When you've finished the course, here's a suggestion:
read the first 4 or 5 pages of the book again - it should all make a
lot more sense this time round. (And you get to enjoy my prose once
more ... )
Check out my "science & maths reading
list" for some leisure reading over the holidays.
The main readings for this course come from my text
Principles
of Mathematics and Logic. Individual chapters are
cited below, unit by unit, so you know when you should read each
chapter (two chapters per unit). A copy of an older edition of the
text is also available on reserve in the library.
(Use this when you
need to but be sure to check with your copy of the current edition
afterwards - changes have been made and typos fixed.)
In addition, some sections of another text, the Alberta
Notes may also be useful - I have made two chapters available
suitably linked in the units where they are relevant. You should be
aware that this
and other texts may treat the material differently
from my text - in cases where there are differences, my text is
definitive for the purposes of this course.
You should also look at the Entertainments section below.
Problems?
Click here if you are having trouble
with PDF files.
Note: When you read mathematics, it is important
to engage the text actively, not passively. You should have pencil
and paper beside you, and try to follow each statement,
doing the suggested calculations or reasoning yourself. It
is not a novel or short story, whose meaning will just flow over you,
but a dialogue, only one side of which is on the page. You must
provide the other side yourself!
Here is an
excellent article on how to read mathematics if you want more
"advice".
(BTW: the book [Emblems of Mind by Edward
Rothstein]
from which the quotes are taken is one I recommend in the
Entertainments below. It's about
Maths & Music, and might give you a different insight into the
nature of maths.)
Note: If you find typos or other errors, or if you have questions about the text, please let me know.
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
We shall cover the second of the following topics this semester
Gödel's Incompleteness Theorem
Categories, logics, & linguistics
Probability and Statistics
General
Unit 1
Unit 2,3
Unit 4
Unit 5
Unit on Gödel's Incompleteness Theorem
Unit on Categories, logics, & linguistics
Note: If you find typos or other errors, or if you have questions about my answers, please let me know.
Additional assignments, comments, solutions, and helpful hints will be posted in this section of the webpage, as relevant. I'll alert you to any additions in class.
Unit 1: Your first reading assignment is Chapter 1
You should do the exercises in Chp 1, especially (Parsing)
Exercise 1.3.6; (Substitution) Exercise 1.3.8; (Truth tables)
Exercise 1.3.10; (Tautology) Exercise 1.3.15; (Translation)
Exercises 1.4.1, 1.4.2.
Next, try the Knights & Knaves Problems (Exercises 1.5.1).
In addition, you will need to read Chapter 2 before the first test.
Unit 2: The main emphasis in this section is Chapter 3. Be sure
to read this chapter carefully, and to do all the exercises. This is a
tricky topic - some find it the hardest of the course - but if you pay
attention to what you can learn from the exercises, you will succeed.
Ask me for help if you need it.
Step-by-step explanation of the
"Vulcans, Romulans, and Klingons" problem. (End of section 3.2)
Summary sheet for natural
deduction (Big print
version for those with poor eyesight)
Note: These will also be useful in Chp 5 (which is why
there are 4 rules you haven't met yet!).
The exercises done in class
(with answers)
(These also appear in the book.)
Chapter 4 is somewhat less technically demanding, but again, do the exercises to get a feel for this topic.
NOTE to those using old editions of the book:
There are some typos in the earlier editions of the text in a
couple of the exercises, specifically on pages 91, 95, and 98:
here are corrected versions of
those pages. This has been fixed in the current Version
("2012.5.31") of the text
We did a worksheet on tableaux (and more derivations!) in Friday's class:
Here are the exercises and solutions to
that worksheet done in class.
Just for fun(!): Some more logic puzzles
(Answers)
Units 3,4: Read Chapters 6, 7 and 8 (Sets, Numbers and Number Theory).
Remember:
you will need a simple (cheap!) calculator, able to do simple
arithmetic. (Or else you can do the calculations in your head!)
Please do not plan to use your cell phone as a calculator, as
this will not be permitted on the next test (indeed as it is not
permitted on any test).
I have put 2 copies of some extra text on the current material (chapters 7-8) in my "binder" in the Maths Lab (H 203). This should help you if you are having problems with mathematical induction, as it contains more worked out examples. You can borrow a copy (from the Maths Lab) and xerox it if you want.
As always, be sure to do all the exercises.
Unit 5: Read Chapter 9 and section 10.2 of Chapter 10.
As ever, there are exercises in the
text; try them (solutions and/or hints at solutions are given at the
end of the section). They will be the basis of Test 4.
You may also find it helpful (even essential!) to look at the extra readings in the Entertainments section.
Practice Test 2 (5 Oct 12)
Some hints at where you can find the solutions.
Practice Test 3 (16 Nov 12)
Test 4 (7 Dec 12)
Hints for Test 4
(And a request for feedback!)
You are permitted to bring to the test an index card (or piece of
paper) 5in by 3in (13cm by 8cm) with whatever notes you want written
on it (but just one side please). Plan it carefully!
I do insist the notes are written by you - no xeroxes!;
do not use somebody else's notes, although you may plan notes together.
Write your name on your notes card -
you must hand in your notes with your test, when you finish it
Friday.
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