MATH 157: Honors Calculus I

Fall 2018

Isaac Newton (L) and Gottfried Leibniz (R), Copyright Royal Society.

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. An essential prerequisite for this course is the intellectual curiosity to learn about a nice piece of mathematics and the willingness to think. Some familiarity with non-rigorous calculus is generally assumed.

References

Syllabus

Assignments

Announcements:

• 12/20: Check out your course grades. Enjoy your break and Happy Holidays!

• 12/18: Check out the final exam solutions. I'll post the grades in a couple of days.

• 12/8: Here are the workshop III problems to be discussed on 12/11 and 12/13. Make sure you think about them ahead of time as you prepare for the final exam. As a reminder, we have an extra session on 12/13 from 11:00am to 12:30pm. As of now it will be in our own room Kiely 277, but I'll notify you in case there is a change.

• 12/5: Here are the solutions to some of HW10 problems.

• 11/19: Here are the solutions to HW8 problems.

• 11/16: Check out your second midterm grades.

• 11/15: Check out the second midterm solutions.

• 11/9: Here are the workshop II problems to be discussed on 11/13. Make sure you think about them ahead of time as part of your preparation for the second midterm.

• 11/8: Have a look at this short article on the sliding ladder problem. It discusses three different scenarios (free slide due to gravity, constrained top, and constant base speed).

• 10/19: Check out your first midterm grades.

• 10/18: Check out the first midterm solutions.

• 10/11: Here are the workshop I problems to be discussed on 10/16. Make sure you think about them ahead of time as part of your preparation for the first midterm.

• 10/4: Here are the solutions to some of HW4 and HW5 problems.

• 9/27: Some examples of graphs in polar coordinates that I have made using MAPLE®:

  a circle, a spiral, another circle, a vertical line, a cardioid, a 4-leaf clover, another 4-leaf clover, a 3-leaf clover, and a 6-leaf clover.

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

  a butterfly, and a maple leaf.

• 9/25: Here are the solutions to some of HW3 problems.

• 9/6: Check out this short note on sums and products of rational and irrational numbers. It's related to Spivak's chapter 2, problem 12.

• 9/5: Here is the schedule of the Math Lab in Kiely 331. Feel free to go there for extra help:

  Mon and Wed 9 am to 8 pm
  Tue and Thu 9 am to 5 pm
  Fri 9 am to 3 pm

• 8/30: In case you haven't received the textbook yet, here is a copy of Spivak's chapter 1 and chapter 2.

• 8/28: Welcome!

General Information and Ground Rules:

• Class lecture meetings are Tuesdays and Thursdays 11:00 - 12:50 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 Exam
  Thursday October 18 (in class)	Thursday November 15 (in class)	Tuesday December 18, 11:00-1:00 in Kiely 277

• 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