materials:

Strang, Gilbert. (1988). Linear Algebra And Its Applications, 3rd ed. Orlando, FL: Harcourt Brace Jovanovich.

Course Description:

At the teacher's discretion, this is either a course in linear algebra or in abstract algebra (other possibilities may be considered). Students enroll in AS I the first time they take this course, regardless of the topic covered. If a student wishes to take the course a second time when a different topic is being taught, they will enroll in AS II.

Linear algebra comprises a standard one-semester university course in linear algebra. Theory and practice of solving linear systems, vector spaces, inner products, determinants, eigenvalues and eigenvectors comprise the core topics. Other subjects of investigation may include Markov chains, Fourier series, and the Fast Fourier Transform. Students have frequently been allowed to bypass their first university linear algebra course after taking this course.

Teaching and Learning Methodology and Philosophy:

This course is intended to model the advanced mathematics courses students will encounter in college and to cover a large amount of material quickly. Thus it is more traditional and lecture-oriented than many other IMSA courses. Student-led discussions and investigations are encouraged, and since the core material does not occupy the entire semester, students have options for directing the course content during the last few weeks.

Student Expectations:

The pre-requisites for this course include at least one other advanced math elective and the permission of the instructor. This is to ensure that only students with the most complete mathematics preparation enroll in the course. The mathematical demands made on the students require this level of preparation.

Regular homework assignments must be completed. These assignments help students solidify concepts in their minds by practicing using important theorems and ideas. Students are also asked to extrapolate and apply ideas to new situation in homework. This practice is essential to understanding the material, and students who do not keep completely up-to-date with homework often find themselves very far behind in understanding.

Students are also required to take careful, complete class notes since classroom presentation may deviate from the order of topics in the text, present alternate approaches to the material, or even present material not contained in the textbook. Students are responsible for all material both from the text and presented in class.

Students will want to form study groups or meet outside of class (either with or without the instructor) in order to discuss and familiarize themselves with the material.

Assessment Practices, Procedures, and Processes:

Students are evaluated on the quality of their written homework and on exam performance. Since much of this material cannot be tested in a short time frame, there may be take-home exams and homework counts for a larger portion of the grade than most other IMSA math courses (about 1/3 of the grade is homework). Additionally, due to the difficulty of the course, the regular 90-80-70 grading scale is often extended so that the "A" range is about 85 - 100, and passing grades begin around 65%.

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