Autumn 2019

Edinburgh

F17LP

"What is truth; said jesting Pilate; and would not stay for an answer." Of truth, by Francis Bacon


logic and proof

Errata page for book


Lecturer Prof Mark V Lawson

Room CM G12

Ext 3210

Email m.v.lawson[at]hw.ac.uk




Please remember: you should work on the exercises in your own time
and use the tutorials to ask questions where you have got stuck.

Tutorials begin in Week 2

Tutorial
Teaching Assistants: 
Alexander Cooper, Spyridon Dimoudis, Alexander Levine
Times
Who
Tuesdays, 16.20 to 17.10 Rooms JN301, JN302
All CS students
Wednesdays, 11.20 to 12.10 Room CMS01
All Maths students



Recommended books

The following are interesting to read:
A. Doxiadis, C. H. Papadimitriou, Logicomix, Bloomsbury, 2009. This is a graphic novel about the early development of logic.
D. Harel, Computers Ltd What they really can't do, OUP, 2012.

D. R. Hofstadter
, G"odel, Escher, Bach: an eternal golden braid, Basic Books, 1999. Mind blowing.

D. Cryan, S. Shatil, B. Mayblin, Introductory logic: a graphic guide, Icon Books, 2008. Student recommendation.
Some of the people involved in the development of logic:

Check out the series of books called Very Short Introductions published by Oxford University Press. There you can find further information about: Aristotle, Logic, Philosophy, Russell, Socrates.

Wikipedia is usually very good in this area with links to other references.

The MacTutor website maintained at St Andrews is good for biographies of all mathematicians.
Ray Monk, Biography of Bertrand Russell: 1872-1920 Volume 1, Vintage, 1997.

Ray Monk, Ludwig Wittgenstein: the duty of genius, Vintage, 1991.

Andrew Hodges, Alan Turing: the enigma, Vintage, 2014.

Richard Tieszen, Simply Goedel, Simply Charly, 2017.

Desmond MacHale, The life and work of George Boole, Cork University Press, 2014.
The following are textbooks rather than reading books:
R. Hammack, Book of proof, VCU Mathematics Textbook Series, 2009. This book can be downloaded for free here.

M. V. Lawson, A first course in logic, CRC Press, 2019.

A PDF of a prepublication version of this book will be made freely available via VISION to all students registered for this course.
The book covers much more than the lecture course. The errata page for this book can be found here.

S. Lipschutz, M. Lipson, Discrete mathematics, second edition, McGraw-Hill, 1997. This is useful for further practice in the mathematical ideas introduced in this course.

P. Teller, A modern formal logic primer, Prentice Hall, 1989. This is now freely available. Just click the title. This is a more sophisticated book than Zegarelli (i.e. no cartoons)
but is still at the same level as this course. It is highly recommended.
M. Zegarelli, Logic for dummies, Wiley Publishing, 2007
Propositional logic. Chapters 1 to 14 inclusive. Things really get going in Chapter 4. Chapter 8 is on truth-trees. You can omit Chapters 9 to 12 inclusive
because I don't do proofs in this course. At the end of Chapter 14 is an introduction to Boolean algebras.
Predicate logic. Chapters 15 to 19 inclusive deal with predicate or first-order logic.
Background reading. Chapters 20 to 25 inclusive.



For typed lecture notes, exercises and all solutions go to VISION

Syllabus


Tuesday  13.20
Wednesday 13.20
Friday 12.20
Homework
Week 1
16 Sept to 20 Sept
CHAPTER 1
Introduction to course
Lecture 2
Lecture 3
You should do the
Introductory Exercises
in the book.
They do not need any special
background to attempt.
Solutions at the back of the book.
Do Exercises 1.1.

Week 2
23 Sept to 27 Sept
Lecture 4
Lecture 5
Lecture 6
Revision of lectures 1 to 5.

Do Exercises 1.2, Question 1 ONLY.
Do Exercises 1.3.

