First Day of Class
1. Introduce yourself. Pass around an attendance sheet. Display the syllabus on the
screen.
2. Divide the class into 6 or 8 groups based on where they are sitting. Give each
group a question about the syllabus (suggestions below).
3. Gi

Metric Spaces
Lecture Notes and Exercises, Fall 2016
M.van den Berg
School of Mathematics
University of Bristol
BS8 1TW Bristol, UK
[email protected]
1
Definition of a metric space.
Let X be a set, X 6= . Elements of X will be called points.
Definition

MTH/CSC 421
Review 1
1. Let a = 0.1 and b = 1. Show that at least 27 steps of bisection method are needed to determine
the root of a function f (x), with an error of at most 12 108 .
Hint: Recall that error
ba
2n+1 .
2. For the bisection method, show that

Numerical Analysis
Grinshpan
Linear Convergence
Let a positive sequence cfw_an converge to 0 and satisfy the condition
an+1
= C,
()
lim
n an
for some C 0.
Condition () implies that C 1. Indeed, since an 0, there exist infinitely many
indices n such that

NUMERICAL SOLUTIONS:
Solved Examples
By
Mahmoud SAYED AHMED
Ph.D. Candidate
Department of Civil Engineering, Ryerson University
Toronto, Ontario 2013
Table of Contents
Part I: Numerical Solution for Single Variable. 2
1.1.
Newton-Raphson Method . 2
1.2.
S

7/27/99
MATH 373 Section H6
Problem Set #2 Solutions
1. Solve the following via the quadratic formula: x2 + 106 x 106 . How will a computer
using single precision floating point arithmetic compute the solutions? How can we alter the
quadratic formula in t

Jim Lambers
MAT 460/560
Fall Semester 2009-10
Lecture 12 Notes
These notes correspond to Section 2.4 in the text.
Error Analysis for Iterative Methods
In general, nonlinear equations cannot be solved in a nite sequence of steps. As linear equations
can be

MA2501 Numerical
Methods
Spring 2015
Norwegian University of Science
and Technology
Department of Mathematics
Solutions to exercise set 7
1 Cf. Cheney and Kincaid, Exercise 4.1.9
Consider the data points
xi
f (xi )
0
1
1
9
2
23
4
93
6
259
a) Find the inte

The International Journal Of Engineering And Science (IJES)
|Volume|2 |Issue| 11|Pages| 05-12|2013|
ISSN(e): 2319 1813 ISSN(p): 2319 1805
On the Rate of Convergence of Newton-Raphson Method
Ranbir Soram1, Sudipta Roy2, Soram Rakesh Singh3, Memeta Khomdram

Introduction to Numerical Analysis
Doron Levy
Department of Mathematics
and
Center for Scientific Computation and Mathematical Modeling (CSCAMM)
University of Maryland
June 14, 2012
D. Levy
CONTENTS
Contents
1 Introduction
1
2 Methods for Solving Nonlinea

MATH 411/511, HOMEWORK #1
DUE THURSDAY, SEPT. 8 AT THE START OF CLASS.
This assignment is based on material covered in class and Sections 1.2, 0.3, and 0.4 from
Nicholson. See also NTNotes.pdf.
1. For each of the pairs of integers, a and b, use the Euclid

Abstract Algebra I
Math 481, Fall 2014
Professor Ben Richert
Exam 1
Solutions
Problem 1 (10pts) Complete the following definitions:
(a4pts) A monoid consists of a . . .
Solution. nonempty set M and a binary operation : M M M with the following properties

1
Solutions to assignment 3, due May 31
Problem 11.26 Use the Euclidean Algorithm to nd the GCD for each of the following
pairs of integers:
(a) 51 and 288
In this case, we write 288 = 5 51 + 33. Following through, we obtain
Solution:
51 = 1 33 + 18
33 =

