THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121 / CSIS1118
Foundations of Computer Science / Discrete Mathematics
Assignment 2
Due Date: October 29, 2014 (Wed)
Question 1: [10%]
For sets A, B, C, prove or disprove each of the following
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121 / CSIS1118
Foundations of Computer Science / Discrete Mathematics
Tutorial 4
Date: Nov. 20, 2014 (Thu.)
1. Suppose we know that 4% of the patients tested in a clinic are infected with avi
Discrete
Mathematics
Course
Introduction
Giulio
Chiribella
Department of
Computer
Science
1
What
2
Topics
Logic and proofs
Sets, relations, and functions
Counting
Probability
Graphs
3
Why
4
Course Learning Outcomes
[O1 Abstract Concepts] Understand a
Appendix
1
Reasoning about sets: example 1
The empty set is a subset of every set.
How to prove it?
Use the logical expression:
A B x [(x A) (x B)]
Choose A to be the empty set and note that the proposition
x [(x ) (x B)]
is always true,
because the propo
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Published: 2nd September, 2016
Due to September 19, 2016
Question 1 (15 Points): English statements and logic (O1)
Let A be the statement The satellite is close to M
Appendix to Lecture 1:
Puzzles, sample exercises,
and more suggestions for you to practice.
1
Back to Knights and Knaves
Zoey
Mel is a knave
Neither Zoey nor
Mel is a knave.
Mel
p: Zoey is a knave
q : Mel is a knave
By the rules of Knights and Knaves,
We
Functions
Giulio
Chiribella
Department of
Computer
Science
1
Why and where
Learning Outcomes:
O1 Understand abstract mathematical concepts
O2 Perform abstract thinking
O3 Analyze and enumerate
Where:
Sections 2.3 and 3.2 of the textbook
2
Menu
What
is
Probability
Giulio
Chiribella
Department of
Computer
Science
1
Why and where
Learning Outcomes:
O1 Understand abstract mathematical concepts
O2 Perform abstract thinking
Where:
Sections 7.1 to 7.4 of the textbook
2
Menu
What
is probability?
Probabilit
Sets
and
relations
Giulio
Chiribella
Department of
Computer
Science
1
Why and where
Learning Outcomes:
O1 Understand abstract mathematical concepts
O2 Perform abstract thinking
Where:
Sections 2.1 and 2.2 of the textbook (sets),
sections 9.1 and 9.5 (re
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Assignment 2: Sets and Relations
Published: 19th September, 2016
Due: 3rd October, 2016
Question 1 (10 Points): Basics on sets (O1)
a) Determine the cardinalities of
Logic
Giulio Chiribella
Department of
Computer
Science
Why and where
Learning Outcomes:
O1 Understand abstract mathemaAcal concepts
O2 Perform abstract thinking
Where:
SecAons 1.1 to 1.5 of the textbook
Menu
ProposiAonal Logic
What
Appendix 2
Sample exercise 1 [O2]
Prove the modus ponens
(p q) (q r) (p r)
Proof.
(p q ) p (p q) p (implica7on law)
(p p ) (q p) (distribu7vity)
F (q p)
q p
q
QED
Sample exercise 2 [O2]
Prove the modus tollens:
(p q) q p
Proof. (p q )
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Published: 3rd October, 2016
Due to 24th October, 2016
Question 1 (20 Points): Paintwork (O2,O3)
A painter has to paint a wall. The wall consists of 7 segments, as d
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Assignment 4, Part 1
November 17, 2015
Due to December 2, 2015, 5:00 PM
Q1
You are standing in a room with N persons in total. Assume for this exercise, that N is no
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Sample solution Assignment 1
Due at 5:00 p.m. on Oct. 5, 2015
Q1 Answer:
(a) (5%)
p(x): a student x likes logic.
q(x): a student x studies for discrete mathematics q
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
October 11, 2015
Due to October 29, 2015
Q1: Recap of week one
i) Show that (x y) (x y) (x y) = x y
ii) What is the conclusion of the following statement? Derive it
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
Assignment 4
November 24, 2015
Due to December 2, 2015, 5:00 PM
Q1 [12 Points]
You are standing in a room with N persons in total. Assume for this exercise, that N i
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF COMPUTER SCIENCE
COMP2121B Discrete Mathematics
October 11, 2015
Due to October 29, 2015
Q1: Recap of week one
i) Show that (x y) (x y) (x y) = x y
ii) What is the conclusion of the following statement? Derive it
Proofs
Giulio
Chiribella
Department of
Computer
Science
1
Why and where
Learning Outcomes:
O1 Recognize a correct proof
O2 Learn how to make proofs
Where:
Chapters 1.6-1.9 of the textbook
2
Beware of the fakes!
All monks wear monk habits.
Jorge wears a
Appendix
5
1
Inclusion-exclusion principle
2
A
Solved exercise
Find how many numbers between 1 and 100 are
multiples of 2, or 3, or 5, or 7.
Fact: the number of multiples of x between 1 and n is
the largest integer n/x
A = multiples of 2 (between 1 and 10
Counting
Giulio
Chiribella
Department of
Computer
Science
1
Why and where
Learning Outcomes:
O3 Analyze and enumerate
O2 Perform abstract thinking
O1 Understand abstract mathematical concepts
Where:
Sections from 6.1 to 6.5 of the textbook
2
Menu
Count
APPENDIX:
COMPUTABLE FUNCTIONS
General functions vs computable
functions
Today you learnt the mathematical definition of function.
In computer science, however, we are usually interested in a
special type of functions, called computable functions.
The com
Appendix
6
1
Exercise 1
We pick 7 cards from from a poker deck.
What is the probability that we get at least one card of each
colour?
2
Solution.
Sample space: S= set of all sequences of length 7 with
entries in cfw_1,2,3,4
(corresponding to the 4 colours
BeBeyond Business
Frameworks Introduction
The table on next page is an abstract of useful frameworks and tools in
Business. You can apply these frameworks to understand better about
marketing, business case analysis.
Who should read these frameworks?
App
CONSULTING AND CASE
INTERVIEW WORKSHOP
GSIA CONSULTING CLUB
October 6, 2001
Agenda
Before the Interview
Interview Summary
Fit Interviews
Case Interviews
Frameworks
Do your research on the firm!
What industries do they serve?
What specialty function
Date updated:
Created by:
What is this data?
Home Page:
Data website:
Companies in each industry:
Variable definitions:
5-Jan-16
Aswath Damodaran, [email protected]
Beta, Unlevered beta and other risk measures
US companies
http:/www.damodaran.com
htt
Valid argument: a sequence of logical implications (a.k.a. deduction)
Logical implication: p logically implies q, if p->q is a tautolofy. P=>q
I have pen and paper, therefore, I have paper is a valid argument:
Translation [O1]:
P: I have pen
Q: I have pap