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: Todd will not hold office hours on Dec 3. Instead there will be a midterm review session from 6-8 pm in E Bridge 201. Siqi He Sundays, 6-7 pm Downs B111 Alex McDonald Saturdays, 12-1 pm Downs B111 Konrad Pilch Thursdays, 5-6 pm Downs B111 and Sundays, 5-6 pm Downs B111 Helene Rochais Fridays, 2-3 pm Downs 107 (Please note Helene's office hours are in 107, not B111) Daniel Siebel Fridays, 4-6 pm Downs B111 Ryan Yoo Wednesdays, 2-3 pm Downs B111 Course Ombuds Thank you to the following students for volunteering to represent your class at the Ombuds meeting. If you have any feedback about the class, please reach out to one of your representatives. If you don't have a representative for your house, please feel free to contact any of the Ombudspeople or become one yourself by contacting Meagan.
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!AssignmentsHomework Dropbox Location - The drop boxes are located on the first floor of Downs, across from the elevator, between rooms 113 and 119. Deposit all completed homework assignments into the dropbox.
Midterm and Final ExamMidterm is available here . The password has been emailed to you. If you have any issues accessing the file, please let Meagan know. It is due on Sunday October 29th at midnight. Turn it in to your section's drop box in Downs, just like homework assignments.It is a take-home exam. You are allowed to spend 4 hours working on the exam. Your 4 hours start the moment you open the exam. Do not look at the exam until you are ready to begin. You must work 4 consecutive hours: for example, 4 pm - 8 pm. You may not break up the 4 hours, such as 4pm - 6 pm and then 7 pm - 9 pm. (Obviously bathroom breaks and such are allowed.) You must write your solutions up in a "blue book." You may not contact any TA while taking the exam to ask a question: ask your TA any questions you may have BEFORE starting the exam. There will be a midterm review session on Friday, October 27 from 8 pm - 10 pm in 142 Keck. I realize not everyone is able to attend so here are my notes. (Please email Todd to report any typos you find!) You are allowed to consult these notes while working on the exam, but Prof. Ramakrishnan's course notes are the authoritative source: if you find any discrepancy go with the professor's notes (and report the discrepancy to Todd). Please observe that each problem was worth 24 points. Problems 1a, 1b, 3a, 3b, 4a, 4b, 5a, 5b were each worth 12 points. Problem 2a was worth 16 points, problem 2b was worth 8 points. Your grade was computed by taking the best 4 of 5 problem scores, and not the best 8 of 10 part a/b scores (so your grade could have been composed of Problems 1,2,4,5 but your grade could not have been composed of 1a, 1b, 2a, 3a, 4a, 4b, 5a, 5b). There were 4 extra points added to each exam to bring the total to 100 points.The Final Exam is available here. The password has been emailed to you. If you have any issues accessing the file, please let Meagan know. It is due on Thursday December 7 at 10 am. Turn it into your section's drop box in Downs. It is a take-home exam. You are allowed to spend 4 hours working on the exam. Your 4 hours start the moment you open the exam. Do not look at the exam until you are ready to begin. You must work 4 consecutive hours: for example, 4 pm - 8 pm. You may not break up the 4 hours, such as 4pm - 6 pm and then 7 pm - 9 pm. (Obviously bathroom breaks and such are allowed.) You must write your solutions up in a "blue book." You may not contact any TA while taking the exam to ask a question: ask your TA any questions you may have BEFORE starting the exam. There will be a final exam review session on Sunday, December 3 from 6-8 pm in East Bridge, Room 201. My notes are here. (Please email Todd to report any typos you find!) You are allowed to consult these notes while working on the exam, but Prof. Ramakrishnan's course notes are the authoritative source: if you find any discrepancy go with the professor's notes (and report the discrepancy to Todd). The final exam has been graded and returned. Each problem was worth 25 points. The best 4 problems were used to calculate your score. In Problem 4 the unnumbered part was worth 10 points, 4a was worth 5 points, and 4b was worth 10 points. The solutions to the final exam are here. Grading questions/complaints: Because we grade such a large number of exams so quickly, we aren't able to leave detailed feedback next to each problem. We try to address the most common errors in the above solutions, so check there FIRST to see if your grading question is addressed. If it is not, follow this procedure: 1. Take a photograph of the specific part of a problem you have a question on (such as 4a). Make sure you have all your solution to that part in the picture, not just part of your solution.2. Email tnorton@caltech.edu with the following subject line: Ma1a Final Exam Question: Problem X, (part a or b) Briefly explain your question 3. Send a separate email for each part of each problem you have a question about. Please keep in mind that each part of each problem was graded by a different TA. A TA can only review the score of a problem that he/she graded. If you use the subject line I suggested above, I can more quickly direct your question to the TA who graded that problem. Please allow them a couple days to respond as they may receive many questions. ALL QUESTIONS MUST BE EMAILED TO TODD BY THE END OF MONDAY, DEC 11. This is to allow the TAs enough time to address your question before final grades are due. Collaboration 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. |