Contact information: Office: Krieger 410 B; Phone: 6-5116; E-mail: kc@math.jhu.edu

When and where: The lectures are on MWF:

Text: Linear Algebra with Applications, Fourth Edition, Otto Bretscher.

The book is required reading. In fact, you are technically required to read the book before the instructor lectures on the material. From the Homework you can usually tell what the instructor is about to lecture on, so you'll know what to read. We will use that material all the time and the instructor will assume it starting day two of classes.

There is a small note about how to read a math textbook on the Supportive material web page for the course.

Homework: Homework will be posted on the course web site sometime on Thursday. Homework will be due at the beginning of the next week's section meeting (on Thursday for all sections). The homework will normally cover the material in the lectures for the week the homework is due. There is no perfect way to time homework. You are allowed, even encouraged, to do your homework in groups. Everyone must hand in their own homework though. Homework is THE essential educational part of the course. You will be graded mostly on your ability to work problems on exams. You cannot work problems on exams if you have not worked lots of problems before and in preparation for these tests. If you misuse homework by not doing it yourself, or not checking that you can solve a problem on your own after having been shown how to do it, then your exam scores and corresponding grade might be disappointingly low. Late homework is not acceptable. Find an agreement with your teaching assistant about how to turn in a homework if you cannot go to class but please do not handle it to the instructor. The TAs grade the homework.

Old Exams: Old exams are posted under the Past Exams website. As with homework, we encourage you to work in groups on these old exams. They are very good study materials and solutions are not always available. However, as with homework, you must use the groups carefully or they will work against you rather than for you. So, some suggestions for study groups. All members should work all problems before the study group meets. At the meeting, the group should hash out differences and help those who couldn't work certain problems. The day after the group each student should work those problems they couldn't work before. A student who goes to a study group and ``learns by watching'' is not likely to do well in the course.

Sections: You must be very careful to physically go to the section you are officially signed up for since that TA will be the one who gives you your grades.

Neither the instructor nor the TAs can move you from one section to another. You should go to the math dept office and read what is posted there about how to switch sections (or get into one if that is the problem). If you still have a problem then you should talk to people in the math office. Do not bring this problem to either the instructor or a TA as we are not authorized to do anything about it.

Exams: Bring your I.D. Do not have any math books or papers anywhere near you. Official grading policy gives you a zero for the exam if you break rules. If you miss an exam with a good excuse (i.e. illness justified with a doctor certificate) then see the instructor as soon as possible. There will be no makeup exams. For excused absences, the grade for a missed exam will be a weighted average of subsequent exam grades. The TA will hand out the exams in section when they are graded. We sometimes make mistakes when we grade exams. Check yours over carefully to see that it was graded properly and the score was added correctly. Do this before you take it out of the room. If you take an exam out of the room we assume that you accept the grade and it will not be changed after that under any circumstances. If you are not sure, return it to the TA and look at it later with the TA.

Personal Problems: If you anticipate, or actually experience, serious problems with an exam because you have physical, mental or psychological problems, then come and talk to the instructor, preferably before the exam, but better late than never. Exams are for the purpose of finding out if you know the material. If you need some sort of special consideration because of a disability or other reason then you should let the instructor know in a timely fashion. If you freeze during an exam, tell the instructor that during the exam, don't wait to tell the instructor the next day.

Grades: Roughly speaking, depending on how the class goes, you can sort of expect that the middle grade might be about a B- and about 25/30% of the class might get As. The instructor will handle two midterm exams, each worth 25% and a final exam worth 40%.

HELP! The department runs a help room, Krieger 213, which is open most of the day; check door for times. This is the easiest, most convenient way to get help if you need it. It is there right when you want it. The instructor office hours are on Wednesday 3:00pm-4:00pm. The instructor is also available by appointment.

The Learning Den on-campus tutoring program will be supporting Linear Algebra this Spring.

The Learning Den: Free Small Group Tutoring; Dunning Hall tutoring@jhu.edu

The tutor is Josh Greenspan (jgreens7@jhu.edu). He will lead tutoring sessions on Wednesdays at 8pm in Dunning Hall, room 408.

To reserve your seat:

1) Sign up online at http://tutoring.jhu.edu (Your User ID and password is your 6-character Hopkins ID; the two fields are identical)

2) Call 410-516-8216 and ask to speak with Ms. Kelly Novic

3) Stop by the Office of Academic Advising, Garland Hall, Suite 3A

Study Habits: All of you are good enough to get an A in the course. What will determine the grade is a combination of motivation and study skills. Motivation shouldn't be a problem since the material is great. Study skills are harder to come by. There are various things around to read like the little pamphlet, How to Study Calculus, by Larry Joel Goldstein. Also, on the Supportive material web page there is something called the Mathematics Survival Guide that is well worth reading. In a nutshell though, the point is, you learn math by doing. You can watch people do math all day and not get much of an education. Do it. Work problems. Memorize every theorem and definition in the book. You need to know them all anyway, why make it up when you need it? Just learn it and remember it. Then work every problem you can find. If you get help from someone, then go back and work it again by yourself the next day. We cannot emphasize enough how important that last statement is. Read it again.

