Math 117: Methods of Analysis
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.
Textbook: Elementary Analysis by Kenneth Ross, second edition
Using the above link, you can...
1) purchase a paperback copy of the textbook for $24.99;
2) download a PDF version for free.
(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
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 8, Solutions 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:
•Homework assignments will be posted on this website and collected during lecture.
•Only the problems marked with an asterisk (*) should be submitted for grading.
•At least one problem on each of the exams will be chosen from the non-asterisked homework problems.
•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.)
•The lowest two homework grades will be dropped and will not count toward the final grade.
Extra Credit Math Movie Competition:
•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.
•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.)
•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