Foundations of Computing Professor Steve Schneider 30BB02 Course - - PowerPoint PPT Presentation

Foundations of Computing

Professor Steve Schneider 30BB02

Course Structure

Two lectures per week One tutorial per week (exercise sheets) Mathematics Surgeries:

Room 44BB02, Wednesdays 10am.

Course material posted on CS189 website. Assessment: Entirely by examination. Everything covered in lectures and tutorials is

examinable.

Course Structure

Monday 3pm: lecture Wednesday 9am: lecture (not week 1) Tuesday 2pm: tutorial (not weeks 1, 2, or 4. I n

week 4, the tutorial will be on Wednesday)

to go through the previous week’s exercise sheet. Bring your solution to the previous week’s exercise sheet; it will be

• marked. Marks do not count towards the final assessment.

Office hours: Monday 4pm and Wednesday 10am.

Sign up for an appointment.

Maths surgery: Wednesday 10am in 44BB02

Foundations of Computing Course Content

Set theory

Sets, relations, functions

Logic

Propositions, truth tables, logical reasoning,

predicates

The Z notation

Use of logic and set theory in specification

Number representations

Representation of values in a computer Dr Roger Peel – weeks 11 and 12

Recommended texts

E Currie: The Essence of Z,

Prentice Hall, (1999), ISBN 0-13-749839-X

R Haggarty: Discrete Mathematics for Computing,

Pearson Education, (2002), ISBN 0-201-73047-2L

Bottaci & J Jones: Formal Specification Using Z.

Thompson, (1995), ISBN 1-850-32109-4

Other background texts

Ben Potter, Jane Sinclair, David Till: An Introduction to

Formal Specification and Z, (Prentice Hall) ISBN 0-13-242207-7

Mike McMorran, Steve Powell: Z Guide for Beginners,

(Blackwell) ISBN 0-632-03117-4

Jim Woodcock and Jim Davies: Using Z, Specification and

Refinement, (Prentice Hall) ISBN 0-13-948472-8

Keith Devlin: Sets Functions and Logic (Chapman Hall), ISBN

1-5848-8449-5

Keith Hirst: Numbers Sequences and Series, (Edward Arnold)

ISBN 0-340-61043—3

Judith Gersting: Mathematical Structures for Computer

Science, (Freeman) ISBN 0-7167-8306-1

Daniel Velleman: How to prove it, (Cambridge University

Press) ISBN 0-521-44116-1

Using the voting handset

Do not press this button or you will not be able to vote To vote, press

• ne of these

buttons FIRMLY and watch the small light (goes green on successful vote) Note: you can

• nly vote when

the green ‘polling

• pen’ indicator is

projected in the top-right of the screen

Sim ulation only

Did you have breakfast today?

Y e s N

• D
• n

’ t k n

• w

0% 0% 0%

1.

Yes

2.

No

3.

Don’t know

0 of 5

Are you familiar with sets and logic?

Y e s , v e r y A l i t t l e N

• t

a t a l l

0% 0% 0%

1.

Yes, very

2.

A little

3.

Not at all

Do you know about truth tables?

Y e s I d i d , b u t I ’ v e f

• r

g

• t

. . . N

• 0%

0% 0%

1.

Yes

2.

I did, but I’ve forgotten them

3.

No

Do you know about power sets and cartesian products?

Y e s I d i d , b u t I c

• u

l d d

• w

i . . N e v e r h e a r d

• f

t h e m

33% 33% 33%

1.

Yes

2.

I did, but I could do with some revision

3.

Never heard of them

Do you know about Karnaugh maps?

Y e s N

• 0%

0%

1.

Yes

2.

No

Have you come across boolean algebra?

Y e s N

• 0%

0%

1.

Yes

2.

No

Motivation

Logic is the foundation of computing. The ability to think and reason logically

is essential in Computing.

Humans are not always very good at

thinking logically.

Thus: formal and systematic ways of

handling logic are necessary.

This lecture

Some exercises and discussion in logical

thinking.

Example 1: quality control

You work in quality control at a games

manufacturer.

A game contains cards with letters on

• ne side and numbers on the other.

They must be printed according to the

rule: If one side has a vowel, the other side must have an even number

Example 1: quality control

You have 4 cards in front of you. Which

cards do you need to turn over to check the rule is being followed? If one side has a vowel, the other side must have an even number

A B C D

Which cards do you need to turn

• ver to check the rule is being

followed?

A C A a n d B A a n d C A a n d D B a n d C A , C a n d D A , B , C , a n d D S

• m

e

• t

h e r c

• m

b i n a t i

• n

0% 0% 0% 0% 0% 0% 0% 0% 0%

1.

A

2.

C

3.

A and B

4.

A and C

5.

A and D

6.

B and C

7.

A, C and D

8.

A, B, C, and D

9.

Some other combination

Example 2: law enforcement

You work in law enforcement. A law states that anyone buying alcohol

in a bar should be at least 18 years old.

Example 2: law enforcement

You have 4 customers in front of you. You can question up to 2 of them.

A: buying a beer B: buying a coke C: a 21 year old D: a 17 year old

Which customers should you question to check the rule is being followed?

A B C D A a n d B A a n d C A a n d D B a n d C

0% 0% 0% 0% 0% 0% 0% 0%

1.

A

2.

B

3.

C

4.

D

5.

A and B

6.

A and C

7.

A and D

8.

B and C

Logical structure

What can we say about the logical

structure of examples 1 and 2?

Example 3: genealogy

You are trying to trace your great-

great-grandfather and you are looking through the records at the Family Records Office.

You have spoken to Aunt Gladys and

Uncle Alan

Your sister has spoken to Grandma

Example 3: genealogy Aunt Gladys and Uncle Alan

Aunt Gladys: He was born in Halifax or

married in Derby.

Uncle Alan: He was married in Derby or he

died in Skipton.

Gladys and Alan together: He was born in

Halifax or married in Derby, AND he was married in Derby or died in Skipton.

Example 3: genealogy: Grandma Carol

Grandma Carol: He was either married

in Derby, or he was born in Halifax and died in Skipton.

Whose information narrows it down more: Gladys&Alan, or Carol?

0% 0% 0% 0% 0%

1.

Gladys & Alan

2.

Carol

3.

Neither - they are just different

4.

They are the same.

5.

No idea

Example 4: truth and lies

Consider two kinds of people: truth

tellers who always tell the truth, and liars who never tell the truth.

Alice says: “If you asked Bob, he would

say that I am a liar.”

What can you deduce?

0% 0% 0% 0% 0%

Alice says: “If you asked Bob, he would say that I am a liar.”

1.

Alice is a truth teller

2.

Alice is a liar

3.

Bob is a truth teller

4.

Bob is a liar

5.

You can’t deduce anything

Summary

Logical reasoning is not always easy or

intuitive.

Treating logic and logical thinking in a

formal and systematic way is necessary.

Please ensure you return your handset before leaving.

The handset is useless outside of this class and non-returns will decease the likelihood of future voting system use on this course.