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 | | |
| | | |
Schedule subject to change.
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.
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Published by Jonathan Novak
Mathematician and Cormac McCarthy enthusiast.
View all posts by Jonathan Novak