Here are my supervision
notes. The process of updating them is clocked by my
supervisions: i post my discussions of an example sheet after i have
concluded all supervisions on that sheet. Discussions of later sheets
(or rather versions of later sheets from earlier years) exist of
course and if you are a Part III student from outside Cambridge or
have a legitimate need for some for other reasons you can email me to
ask for the entire .pdf. I have notes also on example sheets from
Prof Hyland's lectures, but they are more fragmentary and in any case
I am not sure that the examples sheet from as far back as 2007/8 are
visible anywhere. Any reader who finds them on the web and wants my
discussion answers is welcome to email me with the URL, and I will
make my discussions available.
Finally here you can read some
discussion answers of old tripos questions. Thery are a bit scrappy, and definitely work-in-progress, so i won't demur if people want enhancements.
Here is Randall Holmes' very
nice proof (in ZF) that, for all X, the class of things hereditarily
smaller than X is a set (and without using choice!)
are some model tripos questions
that you might find helpful for your revision, and here is a question more in the style of an example
sheet question. These all have model answers which i will show you
(or your supervisor) if you submit an answer of your own.
An answer to Hyland sheet 2 q 9 (2007/8 edition).
It is a proof that for any vector space all its bases are the same size.
a brief discussion of the subtleties of deducing the axiom of the
empty set from the axiom of infinity.
You might like to have a look at my notes (to be published
one day, eventually! by CUP) on the
axioms of set theory. A more recent version is
here. It lacks the chapter on the axiom of choice, but that chapter is itemised separately
Languages and Automata
You will find very useful Prof Pitts' materials on Languages
and Automata on the computer laboratory's course pages; ditto his
CS 1B materials .
There is a slight mismatch between his materials and Dr Chiodo's in
that our course covers push-down automata and context-free languages
(which CS doesn't - i think!) and we do not cover lambda calculus whereas
they do. Nevertheless, Prof Pitts' materials come with the highest
possible recommendation. He is sensationally organised and the
materials are beautifully set out.
Here are my Regular Languages
and Finite Automata materials (originally written for Queen Mary)
in pdf format. I am greatly endebted to Chloë Brown for creating
a version in html . This
version is preferable in various ways to the pdf version, since the
answers to the exercises are not immediately visible in the way they
are in the .pdf version, but can be seen only when you click on the
link. Thank you, Chloë Brown!! Here
is a file of answers to the coursework questions at the end .
Some of you have asked me whether Regular languages are good for
anything. These notes of Arthur
Norman's on the hardness of the equality problem for regular
languages may be of interest to strong students.
Dr Chiodo has
put up a link to some Exam
This discussion answer to Sheet 4 Question 4 Part (i) of Dr Chiodo's 2017 materials might be useful.
Here is a discussion of 2017 paper 4 question 4H.
Here is a discussion of 2017 paper 3 question 11H.
This discussion answer to Sheet 2 Question 1 Part (d) of Dr Chiodo's 2016 materials might be useful.
Here is a discussion of the last part of 2009 paper 6 question 3 of the CS Tripos.
Here is the pdf file of the notes of Richard Crouch's second-year course at
the University of Nottingham on Languages, Computation and Automata. They do not correspond exactly to any course here, but students might find them useful: they are very meaty.
I found this rather nice lambda-calculus reduction workbench. I hope you will find it
Materials for 1b Computer Science.
Materials for 1a Computer Science .
Materials for Part III Mathematics .
Materials for Logic-For-Linguists.
Materials for Part II Mathematics .
Materials for Part IV Mathematics .
Materials for the Computer Science M. Phil .