Math 220A: Lecture 0

Schedule

Lecture	Date	Topic	Modality
0	S 23	Course description	In person
1	S 26	Numbers: complex	In person
2	S 28	Numbers: hypercomplex	In person
3	S 30	Coda	Online
4	O 03	Formal power series: algebra structure	In person
5	O 05	Formal power series: group structure	In person
6	O 07	Coda	Online
7	O 10	Convergent power series: algebra structure	In person
8	O 12	Convergent power series: group structure	In person
9	O 14	Coda	Online
10	O 17	Analytic functions: local inverse function theorem	In person
11	O 19	Analytic functions: local maximum modulus principle	In person
12	O 21	Coda	Online
13	O 24	Convergent power series: partial sums	In person
14	O 26	Convergent power series: Jentzsch’s theorem	In person
15	O 28	Coda	Online
16	O 31	Exponential function: partial sums	In person
17	N 02	Exponential function: Szego’s theorem	In person
18	N 04	Coda	Online
19	N 07	Analytic continuation: logarithm	In person
20	N 09	Analytic continuation: Hadamard gap theorem	In person
	N 11	Veteran’s Day
21	N 14
22	N 16
23	N 18
24	N 21
25	N 23
	N 25	Thanksgiving
26	N 28
27	N 30
28	D 02

Books

• Ahlfors, Complex Analysis.
• Cartan, Theory of Analytic Functions.
• Conway, Functions of One Complex Variable.
• Estermann, Complex Numbers and Functions.
• Flagolet and Sedgewick, Analytic Combinatorics.
• Henrici, Applied and Computational Complex Analysis.
• Kodaira, Complex Analysis.
• Krantz, Handbook of Complex Variables.
• Lang, Complex Analysis.
• Needham, Visual Complex Analysis.
• Pierpont, Functions of a Complex Variable.
• Polya and Latta, Complex Variables.
• Romik, Complex Analysis Lecture Notes.
• Stein and Shakarchi, Complex Analysis.
• Titchmarsh, The Theory of Functions.

Articles

• Buckholtz, A characterization of the exponential function. American Mathematical Monthly 73 (1966), 121-123.
• Gronwall, On the power series for . Annals of Mathematics 18 (1916), p. 70-73.
• Palais, The classification of real division algebras, American Mathematical Monthly 75 (1968), 366-368.

Evaluation

• Problem sets: 70%
• Final exam: 30%

Instructors

• Lecturer: Jonathan Novak, APM 7157. Office hours MW after lecture.
• Teaching Assistant: Shubham Sinha.

Communication

• Piazza. Public posts preferred, private messages when necessary.
• No email.