Credits:
 6 
Level:
 Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2

Assessment:
 EX 100% 
Supplementary Assessment:  MA40188 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take MA30204 
Description:
 NB. This unit is only available in academic years starting in an odd year.
Aims: This is an advanced pure mathematics course providing an introduction
to classical algebraic geometry via plane curves. It will show some of the links with other branches of mathematics.
Learning Outcomes: At the end of the course students should be able to use homogeneous coordinates in projective space and to distinguish singular points of plane curves. They should be able to demonstrate an understanding of the difference between rational and nonrational curves, know examples of both, and be able to describe some special features of plane cubic curves.
Content: To be chosen from: Affine and projective space. Polynomial rings and homogeneous polynomials. Ideals in the context of polynomial rings,the Nullstellensatz. Plane curves; degree; Bezout's theorem. Singular points of plane curves. Rational maps and morphisms; isomorphism and birationality. Curves of low degree (up to 3). Genus. Elliptic curves; the group law, nonrationality, the j invariant. Weierstrass p function. Quadric surfaces; curves of quadrics. Duals.

Programme availability:

MA40188 is Optional on the following programmes:
Department of Computer Science
 USCMAFB13 : BSc (hons) Computer Science with Mathematics (Fulltime)  Year 3
 USCMAKB14 : BSc (hons) Computer Science with Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
Department of Physics
 USXXAFM01 : MSci (hons) Mathematics and Physics (Fulltime)  Year 4
