Advanced Calculus MAT 25
MWF 4:10 - 5 pm, HARING 1204
GENERAL INFORMATION
Instructor : Amitabh Basu
Office Hours : Monday 1:00 pm - 2:00 pm, Friday 1:00 pm - 2:00 pm, email for appointment. Office Hours will be in my office : Mathematical Sciences Building (MSB) 3111.
Email : abasu [at] math [dot] ucdavis [dot] edu
Teaching Assistant : Robert Beck will be the TA for Section B01. The discussion for this section meets in HART 1120, 4:10 - 5pm every Thursday.Robert's email is rbeck [at] math [dot] ucdavis [dot] edu.
Robert's office hours are Wednesday, 2-3pm in MSB 2202.
Nate Merrill will be the TA for Section B02. The discussion for this section meets in STORER 1344, 5:10 - 6pm every Thursday. Nate's email is : ecmerrill [at] math [dot] ucdavis [dot] edu.
Nate's office hours are Thursday, 2-3pm in MSB 2204.
Text : Required - Elementary Real Analysis by Thomson, Bruckner, Bruckner; 2nd Edition, ISBN 143484367X.
Syllabus and Schedule : We will follow the departmental syllabus closely.
This course has two goals:
1) To introduce undergraduate students to rigorous mathematics and how to understand/write proofs.
2) Introduce the foundational mathematical concepts behind all the machinery of calculus that one glosses over in introductory calculus courses.
ANNOUNCEMENTS
- The venue for the Final has been decided:
Venue : Wellman 26.
Date : June 12, 2013.
Time : 1 - 3 pm.
- Practice Midterm II has been put up below under "Midterms and Final".
- The Student Disability Center asks that students interested in serving as paid notetakers for this course please contact Russ Zochowski at [email protected] Notetakers are paid a stipend of $25 per unit, but must have a social security number in order to be paid. Students are asked to put notetaker, the course title, number, and instructors name in the subject lines of their emails. Their information will be passed along to the SDC student in need of notes, and if they are interested they will contact each student accordingly.
- Practice Midterm I has been put up below under "Midterms and Final".
- No HW to be handed in on Monday, April 22 on account of Midterm I.
- The syllabus for Midterm I is posted below.
- Due to unforeseen circumstances, I will not be able to hold my regular office hours TODAY (Monday, April 8). Please email me to schedule an appointment in the afternoon (between 2 and 4 pm).
- Section B01 meets for discussions in HART 1120 from 4:10 - 5pm with Robert Beck.
Section B02 meets for discussions in STORER 1344 from 5:10 - 6pm with Nate Merrill.
Please make a note of the above.
- The HW problems to be handed in for WEEK I are DUE TODAY (Monday, April 8) in class. Please see the pdf file for WEEK I HW problems for the problems that need to be handed in.
EXAM AND GRADING INFORMATION
There will be 2 in-class examinations (Midterm I and Midterm II) and a Final exam. In addition, there will be weekly homework assigments.
Homeworks
- Homework problems will be assigned after every lecture. Every MONDAY, you will be have to hand in 4-5 problems from the HW problems assigned over the previous week (that is, the previous Monday, Wednesday and Friday). These problems that you hand in will be graded, and will count towards your final grade in the quarter. I will announce which problems to hand in on the preceding Friday.
- In case I decide that no assignments need to be handed in on a particular Monday, I will announce this well in advance.
- The HW problems will appear here.
- The lowest of your HW scores will be dropped before computing the final grade.
- HW for WEEK 1. Solutions
Statistics for HW 1: Mean - 32.17/40, Std. Dev - 5.14, Median - 33/40.
- HW for WEEK 2. Solutions. There is a mistake in Problem A.2.3 b). The first ansewr should be R (all reals), and not R\Z (the reals minus the integers). The second answer should be (-1,1) and not the empty set. Thanks to Gongping Niu for pointing this out !
Statistics for HW 2: Mean - 24.61/40, Std. Dev - 8.01, Median - 25/40.
- HW for WEEK 3. Solutions. The solution to 6(iii) appears after the solution to problem 9. Sorry for the scanning mix-up !
- HW for WEEK 4. Solutions.There was a typo in Problems 5 and 6. A and B are arbitrary subsets of the real numbers, there is no hypothesis about A subset of B. This hypothesis is there in Question 4, but not in Problems 5 and 6.
