MAT1830 - Discrete Mathematics for Computer Science
Assignment #7
To be handed in at the beginning of your support class in week 9 (2 6 May)
Show your working for all questions.
1. Find expressions fo
MAT1830 - Discrete Mathematics for Computer Science
Assignment #6 Solutions
1. E is reflexive and symmetric and transitive.
E is not antisymmetric (for example, aEb and bEa).
F is reflexive and antisy
MAT1830 - Discrete Mathematics for Computer Science
Assignment #7 Solutions
1. (a) A ternary string of length 10 is an ordered selection of 10 elements from the set cfw_0, 1, 2 with
3 elements. There
MAT1830 - Discrete Mathematics for Computer Science
Assignment #3 Solutions
(1) (a) This is true. For any integer, there is another integer which is double the first.
(b) This is false. It is not the
MAT1830 Sample Exam 2
When you are instructed to write down something, no explanation is required. Everywhere else,
you must justify your answers. Marks will be allocated for clarity of explanation. I
MAT1830 - Discrete Mathematics for Computer Science
Assignment #7
To be handed in at the beginning of your support class in week 9 (1 5 May)
Fully explain your answers for all questions.
1. Find expre
MAT1830 - Discrete Mathematics for Computer Science
Assignment #9
To be handed in at the beginning of your support class in week 11 (15 19 May)
Fully explain your answers for all questions.
1. A biase
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #10 Solutions
1. (a) Note that a0 = 20 = 1.
Also, an = 2n = 2(2n1 ) = 2an1 for n 1.
So a0 = 1 and an = 2an1 for all integers n 1 is a
Lecture 22: Conditional probability and Bayes
theorem
Your friend believes that Python coding has become more popular
than AFL in Melbourne. She bets you $10 that the next person to
pass you on the st
Lecture 29: Graph Theory
What graph theory is NOT about
Supply
Demand
What graph theory IS about
A graph consists of a set of objects called vertices and a list of
pairs of vertices, called edges.
Gra
Lecture 25: Discrete distributions
In this lecture well introduce some of the most common and
useful (discrete) probability distributions. These arise in various
different real-world situations.
Discr
Learning Outcomes for MAT1830
At the completion of this unit, students should be able to:
I
identify basic methods of proof, particularly induction, and
apply them to solve problems in mathematics and
MAT1830 - Discrete Mathematics for Computer Science
Assignment #8
To be handed in at the beginning of your support class in week 10 (8 12 May)
Fully explain your answers for all questions.
1. One side
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #9 and Additional Practice Questions
Tutorial Questions
1. (a) Find the expected value and variance of a random variable X with proba
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #8 and Additional Practice Questions
Tutorial Questions
1. A fair coin is flipped three times. Let X be the number of times heads is
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #8 and Additional Practice Questions
1. The sample space is cfw_HHH, HHT, HTH, HTT, THH, THT, TTH, TTT (where HTH means heads
on the
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #11 Solutions
1. (a)
V1
V2
V3
V4
(b) 1. The walk is V1 , V2 , V1 , V2 .
(c) For any n 2:
- The 1st entry in the top row of M n is the
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #10 and Additional Practice Questions
Tutorial Questions
1. Find recursive definitions for the following.
(a) The sequence a0 , a1 ,
MAT1830 Sample Exam 1
When you are instructed to write down something, no explanation is required. Everywhere else,
you must justify your answers. Marks will be allocated for clarity of explanation. I
Office Use Only
Monash University
Semester One Examination Period 2013
Faculty Of Science
EXAM CODES:
MAT1830
TITLE OF PAPER:
Discrete Mathematics for Computer Science
EXAM DURATION:
3 hours writing t
Lecture 21: Probability and Independence
Lecture 21: Probability and Independence
Why should you care?
I Many algorithms work better if they make random choices.
For example, quicksort can avoid its w
Lecture 30: Walks, paths and trails
There are several ways of travelling around the edges of a graph.
A walk is a sequence
V1 , e1 , V2 , e2 , V3 , e3 , . . . , en1 , Vn ,
where each ei is an edge joi
MAT1830 - Discrete Mathematics for Computer Science
Assignment #6 Solutions
1. E is reflexive and symmetric and transitive.
E is not antisymmetric (for example, aEb and bEa).
[2]
F is reflexive and an
MAT1830 - Discrete Mathematics for Computer Science
Assignment #4 Solutions
(1) Let P (n) be the statement 2n divides an .
Base steps. a1 = 4 and 21 = 2 divides 4, so P (1) is true.
a2 = 12 and 22 = 4
MAT1830 - Discrete Mathematics for Computer Science
Assignment #5
To be handed in at the beginning of your support class in week 7 (10 13 April)
If youre missing out on your usual support class on Fri
MAT1830 - Discrete Mathematics for Computer Science
Assignment #4
To be handed in at the beginning of your support class in week 6 (37 April)
Show your working and give full explanations for all quest
MAT1830 - Discrete Mathematics for Computer Science
Assignment #1
To be handed in at the beginning of your support class in week 3 (1216 March)
Show your working and give full explanations for all que