Lectures for Mathematics 311, Spring 201112
 Monday 1/23: Introduction, preview
 Tuesday 1/24: More preview
 Wednesday 1/25: Complex numbers
 Friday 1/27: Point set topology
 Monday 1/30: [Assignment 1 due]
Uniform continuity, uniform convergence
 Tuesday 1/31: [Add/sectionchange deadline]
Complex differentiability, CauchyRiemann equations
 Wednesday 2/1: More CauchyRiemann, harmonic functions
 Friday 2/3: Complex functions as mappings: exp, log, powers
 Monday 2/6: Complex functions as mappings: (z+1/z)/2
 Tuesday 2/7: [Assignment 2 due]
Complex integration
 Wednesday 2/8: More integration
 Friday 2/10: Cauchy's Theorem
 Monday 2/13: [Assignment 3 due]
Finish Cauchy's Theorem, Cauchy's formula, higher derivatives
and power series representation modulo technicalities
 Tuesday 2/14: Technicalities of higher derivatives and power series representation
 Wednesday 2/15: Homology and homotopy, Morera's theorem, recap
 Friday 2/17: [Inclass quiz]
 Monday 2/20: Uniform limit of continuous functions, limsup
 Tuesday 2/21: [Assignment 4 due]
Power series radius of convergence,
differentiability of power series
 Wednesday 2/22: Differentiability of limits more generally
 Friday 2/24: Uniqueness theorem
 Monday 2/27: [Assignment 5 due, noW drop
deadline]
Maximum principle, Fundamental Theorem of Algebra, state
CasoratiWeierstrass
 Tuesday 2/28: Prove CasoratiWeierstrass, Laurent expansion, examples
 Wednesday 2/29: Classification of singularities, Residue Theorem,
Argument Principle
 Friday 3/2: Rouche's Theorem, behavior at infinity,
Local Mapping Theorem, Open Mapping Theorem
 Monday 3/5: [Assignment 6 due,
midterm out  due in hardcopy
form Saturday 7 p.m.]
General CasoratiWeierstrass Theorem, Riemann's Theorem,
the Hurwitz Theorem
 Tuesday 3/6: Examples of the residue theorem
 Wednesday 3/7: More examples of the residue theorem: zeta(k) for even k,
Fourier transform of the Gaussian
 Friday 3/9: Miscellany on cotangent and zeta
 Saturday 3/10: [midterm due in hardcopy form 7 p.m.]
 Spring break week
 Monday 3/19: Conformality, stereographic projection is conformal
 Tuesday 3/20: Fractional linear transformations, circles and lines
 Wednesday 3/21: Associativity
 Friday 3/23: Triple transitivity, reflection in a circle, cross ratio,
conformal mappings examples
 Saturday 3/24: [Junior Qual]
 Monday 3/26: More conformal mapping examples, dynamics
 Tuesday 3/27: [Assignment 7 due] Automorphisms
 Wednesday 3/28: Automorphisms of the plane and of the sphere,
rotations of the sphere
 Friday 3/30: Automorphisms of H and D, Schwarz's lemma
 Monday 4/2: [Assignment 8 due,
withdraw/leave deadline]
ArzelaAscoli Theorem (student lecture)
 Tuesday 4/3: Start Riemann Mapping Theorem
 Wednesday 4/4: Finish Riemann Mapping Theorem,
start Dirichlet's Problem on the disk
 Friday 4/6: finish Dirichlet's Problem on the disk
 Monday 4/9: [Assignment 9 due,
final out  due in hardcopy form
5/9 5 p.m.]
Topology of compact Riemann surfaces and their universal covers
 Tuesday 4/10: Complexisomorphism classes of tori
 Wednesday 4/11: Escher's "Print Gallery," isogenies of tori
 Friday 4/13: Necessary conditions, Weierstrass P and P'
 Monday 4/16: Complex tori as elliptic curves
 Tuesday 4/17: Sufficient conditions (student lecture), elliptic integrals
 Wednesday 4/18: Duplication law for P, Klein's jfunction,
 Friday 4/20: Elliptic curve isomorphisms, rational j => rational curve,
RS structure of X(1)
 Monday 4/23: Continuation of zeta (student lecture)
 Tuesday 4/24: RS structure, modular curves, Modularity Theorem
 Wednesday 4/25: Picard's Theorem, course evaluations
 Friday 4/27: (No meeting)
 Wednesday 5/9: [Final due in hardcopy form 5 p.m.]
Assignments

Materials

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