| 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 |
Why is this unit important?
Algebraic geometry explores systems of polynomial equations on the algebraic side, structures known as algebraic varieties that emerge as the solution sets. This course is designed to equip students with fundamental algebraic tools essential for understanding and analysing the algebra-geometric properties of these algebraic varieties. Furthermore, the course delves 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 from a combinatorial and polyhedral point of view.
Algebraic geometry is taught as a foundational advance course in any major department in mathematics. Understanding algebraic varieties is vital across diverse fields like number theory, cryptography, combinatorics, probability and physics. Toric varieties provide a fertile testing ground and providing examples in algebraic geometry and related topics. This unit enhances students' analytical skills, preparing them to explore modern mathematical research landscapes which is aligned with the University of Bristol’s research strategy.
How does this unit fit into your programme of study
This unit is integral to our mathematics curriculum and our strategy to expand algebraic geometry within the department. This course is aligned with courses in algebra, geometry, and combinatorics, it deepens students' understanding of abstract algebra and computational aspects, laying a solid foundation for research pursuits. Complementing advanced topics like Algebra 2, number theory, and algebraic topology, it provides a good mathematical education. A basic course in algebraic geometry with an eye towards combinatorial algebraic geometry equips students with advanced problem-solving abilities, encouraging them for further studies and research in mathematics.
An overview of content
The course covers the following topics.
How will students, personally, be different as a result of the unit
The students will develop a keen appreciation for the intricate interplay between algebra, geometry and combinatorics. Furthermore, they will also gain maturity as they reconsider and substitute foundational concepts like Euclidean topology with Zariski topology, thus building their mathematical understanding upon a different framework. Also, the student-led problem classes will help the students to practice presentation skills and boost their ability to articulate complex abstract ideas in simpler terms
Learning Outcomes
The students completing this course successfully will be able to
The unit will be taught through a selection of lectures, online materials, independent activities such as problem sheets and other exercises, problem classes and office hours.
Tasks which help you learn and prepare you for summative tasks (formative):
Non-assessed formative coursework and problem classes during the term which help the students prepare for the assessment. Student-led problem classes are with group discussion.
Tasks which count towards your unit mark (summative):
50% timed examination, two coursework assignments each worth 25%
When assessment does not go to plan
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. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
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.