Linear Algebra: Linear algebra is everywhere. You've been using it for years without naming it. The integral is linear, the derivative is linear. Most applications of mathematics to the `real' world only work when you only look at the linear part. It is great material which will be with you always.

Calculus: Calculus I is a prerequisite for this course. Technically, you can certainly do linear algebra without calculus, but calculus supplies us with lots of examples so we use it. Even though there are few real prerequisites, there is an abstraction about linear algebra that makes it more difficult to grasp for some people. This is why many of you find yourself taking it after Calculus III or differential equations. The more mathematical sophistication you have, the easier it is to learn linear algebra. There are two distinct new levels of abstraction in this course. The intellectual transition for each of these is quite difficult so if you find yourself having a hard time with the material it might not be your imagination. The best way to make these transitions is, as usual, to work lots of problems. Although these transitions can be difficult, they are well worth the investment. Successfully making these transitions opens up a whole new type of thought process which will remain available to you even if you never do math again. As great as the material is and as ever present as linear algebra will be for those who continue to use mathematics, this ability to understand a new level of abstraction may well be the most important thing in the course, should you manage it.

Final Exam: The final exam for the course is scheduled on Monday May 10, 9:00am-12:00pm:

Attendance: Not all students come to class every day. There are a couple of reasons why this can adversely affect a student's grade in the course. One type of student isn't really interested and doesn't really care. The consequences are obvious. Another type of student learns better by reading and seldom gets much out of a lecture and so they don't go. There is a problem with this too. During the lectures the instructor will let students know what she thinks is important in the course and it turns out that the instructor makes up the exams and she tends to put what she think is important on the exams. A student who doesn't pay any attention to what happens in class might miss this important connection. So, if you are among those who regularly cut class, we advise you to stay in close contact with someone who does go so that you will know what the instructor is doing in class and what she thinks is important. You will not get that from the book. The point of this paragraph is that there are good students who don't come to class but who study very hard and then find that their decisions about what was most important to study were wrong.

Calculators: You will not be allowed to use calculators on your exams in this course. Thus it is not a good idea to use them on homework since the homework is designed to prepare you for the exams. The reason for this ``no calculator'' rule is simple. The purpose of this course is to give you a basic understanding of linear algebra and develop your problem solving skills in this new context. There is no mathematics concept in this course that requires the use of a calculator (or computer) for you to learn it or for me to test you on it. The same can be said for all previous mathematics that you have learned. Calculator dependency is a BAD thing.

Ethics: We have rarely had problems with cheating in my classrooms and we don't expect to have it in this class. If, however, you know of cheating going on or feel that anything about the course is unfair, then please, report it to the instructor. In the event of cheating then let the instructor know how it is being done so that we can stop it. Cheating does not cheat me but cheats the other students in the class since cheating that raises one person's grade can lower everyone else's grades.

week	beginning	topics
1.	Jan. 25	Introduction to linear systems, Gauss-Jordan elimination, solutions of linear systems: 1.1, 1.2, 1.3.
2.	Feb. 1	Linear transformations: linear transformations and their inverses, linear transformations in geometry: 2.1, 2.2.
3.	Feb. 8	Snowstorms: no classes
4.	Feb. 15	Continue on 2.2; matrix products, the inverse of a linear transformation: 2.2, 2.3, 2.4
5.	Feb. 22	Subspaces of Rn and their dimension: 3.1, 3.2, 3.3.
6.	Mar. 1	Continue on 3.3, 3.4; Linear spaces: 4.1, 4.2
7.	Mar. 8	The matrix of a linear transformation: 4.3; Orthogonality: 5.1
8.	Mar. 15	Spring break: no classes
9.	Mar. 22	Orthogonality (continue) 5.1, Gram-Schmidt process and QR factorization 5.2, Orthogonal transformations 5.3
10.	Mar. 29	Orthogonal transformations (continue) 5.3, Least squares and data fitting 5.4, Inner product spaces 5.5
11.	Apr. 5	Inner product spaces 5.5 (continue), Introduction to determinants 6.1, Introduction to eigenvalues and eigenvectors 7.1 and 9.1
12.	Apr. 12	Determinants 6.2, 6.3.
13.	Apr. 19	Eigenvalues and eigenvectors (continue): 7.2, 7.3, 7.4.
14.	Apr. 26	Complex eigenvalues and eigenvectors 7.5, Symmetric matrices and diagonalization 8.1
15.	May 3	Symmetric matrices and diagonalization, Spectral Theorem and decomposition, quadratic forms 8.1, 8.2