Lectures for Mathematics 311, Spring 202021
 Monday 1/25: Introduction, preview
 Tuesday 1/26: More preview
 Wednesday 1/27: Complex numbers
 Friday 1/29: Point set topology
 Monday 2/1: [Assignment 1 due]
Uniform continuity, uniform convergence
 Tuesday 2/2: Complex differentiability, CauchyRiemann equations
 Wednesday 2/3: More CauchyRiemann, harmonic functions
 Friday 2/5: [Add/sectionchange
deadline]
Complex functions as mappings: exp, log, powers
 Monday 2/8: Complex functions as mappings: (z+1/z)/2
 Tuesday 2/9: [Assignment 2 due]
Complex integration
 Wednesday 2/10: More integration
 Friday 2/12: Cauchy's Theorem
 Monday 2/15: [Assignment 3 due]
Finish Cauchy's Theorem, Cauchy's formula, higher derivatives
and power series representation modulo technicalities
 Tuesday 2/16: Technicalities of higher derivatives and power series representation
 Wednesday 2/17: Homology and homotopy, Morera's theorem, recap
 Friday 2/19: Uniform limit of continuous functions, limsup
 Monday 2/22: Power series radius of convergence,
differentiability of power series
 Tuesday 2/23: [Assignment 4 due]
Differentiability of limits more generally
 Wednesday 2/24: Uniqueness theorem
 Friday 2/26: Maximum principle, Fundamental Theorem of Algebra, state
CasoratiWeierstrass
 Monday 3/1: [Assignment 5 due,
Prove CasoratiWeierstrass, Laurent expansion, examples
 Tuesday 3/2: Classification of singularities, Residue Theorem,
Argument Principle
 Wednesday 3/3: Rouche's Theorem, behavior at infinity,
Local Mapping Theorem, Open Mapping Theorem
 Friday 3/5: General CasoratiWeierstrass Theorem, Riemann's Theorem,
the Hurwitz Theorem
 Monday 3/8: [Assignment 6 due,
midterm out  due in electronic
form Saturday 7 p.m.]
Examples of the residue theorem
 Tuesday 3/9: More examples of the residue theorem: zeta(k) for even k,
Fourier transform of the Gaussian
 Wednesday 3/10: No meeting
 Friday 3/12: Miscellany on cotangent and zeta
 Saturday 3/13: [midterm due in electronic form 7 p.m.]
 Monday 3/15: Conformality, stereographic projection is conformal
 Tuesday 3/16: Fractional linear transformations, circles and lines
 Wednesday 3/17: Associativity
 Friday 3/19: Triple transitivity, reflection in a circle, cross ratio,
conformal mappings examples
 Monday 3/22: More conformal mapping examples, dynamics
 Tuesday 3/23: [Assignment 7 due] Automorphisms
 Wednesday 3/24: Automorphisms of the plane and of the sphere,
rotations of the sphere
 Friday 3/26: Automorphisms of H and D, Schwarz's lemma
 Monday 3/29: [Assignment 8 due,
noW drop deadline,
withdraw/leave deadline]
ArzelaAscoli Theorem
 Tuesday 3/30: Start Riemann Mapping Theorem
 Wednesday 3/31: Finish Riemann Mapping Theorem,
start Dirichlet's Problem on the disk
 Friday 4/2: finish Dirichlet's Problem on the disk
 Monday 4/5: [Assignment 9 due,
final out  due in electronic form
5/12 5 p.m.]
Topology of compact Riemann surfaces and their universal covers
 Tuesday 4/6: Complexisomorphism classes of tori
 Wednesday 4/7: Escher's "Print Gallery," isogenies of tori
 Friday 4/9: Necessary conditions, Weierstrass P and P'
 Spring break week
 Monday 4/19: Complex tori as elliptic curves
 Tuesday 4/20: Sufficient conditions, elliptic integrals
 Wednesday 4/21: Duplication law for P, Klein's jfunction,
 Friday 4/23: Elliptic curve isomorphisms, rational j => rational curve,
RS structure of X(1)
 Monday 4/26: Continuation of zeta
 Tuesday 4/27: RS structure, modular curves, Modularity Theorem
 Wednesday 4/28: Picard's Theorem, course evaluations
 Friday 4/30: (No meeting)
 Wednesday 5/12: [Final due in electronic form 5
p.m.]
Assignments

Solutions
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