Course Description:

This is an introduction to linear algebra, including the following topics: vectors and matrices; solutions of linear equations; determinants; abstract vector spaces and linear transformations; real and complex inner product spaces; orthogonal bases; eigenvalues and eigenvectors; similarity and change of basis; least squares; quadratic forms; positive definite matrices; numerical methods; selected applications to geometry, differential equations, probability, and other areas.

Theory and applications will be emphasized equally, and the course is suitable both for math majors and non-majors. It will develop technical tools that play an important role in more advanced mathematics courses and in other subjects. The course has a substantial focus on computation, but will also frequently employ the formal "mathematical" language of definitions and proofs to make precise statements and justify results carefully. For students who have not previously experienced this mode of discourse, the course will provide an introduction.

If you are undecided whether this course is your best choice, please see the comments at the end of this document.

Linear Algebra and its Applications (Fourth edition), by Gilbert Strang (Thomson/Brooks-Cole, 2006).

Three lectures per week (MWF 10:30-11:30), plus one additional discussion hour, at times to be determined during the first week of classes.

Weekly homework, two midterm exams (each will consist of an in-class quiz plus a take-home supplement), and a self-scheduled final. In addition, there will be a term project (in an application area chosen by you) culminating in a poster presentation and/or a short written report. These will be weighted as follows in determining the overall course grade:

Each weekly homework assignment will consist of two parts, counted equally in determining the final homework grade.

(1) Standard problems. These are designed to give practice with the routine aspects of material covered each week in lectures. This part of the assignment will normally be handed out on Wednesdays and due the following Wednesday.

Standard homework

(2) Special problems. Generally one additional "special problem" will be assigned each week. These will be more challenging, often covering material not directly related to the current lectures and drawing on topics from different parts of the course.

Special problems have an extended due date: you should try to do them each week along with the standard problems, but they are officially due four weeks after they are assigned. You may resubmit problems until they are done correctly, within the four-week time limit. I will return them with hints, and record only the grade for the final version. I will accept interim submissions on Fridays (only), and these will be returned the following Monday.

I hope (and expect) that you will find the special problems interesting and perhaps even fun.

Collaboration:

I encourage collaboration on the homework, both standard and special problems. Indeed, I expect you will learn a great deal about this course from each other. It will be to your advantage to form study groups, and many students facilitate this by working together in the Math Question Center (Sunday through Thursday 7-9PM, Hilles 012). This semester I will be in the MQC on Monday nights.

Collaboration on homework naturally raises the question, "how much is OK?" I expect that you will share ideas, and perhaps work together at a blackboard, but eventually each student must write up his/her work independently, without reference to another students work or to written work that has been produced jointly. Verbatim copying from another person's paper or blackboard work is definitely "not OK". The safest approach is to write up your final solutions in a different place, and on a fresh sheet of paper.

It's important not to misunderstand these guidelines, so please ask me if you have any questions. You might also want to refer to the department's published guidelines on homework collaboration, which are available on the department website. Collaboration on tests is never permitted. All inquiries about problems on the tests should be directed to me.

Honor code principle:

You must never present others' work as your own. If you have used other students' work in the preparation of homework you must acknowledge it. If you obtain solutions to assigned problems (on homework or take-home tests) from sources other than the textbook or class notes, you must acknowledge such sources. This especially applies to material obtained electronically, e.g., on the web. 

If there are questions about honor code issues, you should seek clarification and guidance from me.

Electronic Resources:

(1) Blackboard will be the primary source for course materials. You are responsible for getting the weekly homework assignments from Blackboard. I will also post solutions to homework and tests, handouts, links to course-related websites, sample Mathematica notebooks, and other items that might be quite important (e.g. corrections to and hints to homework assignments, reminders of test dates, etc.). Please check Blackboard regularly.

(2) Mathematica is a powerful software system for doing symbolic calculation and displaying graphics, and we will use it extensively. Since it may also be useful in other courses, it is worthwhile becoming adept with Mathematica at an early stage of your Haverford career. If you are not familiar with Mathematica, please acquaint yourself with it as soon as possible, e.g., by coming to the Math Question Center. In this course you will especially want to acquaint yourself with the Solve command.

This year Haverford has a site license that permits unlimited use by students, as long as they are on the campus network. Complete details on how to download Mathematica and install it on your own computer can be found at http://www.haverford.edu/math/Mathematica/. The installation process requires obtaining a password from the publishers. If you have any difficulty doing this, please come to the MQC and/or contact David Lippel (Math Department lab support person) for assistance.

Who should take this course?

• Prerequisite: You should have had a full year of calculus, or the equivalent, either at Haverford or elsewhere. We won't use particular results or techniques from calculus very much; this requirement is primarily to insure a certain level of experience and mathematical maturity.
• You should enjoy math, and be fairly good at it. It will be a challenging, fast-paced course!
• You absolutely must take this course if you a sophomore considering a major in mathematics. First year students who are potential math majors have other options, e.g., waiting until next fall and then taking Math 215-216.
• If you are majoring in physics, chemistry, or economics (or related fields) and are interested in developing your mathematical skills to a high level, you should take this course eventually.
• Aside from practical issues, there are plenty of other good reasons for studying linear algebra. It is a deep and (potentially) beautiful subject, and it reveals a mode of "mathematical thinking" that you may not have observed in your previous math courses. For mathematicians, linear algebra is an indispensable tool: it permeates virtually every corner of the subject. And finally, one cannot overemphasize the fundamental role that linear algebra plays in such subjects as economics, multivariate statistics, differential equations, computer graphics, and many others. Take the time to learn linear algebra well, and your efforts will be repaid many times over.