Aimed primarily at future math majors, this course covers linear algebra more thoroughly and more theoretically than our other linear algebra courses (MAT202 and MAT204). This course is a rigorous introduction to linear algebra and matrices, with emphasis on proofs rather than on applications. Topics include vector spaces, linear transformations, inner product spaces, determinants, eigenvalues, the Cayley-Hamilton theorem, Jordan form, linear systems of differential equations, the spectral theorem for normal transformations, bilinear and quadratic forms.

# Course MAT217 in Fall 2011

## Honors Linear Algebra

Classes are usually taught in a single section in the fall semester and two sections in the spring semester. The two spring sections are closely coordinated, with the same problem sets and exams.

Challenging weekly problem sets count for about 30% of the course grade. There is an in-class midterm exam that counts for an additional 30% of the grade and an in-class final exam that counts for the remaining 40%.

- Most students will be continuing from MAT215 or from MAT214 and the instructor will assume that students have some prior experience with formal proofs.
- This course is usually followed by MAT218 (analysis in several variables) or by MAT203 in some cases. Students who are pressed for time to complete prerequisites for the major may take MAT217 and MAT218 in the same semester if absolutely necessary. Obviously this makes for an unusually demanding schedule, so plan your other courses accordingly!

Primarily prospective math majors. Some physics or computer science majors with a strong interest and background in (rigorous) mathematics may also take this course.

Students who are undecided between math and physics as a major, but leaning toward physics, should perhaps consider the somewhat less abstract MAT204 instead.

A very strong aptitude for mathematics and real mathematical curiosity with a taste for rigorous proof is essential.

Most students are continuing from either MAT214 or from MAT215, where they should have already learned how to understand and contruct formal mathematical arguments.

Incoming freshmen who have taken at least one rigorous proof course at another university may be able to start in this course. However, in most cases, we recommend taking MAT215 or MAT214 here to get a good foundation in formal mathematical argument. If in doubt, consult the math placement officer at freshman registration or at the Academic Expo during orientation. It may be helpful to bring your graded work from previous courses to show the placement officer when you meet.

A math major who took this course in the Spring of 2011 has prepared this list of sample problems designed to help you understand for yourself what MAT217 will be like. If these questions seem intriguing to you, then take the course to find the solutions! (Warning: the first problem on this list is a theorem that will be proved in class, not really a homework problem. The later questions are more typical homework problems for the course, representing some (but not all) of the important topics you will learn about.)

**How hard should I expect to work in this course?**

• Pretty hard. If you already took MAT214 or MAT215 then you should have a pretty good idea of what is involved. It requires a steady time commitment, but the time you will need to invest can vary quite a lot depending on your background and goals. It is quite difficult to judge how much time you will need to master the more abstract parts of the course. To do well on exams, you need to spend a lot of time digesting the course material, learning the proofs well enough to adapt them to new situations and combine various standard ideas in new ways on an exam.**I have never had a course with rigorous proofs -- will this course be too hard for me?**If you have time, consider starting in MAT215 or MAT214 instead. If that is not an option but you have a serious interest in being a math major, then you should give it a try. The first few classes will tell you whether you find this way of doing mathematics appealing or not. Students who have had the expected previous experience constructing mathematical proofs will have an advantage, but it is not impossible to catch up. You will certainly need to work much harder for the first few weeks since you will be learning both new mathematics and a new way of thinking about mathematics. Go to your instructor's office hours and take advantage of the help available at the McGraw Study Halls, where enthusiastic math majors will help you learn to think like a mathematician.

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• Consider attending both this course and MAT204 for the first few weeks of the semester until you can tell which course will work better for you. Discuss the decision with your instructor if you are not sure.

• This course (like MAT204) is graded on a generous curve to encourage interested students who want to give this kind of thinking a serious try without undue academic risk. Consult your instructor for advice after the first few weeks if you are worried about the decision.**I can't fit this course into my schedule. Can I take this course for Princeton credit at another university?**

• Probably not. If you want to be a math major you should take this course here at Princeton. Courses like MAT217 and MAT218, along with MAT215 or MAT214, set the foundation for all the more advanced courses for math majors and you really need to be sure that this foundation is as solid as possible. Credit for this course at another university will be granted only under very exceptional circumstances and we strongly prefer that you take this course here at Princeton.**My question is not listed above. Where can I find an answer?**

• Try the undergraduate home page. You will find links there to more information for future math majors and contact information for the various people who can advise you. Representatives from the math department will be available at the academic expo during orientation and at freshman registration.