Math 434
Practice Midterm
Fall 2015
The actual exam will have one fewer problem.
Problem 1. Consider the two points P = (2, 2) and Q = (2, 2) in the hyperbolic
plane (H2 , dhyp ).
!
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a. Compute the hyperbolic length hyp [P, Q] of the line segment [P, Q].
Math 434, Fall 2015
Geometry and Transformations
Practice Final Exam
Remember: no book, no notes for the final exam.
Problem 1. Let (X, d) be a metric space where the metric d satisfies the property that
d(P, R) 6 max d(P, Q), d(Q, R)
for every P , Q, R
MATH 434
Fall 2015
Homework 1, due on Wednesday 9/2
Problem 1. Let z = 2 + i and z = 3 2i. Write the product zz and the quotient
z
in the form a + ib, with a, b R.
z
Problem 2. Let z C be a complex number, and let z be its conjugate. Show
that z is a real
Notes for MATH 434
Geometry and Transformations
Francis Bonahon
Fall 2015
Version: September 7, 2016
Department of Mathematics
University of Southern California
Los Angeles, CA 90089-2532, U.S.A.
E-mail address: fbonahon@math.usc.edu
URL: http:/www-bcf.us
Notes for MATH 434
Geometry and Transformations
Francis Bonahon
Fall 2015
Version: October 23, 2015
Department of Mathematics
University of Southern California
Los Angeles, CA 90089-2532, U.S.A.
E-mail address: fbonahon@math.usc.edu
URL: http:/www-bcf.usc