All posts by Ian Stark

Festival of Creative Learning

As noted in Tuesday’s lecture, next week gives a break from all classes with the University’s Festival of Creative Learning. There’s a cascade of events at the calendar and blog; I’ve just picked out a few here that I liked.

Links: Festival home page; Event calendar; Blog

Picture of baked goods Mathematical Bake-Off
Monday 20 February

“Leading mathematicians from the School will explain their cutting-edge research using delicious pastries”

Links: Book event; More information

Workshop poster Data and Democracy
Monday 20 February

Data collection and digital footprint; workshops on mass surveillance, anonymity and advertising.

Links: Book event; More information

Escape with Fermat’s Lost Proof
Wednesday 22/Thursday 23 February

Find the missing proof and escape the locked room.

Links: Book Wednesday; Book Thursday; More information

Escher tesselation
Exploring Escher: Mathematical Printmaking
Wednesday 22 February

Create your own linocut prints.

Link: Book event

Lecture 9: Trees and XML

Title slide

Slides : Recording

From the strict rectangles of structured data to the more generous triangles of semistructured data. This morning’s lecture gave an overview of what kind of data is seen as “semistructured”; the idea of trees as a mathematical model of data; the particular form of trees in the XPath data model; and their textual representation in XML — the Extensible Markup Language.

XML also has a large number of domain-specific variants. These are all valid XML, and use standardised sets of element types to give a custom language for representing data relevant to a particular field: from musical scores to financial trading.
Continue reading Lecture 9: Trees and XML

Tutorial Notes and Exercises

Tutor notes and solutions for Tutorial 2 are now on the tutorial page, together with next week’s exercises. Tutorial 3 is about formulating queries in tuple relational calculus and finding ways to compute them in relational algebra.

Have a look at the exercises now, and if you have questions about anything then ask on Piazza or after lectures.

Lecture 6: Tuple Relational Calculus

Title slideToday, another language for talking about databases. This one is the Tuple Relational Calculus for writing queries that describe information to be extracted from the linked tables of a relational database. There’s a separation of roles here: the tuple relational calculus is good for succinctly stating what we want to find out; while relational algebra from the last lecture describes how to combine and sift tables to extract that information from the data. We distinguish what information we want from how to compute it.
Continue reading Lecture 6: Tuple Relational Calculus

Lecture 5: Relational Algebra

Title slideThis morning’s lecture presented a mathematical language for slicing and dicing the structured tables of the relational model: selection, projection, renaming; union, intersection, difference; cross product, join, equijoin and natural join. A key feature of this relational algebra is that just six of these operations are enough to capture an extremely wide range of queries and transformations of data. Database implementors work hard to build highly efficient engines to carry out these operations, which can then support many different kinds of user application.
Continue reading Lecture 5: Relational Algebra

Lecture 4: From ER Diagrams to Relational Models

Title slideToday’s lecture reviewed the high-level conceptual language of ER diagrams and the more concrete structures of the relational model; followed by some recipes for translating from the first into the second. This isn’t always an exact match, and for any particular ER diagram we might go back to its original scenario description to decide how to best represent it as a relational model. Even so, this kind of step-by-step staging towards a fully formal representation is an effective route to capturing the subtleties of real-world systems.
Continue reading Lecture 4: From ER Diagrams to Relational Models