Elliptic Curves have motivated a large part of the mathematics of the last century: in particular, they have allowed for the famous proof of Fermat's Last Theorem. They still are an area of active research, in pure mathematics (for example, motivated by the Birch and Swinnerton-Dyer conjecture, one of the seven Clay Math problems) but also in applied mathematics in relation to many applications in cryptography.

Over the complex numbers, elliptic curves have a particularly simply description: an elliptic curve is just a complex torus. But this conceals a lot of their inner structure! Trying to classify them up to isomorphism leads into many interesting problems, such as the idea of moduli spaces, the mysterious j-invariant and doubly periodic functions on the complex plane.

These elliptic curves come with a group structure (either coming from their description as a torus or by considering a chord-tangent group law, the two being related by the Weierstrass function), and we can thus consider their endomorphisms (the group homomorphisms from the elliptic curve to itself). Every elliptic curve over the complex numbers comes with a multiplication by endomorphism for every integer , but for most of them, that's the end of the story. Special elliptic curves, with more endomorphisms, are said to have complex multiplication.

The study of elliptic curves with complex multiplication relates perhaps surprisingly with class field theory and the study of quadratic imaginary fields (fields of the form for positive integers ); there is a direct relation between isomorphism classes of elliptic curves with given endomorphisms and corresponding quadratic imaginary fields.

Join us in MS.04 at 7:30 to learn about all this and more! Don't miss it - this is probably the last Discussion Group for a while due to exams starting for many of us. We will of course translate ourselves to the pub afterwards.

This term only, for all your revision and coffee based needs, Maths Café will be running twice a week under the guise of Revision Café. Every Wednesday and Friday from 1 PM to 3 PM, feel free to come have a cup of tea/coffee and get help with any course you need to revise for.

This term only, for all your revision and coffee based needs, Maths Café will be running twice a week under the guise of Revision Café. Every Wednesday and Friday from 1 PM to 3 PM, feel free to come have a cup of tea/coffee and get help with any course you need to revise for.

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

1st Year Linear Algebra Crash Course.

Run by Ben Simpson and Colin Dold.

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

1st Year Differential Equations Crash Course.

Run by Sam Derbyshire.

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

2nd Year Differentiation Crash Course.

Run by Praveen Amarasinghe

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

2nd Year Algebra II Crash Course.

Run by Cosmin Davidescu and Richard Howell-Peak.

WMS Module Crash Courses for first and second year modules are already underway! Details are as follows:

1st Year:

Mon 25th May: GEOMETRY AND MOTION (MS.01, 3pm-5pm)

Tues 26th: ANALYSIS 2 (MS.01, 3pm-5pm)

Wed 27th: LINEAR ALGEBRA (MS.01, 3pm-5pm)

Thurs 28th: DIFFERENTIAL EQUATIONS (MS.01, 3pm-5pm)

Second Year:

Fri 29th: DIFFERENTIATION ( MS.04, 3pm-5pm )

Thurs 4th: ALGEBRA 2 (MS.01, 3pm-5pm)

Fri 5th: PDE'S (MS.01, 3pm-5pm)

Mon 8th: METRIC SPACES ( MS.04, 3pm-5pm )

Sorry for the delay!

(Updated places in red.)

2nd/3rd Year Introduction to Partial Differential Equations Crash Course.

Run by Mike Scott.

2nd/3rd Year Metric Spaces Crash Course.

Run by Dave McCormick and Justin Millette.

NB: Time Subject to Change.

DGs are back this Monday for a look at the fascinating world of algebraic number theory! If you feel like learning about some interesting mathematics in a relaxed setting after all those boring exams, feel free to join us in MS.04 this evening at 7:30 PM. Following the DG we'll, as usual, head on to the pub.