Syllabus and Facts of Life

Linear Algebra, 110.201, Spring 2018

Professor W. Stephen Wilson

Contact information: Office: Krieger 421 E-mail:

Course web site.

When and where: There are two lectures (nearly identical), one at 10-10:50 and the other at 11-11:50. Both lectures are MWF. The first is in the Maryland 110, and the second is in Shaffer 3. This change was made recently (in the middle of the night, of Jan 23-24). I assume this is the way it will be.

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

The book is required reading. In fact, you are technically required to read the book before I lecture on the material. That way I can feel free to cover the material, or not, in lecture, since I know you have already read it. At any rate, if it is in the reading assignment then you are responsible for it whether I mention it in lecture or not. From the syllabus you can usually tell what I am about to lecture on so you'll know what to read. Actually, there is too much stuff in the book for me to lecture, in detail, on all of it anyway. Thus you should read the material both before and after the lecture. If you don't, then don't expect to do well.

In particular, on the second day or so of the material there are about 20 definitions and I will not do them all in class but expect you to have read them already. Another very special assignment: You must read appendix A on vectors on your own outside of class. We will use that material all the time and I will assume it starting day two.

Homework: I believe that homework will be posted on Blackboard on Wednesday. Homework will be due at the beginning (or end, depending on your TA) of the next week's section meeting (Tuesday or Thursday). The homework will normally cover the material in the lectures for the previous week. (There is no good way to deal with the timing of homework, sorry.) You are allowed, even encouraged, to work in groups. When it comes to handing in the homework though, please do your own solutions. 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 the exam, thus: homework. 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 will be disappointingly low. My experience with homework is that students with slightly lower than average scores on homework tend to have higher grades on exams. Both are because they did the homework on their own. It is also my experience that pretty much the only students who don't do the homework are those in the D and F category. Late homework is not acceptable. Work something out with your Teaching Assistant about how to turn in a homework if you cannot go to class. DO NOT GIVE IT TO ME. The TAs deal with the homework.

Videos (click here):

A few years back I made a complete set of video lectures (Khan Academy style (without the charm)). I went through the entire book (probably the third edition) in roughly 10 minute segments. I also worked a lot of problems, particular the interesting but obscure problems in the book, but also the problems I gave on exams, see links below for when I taught the course.

In principle, I could just assign watching the lectures on line, and we could find something more interesting to do in class than have me give similar lectures again. However, with such a large class, I can't think of what we could do. However, rather than read the book before class, you could watch the lecture before it happens. This could cause problems with your personal concept of the linear flow of time, but you'll adapt.

Old Exams: are posted on the web. These are from many years of previous versions of this course. There are lots of exams and some solutions. Lots of great practice materials.

It has been awhile since I've taught the regular linear algebra course, but here are all the course links for those times.

  • Linear Algebra 110.201, Fall 2004, Course pages.

  • Linear Algebra 110.201, Spring 2004, Course pages.

  • Linear Algebra 110.201, Fall 2003, Course pages.

  • Linear Algebra 110.201, Spring 2003, Course pages.

    As with homework, I 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 meets, 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. I do not grade on the basis of how well you can watch others do problems.

    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. There will be quizzes every week in section and they will count as 20% of your grade. Quiz scores cannot move from one section to another. Neither I nor the TAs can move you from one section to another.

    You should go to the math dept office and learn what they say there about how to switch sections (or get into one if that is the problem). Do not bring this problem to either me or a TA as we are not authorized to do anything about it.

    Exams: I have been known to assign seating for exams. Come early enough so you can find your seat if I do. 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 then see me 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 me, preferably before the exam, but better to do it during the exam than after. Exams are for the purpose of finding out if you know the material, not to see if you can function when your mother just ran off with a Hitler clone, your girl/boy-friend just ran off with your roommate or any of the other natural and unnatural disasters which happen to students every year. If you need some sort of special consideration because of a disability or other reason then you should let me know in a timely fashion. If you freak or freeze during an exam then tell me then, during the exam, don't wait to tell me the next day. Read that last sentence again and remember it so that it floats to the surface if all other mental functions fail you.

    Grades : Roughly speaking, depending on how the class goes, you can sort of expect that the middle grade might be about a B/B-/C+ and about 30-40% of the class might get As. However, if you all learn the material really well then I would be delighted to give you all As. I like to give hard exams because I don't think the best students should be cheated out of their tuition; they should have something to do too. So, don't get demoralized if the average is 50%, I grade on the proverbial 'curve'. I will give two midterm exams, each worth 20%. Your weekly section quizzes given and graded by your TA count for another 20%. The final will count 40%. I adjust the lowest of the 3 20% grades up to the middle one. This is done after I have adjusted the grades so they can be compared. If you do better on the final than you have during the term (after I have adjusted the numbers so I can compare them) then I will give a fudge factor for that equivalent to counting the final 60%. I adjust things so that fully 1/2 of the class gets this fudge factor. I reserve the right to count in-class participation towards (or against) the grade but should point out that I have never done it. Grading will not be consistent from section to section. However, I will adjust the grades of each section so that they are comparable and no section will be hurt because of a 'tough' grader or helped because of an 'easy' grader.

    Every semester there are a number of students who are unhappy with their course grade. Only one or two of these students push very hard for a grade change. These students are usually ones who neglected some important part of the course like doing the homework, studying, or they want some sort of special consideration. Special consideration is patently unfair to all of the other students. I will not do something for one student that I would not do for all. I will not be unfair to the many students who would like a better grade but who do not bug me daily for a week or two. Students who do push hard for a grade change will experience my insistence on fairness for all students as personal brutal abuse. I will be able to defend any grade I give and my chairman and my dean will back me up. The point of this little tirade is two-fold. First, I would really like to save the incredible amount of time these one or two students cost me each semester, and, second, I want to reassure all of the other students that I will not unfairly change someone else's grade just because they made a pest of themselves. I take grades seriously because I know most students do too. That means that they should be fair.

