Algebraic Geometry is the study of algebraic sets (or varieties), all those defined by polynomial equations in several variables. Although the subject probably goes back to Descartes, it is still one of the most thriving research areas of pure mathematics. In addition, Algebraic Geometry is connected to many other areas of mathematics such as number theory for example. Our aim is to introduce basic notions of algebraic geometry in the most down-to-earth fashion. After defining affine and projective algebraic sets and studying their basic properties, we will mostly focus on the case of algebraic curves. One of the main aims of the course is to prove the Bezout's theorem about intersection of two plane projective curves.

In this course, we will aim to introduce a language for (first order predicate) mathematical logic and proceed to study the interplay between the notions of 'truth' and 'provability' in the propositional and first order predicate 'versions' of logic. We will then aim to study computability, via register machines, recursive functions and coding, and try to use these concepts to show that first order predicate logic is undecidable.

The purpose of this course is to provide an elementary introduction to the methods of Algebraic and Geometric Topology via the homology of simplicial...

The purpose of this course is to provide an elementary introduction to the methods of Algebraic and Geometric Topology via the homology of simplicial complexes. A good grounding in Linear Algebra is assumed, but with that exception the course is self contained.

Ancient Languages and Cultures|Classics|Early Modern History|Latin

Teaching Delivery: This module is taught in 10 weekly lectures.

Content: Due to the practical nature of this module, there are only 20 places available.

The...

Teaching Delivery: This module is taught in 10 weekly lectures.

Content: Due to the practical nature of this module, there are only 20 places available.

The aim of the module is to introduce students to the materials and methods employed in the production of written documents on stone, papyrus and parchment and to familiarize them with the historical development of Latin scripts. These include Roman capitals and cursives, and Insular, Merovingian, Caroline, Beneventan and Gothic scripts. This module will also train students in the skills of identifying different writing styles and transcribing Latin texts.

Skills: Participants should develop an eye for detail, gain an appreciation of the links between the history of writing and its cultural context, and acquire useful tools and techniques for deciphering difficult handwriting of any kind.

Module texts: Students will be provided with handouts.