ACMS 40485, Spring 2015
Hayes-Healy 231; T+Th 11:00AM-12:15PM
Course Syllabus
Course Organization
Instructor: Andrew Sommese (Hurley 291).
Email: sommese@nd.edu
Office Hours: After class and
by appointment.
Exam Schedule
Exam 1: Take home test will be given
out in class on Tuesday Feb. 10 and will be due Thursday, Feb. 12 at
start of class. Test and Answers.
Exam 2: Take home test: Handed out Thursday,
March 26 at end of class and
due Tuesday, March 31 at start of class. Test and
Answers.
Final: Take home test. Will be sent out on Monday, may 4 and
will be due by Friday, May 8, 12:30PM.
Handouts
RungeFunction Runge’s function showing a potential bad property of
inter-polation polynomials
AnalyticContinuation
Analytic continuation by means of differential equation marching methods
A Short Introduction to the Euler Characteristic
Computing analytic one-forms on smooth curves
Homework
Homework 1
Make
sure you understand the review material! (Manipulating complex numbers, basic
residue integration, convergence of power series, Laurent series, exponential,
log, Euler’s relation, ...)
Homework 2 (Due Tuesday, February 3) Answers
Pg.
44: 1bc, 2bd, 3, 5.
Pg.
59: 1, 2, 3, 6c.
Pg.
79: 1, 8.
Pg.
90: 2.
Homework 3 (Due Thursday, February 5) Answers
Pg.
80: 3.
Pg.
90: 3, 4, 6.
Pg.
101: 1abde, 2acd.
Homework 4 (Due Tuesday, February 10) Answers
Pg.
135: 1, 2, 3ac, 4abce.
Homework 5 (Due Thursday, February 19) Answers
Pg.
216: 1abce, 3, 5.
Pg.
235: 1bd, 2abehi.
Homework 6 (Due Thursday, February 26) Answers
Pg.
235: 3, 5, 6, 7, 8a, 9.
Homework 7 (Due Thursday, March 5) Answers
Pg.
253: 1, 2, 4, 7, 11, 13.
Homework 8 (Due Tuesday, March 24) Answers
Pg. 265: 2, 5.
Pg. 282: 11bc, 12, 13ab, 16, 18.
Pg. 316: 3.
Show the cross-ratio is left unchanged by a linear
fractional transformation.
Homework 9 (Due Thursday, April 9) Answers
Pg. 421: 1a, 2, 3, 4.
Pg. 438: 1, 2, 3, 7.
Homework 10 (Due Thursday, April 16) Answers
Pg. 438: 4, 5.
Pg. 447: 1.
What is the Euler characteristic of
the complex plane minus the disc consisting of all points of absolute value
strictly less than 1?
What is the Euler characteristic of
the complex plane minus the disc consisting of all points of absolute value
less than or equal to 1?
Homework 11 (Due Thursday, April
23) Answers
1) Attend the two Trefethen
talks.
2) Homogenize 
3) Dehomogenize
with respect
to the hyperplane z = 0.
4) Find
the singular points of 
5) Find
the singular points of V(
What is the Euler characteristic of the Riemann sphere minus 10
closed disks?
Homework 12 (Due Tuesday, April 28)
Answers
What are the analytic one-forms on
V(x^4+y^4+z^4)?
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