    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. My office hours are Monday Noon to 1. I will only stay for the first 15 minutes unless someone has emailed me telling me that they will come later in the hour. I am also available by appointment and you can always send me an email at any time. Also, feel free to grab me after class as I am almost always available right then. The course TAs spend time in the math dept help room. We will post the times for all our TAs on Blackboard (I hope).

    HOURS YOU OWE: This is a 4 credit course. I assume that you take 15 credits and you work 45 hours a week. That means you owe this course 45 x (4/15) = 12 hours, minus the 4 in class if you come, to get 8. If you are not working 8 hours outside class then don't be surprised if you're not doing well. Work harder before you complain or even before you ask for too much help. You are not working hard in this course until you put over 12 hours a week into it outside of class if you come to class, 16 if you don't. If you are taking more credits then you have chosen to work more hours.

    BOSS: I'm the boss for the course. If the TA tells you something that contradicts what I said, get it straightened out. This could be quite serious. If, for example, they said you didn't have to go to a midterm because they don't count, you probably should check with me because that contradicts what I said. If you don't, and you listen to them, then you could lose big. We have very good TAs so I do not anticipate any problems, but if you have problems with your TA then you must bring it to my attention as quickly as possible if you want the problem to end. For some reason students don't take this admonition seriously. If you have complaints about your TA then see me about them. We'll fix it.

    Study Habits: I should give you a little speech here about 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 and you are paying a fortune to get it (although I have met students who were unaffected by these motivational tools). Study skills are harder to come by. I have collected a number of useful things that might help with learning how to study. 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. I cannot emphasize enough how important that last statement is. Read it again. Do it. Many of you will notice that there is a slight difference between this course and the last math course you took in high school. We have roughly 125 students in this lecture. How big was your last math class in high school? Did your teacher in high school actually know your name? Did you have to read the book to learn the material in high school or could you get it all out of the class? How many class hours did you have in high school to learn one semester of Calculus? How many are you going to get for Linear Algebra here? You MUST be able to read the book in this class.

    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.

    From the Course Catalogue: 110.201 (Q) Linear Algebra
    Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations. Prerequisite: Calculus I. 4 credits

    The official Short Syllabus for Linear Algebra

    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. On the other hand, the more linear algebra you know, the easier it is to understand the content of courses like Calculus III and differential equations, because they are full of linear things, obvious to those who have had linear algebra. Some years back we found that students were getting random advice as to what order to take courses in. I decided to figure out if there was a best order. What I found didn't help. Students who took Calc III first and then Linear Algebra did about the same in each. Students who did Linear Algebra first and then Calc III didn't do as well in Linear Algebra as might have been expected (they didn't have the advantage of the extra mathematical maturity of having taken Calc III) but then they did better than expected in Calc III (because the content knowledge of Linear Algebra that they had helped them with Calc III). We decided not to tell people what order to recommend the courses be taken in.

    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. Go for it!

    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. Some just sleep better in a bed than in a class; I can sympathize with this. Another type of student learns better by reading and seldom gets much out of a lecture and so they don't go. (I was that type, and anyway, I've only recently learned how to sleep in lectures.) There is a problem with this too. During the lectures I let students know what I think is important in the course and it turns out that I make up the exams and I tend to put what I 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, I advise you to stay in close contact with someone who does go so that you will know what I am doing in class and what I think 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. There are also those students who get the day of the exams wrong. A little contact with the class can help avoid those embarrassing situations.

    Calculators: You will not be allowed to use calculators on your exams or quizzes in this course. Thus it is not a good idea to use them on homework (with exceptions) since the homework is designed to prepare you for the exams and quizzes. 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. You can check my web page to see a paper that shows that the students at Johns Hopkins who had calculators "encouraged and emphasized" in K-12 had somewhat lower grades in their JHU mathematics courses. The paper shows that this is independent of math SAT scores.

    Ethics: I have rarely had problems with cheating in my classrooms and I 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 me. In the event of cheating, let me know how it is being done so that I 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 class standing.

    Weekly Reading Assignments and Exam Dates:

    Week # 1: Jan 29--Feb 2, Sections 1.1, 1.2 ,and 1.3.

    Week # 2: Feb 5--Feb 9, Sections 2.1 and 2.2.

    Week # 3: Feb 12--Feb 16, Sections 2.3 and 2.4.

    Week # 4: Feb 19--Feb 23, Sections 3.1, 3.2, and 3.3.

    Week # 5: Feb 26--Mar 2, Section 3.4. Midterm exam, Friday, March 2.

    Week # 6: Mar 5--Mar 9, Sections 4.1, 4.2, and 4.3.

    Week # 7: Mar 12--Mar 16, Sections 4.3, 5.1, and 5.2.

    Spring Break: Mar 19--Mar 23.

    Week # 8: Mar 26--Mar 30, Sections 5.3, 5.4, and 5.5.

    Week # 9: Apr 2--Apr 6, Sections 5.5, 6.1, and 6.2.

    Week # 10: Apr 9--Apr 13, Sections 6.2 and 6.3. Midterm exam, Friday, April 13.

    Week # 11: Apr 16--Apr 20, Sections 7.1, 7.2 and 7.3.

    Week # 12: Apr 23--Apr 27, Sections 7.3, 7.4 and 7.5.

    Week # 13: Apr 30--May 4, Sections 8.1, 8.2 and 8.3.

    The Final Exam is Wednesday May 9, 9am - Noon.

    Many of you have conflicts with the final exam. We have a system to take care of that. Just don't try to leave town at noon the day of your conflicts.