MATH 157: Honors Calculus I

Fall 2009

Description and goals: A closer, more rigorous look at the fundamental concepts of differential calculus in one variable. The main focus will be on the structure of real numbers and the key notions of limit, continuity and derivative; standard applications will be presented as mere examples. The course provides a good opportunity for students to learn how to read and write proofs. The true prerequisite for this course is the intellectual curiosity to learn about a nice piece of mathematics and the willingness to think. Familiarity with non-rigorous calculus is generally assumed, but not essential. Picture: Isaac Newton (L) and Gottfried Leibniz (R), Copyright Royal Society.

References

Syllabus

Assignments

Announcements:

• 11/20: Check out your grades as of today.

• 11/17: Check out the midterm II solutions.

• 11/8: Here are the workshop II problems to be discussed on 11/12. Make sure you think about them ahead of time.

• 10/22: Check out this note on an example which shows the completeness axiom does not hold in the field of rational numbers.

• 10/16: Check out your grades as of today.

• 10/13: Check out the midterm I solutions.

• 10/6: Check out the solutions to the remaining homework problems from chapter 4 that we did not discuss in class.

• 10/3: Here are the workshop I problems to be discussed on 10/8. Make sure you think about them ahead of time.

• 9/25: Here are some examples of graphs in polar coordinates that I have made using MAPLE®. In each case the polar equation of the curve is shown at the top of the frame:

  circle, cardioid, 4-leaf clover, 3-leaf clover, and 6-leaf clover.

  By playing with more complicated equations, you can produce graphs that are quite interesting. Here are two examples:

  A "maple leaf" and a "butterfly".

• 9/15: Well, some of you are still waiting to receive your copy of the textbook. In the meantime, here is a scan of Spivak's chapter 3.

• 9/10: Check out this note on sums and products of rational and irrational numbers.

• 9/2: Just asked the bookstore to order copies of Spivak. They should arrive in a few days. I also noticed that there is a 4th edition out which adds only a small amount of material and some problems. It will probably not be of interest to those who already have the 3rd edition.

• 9/2: Here is a copy of the relevant pages of Spivak's first two chapters.

• 9/1: Welcome!

General Information and Ground Rules:

• Class lecture meetings are Tuesdays and Thursdays 4:30 - 6:20 in Kiely 277.

• Homework is an absolutely essential part of this course. You cannot master the course material without solving many problems consistently throughout the semester. Homework will be assigned on a weekly basis and will be discussed in class, as much as time allows. You are encouraged to work in groups and discuss these problems with one another, but the work that you hand in must be your own write up.

• Course grade is based on the following scheme:
  
  

  Home/Class Work	Two Midterms	Final Exam
  20%	20% each	40%

• Exams are scheduled as follows:
  
  

  Midterm 1	Midterm 2	Final
  Tuesday October 13 (in class)	Tuesday November 17 (in class)	Tuesday December 15, 4:00-6:00 room TBA

• If a midterm exam is missed because of a documented illness or valid emergency, the course grade will be determined on the basis of the other work done during the semester. Exams missed for other reasons will count as failures.

• At the end of the semester, everyone who has not withdrawn from the class will receive a grade. Incompletes will not be given to avoid F's.

Saeed Zakeri