limitations. . Key infrastructure technologies for workflow
management Efficient and reliable support for workflow
implementation and execution requires a distributed computing
environment that: supports integration and interoperability
among loosely-coup
Math 4383
Spring 2012
Homework 5
Sections 4.2, 4.3, 4.4
The notation [ x ]n denotes the congruence class of the integer x modulo n.
The set n is the set of all distinct congruence classes (residue classes) modulo n. See the extra
4.2 notes for definitions
Number Theory
Spring 2012
Homework 6
Sections 4.4 and 5.2
1. Show that if p is an odd prime number, then 1p + 2 p + 3 p + . + ( n 1) 0 ( mod p ) .
p
2. Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives
a remainder of
Math 4383
Section 2.2
Page 1 of 3
Number Theory
Chapter 2
Section 2.2: The Division Algorithm
Remember that the basic premise of number theory is the study of the properties of the integers.
So, when we perform arithmetic operations, we are looking for in
Math 4383
Section 2.2
Page 1 of 3
Number Theory
Chapter 2
Section 2.2: The Division Algorithm
Remember that the basic premise of number theory is the study of the properties of the integers.
So, when we perform arithmetic operations, we are looking for in
Math 4383
Section 2.3
Page 1 of 7
Number Theory
Chapter 2
Section 2.3 Greatest Common Factor
Language for Division
3 is a factor of 12
3 is a divisor of 12
12 is a multiple of 3, 12 is a multiple of 4
12 is divisible by 3, 12 is divisible by 4
Formal Lang
Math 4383
Section 2.3
Page 1 of 7
Number Theory
Chapter 2
Section 2.3 Greatest Common Factor
Language for Division
3 is a factor of 12
3 is a divisor of 12
12 is a multiple of 3, 12 is a multiple of 4
12 is divisible by 3, 12 is divisible by 4
Formal Lang
Math 4383
Section 2.3
Page 1 of 7
Number Theory
Chapter 2
Section 2.3 Greatest Common Factor
Language for Division
3 is a factor of 12
3 is a divisor of 12
12 is a multiple of 3, 12 is a multiple of 4
12 is divisible by 3, 12 is divisible by 4
Formal Lang
Math 4383
Section 2.4
Page 1 of 5
Number Theory
Chapter 2
Section 2.4 The Euclidean Algorithm
We know that the greatest common divisor of two nonzero integers is always defined, but how
do we find it? The Euclidean Algorithm is a systematic way of finding
Math 4383
Section 2.4
Page 1 of 5
Number Theory
Chapter 2
Section 2.4 The Euclidean Algorithm
We know that the greatest common divisor of two nonzero integers is always defined, but how
do we find it? The Euclidean Algorithm is a systematic way of finding
applications are submitted as DBMS or TP display transactions.
Transactional workflows involve coordinated execution of multiple
duties that (i) could contain people, (ii) require entry to HAD systems,
and (iii) help selective use of transactional homes (
decrease know-how method rate or reduce waste of material in a
approach. As a result, this technique is not appropriate for modeling
industry strategies with objectives rather than consumer delight. Yet
another dilemma is that this system with the aid of
performed). WFMSs that support creation workflow must provide
facilities to outline task dependencies, and manage assignment execution
with little or no human intervention. Construction WFMSs are most
commonly mission central and need to deal with the com
for materials. Within the efficiency of procurement, the procurement
office instructs the accounts administrative center to verify the account
reputation of the customer. The procurement place of work then contacts
vendors for bids, and ultimately selects
implement work- flows, and (ii) keeping workflow structure (i.e.,
the rules for sequencing of tasks) separated from the task
implementation code. The latter allows changes in workflow
structure without modifying the programs that implement the
workflow ta
Number Theory
Homework #3
Sections 2.5, 3.1 and 3.2
1. Liz recently downloaded some songs and movies from her internet account. Songs cost $1.89
to download, movies cost $5.88 to download and Liz spent a total of $255.15.
A. State all solutions to the lin
Number Theory
Section 2.5
Linear Diophantine Equations
A Diophantine equation is an equation in one or more unknowns that is to be solved in the
integers. The name honors the mathematician Diophantus, who may have lived in the 3rd century
AD in Alexandria
Number Theory
Section 2.5
Linear Diophantine Equations
A Diophantine equation is an equation in one or more unknowns that is to be solved in the
integers. The name honors the mathematician Diophantus, who may have lived in the 3rd century
AD in Alexandria
Math 4383
Section 4.2 Extra
Page 1 of 5
Number Theory
Chapter 4
Section 4.2 Extra Information on Congruence
Any set of n integers that are incongruent modulo n is called a complete set of residues mod n.
The standard set is the set of numbers 0,1,2, n-1.
Math 4383
Section 4.2 Extra
Page 1 of 5
Number Theory
Chapter 4
Section 4.2 Extra Information on Congruence
Any set of n integers that are incongruent modulo n is called a complete set of residues mod n.
The standard set is the set of numbers 0,1,2, n-1.
Math 4383
Section 4.2 Extra
Page 1 of 5
Number Theory
Chapter 4
Section 4.2 Extra Information on Congruence
Any set of n integers that are incongruent modulo n is called a complete set of residues mod n.
The standard set is the set of numbers 0,1,2, n-1.
Math 4383
Section 4.3
Number Theory
Chapter 4
Section 4.3 Binary and Decimal Representation of Integers
Place Value Systems of Numeration
Expanded form in base b
Short form
Page 1 of 6
Math 4383
Section 4.3
We work in base 10, WHY?
3526
The base 10 plac
Math 4383
Section 4.3
Number Theory
Chapter 4
Section 4.3 Binary and Decimal Representation of Integers
Place Value Systems of Numeration
Expanded form in base b
Short form
Page 1 of 6
Math 4383
Section 4.3
We work in base 10, WHY?
3526
The base 10 plac
Number Theory
Chapter 4
Linear Congruence and the Chinese Remainder Theorem
Linear Congruence
Given integers a and b and n>1, find a solution to the equation
ax b ( mod n ) .
What this means:
Congruent solutions versus incongruent solutions:
Solutions in
Math 4383
Sections 5.1 and 5.2
Page 1 of 9
Number Theory
Chapter 5
Sections 5.1 and 5.2 Fermats Theorem
Pierre de Fermat 1601-1665
Fermat was a lawyer and magistrate in provincial parliament in Toulouse, France.
Mathematics was his hobby.
Most of his work