49 pages + 13 pages of solutions

Full notes from omegasets.dvi.gz or omegasets.ps.gz or omegasets.pdf.gz .

**Forms of recursion and induction**

**Abstract**:
A brief introduction to subrecursive hierarchies and related
topics, but not intended as a detailed account. The notes deal with
such topics as the various kinds of recursions (over the natural
numbers), the primitive recursive functions and the way these are
stratified, the complexities beyond primitive recursion as can be
generated by jump operators.

60 pages + 17 pages of solutions

Full notes from
FormsRec.dvi.gz
or
FormsRec.ps.gz
or
FormsRec.pdf.gz
.

**$\lambda$-calculi**

**Abstract**:
An introduction to the untyped, and the simply typed
$\lambda$-calculus, and G\"odel's T as a $\lambda$-calculus. The
emphasis is on the way natural number gadgets are simulated amd
represented in the various calculi.

46 pages + 12 pages of solutions

Full notes from
lcalculus.dvi.gz
or
lcalculus.ps.gz
or
lcalculus.pdf.gz
.

** While loops and programs**

**Abstract**:
An short introduction to the denotational semantics of While loops.

29 pages + 6 pages + 8 pages of solutions

Full notes from
While.dvi.gz
or
While.ps.gz
or
While.pdf.gz
.

** Category theory**

**Abstract**:
An introduction to category theory in four chapters dealing with the
basics, functors and natural transformations, various kinds of limits
and universal solutions, and cartesian closed categories. Contains
many exercises (and eventually will contain a fairly full set of
solutions). The best introduction to the subject ever written.

133 pages + solutions to be written

Full notes from
CatTheory.dvi.gz
or
CatTheory.ps.gz
or
CatTheory.pdf.gz
.

** Domains for recursion**

**Abstract**:
A short introduction to domains from various forms of recursion over
the natural numbers.

19 pages + 14 pages of solutions

Full notes from
Domains.dvi.gz
or
Domains.ps.gz
or
Domains.pdf.gz
.

** The coverage technique for enriched posets**

**Abstract**:
The coverage technique is used to convert a poset (perhaps with some
extra structure) into a complete poset of a certain kind, usually a
frame or quantale. These notes describe the basics of the method with
a decent selection of examples. Especially written for the hard of
hearing.

84 pages

Full notes from
Coverages.dvi.gz
or
Coverages.ps.gz
or
Coverages.pdf.gz
.