Textbook

Chapters 1 - 4 of A Course in Linear Algebra by David Damiano & John Little
(This book is out of print, but a course packet with these chapters is available in the bookstore.)
We will cover all of the chapters in the course packet, omitting certain sections and emphasizing others. This material breaks up into four basic units:

• Vector spaces, linear combinations, linear independence, bases, and dimension.
  
• Linear transformations, matrices, kernel and image, composition of linear transformations, inverse transformations, change of basis.
  
• Determinants.
  
• Eigenvalues, eigenvectors, diagonalization, spectral theorem for symmetric matrices.
  

Between classes, I expect you to read the upcoming sections of the book, and to study the sections which were covered in the previous class. Read the book with paper and pencil at hand, working out the examples, trying to reconstruct proofs of theorems without looking at the book or your notes, and writing down any questions you have about the material. Trust me, you will get much more out of the course by following this advice!

Pre-requisites

Math 243, Algebraic Structures. I will assume that you all have a strong working knowledge of the following topics which were discussed in that course:

• the basic language of sets and properties of set operations such as union, intersection, complement,
  
• mappings (functions) and the one-to-one and onto properties,
  
• relations and binary operations,
  
• the method of proof by mathematical induction.
  

If you have not taken Math 243, you should see me immediately. I will give you a copy of the appendices from our course text which cover these topics. You must master this basic material to understand almost everything we talk about in this course. In addition, even if you have seen most of these topics before, you may need to adjust your thinking and study skills in order to succeed in a 200-level mathematics class. (See notes at the end of this syllabus).

Instructor

Professor Sharon M. Frechette

Office: Swords 321

Office Hours: here

Phone: 508-793-2257 or email (preferred)

Exams

There will be three in-class midterm exams, tentatively scheduled for February 20, March 26, and April 30. A cumulative final exam will be given on Wednesday, May 12, at 2:30pm

There will be no makeups for missed exams. If you miss an exam without legitimate reason, you will receive a score of 0. If you miss an exam due to legitimate circumstances confirmed by your class dean, the percentages for your remaining exams will be adjusted, to maintain the 40 % total. If you know in advance that you must miss an exam day, notify me as soon as possible. I can arrange for you to take your exam early.

Grades

Course grades will be computed according to the following percentages:

Weekly homework	20 %
Class participation, and group discussion write-ups	10 %
Weekly Definitions Quizzes	5 %
3 in-class Midterm Exams (lowest: 10 %, others: 15 % each)	40 %
Final Exam	25 %
Total	100 %

Homework Guidelines

Will be assigned on Fridays and collected the following Friday at the beginning of class. Each student is entitled to two late assignments which may each be turned in one class period late. Other than that, late homework will not be accepted.

Some things to keep in mind while doing your assignment, for our mutual benefit:

• Please be neat! Write up the problems in order, write only on one side of the page, and staple your assignment together. Leave lots of space for me to write comments.
  
  
• Copy out the problem statement before giving the solution.
  
  
• Show enough detail so that a confused student in the class could follow your solution. Don't expect that the reader already knows how to solve the problem. Just writing the answer is almost never sufficient.
  
  
• Proofs should be written in complete sentences, although your sentences will often contain mathematical symbols and statements. Proofread what you have to be sure it makes sense.
  
  
• No "miracles" during proofs, please! If you are left with a small gap in the proof that you just can't bridge, acknowledge it. I will write helpful hints when grading, so you can give it another try.
  
  
• Start the assignment early (i.e. the day it is handed out). This will allow you ample time to consult with me or your classmates if you get stuck on some problems. If you start the assignment on the day before it is due, you will be very unhappy!
  
  
• Work on making your arguments clear and concise. Make good use of notation and diagrams. Your proofs will be graded for both accuracy and presentation.
  
  
• I encourage you to discuss homework problems with other students and/or with me. Most of us learn math better when we have to verbally communicate about it! However, even if you work with other students to solve a problem, all solutions that you turn in must be written in your own words. (Plan on taking scrap notes when you work out the problem first, and then ``writing it up" in a clean form by yourself afterwards, without other students in the room.)
  
  
• If you discuss homework assignments with other students or with me, you must list the names of all such "consultants" at the top of your assignment.

Academic Integrity

The College's policy on Academic Integrity, as well as the more specific Mathematics Departmental Statement on Academic Integrity must be strictly observed. For this course, the following addenda apply:

• All exams will be closed-book, and no sharing of information in any way is allowed during an exam.
  
  
• If you discuss homework assignments with other students or with me (as you are encouraged to do!), you must list the names of all such "consultants" at the top of your assignment.
  
  
• On write-ups for group discussions, the collaboration of all members in a group is expected. However, all final solutions to discussion assignments must be a group's own, and are not to be shared across groups.
  

Definitions Quizzes

Now that you all have some experience in 200-level math classes, you know that a firm grasp of definitions is absolutely essential! Without it, one cannot understand the significance of theorems, nor construct their proofs. Moreover, since concepts build on one another in layers, definitions from the early part of the course will still need to be "in the front of your brain" later in the course. To keep everyone on their toes in this regard, we will have a Definitions Quiz once a week at the beginning of class. The definition of any term or object introduced in the course before the date of the quiz is fair game on any of these quizzes.

Advice on Succeeding in a 200-level Math Course

Almost all of you now have some experience writing proofs. Writing clear, convincing arguments which convey a mathematical concept is the cornerstone of higher mathematics. The skills you develop in this course will have a significant impact on your success in future courses. Giving your best effort now will have a huge payoff later! Some advice:

• I encourage you to not be satisfied with simply getting through a proof. Once you have the framework in your scrap notes, think about how to construct the proof in the most logical, easily readable and convincing fashion. Work on using notation well and being concise while conveying the necessary information.
  
  
• Study your notes and the sections covered, and read ahead for the sections to be covered during the next class. This should be done with paper and pencil at hand. It is very helpful to work out additional examples, and to fill in extra details on proofs done at the board in class. Also, make a note of any questions that arise, and come to office hours to ask them.
  
  
• Be persistent and realize that some homework problems will take both time and inspiration. Expect to work hard, and always start assignments early. If you start an assignment the day before it is due, you will be very unhappy. Trust me on this one -- don't find out the hard way!
  
  
• When doing a proof, you may want to first verify the principle to be proved, by putting in numbers and trying a few examples. This helps you get a feeling for what you're trying to prove, and why it's valid! If you've been beating you head against a proof for a while, it's best to leave the problem and do something else for a while. You'll be surprised at how much your brain can accomplish on "simmer."
  
  
• When doing proofs, always remember to think "what do I know, what must I show?" Take the hypotheses and the conclusion(s), and translate them all into useful terms. This involves applying definitions for abstract objects, and knowing how to specialize them to the given situation. You will be surprised at how often this simple strategy helps you to at least see how to get started.
  
  
• Remember that doing a proof is a multi-stage process. Generating several pages of scrap work with various attacks, some completely unsuccessful, is the rule rather than the exception! If you would like to save trees, feel free to come get some scrap paper from the big stack in my office whenever I am around.
  
  
• Expect to spend a minimum of 3 hours studying and doing homework for every hour spent in class. However, if you find you are spending considerably more time than this, please discuss it with me.