Math 829 Spring 2020 course homepage
The classes are on MWF: 10:20 -- 11:10am at A218 Wells Hall.
Instructor: Ilya Kachkovskiy,
ikachkov@msu.edu
Instructor office: C300 Wells Hall
Office hours: Monday 2-3pm, Thursday 1:30-2:30pm. Additional hours available on request.
Grader: Dimitris Vardakis.
Syllabus: pdf.
Book: Serge Lang, Complex Analys, 4th edition. Available for free for MSU users, requires MSU login.
Additional notes: Notes by Dapeng Zhan.
Homework 1: due Friday, Jan 17. Use problems from the notes.
a) All problems on pages 3,6,8 (not to hand in). References are to Lang's book.
b) Pages 12, 14, 18: all problems to hand in.
Homework 2: due Wednesday, Jan 29.
Lang, Section II.1 (page 46): 3,4,5.
Lang, Section II.2 (page 58): 6,7,9,11.
Lang, Section III.1 (page 93): 2.
Lang, Section III.2 (page 102): 3,4,5,8.
Lang, Section III.5 (page 118): 1,2,4.
Homework 3: due Wednesday, Feb 5.
Lang, read Section III.6 about logarithms. (N) means "not to hand in"
Lang, III.6 (page 125): 1(N), 2(N), 3,4,6.
Lang, III.7 (page 132): 1,2.
Lang, IV.2 (page 149): 1.
Lang, V.1 (page 158): 1,3,4,7,8.
Homework 4: due Wednesday, Feb 12.
Lang, V.2 (page 163): 2(N), 3, 4, 6, 12, 14(N), 15(N).
Lang, V.3 (page 170): 1bc, 2, 4(N), 7, 8, 9.
Lang, VI.1 (page 186): 6, 11,13, 19.
Homework 5: due Wednesday, Feb 19.
Lang, VI.1 (page 186): 21, 26bce, 28, 31.
Lang, VI.2 (page 204): 1b, 3, 7, 8, 11, 15.
Homework 6: due Wednesday, Mar 12.
Lang, VII.2 (page 213): 2, 3(N), 4(N), 5(N).
Lang, VII.3 (page 217): 4(N), 6.
Lang, VII.4 (page 229): 1(N), 2, 3, 4, 5(N).
Lang, VII.5 (page 237): 3ab, 4a, 6(N), 9 (only answers), 12(N).
Homework 7: due Wednesday, Apr 1.
Lang, IX.2 (page 302): 1, 2, 3, 4, 5, 6.
Lang, X.2 (page 310): 6, 7.
Complete the last claim of the proof of Caratheodory's theorem:
suppose $f$ is continuous in the open unit disk $\mathcal D$. Suppose that $f$ satisfies the following property: for any point $z\in \partial D$ and any two continuous curves $\gamma_1, \gamma_2 \colon [0,1]\to \overline {\mathcal D}$ such that $\gamma_i([0,1))\subset \mathcal D$ and $\gamma_i(1)=z$, we have $\lim f(\gamma_1(t))=\lim f(\gamma_2(t))$ as $t\to 1$. Show that $f$ contiuously extends to $\overline D$.