Week 3
30 Sept to 4 Oct
Lecture 7
Lecture 8
Lecture 9
Do Exercises 1.4.
Do Exercises 1.5, Question 1 only.
Week 4
7 Oct to 11 Oct
Lecture 10
Lecture 11
TEST 1 DURING LECTURE
Lectures 1 to 6 inclusive only
Test lasts 15 minutes
You can stay as long as you like after that
to complete it
Exercises 1.6.
Exercises 1.7. Question 1 only.


Week 5
14 Oct to 18 Oct
Lecture 12
Revision of lectures 1 to 11.
Lecture 13
Lecture 14
Exercises 1.8.
Week 6
21 Oct to 25 Oct
Lecture 15
Lecture 16
Lecture 17
Exercises 1.9.
Exercises 1.10 Questions 1 and 2.
You can do Question 3 if you want but
it is not essential.

Week 7
28 Oct to 1 Nov
Lecture 18
Lecture 19
Lecture 20
Revision: Question 2 of last year's exam paper.
Exercises 1.11.
THIS CONCLUDES CHAPTER 1
Week 8
4 Nov to 8 Nov
CHAPTER 2
Lecture 21
Lecture 22
TEST 2 DURING LECTURE
Lectures 7 to 16 inclusive
(and assuming lectures 1 to 6 inclusive)
Test lasts 15 minutes
You can stay as long as you like after that
to complete it
Exercises 1.2 Questions 2 and 3.
Exercises 2.1.
Week 9
11 Nov to 15 Nov
Lecture 23
Lecture 24
Lecture 25
Exercises 2.2.
Exercises 2.3.
THIS CONCLUDES CHAPTER 2
Week 10
18 Nov to 22 Nov
CHAPTER 3
Lecture 26
Lecture 27
Lecture 28
Exercises 3.1.
Exercises 3.2.

Week 11
25 Nov to 29 Nov

Lecture 29
THIS CONCLUDES CHAPTER 3
Lectures are concluded





Interesting links


                                                       


C. Elegans (and its small brain)

Alan Turing

 Algorithm

Transistor

Transistor count

Moore's law

Millennium prize problems

Turing award

Logic is the calculus of computer science

An article by Jonathan Jacky on safety-critical computing

G"odel, Escher, Bach Check out the link to the lecture course at MIT

The 25 billion dollar eigenvalue an article by Kurt Bryan and Tanya Leise

Quantum tunnelling

Reversible computing
Lecture on reversible computing

Alphago

A circuit for adding two 4-bit binary numbers

Building logic gates from transistors



                                             

Material implication
This is just an example of the amount of debate
that the definition of this logical connective generates

Truth table generator
By Lawrence E. Turner
Southwestern Adventist University

Truth tree solver
Merci a Gabriel Lemonde-Labrecque
 
His notation is slightly different from mine
but the translations are obvious.
Watch your syntax!

Prime numbers

AKP Primality test

NP-complete problems

Minesweeper is NP-complete

Article by Richard Kaye on minesweeper

SAT-solvers

Article (2009) by Lance Fortnow
on the status of P versus NP


Time complexity


 


TESTS

Each test contributes 10% towards your final grade.
These are closed book tests based on the exercises. They are very important for your personal feedback.


Test 1. Week 4. Test paper and solutions.

Test 2. Week 8. Test paper and solutions.

Please note. In exams and tests, you do not have the right to question the academic criteria used in marking your work. That is for the lecturer to decide. However, if marks are added up incorrectly or not all of your answers have been marked, then you can inform the lecturer.



Calculators are neither required nor allowed in this course

In mathematics, we provide only one past exam paper and its solutions.

This is so that you will have an idea of the format of the exam paper.
To prepare for the exam, you should work through all the exercises referring to the lecture notes as and when needed.


2019 Exam paper and solutions


Highest mark = 88; average mark = 53; lowest mark = 3.




Turing

 


2.IX.2019