Math 250
Here is the catalog description of the course:

The ideas and computations of linear algebra are everywhere in mathematics and its applications. They are used in every area of science, technology, and engineering.

I last taught linear algebra many years ago. At that time matrices were triangular (to the right are some student notes from that course written on a rock). Since then, matrices have evolved and become four-sided: they are rectangular.

More spectacularly, the ideas of linear algebra led directly to the overwhelming success of Google (a discussion of the specific ideas involved is here with some supporting computational framework here).

I believe it is nearly educational malpractice to present linear algebra without some computational support in this century, but we will try to teach and learn without such. In "real life", the ideas and algorithms of linear algebra are almost always implemented by silicon friends but in this course we will be stuck with examples that can be done by hand.

Not only are real examples usually on a much larger scale than what can be presented in Math 250, but also much of linear algebra uses only (?) arithmetic (+,–,x,/) so all sorts of collections of "numbers" or any objects which can be added, subtracted, multiplied, and divided are candidates for linear algebra and its ideas and computations. This includes such familiar collections as the rational numbers (fractions involving integers) and the complex numbers (a+bi with a and b real and i²=–1) and also includes less familiar examples such as finite fields, which students who study digital signal processing and the finite Fourier transform will learn much about. That sort of linear algebra is also important in coding theory and cryptography.

The phrase "linear algebra" has almost two and a half million Google links today. There is certainly enough information available! If you would like to see some simple but very clever elementary applications of linear algebra, look at Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra by Jiri Matousek (briefly: "This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra."), published by the American Mathematical Society. The Amazon web page about this book is here and allows you to see some of the contents.

Text
From the Math Department's web page:

Spence, Insel, & Friedberg: Elementary Linear Algebra: A Matrix Approach, 2nd Edition , Prentice-Hall   (ISBN # 978-0-13-187141-0).

The authors of the textbook also have a companion web site containing supplementary material, including multiple choice tests covering the topics in the course. Students can take these tests on-line and have graded results of each test e-mailed to themselves (and their instructors, if desired).

I hope to follow the suggested syllabus for the course and would like students to do the suggested homework problems. I'll ask that solutions to some textbook problems be handed in.
Here are both the syllabus and the suggested homework list combined so you can save paper by printing this file two-sided.

One student (Ms. Steiner) reported that the website http://www.onlinemathlearning.com/linear-algebra-help.html has links to some helpful video tutorials about linear algebra.

Every computational algebra system I know (certainly including Maple, Mathematica, and Matlab) supports linear algebra very well. You may wish to investigate this. Almost surely you'll need to learn how to use such programs sometime in your life -- in school or at work. Here is a webpage at Duke University which has modules which can help you learn about linear algebra computations in Maple, Mathematica, Matlab, and Mathcad.

Background
You need to know how to do arithmetic and how to think logically.
One interesting aspect of the course is the contrast between formulas and algorithms. This course can briefly (and almost accurately!) be described as one algorithm and how to interpret the output. What may surprise students is that although explicit formulas can sometimes be given to get the computational results desired, the formulas are usually quite inefficient. I'll try to address this contrast during the course. The logical thought mentioned above is needed to deal with the output of the algorithms. We will solve systems of linear equations. Because we're doing this by hand, most of our systems will have a relatively small number of variables and equations. You need to learn to cope with many variables and equations. Therefore you need to learn the underlying logic: definitions and theorems. The simple examples we will do in this course are generally not realistic, and the logic will prepare you for what you will need to do.

Instructor
The lecturer is S. Greenfield.
Office: Hill 542 on Busch Campus; (732) 445-2390 X3074 (there's an answering machine);
My e-mail address is greenfie@math.rutgers.edu. I usually check e-mail several times a day, so that's probably the best way to leave a message.
Office hours: Monday and Wednesday from 3 to 4 PM and by appointment (e-mail is best for arranging appointments).

Grading

• Possible cheating
  Suspected violations of academic integrity (cheating) will definitely be reported. Students should be familiar with Rutgers policies on academic integrity. The penalties for infractions (breaking the rules) can be quite severe.
  Please: if you are uncertain about what the policy requires in any situation specific to this course, then discuss this uncertainty with the lecturer. The course should support efficient and comfortable learning of the material. I'll try to grade and do any sort of assessment of student work accurately, carefully, and honestly.
• Formal exams
  
  • Several formal exams will be given during classes. These exams will be announced in advance.
    Almost surely there will be special review sessions and office hours before each exam. Review material is also likely to be provided.
  • Make-up exams will be given only in the case of illness, a major emergency, or a major outside commitment. Verification of each of these should be done through the appropriate Dean's office, and a written note from the Dean requesting a make-up exam should be presented to the lecturer. You will need some form of proof (like a doctor's note, a police report, a towing bill etc.). The lecturer must approve each request for a make-up exam.
    If the reason for the make-up is known in advance you must ask for permission before the exam. In all other cases, please notify the lecturer as soon as possible using e-mail (preferred: greenfie@math.rutgers.edu), by phone (at (732) 445-2390 X3074 [equipped with an answering machine]), or through the Math Department Undergraduate Office (at (732) 445-2390).
    Make-ups will not be given for reasons like "the alarm clock didn't go off", "not knowing when the exam will be", or "not feeling prepared".
  • The final exam for section 1 is scheduled to be on Tuesday, May 10, from 12 to 3 PM.
    The final exam for section 5 is scheduled to be on Friday, May 6, from 4 to 7 PM.
    The location of the final exams will be announced later.
    
• Homework
  Students should do homework. Students at or above C-level should be able to successfully complete most of the suggested problems. Some homework problems will be collected.
• Quizzes
  There will be several brief quizzes. These may or may not be announced in advance and the time needed will be 10 to 15 minutes. They likely will reflect closely homework which should have been done.
• A precise formula?
  I don't have an exact formula for grades yet. Something resembling the following will be used:
  

  	Exam 1	100
  	Exam 2	100
  	Final exam	200
  	Quizzes	50
  	Homework	50
  	Total	500

  The total score will then be converted to a course grade. There are two additional comments on course grades.
  • Students who miss a significant number of classes may have their course grades lowered one step (for example, from a C+ to a C). When I've most recently done this in a calculus course, almost all of the students to whom it applied could not have their grade decreased (think about what this means). Attendance can be useful!
  • Students whose exam grades all are near bare passing or are failing may fail the course in spite of numerical averages: students must show that they can do adequate work connected with this course independently and verifiably.

Maintained by greenfie@math.rutgers.edu and last modified 1/15/2011.