Date	Topics	Assignments
Jan 29 & 31	Class starts: Tuesday Jan 29 1. Introduction 1.1 Review of complex numbers 1.2 Dynamical Systems and the Logistic Family
Feb 5 & 7	1.3 Background Material and Notation 2. First Steps in Complex Iteration 2.1 & 2.2 Orbits and Iteration	Homework I
Feb 12 & 14	2.3 Iterating the Logistics Maps 2.4 Periodic Points and their Multipliers
Feb 19 & 21	30 min. Student Presentations Start 2.5 The Basin of Infinity of a Polynomial 2.6 Iterating Transcendental Functions 2.7 Affine Conjugacy 2.8 Equicontinuity	Feb 19 2.5 Alexander Pacun 2.6 Moshe Stein Feb 21 2.7 Jiayong Zhu 2.8 Emi Brawley Homework II
Feb 26 & 28	3. Riemann Sphere 3.1 Stereographic Projection/Chordal Distance 3.2 Spherical Derivative and Meromorphic Functions 3.3 Moebius Transformations I 3.4 Moebius Transformations II	Feb 26 3.1 Sachin Seth 3.2 Kunhui Luan Feb 28 Nicole Sayad Janine Villarreal Homework III
March 5 & 7	4. Fatou and Julia sets 4.1 Definitions of the Fatou and Julia sets I 4.1 Definitions of the Fatou and Julia sets II The Geometry of Julia Sets I The Geometry of Julia Sets II	March 5 4.1-I 4.1-II Jinzheng Li March 7 Geometry-I Brandon Gontmacher Geometry-II Moshe Dinowitz
March 12 & 14	4.2 The Filled-in Julia set of a Polynomial and Exceptional Set I 4.2 The Filled-in Julia set of a Polynomial and Exceptional Set II	March 12 4.2-I Hubert Puszklewicz 4.2-II Pete Coletti March 14 No class
March 19 & 21	Spring Break !
March 26 & 28	4.3 The Boundary of the Filled-in Julia Set I 4.3 The Boundary of the Filled-in Julia Set II	March 26 4.3-I Liuming Wang 4.3-II Connor Stewart Homework IV March 28 No class
April 2 & 4	5. Components of the Fatou set/Normal Families 5.1 Normal Families and Compact Convergence I 5.1 Normal Families and Compact Convergence II 5.2 Components of the Fatou Set: Constant Limit Functions I 5.2 Components of the Fatou Set: Constant Limit Functions II	April 2 5.1-I Hanning Wang 5.1-II Yanming Cao April 4 5.2 I Spencer Jarrad 5.2-II Pablo Mingwang Zhou Wang
April 9 & 11	Second round of presentations start 5.3 Parabolic Points I 5.3 Parabolic Points II 5.4 Non-Constant Limit Functions and the Classification of Fatou Components 6. Further Properties of the Julia sets; The Fundamental Theorem 6.1 Essential Singularities	5.3-I Jiayong Zhu 5.3-II Jinzheng Li 5.4 Nicole Sayad 6.1 Pablo Mingwang Zhou Wang Homework V
April 16 & 18	6.2 The Julia Set of an Entire Function 6.3 Montel's Theorem and Properties of the Julia Set 6.4 Connecting Normal Families and the Entire Functions: Zalcman's Lemma I 6.4 Connecting Normal Families and the Entire Functions: Zalcman's Lemma II	6.2 Janine Villareal 6.3 Pete Coletti 6.4-I Liuming Wang 6.4-II Connor Stewart
April 23 & 25	6.5 Density of Repelling Periodic Points 7. Singular Values and the Mandelbrot Set 7.1 Singular Values I 7.1 Singular Values II 7.2 The Influence of Singular Values	6.5 Emi Brawley 7.1-I Yanming Cao 7.1-II Hanning Wang 7.2 Sachin Seth Homework VI
April 30 & May 2	7.3 The Mandelbrot Set 7.4 The Boundary of the Mandelbrot Set The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics I The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics II	7.3 Spencer Jarrad 7.4 Kunhui Luan Exp-I: Moshe Dinowitz Exp-II: Brandon Gontmacher Homework VII
May 7 & 9	The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics III The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics IV The Exponential Map is Chaotic: An Invitation to Transcendental Dynamics V	Exp-III Alexander Pacun Exp-IV Moshe Stein Exp-V Hubert Puszklewicz