| Unit name | Algebraic Geometry |
|---|---|
| Unit code | MATHM0036 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Babaee |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
MATH21800 Algebra 2 MATH20006 Metric Spaces |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
N/A |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit Aims
The objective of this unit is to provide an introductory overview of algebraic geometry while also touching upon the fascinating interplay between algebra, geometry, and combinatorics within the field of combinatorial algebraic geometry.
Unit Description
Algebraic geometry delves into the exploration of systems of polynomial equations, investigating the geometric structures known as algebraic varieties that emerge as solution sets. This course is designed to equip students with fundamental algebraic tools essential for understanding and analysing the geometry of these algebraic varieties. Furthermore, we delve into the study of combinatorial algebraic geometric objects known as toric varieties. This exploration allows us to revisit numerous examples from the course, offering fresh insights and perspectives.
Relation to Other Units
This unit replaces Lie Groups, Lie Algebras and their Representations
Students who are successful in this course will learn basic constructions and theorems of algebraic geometry. They will be able to compute certain algebraic invariants of geometric objects such as degree and dimension. They will understand the proofs of basic results in algebraic geometry. They will gain an appreciation of the interplay between algebra and geometry, and finally. they will be able to define toric varieties and read off certain algebro-geometric properties of toric varieties from combinatorial data.
Syllabus
There are 3 lecture per week and every other week one session is designed as a problem session. The course is based on the lectures and exercises. The basic lecture notes will be posted and solutions to most of the exercises will be distributed. The last 2 weeks of the course will be devoted to review and revision, and in this time exercises (both assigned and not assigned) will be addressed. Besides the problems classes, there is also a weekly office hour during which students can ask questions about lectures and exercises.
The pass mark for this unit is 50. The final mark is calculated as follows:
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0036).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
