Information.

Problem Set 1. Due in class on Thursday , September 22.

Problem Set 2. Due in class on Thursday , September 29.

Problem Set 3. Due in class on Thursday , October 6.

Problem Set 4. Due in class on Thursday , October 13.

Problem Set 5. Due in class on Tuesday , October 25.

Problem Set 6. Due in class on Tuesday , November 15.

Problem Set 7. Due in class on Tuesday , November 22.

Problem Set 8. Due in class on Thursday , December 1.

Problem Set 9. Due in class on Thursday , December 8.

Problem Set 10. Due in class on Friday, December 16.

Sep. 15: Introduction to Complex Analysis, holomorphic functions.

Sep. 16: The Cauchy-Riemann equations, power series.

Sep. 20: Integration along curves, Goursat's theorem.

Sep. 22: The Cauchy theorem, Cauchy's integral formulas, analytic functions.

Sep. 23: Applications: Liouville's theorem, the fundamental theorem of algebra, Morera's theorem, analytic continuation.

Sep. 27: Sequences of holomorphic functions, Schwarz reflection principle.

Sep. 29: Removable singularities, poles, the residue formula.

Oct. 04: The argument principle, Rouche's theorem, Cauchy's theorem in simply connected domains.

Oct. 06: The complex logarithm, Fourier series, the Riemann sphere.

Oct. 07: The Fourier transform: the Fourier inversion formula and Plancherel theorem.

Oct. 11: The Fourier transform on holomorphic functions.

Oct. 13: The Poisson summation formula.

Oct. 14: The Paley-Wiener theorem.

Oct. 18: Entire functions: Jensen's formula.

Oct. 20: Functions of finite order, infinite products.

Oct. 21: Weierstrass infinite products, examples.

Oct. 25: Hadamard's factorization theorem.

Oct. 27: Midterm exam.

Oct. 28: The Gamma function: definition and basic properties.

Nov. 08: The Gamma function: meromorphic extension and further results.

Nov. 10: The zeta function: definition and the functional equation.

Nov. 11: The zeta function: meromorphic extension and bounds.

Nov. 15: The Prime Number Theorem: outline of the proof.

Nov. 17: The zeta function in the critical strip.

Nov. 18: Proof of the Prime Number Theorem.

Nov. 22: Conformal mappings, examples.

Nov. 29: The Schwarz lemma, automorphisms of the disk, the Riemann mapping theorem.

Dec. 01: Proof of the Riemann mapping theorem.

Dec. 02: Conformal mappings onto polygons: extension to the boundary.

Dec. 06: Conformal mappings onto rectangles.

Dec. 08: Elliptic functions: definitions and main properties.

Dec. 09: The Weierstrass p function.

Dec. 13: Theta functions: definitions and basic properties.

Dec. 15: The two-squares theorem: main ideas.

Dec. 16: Proof of the two-squares theorem.