There is a typo in the last 2 lines of the solution to 11. It should be "y = f(x) = 1 - e^{-x} = 1 - \epsilon/2 > 1-epsilon, because epsilon > epsilon/2." Thanks to Zheng Yan for pointing this out !
Statistics for HW 4: Mean - 21.40/30, Std. Dev - 5.57, Median - 22/30.
- HW for WEEK 5. Solutions. Solution to Problem 12. Alternate solution to density of irrationals using cardinality of sets.
There is a typo in Problem 6. The last sentence should be "Show that A is also dense in R (reals)". Thanks to Zheng Yan for catching this !
Statistics for HW 5: Mean - 25.51/30, Std. Dev - 3.84, Median - 26/30.
- HW for WEEK 6.Solutions.
- HW for WEEK 7.Solutions.
Statistics for HW 7: Mean - 20.39/30, Std. Dev - 6.04, Median - 21/30.
- HW for WEEK 8.Solutions
There was a typo in Problem 12. The bound should be "s_{2^n-1} <= 2 - 1/2^{n-1}" instead of "s_{2^n-1} <= 2 - 1/2^n".
- HW for WEEK 9.Solutions. Pages 9 and 10 should switched in the solutions - thanks to Yankun Lin for catching that.
There were a couple of typos and issues with the original posting. Problem 2 has been changed slightly - thanks to Lila Zen for catching that. Problem 5 has also been fixed - thanks to Zheng Yan for catching that.
- HW for WEEK 10.Solutions.
Midterms and Final
- Practice Midterm I. There was a typo in Problem 6(b). It is fixed now. Thanks to Gonping Niu for catching this.
There was a typo in the solution to Problem 6(d). The second line should appeal to Axiom 7, not Axiom 3. Thanks to Zheng Yan for catching this.
There is a typo in Problem 7 (b)(ii). E should be a subset of Q, and not R. So E = { x in Q : 0 <= x < 5}
Solutions to Practice Midterm I.
Midterm I will be on Monday, April 22, 2013 in class.
The syllabus for Midterm I will be everything from the beginning of the quarter upto, and including, the material covered on Wednesay, April 17, 2013.
The relevant sections from the textbook are : A.2.1, A.5, A.6, A.7, A.8, A.9, 1.3, 1.4, 1.5, 1.6 and 2.3.
HWs for Weeks 1,2 and 3 are relevant.
The material on cardinality of sets appears in Section 2.3 - but is not very detailed. Please study your class notes and HWs.
Solutions to Midterm I.
Statistics for Midterm I:
Class Average : 52.92/100
Median : 54/100
Std. Dev. : 13.44
- Practice Midterm II.
Solutions to Practice Midterm II.
Midterm II will be on Monday, May 13, 2013 in class.
The syllabus for Midterm II is everything after Midterm I, and upto and including the lecture on Wendesday, May 8, 2013.
The relevant sections from the textbook are : 1.6, 1.7, 1.9, 1.10, 2.2, 2.4, 2.5.
HWs for Weeks 4, 5 and 6 are relevant.
Solutions to Midterm II.
Statistics for Midterm II:
Class Average : 52.35/80
Median : 55/80
Std. Dev. : 14.17
- The Final exam will on Wednesday, June 12, 2013 in Wellman 26 from 1-3pm. Please note that the final will not be held in the same location as the lecture. The venue is Wellman 26.
The syllabus for the Final will be everything we have covered in the quarter.
The relevant sections from the textbook :A.2.1, A.5, A.6, A.7, A.8, A.9, 1.3, 1.4, 1.5, 1.6, 1.7, 1.9, 1.10, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.11, 2.12, 2.13, 3.4, 3.5 and 3.7 (In section 3.7 Reimann's theorem is not included).
All HWs 1 -10 are relevant.
- Both Midterms and the Final Exam will be closed book.
Grades
- Your final grade will be based on the following weightage :
Homework - 20%
Midterm I - 20%
Midterm II - 20%
Final - 40%
- SmartSite will be used to post the exam grades. You should be able to access your grades there.
FEEDBACK
You can use the form below to give me any feedback anonymously. Your feedback can be about anything related to course - pace of lectures, homework, exams etc. I welcome your suggestions !