OverviewAt the very basic level, Linear Algebra is concerned with solving systems of linear equations like
2x + 3y + 2z = 10 x - 6y + 2z = 2The beauty of Linear Algebra is that these seemingly mundane algebraic questions have very deep geometric interpretations. We will be able to play off the algebraic and geometric views against each other to gain insights and build intuition about both. Fundamental to developing this intuition is an understanding of the relationship between matrices and linear transformations, which are special types of maps from n-space to m-space.
The interconnections among systems of linear equations, matrices, and linear transformations provide a framework for applications to vastly different areas. Some of the applications we will look at this semester include applications to population dynamics, computer graphics, and the long-term behavior of dynamical systems. This is going to be a really fun semester.
Reading the Text and Working with Other StudentsTwo of the goals of this course are that you learn to read a math text and that you learn to communicate mathematics with other students. Mathematics is a very personal discipline that is best learned by doing rather than by observing.
Therefore, the class will be structured with some lectures to emphasize particular topics, but much of the time will be spent on in-class work. The class meetings are not intended to be a complete encapsulation of the course material -- There will be material in the text for which you are responsible that we will not cover in class.
Many of the assignments this term will be group assignments where you will work in groups of two or three (of your choosing). Each assignment will receive a grade, and the group will determine how the points are allocated to each member. For example, if a group of three receives an 85 on an assignment, then the group will have 3 x 85=255 points to distribute among them. I will be available to mediate this process, if necessary.
You will have a reading assignment for nearly every class meeting, and it is extremely important that you complete the reading before the next class meeting! See the section below on Reading Assignments and the Guidelines for Submitting Reading Assignments for more information.
EvaluationYour final grade will be determined by
ExamsThe takehome exams will have some problems that are similar, but not identical, to homework exercises. However, most of the exam problems will ask you to combine your knowledge of several different topics from the course. Although you may not discuss the exams with anyone else, you can ask me as many questions as you want about the exams. You will always have at least one week to complete the takehome exams.
The quizzes will be quite short on very specific topics. They will be mostly computational, but you may also need to state definitions or theorems precisely. I will tell you the exact topics that each quiz will cover.
Group ProjectsThere will be two group projects assigned during the semester. You will always have at least a week to complete the assignment (see the syllabus for the due dates).
One of the main goals of the projects is that you learn to communicate mathematics precisely, both verbally with your group and in writing. The reports should be written in complete sentences explaining the results and major ideas involved. You may divide the writing of the report in whatever way is agreeable to the group, but everyone should completely understand the whole of the paper. Further, each member should proofread the entire paper for consistency and typos.
HomeworkHomework will be collected on most Tuesdays. I will carefully grade three or so ``spotlight'' problems from each homework assignment, and very quickly scan the rest of the assignment. I will tell you which are the spotlight problems, and these should be especially well-written and placed at the beginning of your assignment. Each spotlight problem will be receive a score between 0 and 4, and I will also assign a total score of 0-4 for the non-spotlight problems.
The homework assignments will alternate between Individual assignments and Group assignments. For the Group assignments, each student should attempt all of the homework problems, and the group should meet to complete the assignment. Each group will turn in one paper with one student designated as the primary author who writes-up the solutions for that assignment. The role of primary author must rotate among the members of the group.
You may discuss the Individual assignments with other students, but each person must turn in a separate paper that represents his/her own work.
Here are a few guidelines for the presentation of your homework. If you do not follow these, I reserve the right to return your homework ungraded!
Reading AssignmentsI will put a copy of each reading assignment on the course homepage. Each assignment will indicate which parts of the section are especially important and which can be skipped. Each assignment will also have three (or so) questions that you should be able to answer after you have read the section.
See the Guidelines for Submitting Reading Assignments for more information.
Class AttendanceAlthough class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.
Getting HelpPlease come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.
If you want to know check on your grade at any time during the semester, please ask me and I can give you a rough idea of your current standing.