Course Description and Grading BreakdownThis course will introduce the mathematical method through (One Variable) Calculus, with which the Caltech freshmen have reasonable familiarity, at least for doing calculations (assuming various results as black boxes). The typical high school courses, and the AP tests themselves, are woefully inadequate in 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. Learning to think precisely and rationally will come in handy in life, regardless of which subject one majors in. The first nine topics below, and as much as possible of the tenth topic, will be treated during the Fall quarter: (1) Mathematical Induction and the real number system (2) Sequences and Series (3) Continuous Functions (4) Differential Calculus (5) Integral Calculus (6) Polynomial Approximations (7) L’Hôpital’s rule for 0 (8) Improper Integrals (9) Complex Numbers (10) Integral Tests, Abel summation for series There will be weekly
homework assignments, as well as a Midterm and a Final examination, each of the
Take Home variety lasting three hours. The final grade (of Course Meeting Time and LocationLecturesMonday, Wednesday and Friday 10:00 - 10:55 Baxter Lecture Hall (BAX) Recitations Thursday
If you would like to switch your recitation section, please email Meagan with your preferred recitation time. Course Instructor Contact Information and Office Hours256 West Bridge TA Contact Information and Office HoursTodd Norton (Head TA) Office Hours: Sundays, 7-9 pm Location: TBD Siqi He Sundays, 6-7 pm TBD Alex McDonald Saturdays, 12-1 pm TBD Konrad Pilch Thursdays, 4-6 pm TBD Helene Rochais Fridays, 2-3 pm TBD Daniel Siebel Fridays, 4-6 pm TBD Ryan Yoo Wednesdays, 2-3 pm TBD Course Schedule
Course PoliciesHomework- Homework is due Sundays by
12 Midnight, just before the advent of Monday, and will be posted on the course
web site on Tuesday before noon during the previous week; for example, the
first HW will be due on Oct.1 (by midnight) and the problem set will be posted
on Sep. 26. All problems may be done in collaboration with others. However,
each student must write down the solution in his/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 problems. At most one
late homework set will be accepted throughout the quarter, and only at your TA’s
discretion, if arrangements have been made in advance with your TA, and if the
work is less than a week late. Beyond this, late homework will NOT be accepted,
except with 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.Recitations - 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!Assignments
Midterm and Final ExamCollaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |