**MATH 131AH: Winter 2023**

**Honors Analysis**

lecturer: Marek Biskup, MS 6180

lecture: MWF 10-11 in MS 6229

office hours: (tentatively) MWF 9:30-10, 11-noon

discussion: T 10-11 in Geology 4645, TA: Haiyu Huang

**Board photos & lecture notes: **
can be found here, including a brief synopsis of material covered.

**Homework: **

HW#1 HW#2 HW#3 HW#4 HW#5 HW#6 HW#7 HW#8 HW#9 HW#10

**Course content: **

**Textbooks:**

- W. Rudin,
*Principles of Mathematical Analysis*, 3rd Ed, McGraw-Hill Higher Education - E. Copson,
*Metric Spaces*, Cambridge University Press

**Topics to be covered:** Rigorous treatment of the foundations of real analysis, including construction of the naturals, rationals and reals. Metric space (a.k.a. point set) topology, compactness and its consequences. Numerical sequences and series. Continuity, including connections with compactness. Rigorous treatment of the main theorems of differential calculus.

While being marked as an honors version of MATH131A, the content of the course contains a number of additional topics generally treated in MATH131B. If you need to take the whole MATH131AB sequence (and, in particular, learn also the Riemann integration theory), then plan to take MATH131BH as well.

**Course policies: **

**Midterms:** in class on Friday, February 10 (week 5) and Friday, March 3 (week 8)

**Final exam:** Thursday, March 23, 3-6PM

**Exam policy: ** No make-ups, no open book or calculators, ID required

**Homework:** assigned via this website, due on the date posted at the beginning of class

**Homework policy: ** lowest HW score dropped, no late HW accepted

**Grading:** Homework 10% and the better of the following: Midterms 30% + Final 60% OR Final 90%. The two midterms contribute to overall midterm score equally.