Math 117: Methods of Analysis

Professor: Katy Craig, SH 6507, katy•craig•math at gmail • com

Teaching Assistant: Eleni Panagiotou, SH 6617 U, panagiotou at math • ucsb • edu

Lecture/Office Hours:

Attendance in lecture is mandatory. Students who do not attend lecture may be unenrolled in order to admit students who do attend lecture.

Attendance in section is optional.

Using the above link, you can...

1. 1) purchase a paperback copy of the textbook for \$24.99;

(Do both.)

Other Recommended References:

Principles of Mathematical Analysis, Walter Rudin

Exams: There will be two midterms and one final exam. The examinations will be closed book and closed note. There will be no retaking or rescheduling of exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

First Midterm: Tuesday, May 2nd, 12:30-1:45PM

Second Midterm: Thursday, May 25th, 12:30-1:45PM

Final Exam: Monday, June 12th, 12:00-3:00PM

Grading Scheme: homework: 10%, highest midterm score: 40%, final: 50%

If you have questions about the grading of any assignment or exam, you have one week after it is handed back to request a regrade.

Prerequisites: Math 8

Outline of Course:

Part I: Sequences                                                     Part II: Functions
the real numbers, inf, and sup                                        continuous functions
limit, liminf, limsup                                                 cts functions attain max and min on closed interval
bounded, monotone, and Cauchy sequences                               intermediate value theorem
subsequences and the Bolzano-Weierstrass theorem

Syllabus:
topic                                read for today    due today        notes and review materials
1   Apr 4  (T)   N,Z,Q,R and triangle inequality      1-2, appendix                      Lecture 1
2   Apr 6  (Th)  properties of real numbers           3                 HW 1, Solutions  Lecture 2 (Updated)
3   Apr 11 (T)   def’n of R and Archimedean Property  4                 HW 2, Solutions  Lecture 3
4   Apr 13 (Th)  Q is dense in R; + and - infinity    5                                  Lecture 4
5   Apr 18 (T)   sequences                            7-8               HW 3, Solutions  Lecture 5
6   Apr 20 (Th)  limit theorems                       9                                  Lecture 6
7   Apr 25 (T)   monotone sequences                   10                HW4 , Solutions  Lecture 7
8   Apr 27 (Th)  limsup and liminf                    10                                 Lecture 8
-   May 2  (T)   first midterm, over lectures 1-7                       Mid1, Mid1Sols   PractMid1, RevSheet1,PractSols1
9   May 4  (Th)  limsup and liminf                    10                                 Lecture 9
10  May 9  (T)   Cauchy sequences                     10                HW 5, Solutions  Lecture 10
11  May 11 (Th)  subsequences                         11                                 Lecture 11
12  May 16 (T)   more subsequences                    11                HW 6, Solutions  Lecture 12
13  May 18 (Th)  Bolzano-Weierstrass, limsup/liminf   12                                 Lecture 13
14  May 23 (T)   continuous functions                 17                HW 7, Solutions  Lecture 14
-   May 25 (Th)  second midterm, over lectures 1-13                     Mid2, Mid2Sols   PractMid2, RevSheet2, PractSols2
15  May 30 (T)   properties of cts fns                18                math movies      Lecture 15
16  Jun 1  (Th)  intermediate value theorem           18                                 Lecture 16
17  Jun 6  (T)   catch up                                               HW 8Solutions  Lecture 17
18  Jun 8  (Th)  review and math movie competition                                       Lecture 18

-  Jun 12 (M)   final exam, 12:00-3:00PM                                                 PractFinal, RevSheetFin, PracFinSol

Homework:

1. Homework assignments will be posted on this website and collected during lecture.

1. Only the problems marked with an asterisk (*) should be submitted for grading.

1. At least one problem on each of the exams will be chosen from the non-asterisked homework problems.

1. No late homework will be accepted.

(Talk to me if you transfer into the course partway through the quarter, and we’ll work something out.)

1. The lowest two homework grades will be dropped and will not count toward the final grade.

Extra Credit Math Movie Competition:

1. As an opportunity for extra credit, we will hold a math movie competition. The goal is to make the best math movie, lasting three minutes or less. Submissions are due on May 30th. The winner of the competition will receive ten points of extra credit on their final exam. Second place will receive five points of extra credit, and third place will receive three points of extra credit.

1. Submissions should be uploaded to YouTube or a similar site. Links to the movies can be sent to me at katy•craig•math at gmail • com. (Please do not send the movies as email attachments.)

1. Potential topic ideas for inspiration...

- Why we should celebrate square root of two day on January 4th

- Why series and sequences are actually the same thing

- Why sequences are the most important mathematical concept in finance

- Why real numbers are uncountable

- The entire history of the real numbers in three minutes

- Epsilons, deltas, and data science