MATH 411/511, HOMEWORK #3
DUE TUESDAY, SEPT. 20 AT THE START OF CLASS.
1. Suppose a, b Z, and n Z+ . Prove that
a b (mod n)
if and only if a and b have the same remainder when divided by n.
2. Let c, n Z+ .
a. Show that if c and n are relatively prime, th

Mathematics 310
Robert Gross
Homework 3
Answers
1. Let
!
a b
2
2
a,
b
R,
a
+
b
=
6
0
.
G1 =
b a
Last week, we saw that G1 is an abelian group with group operation matrix
multiplication.
!
a b
Define a function : C G1 with the formula (a + ib) =
. Show

Math 417
Exam 1 (Solutions)
Prof. I.Kapovich February 27, 2009
Problem 1.[20 points]
For each of the following statements indicate whether it is true or false.
You DO NOT need to provide explanations for your answers in this problem.
(1) The set cfw_a : a

Problem 1. Let G be a group and let H, K be two subgroups of G such that H K
is also a subgroup. Prove that either H K or K H.
Solution: Suppose that neither H K nor K H. Then there is h H,
h 6 K and there is k K, k 6 H. Since H K is a subgroup, we have h

Section 5.2 Compound Interest
With annual simple interest, you earn interest each year on your original investment. With
annual compound interest, however, you earn interest both on your original investment and
on any previously earned interest.
EXAMPLE:

Rational Numbers
There are four standard arithmetic operations: addition, subtraction,
multiplication, and division.
Just as we took differences of natural numbers to represent integers, here the
essence of the process is to use ordered pairs representi

MATH 125 Mathematics and its Applications
Section *
Fall 2016
Instructor: Your Name
Office: RB *
8640
Office Hours: Your office hours
Phone: 285-*
Leave messages at: 285Email: [email protected]
Text and Materials: Our text is Thinking Mathematically, 6th editio

Compound Interest
USE THIS POWER POINT AFTER
COMPLETING VIZI LESSON 6 SEGMENT 3.
NOTICE THAT VIZI USES WHERE OUR
TEXT USES .
Compound Interest Formula
Compound interest is interest computed on the
original principal as well as on any accumulated interest

MATH 411/511-Abstract Algebra 1
Fall Semester, 2016
Instructor: Dan Rutherford
Email: [email protected]
Office: RB 470
Office Hours: T 4:00-5:00pm, W 10-11am, R TBA.
Class Location: Robert Bell Building (RB) 450
Meeting time: TR 6:30-7:45pm
Text: Introdu

TR Calendar and Assignment List
X3 means multiples of 3.
CVC refers to a quiz modeled after the Concept and Vocabulary Check found at the
end of each text section, right before the problem set. These are submitted through Bb.
FTP refers to Finish the Prob

Math 333 Problem Set 2
Due: 02/17/16
Solutions
1. Find the quotient and remainder when a = 614 is divided by b = 13.
We have 614 = 13(48) + 10, so q = 48 and r = 10.
2. Prove that the square of any integer a is either of the form 3k or 3k + 1
for some int

Transition to Mathematical Proofs
Chapter 7 - Peano Arithmetic Assignment Solutions
Theorem 1 (Commutativity). For all a, b N, the following hold:
a+b=b+a
ab=ba
Theorem 2 (Associativity). For all a, b, c N, the following hold:
a + (b + c) = (a + b) + c
a

MATH 125: Mathematics and Its Applications (3 hours)
1. Course Description: A diverse course including statistics and other topics such as mathematical
modeling, problem solving, finance, geometrical concepts, growth patterns, and applications to the
phys

MATH 125: Quiz-01
Your Name:
1. Explain the idea of Percents.
2. Express
1
8
as a percent.
3. Express
1
4
as a decimal.
4. What you mean by Interest.
MATH 125: Quiz-01
Your Name:

8
Personal Finance
Compound Interest
Annuities
Amortization and Sinking Funds
8.3
Simple Interest
To calculate simple interest:
Interest = principal rate time
I = Prt
The rate r, is expressed as a decimal when
calculating simple interest.
Compounding M