Math 20, Introduction to Linear Algebra and Multivariable Calculus

Spring 2000

• Instructor: Nathan Dunfield, with help from the CA's.
  
• Time and Place: MWF 9:00am in Science Center 309, plus a weekly problem session (see below).
  
• E-mail: nathand@math.harvard.edu.
  
• Office: Science Center 334. Office Phone: 5-5349.
  
• Web page: http://www.math.harvard.edu/~nathand/
  

Course Outline:

The material which will be covered falls into three interconnected parts. Linear Algebra: Systems of linear equations, row reduction, vector spaces, matrices, linear transformations, determinants, eigenvalues and eigenvectors. Multivariable Calculus: Functions of several variables, partial derivatives, chain rule, optimization problems (both constrained and unconstrained). Applications: Possible topics include: Cobb-Douglas production function, Leontief economic models, Markov chains, population models, linear programming, least squares curve fitting.

Although many of the examples in the course will be drawn from economics and other social sciences, knowledge of these subjects will not be assumed.

Textbook

Elementary Linear Algebra, Applications version, Anton and Rorres, 7th or 8th edition (If you use the 7th edition, you may occasionally have to look up a problem that is in the 8th but the not the 7th ed. Otherwise the texts are the same, except that the 8th ed. is much uglier). The multivariable calculus part of the course will be taught out of a course packet that will be sold in the Science Center basement. This packet will be available later, when it is needed (about the 5th week of class).

Prerequisites

Math 1b or equivalent, or an A or A- in Math 1a, or a 5 on the AB or a 3 on the BC Advanced Placement exam in Mathematics.

Problem Sessions:

There will be weekly problems sessions run by the Course Assistants. Attending a problem session each week is strongly encouraged. Not only are these sessions a great place to get help, but due to the large amount of material to be covered in the course, it's not possible to do as many examples in class as I would like. Times and places will be announced.

Exams:

There will be two in-class midterm exams and a final. The first midterm will be on Friday, March 10. The second will be Monday, April 17. The final will be in its standard, university scheduled, time slot. Makeup exams will only be given in cases of extreme human tragedy.

Note: Calculators will not be allowed on exams.

Homework:

There will usually be two homework sets per week. The first set will be given out on Monday and due Friday of the same week. The second will be given out on Friday and collected the following Wednesday. Assignments will be graded and returned promptly. Solutions will be put on reserve in Cabot Library after the assignment is due. Homework assignments must be turned in on time -- no late homework will be accepted. However, your two lowest homework grades will be dropped. Homework assignments (but not solutions) are also posted on the course web page.

You are allowed, nay encouraged, to work together on homework problems. However, you must write up your solutions individually.

Grading policy:

Homework will be worth 20% of the final grade, each midterm 20% and the final 40%.

Office Hours:

My office hours will be:
• Monday: 2:30 - 3:30
• Tuesday: 3:00 - 4:00
• Friday: 2:30 - 3:30
and by appointment. For an appointment, just talk to me before/after class or send me e-mail.

The course assistants will also have office hours at times and places to be arranged.

There's also the Question Center which is open from Sunday-Thursday from 8-10 pm in Loker Commons, and which is stocked with CA's and grad students to answer your questions.