Wed 5/17: Final Oral Exam questions.
- Note: Some typos have been fixed from the original printed version, and one additional question has been added.
Tue 5/16: Moduli space of lattices; modular forms.
- Reading V.7, V.8.
- Sign ups for Final Oral Exam
Thu 5/11: Addition formula for an elliptic curve.
- Reading V.3, V.4
Tue 5/9: Theta function and functional equation for Riemann zeta.
Thu 5/4: Fourier inversion, Poisson Summation.
- Lecture by Prof. McDonald
Thu 4/27: Field of elliptic functions, the torus as an elliptic curve.
- Reading: Section V.3, V.3.A
Tue 4/25: Weierstrass P-function.
- Reading: Section V.2
Thu 4/20: Elliptic functions.
- Reading: Section V.1
Wed 4/19: Homework 6.
Due on Thursday 4/27.
- Section IV.1: #3.
- Section IV.2: #2, 3.
- Section IV.3: #4.
- Section V.1: #1, 2, 5.
Tue 4/18: Weierstrass products, Mittag-Leffler theorem.
- Reading: Section IV.2, IV.3.
Thu 4/13: The Gamma function continued.
- Reading: Section IV.1
Tue 4/11: The Gamma function.
- Reading: Section IV.1
Thu 4/6: Homework 5.
Due on Thursday 4/13.
- Section III.6: #1, 6, 7.
- Section III.7: #1, 9, 11.(a), 13.(a).
Thu 4/6: Residue Theorem continued.
- Reading: Section III.6, III.7.
Tue 4/4: Residue Theorem.
- Reading: Section III.6, III.7.
- Office Hours Today: 3-4 instead of the usual 4-5.
Tue 3/21: Meromorphic functions.
- Reading: Section III.A.
Thu 3/16: Laurent decompositions and series.
- Reading: Section III.5.
Tue 3/14: Singularities of analytic functions.
- Reading: Section III.4.
Thu 3/9: Homework 4.
Due on Thursday 3/16.
- Section III.2: #9.
- Section III.3: #1, 3, 5, 6.
- Section III.4: #1, 4, 5, 7.
Thu 3/9: Analytic continuation.
- Reading: Section III.3.
Tue 3/7: Power series.
- Reading: Section III.2.
Thu 3/2: Morera’s Theorem; sequences and series of functions.
- Reading: Section II.3, III.1.
Wed 3/1: Homework 3.
Due on Thursday 3/9.
- Section II.3: #1, 2, 4, 7, 8
- Section III.1: #4, 5
- Section III.2: #1, 3
Tue 2/28: Cauchy’s Integral formulas.
- Reading: Section II.3.
Thu 2/23: Cauchy’s Theorem.
- Reading: Section II.2.
Tue 2/21: Homework 2.
Due on Tuesday 02/28.
- Section 1.5: #1, 2, 4, 7
- Section 2.1: #1, 5
- Section 2.2: #4, 7, 12, 13
Tue 2/21: Complex line integrals.
- Reading: 2.1, 2.2 (we will spend several lectures on 2.2).
Thu 2/16: Complex differentiability continued.
- Reading: 1.5
Tue 2/14: Complex differentiability.
- Reading: 1.4, 1.5.
Thu 2/9: Complex exponential, trig functions and logarithms. Review of topological concepts..
- Reading: 1.2, 1.3
Wed 2/8: Homework 1.
Due on Thursday 02/16.
- Section 1.1: #1, 2 (on 1 and 2, pick three of the examples), 3, 8, 9, 13
- Section 1.2: #1, 7, 9, 20
- Section 1.3: #2
- Section 1.4: #2, 3, 5, 6
Tue 2/7: Complex numbers, sequences and series.
- Reading: 1.1, 1.2