Math 131B FALL 2016
Analysis
MWF 12:00-12:50PM Math Sciences Building 5137
Instructor:
Email:
Course Websites:
Personal Website:
Office:
Office hours:
Evan Randles
[email protected]
https:/ccle.uc
Math 131B-2
Homework 4
Due: October, 25th, 2016
This assignment is due on October 25th, 2016 in the discussion section. Provide complete well-written solutions to
the following exercises. In what foll
Math 131B-2
Homework 5 Solutions
Due: November 8, 2016
Exercise 1. Use the Weierstrass approximation theorem to prove the following proposition.
Proposition 1. Let I = [0, 1] and suppose that f : I R
Math 131B-2
Homework 2 Solutions
Due: October, 11th, 2016
Exercise 1. Let (X, d) be a metric space and Y X. A collection cfw_V I (where I is an index set) of open sets
in X is called an open cover of
Math 131B-2
Homework 7 Solutions
Due: December 2, 2016
Exercise 1. In this exercise, you will give another proof of Theorem 42 from the notes.
For each R, define
[] = cfw_ + 2k R : k Z
The collection
HW: 10
Course: M339D/M389D - Intro to Financial Math
Page: 1 of 4
University of Texas at Austin
HW Assignment 10
Asian options. Barrier options.
Provide your final answer only for the following proble
Homework 2 Solutions
Math 131B-1
(3.29) Let (M, d) be a metric space, and
d (x, y) =
d(x, y)
.
1 + d(x, y)
d(x,x)
1+d(x,x)
0
1
We check that d is a metric.
For any x M , d (x, x) =
=
= 0.
(Positivi
Math 131B-2
Homework 1 Solutions
Due: October, 4th, 2016
Exercise 1. Let H be a vector space over R and let h, i be an inner-product on H, i.e., H paired with h, i is a
real inner-product space. For x
Math 131B
Spring 2017
UCLA
Homework 2
Due on Friday, April 14th
Exercises from the text:
Section 1.1: 13, 15, 16
Section 1.2: 3fgh, 4
Additional problems:
(1) Let (X, d) be a metric space. The triangl
Math 131B
Spring 2017
UCLA
Homework 7
Due on Friday, May 19th
Exercises from the text:
Section 3.4: 1, 2
Section 3.6: 1
Additional problems:
(1) Prove the Weierstrass M -test as stated here:
Theorem (
Math 131B
Spring 2017
UCLA
Homework 1
Due on Friday, April 7th
Exercises from the text:
Section 1.1: 3, 8, 9, 10
Hint for 1.1.8: You may use (without proof) any part of Exercise 1.1.5.
Additional prob
COUNTABLE PRODUCTS
ELENA GUREVICH
Abstract. In this paper, we extend our study to countably infinite products of topological
spaces.
1. The Cantor Set
Let us constract a very curios (but usefull) set
Math 112
Solutions for Problem Set 2
Spring, 2013
Professor Hopkins
1. (Rudin, Ch 1, #6). Fix b > 1.
(a)
If m, n, p, q are integers, n > 0, q > 0, and r = m/n = p/q, prove that
(bm )1/n = (bp )1/q .
H
Math 131B
Spring 2017
UCLA
Homework 3
Due on Friday, April 21st
Exercises from the text:
Section 1.1: 12
Hint for 1.1.12: Use the inequalities (1.1) and (1.2) (on pages 4 and 5, respectively)
which yo
Math 140B
HW 7, May 20 Chapter 7, Page 167-168: #13(a), 15, 16, 18.
#13. Assume that ffn g is a sequence of monotonically increasing functions on R with 0
fn (x) 1 for all x and all n:
(a) Prove that
ECON 122
INTERNATIONAL FINANCE
PROF. ARIEL BURSTEIN
Department of Economics, UCLA,
2017, Winter Quarter
Summary of material covered in chapters 5-10
Chapter 5: Balance of payments accounting
Full cha
Math 131B
Fall 2016
Midterm Exam
October 28th, 2016
Name (Print):
UID:
This exam contains 5 pages (including this cover page) and 4 problems. Check to see if any pages
are missing. Enter all requested
Basic Properties of Open and Closed Sets
David Jekel
January 16, 2017
The following notes cover material from Taos Analysis 1.2, especially Proposition 1.2.15.
1
Interior, Exterior, Boundary, Closure
A Short Guide to Learning Mathematics
David Jekel
January 17, 2017
Preface and Disclaimers
This guide is primarily aimed at undergraduates in proof-based math classes,
but some of it may apply to othe
Lecture: 6
Course: M339D/M389D - Intro to Financial Math
Page: 1 of 5
University of Texas at Austin
Lecture 6
An introduction to European put options. Moneyness.
6.1. Put options. A put option gives t
ECON 122
INTERNATIONAL FINANCE
PROF. ARIEL BURSTEIN
Department of Economics, UCLA,
2017, Winter Quarter
Summary of IS-LM framework, based on Chapter 7,
Feenstra-Taylor textbook
Model assumptions
UIP
Math 131B
Spring 2017
UCLA
Homework 4
Due on Friday, April 28th
Exercises from the text:
Section 1.5: 3, 4, 5
For 1.5.3: When the book references Theorem 9.1.24, the thing to use is the BolzanoWeierst
Mathematics 131B/2
Winter, 2017
MIDTERM 1 INFORMATION
The examination will be at 1:00 on Friday, February 3, NOT in the usual
classroom but in
FRANZ 1260
It is a closed book examination. You will work
NOTE: Throughout the exam, (X, d) is a metric space. For all
the proofs, you may assume any fact from the course except the
result you are proving.
1. (a) Define: x0 is an adherent point of E X. (b) P
The Chain Rule
It is easy to get confused by the chain rule for functions of more than one
variable. When f and g are functions of one variable, you learned long ago that
the derivative of h(x) = f (g
Solutions to Some Old Hour Exam Questions
1. For each of the following sets in R1 or R2 with the distance function d(x, y ) =
|a y | give its interior, exterior and boundary, and state whether it is o
The shortest proof I know for
I will assume that f ,
f
x ,
f
x ( y )
f
x ( y )
=
f
y ( x )
f
y are defined and continuous
f
y ( x ) are defined on that disk
and
on a disk centered
at (x, y) and th