# Unit information: Topics in Modern Geometry 3 in 2018/19

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Unit name Topics in Modern Geometry 3 MATH30001 10 H/6 Teaching Block 1A (weeks 1 - 6) Dr. Jordan Not open MATH20200 Metric Spaces and MATH21800 Algebra 2. MATH33300 Group Theory is helpful but not essential. Students may not take this unit if they have taken the corresponding Level H/6 unit Topics in Modern Geometry 3. Math 33300 (Group Theory) is helpful but not essential. School of Mathematics Faculty of Science

## Description

Unit aims

To provide an introduction to to various types of geometries which are all central to modern research. The unit will look at basic concepts in algebraic geometry which is a requirement for research projects in areas of geometry, number theory, and advanced algebraic geometry.

Unit description

The aim of this course is to develop basic geometric tools to explore properties of systems of polynomial equations and varieties. The unit will start by giving the key definitions of affine varieties, the Zariski topology and manifolds with several examples given to illustrate the definitions. The unit will provide an introduction to algebraic curves, smoothness and tangent spaces of varieties.

Relation to Other Units

The course expands ideas introduced in MATH21800 Algebra 2, and has relations to MATH20200 Metric Spaces, MATH33300 Group Theory and MATHM1200 Algebraic Topology.

## Intended learning outcomes

Learning Objectives

Students who successfully complete the unit should:

• be able to clearly define topological groups, discrete groups and manifolds and *be familiar with examples of all three;

use techniques from abstract algebra and mathematical analysis to solve problems in geometry;

• be familiar with aspects of Lie groups;
• be familiar with aspects of algebraic curves.

## Teaching details

Lectures, including examples and revision classes, supported by lecture notes with problem sets and model solutions.

## Assessment Details

80% Examination and 20% Coursework.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.