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Stein and Shakarchi: Complex Analysis

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	WEEK LECTURE 1 LECTURE 2 NOTES READING HOMEWORK DUE Week 1 9/01, 9/04 Introduction Complex Numbers Holomorphic Functions Cauchy-Riemann Equations 09/01 Notes 09/04 Notes 09/04 Mathematica File Chap. 1: Sec 2.1 -- 2.2 Pset1 -- Chap. 1, #1-10 due 9/11 Week 2 NO 9/08, 9/11 NO CLASS MON SCHEDULE Power Series Hadamard's Formula 09/11 Notes 09/11 Mathematica File (thanks to Thomas!) Chap. 1: Sec 2.3 -- 2.4 Pset 2 -- Chap. 1, #11-19 And Exercise from lecture 9/11 due 9/18 Week 3 9/15, 9/18 Integration on Curves Goursat's Theorem 09/15 Notes 09/18 Notes Chap. 1: Sec 3, Chap. 2: Sec 2 -- 3 Pset 3 -- Chap. 1, #20-26 Chap. 2 #1-2 due 9/25 Week 4 9/22, 9/25 Cauchy Integrals Liouville's Theorem Fundamental Theorem of Algebra 09/22 Notes 09/25 Notes Chap. 2: Sec 1 -- 4 Pset4 -- Chap. 2 Exercises #3-9, 11, Problems #1a, 2 Write up any problem on Hwk1, Hwk2 or Quiz1 that did not receive full credit due 10/02 Week 5 9/29, 10/02 Analytic Continuation Moreira's Theorem Residue Calculus 09/29 Notes 10/02 Notes Chap. 2: Sec 4 -- 5 Chap. 3: Sec 1 -- 2 Pset 5 -- Chap. 2 Exercises #12-13 Chap. 3 Exercises #1-6 Problem #3 due 10/09 Week 6 10/06, 10/09 Riemann Sphere Argument Principle Open mapping theorem Maximum Modulus 10/06 Notes 10/09 Notes Chap. 3: Sec 3 -- 4 Watch this video on conformal maps of the plane/sphere Pset 6 -- Chap. 3 Exercises #7-15 Problem #2 due 10/16 Week 7 10/13, 10/16 Homotopy Complex Logarithm Fourier Series Mean Value Property 10/13 Notes 10/16 Notes Chap. 3: Sec 3 -- 7 Chap. 4: Sec 1-- 3 Pset 7 -- Chap. 3 Exercises #16 - 22 Problems #4, 5a Write up any problem on Hwk3-Hwk6 or Quiz2 that did not receive full credit due 10/23 Week 8 10/20, 10/23 The Fourier Transform Poisson Summation 10/20 Notes 10/23 Notes 10/23 Mathematica File Chap. 4: Sec 1-- 3 Nice exposition for the Riemann surface of sqrt z Pset 8 -- Chap. 4: Exercises #2, 3, 4, 6, 7 Problem #2 due 10/30 Week 9 10/27, 10/30 Trace Formula Paley-Weiner Phragmen-Lindelof 10/27 Notes 10/30 Notes Chap. 4: Sec 3 Pset 9 -- REVIEW! due 11/06 Week 10 11/03, 11/06 Conformal maps Schwarz lemma 11/03 Notes 11/06 Notes Chap 8: Sec 1 -- 2 Pset 10 -- Chap. 4: Exercises #2, 8 Chap 8: Exercises #1-5, Chap 8: Problem #2 due 11/13 Week 11 11/10, 11/13 Schwarz lemma Automorphisms of the Disk and Half-Plane Riemann Mapping Theorem 11/10 Notes 11/13 Notes Chap 8: Sec 3 -- 4 Optional: Read this on "Inversive Geometry" Pset 11 -- Chap 8: Exercises # 10-16 Problems #3(a-d), 4 due 11/20 Week 12 11/17, 11/20 Montel's Theorem (Arzela-Ascoli) Explicit Riemann Mapping Theorem Dirichlet Problem Grotzsch's Thm, quasiconformality 11/17 Notes 11/20 Notes Chap 8: Sec 3 -- 4 Pset 12 -- Write up any problem on Hwk7-Hwk11 or Quiz3 that did not receive full credit due 11/25 Week 13 11/24, 11/25 Wed 11/25 Class Basel Problem Riemann Zeta Function Euler Product Sum Reciprocals of Primes Diverges Jensen's Formula Hadamard Factorization 11/24 Notes 11/25 Notes Chap 5 Pset 13 -- Chap. 5: Exercises #2, 4, 6, 8, 9, 10, 11 due 12/04 Week 14 12/01, 12/04 Zeta Function Gamma Function Mellin Transform/Inverse (see this Appendix) Perron's Formula Skewes's Number Analytic Continuation, Functional Equation for Zeta Riemann's Explicit Formula Legendre-Gauss Conjecture 12/01 Notes 12/01 Mathematica File 12/04 Notes Chap 6,7 Pset 14 -- Exercises from Lectures (12/1, 12/4) due Wed 12/09 Week 15 12/08 FINAL EXAM Due 10:20 am on Tues, 12/15 Nonvanishing of Zeta on 1-Line Prime Number Theorem 12/08 Notes 12/08 Mathematica File Extra Innings! Added 2023 12/01 Elliptic Integrals, Functions, Double Periodicity Lecture 29 Notes 12/05 12/08 Weierstrauss P-function, Elliptic Curves Lecture 30 Notes Eisenstein series, modularity, BSD Lecture 31 Notes 12/12 Jacobi Theta Function, Sums of Two Squares Lecture 32 Notes