PROFESSOR OF MATHEMATICS
- Section 2: Peter Burton 9:00-9:55 151 SLN
- Section 3: Angad Singh 9:00-9:55 153 SLN
- Section 4: Nathan Lawless 10:00-10:55 153 SLN
- Section 5: Konrad Pilch 10:00-10:55 151 SLN
- Section 6: Joshua Lieber 13:00-13:55 153 SLN
- Section 7: Gene Yoo 13:00-13:55 257 SLN
- Section 8: Nathan Lawless 14:00-14:55 257 SLN
- Section 9: Andrei Frimu 9:00-9:55 B111 DWN
- Section 10: William Chan 10:00-10:55 103 DWN
- Section 11: Todd Norton 14:00-14:55 103 DWN
- Thursday, 7 pm
Nets Katz, Sloan 164
- Thursday, 8 pm
Angad Singh, Kellogg 307
- Friday, 11 am
Gene Yoo, Sloan 274
- Friday, 2 pm
Nathan Lawless, Sloan 280
- Friday, 5 pm
Nathan Lawless, Sloan 280
- Friday, 6 pm
Andrei Frimu, Sloan 160
- Saturday, 3 pm
Peter Burton, Sloan 156
- Saturday, 4 pm
William Chan, Sloan 160
- Sunday, 1 pm
Todd Norton, Kellogg 307
- Sunday, 2 pm
Joshua Lieber, Sloan 274
- Sunday, 3 pm Konrad Pilch, Sloan 158
- Sunday, 4 pm
Nets Katz, Sloan 164
There will be weekly assignments, as well as a Midterm and a Final examination, each of the Take Home variety lasting five hours. The final grade (of P or F) will depend on a composite of these factors. To be precise, the homework will be worth 40 percent, while the final and midterm will be worth 30 percent. No one will be excused from the final exam.
The use of calculators, computer software, homework assignments and solution sets from previous terms, books and notes and or other such tools is NOT permitted on the exams. Collaboration on exams is not allowed.
Collaboration is allowed on the homework but you must write the solutions in your own language. Use of books and notes is allowed on the homework but you may not use solution sets from previous terms if they do the exact same problems. Use of calculators and computer software is allowed for homework but you are encouraged (unless software is specifically mentioned in the homework) to only use these tools to check your work.
Please go to the recitations! Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA and bug him/her to death (figuratively speaking) with your questions, and try to fill in all the holes in your understanding. Don't wait till the midterm to start doing that.
Extra Help: Tutoring is available for anyone who feels they would benefit from some extra assistance.
Homework is due Mondays at 2 AM to be turned in in the locked boxes outside Sloan 253 and will be posted on the course website by Tuesday the previous week. All problems may be done in collaboration with others. However, each student must write down the solution in his or her own individual way, and there should be no two identical solutions to any problem. Do not consult the solution sets from previous years in working this year's problem.
At most one late homework set will be accepted throughout the quarter, and only at your TA's discretion. Arrangements must be made in advance with your TA, and the homework set in question must be submitted no later than Wednesday 10 a.m. of the same week. Beyond this, late homework will NOT be accepted, without a letter from the Infirmary or from the Dean (or Associate Dean). Every week, graded homework can be picked up from the TA during the recitation on Thursday.
This course will introduce the mathematical method through (One Variable) Calculus. By the mathematical method, what we primarily mean is the ability to express one's self with absolute precision, and then to use logical proofs to establish that certain precise statements are universally true. We assume that the Caltech freshman has reasonable familiarity with single variable calculus as a computational system, but we emphasize explaining, or testing, why things work and how to justify one's propositions. In Ma 1a, the underlying concepts will be stressed, as well as the need for checking the hypotheses precisely as to where the results apply. A main focus will be on the writing of complete proofs so the case one is making is ironclad and unassailable. It will emerge that when we do this, we actually know more than the standard computational aspects of single variable calculus and that we can answer questions which are new to us and come up naturally once all the terms in Calculus are carefully defined and the definitions used. Some of these questions are also quite natural from the point of view of the scientist and engineer.
The topics listed below will be treated during the Fall quarter:
- Mathematical induction and the real number system.
- Sequences and Series
- Continuous Functions
- Differential Calculus
- Integral Calculus
- Polynomial Approximations
- L'Hopital's rule for 0/0
- Improper Integrals
- Complex Numbers
- Integral Tests, Abel summation for series
TEXTBOOKSThe classic textbook for the course is Apostol's book below. We will use it only as a reference
Apostol, Tom M., Calculus, Volume 1, 1991, Wiley, ISBN: 0-471-00005-1.
Katz, Nets Hawk, Official Course Lecture Notes (under construction). These will serve as the course textbook and have the problems for your problem sets.
|10/19||This is how we used to teach the Mean Value theorem|
|October 3||Problem set 1|
|October 10||Problem set 2|
|October 17||Problem set 3|
|October 24||Problem Set 4|
|November 7||Problem Set 5|
|November 14||Problem Set 6|
|November 21||Problem Set 7|
|November 28||Problem Set 8|