MATH/MTHE 472/872
Winter 2014
Homework Assignment 1
Every question is worth 10 points, a random subset will be graded.
Problem 1
a) Let F be a eld of subsets of some space X for all where is some set. Let
F=
F
Show that F is also a eld on X.
For a space X
MATH/MTHE 472/872
Winter 2014
Homework Assignment 2
Solve at least 3 out of the total 5.
Problem 1: Dynamic Programming and Control
Consider the following problem. A investors wealth dynamics is given by the following:
xt+1 = ut wt ,
where cfw_wt is an i
MATH/MTHE 472/872
Winter 2014
Homework Assignment 4
Problem 1
Consider the MDP with components (X, A, p, c) and average cost J. Let (, h, f ) be a canonical
triplet. Prove that if h satises
lim Ex [h(xn )]/n = 0, for every R , x X,
n
then the policy cfw_f
MATH/MTHE 472/872
Winter 2014
Homework Assignment 3
Problem 1
Consider the following model.
xt+1 = f (xt , ut , wt ),
yt = g(xt , vt ),
where X, U , W and V are assumed to be nite spaces. Here, cfw_wt t1 and cfw_vt t1 are i.i.d. noise
2
2
processes with z
Final Project
The classication of compact surfaces
Rules of the Game
This worksheet is your nal exam for this course. You will work on these
problems in class. Douglas will be there to help you for the last two weeks of
classes, take advantage of him. You
LECTURE PLAN FOR MATH 472
INTRO TO TOPOLOGY
Fall 2010
1
Aug 23
Announcements
1. Exams
2. Hwk
3. Oce times/talk to each other rst
4. Feedback
Draw pictures about things that are equal or dierent in dierent geometries. Explore:
euclidean 3d (LENGTH, ANGLES
The Fundamental Group
Renzos math 472
This worksheet is designed to accompany our lectures on the fundamental
group, collecting relevant denitions and main ideas.
1
Homotopy
Intuition: Homotopy formalizes the notion of "wiggling". Homotopy
is a way to com
Projects
Renzos math 472
1
Compactications
Compact spaces are very nice for many dierent reasons, most of which
will only become evident much further along in your mathematical journey.
Given a non compact space X, one would sometimes like to construct a
Projects
Renzos math 472
The list of questions/projects below will lead the discussion for this week.
Dont be shy, put forth your ideas
1
Dense Sets
Let X be a topological space. A set A is called dense if its closure is X.
Warm-up 1. Give some example of
Renzos Math 490
Introduction to Topology
Tom Babinec
Chris Best
Michael Bliss
Nikolai Brendler
Eric Fu
Adriane Fung
Tyler Klein
Alex Larson
Topcue Lee
John Madonna
Joel Mousseau
Nick Posavetz
Matt Rosenberg
Danielle Rogers
Andrew Sardone
Justin Shaler
Smr