MATH1081 Discrete Mathematics
D. Angell/D.Trenerry
4.1 Counting
Counting is probably the earliest mathematical operation you learn, and it
might seem rather strange to have part of a university course
MATH1081 Test 2 2009 S1 v2A
February 25, 2015
These solutions were written by Johann Blanco and typed up by Georgia Tsambos. Please be
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UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
Exercise. Given the formulas
n
X
n(n + 1)
k =
2
k=1
and
n
X
n(n + 1)(2n + 1)
k =
,
6
k=1
2
evaluate
10
10
X
X
(k 3
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
Laws of set algebra:
Laws of set algebra:
Commutative laws A B = B A
AB =BA
Laws of set algebra:
Commutative laws
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
Recall that if f is a function from X to Y , then
for every x X, there is exactly one y Y such that f (x) = y.
Rec
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
Welcome !
UNSW Australia 201
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
The identity function on a set X is the function iX : X X, iX (x) = x.
The identity function on a set X is the fun
You should print the Topic Lecture Notes before the start of each
topic, and bring them along to lectures, together with some extra
notepaper for making handwritten notes.
The pages have useful but no
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
Example. The complete bipartite graph Km,n is the simple bipartite graph with
V1 containing m vertices and
V2 cont
F.Kuo and D.Angell / D.Trenerry
C
N O
SW P
M
Y
AT S R
AN H C IG
H
D EM O HT
ST A O :
L
T
AT IC O
IS S F
TI
C
S
MATH1081 Discrete Mathematics
Topic 3 Logic, Proof and Induction
3.1 Symbolic Logic
A pro
F.Kuo and D.Angell / D.Trenerry
N CO
SW P
M S YR
A
AN T CH IG
H
H
D E O T
ST M OL :
A
AT T O
I
F
C
IS S
TI
C
S
MATH1081 Discrete Mathematics
Topic 4 Counting and Recursion
4.1 Counting
Counting is pro
MATH1081 Discrete Mathematics
F.Kuo and D.Angell / D.Trenerry
Topic 3 Logic, Proof and Induction
3.1 Symbolic Logic
A proposition (or statement) is a sentence or clause that is unambiguously
true or f
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
Semester 2 2011
MATH1081
DISCRETE MATHEMATICS
(1) TIME ALLOWED TWO (2) HOURS
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUEST
UNSW Australia 2016 S1
MATH1081 Discrete Mathematics
Thomas Britz and Dennis Trenerry
An ordered pair is a collection of two objects in a specified order.
We use round brackets to denote ordered pairs
MATH1081 Discrete Mathematics
3.1: Title
MATH1081 Discrete Mathematics
3.2: Introduction
The defining characteristic of modern mathematics is proof .
In ancient times mathematics consisted of a collec
MATH1081 Discrete Mathematics
Frances Kuo
3.1 Logic
A proposition (or statement) is a sentence that is unambiguously true or false.
Example.
Canberra is the capital of Australia is a proposition which
MATH1081 Test 1 2010 S1 v1A
February 10, 2015
These answers were written by Johann Blanco and typed up by Georgia Tsambos. Please be
ethical with this resource. It is for the use of MathSOC members, s
MATH1081 Test 3 2008 S1 v3A
February 10, 2015
These solutions were written by Johann Blanco and typed up by Evgeny Martynov. Please be
ethical with this resource. It is for the use of MathSOC members,
MATH1081 Test 3 2008 S2 v1A
February 25, 2015
These solutions were written by Johann Blanco and typed up by Evgeny Martynov. Please be
ethical with this resource. It is for the use of MathSOC members,
MATH1081 Test 3 2009 S1 v2A
February 10, 2015
These solutions were written by Johann Blanco and typed up by Evgeny Martynov. Please be
ethical with this resource. It is for the use of MathSOC members,
MATH1081 Test 3 2009 S2 v1A
February 16, 2015
These answers were written by Johann Blanco and typed up by Evgeny Martynov. Please be
ethical with this resource. It is for the use of MathSOC members, s
MATH1081
Discrete Mathematics
Topic 2
Integers and Modular Arithmetic
Dr. Brian Jeeries
School of Mathematics and Statistics
University of New South Wales
Semester 2 2012
Factorisation
B.Jeeries
MATH1
MATH1081 Discrete Mathematics
1 Sets, Functions, and Sequences
A set is a well-defined collection of distinct objects.
An element of a set is any object in the set.
- belongs to or is an element of
/
MATH1081
Discrete Mathematics
Topic 1
Functions and Sequences
Dr. Brian Jeeries
School of Mathematics and Statistics
University of New South Wales
Semester 2 2012
Cartesian Product of Sets
An
ordered
MATH1081
Discrete Mathematics
Topic 2
Relations
Dr. Brian Jefferies
School of Mathematics and Statistics
University of New South Wales
Semester 2 2012
MATH1081 Discrete Mathematics
B.Jefferies
1 Relat
MATH1081 Test 4 2010 S1 v2A
May 25, 2015
These answers were written by Johann Blanco and typed up by Georgia Tsambos. Please be
ethical with this resource. It is for the use of MathSOC members, so do
MATH1081 Test 2 2008 S1 v2A
May 6, 2015
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ethical with this resource. It is for the use of MathSOC members, so do
MATH1081 Test 4 2009 S2 v2B
May 25, 2015
These answers were written by Johann Blanco and typed up by Georgia Tsambos. Please be
ethical with this resource. It is for the use of MathSOC members, so do
MATH1081 Test 4 2008 S1 v3B
May 25, 2015
These solutions were written by Johann Blanco and typed up by Georgia Tsambos. Please be
ethical with this resource. It is for the use of MathSOC members, so d