## Teaching Mathematics at RHUL

If you are a mathematics student interested in a third year or MSc project in the area of quantum computation or quantum cryptography, please contact me directly.

If you are an undergraduate looking for the course selector page, where you can check out the dependencies of different courses, you need to look here.

Lego Skills

In the Autumn Term 2014, I ran a trial series of workshops for a writing skills course based on using LEGO. This has since been incorporated into the MT121 course.

MT121 - Introduction to Applied Mathematics

In the Introduction to Applied Mathematics course, which is compulsory for all first year mathematics undergraduates, we take some of the fundamental concepts already developed in other courses, particularly those of differential equations and vectors, and apply them. We see that they can be used to describe many aspects of the world around us, from how to line up your shot in snooker, how to fire a catapult (we try not to hit anybody during lectures!) to how to send a rocket to the moon, and how planets orbit the sun.

The final exam only contributes 75% of you mark for this course. There are several sources of continuous assessment that mean you can go into the final exam with a lot of confidence. These include the standard 10% continuous assessment for successful completion of homework, 10% from a writing skills workshop where you build LEGO models, and 5% for completing a Mathematica programming project. There's lots of support available to help you through these various activities.

The course is administered via moodle, where you can find question sheets and lecture notes.

MT345 & 445 - Quantum Information and Coding

The Quantum Information course is available to third and fourth years. The only prerequisite is Linear Algebra, MT280. You do not need to have completed another course in quantum as we work from a completely different perspective, and often different notation a well! After revising all the linear algebra that you need (which we have to extend to complex vector spaces), we use this to set some simple postulates for the way that the world works, and we explore their consequences. This touches on current research in places.

We discuss concepts such as determinism - we are used to thinking of the world as being entirely predictable. Perhaps there are some things we can't predict (such as the result of tossing a coin), but this is only down to a lack of knowledge. If we knew enough, we believe we could predict it. However, Quantum Mechnics throws this notion out the window. We prove that Quantum Mechanics is inherently unpredictable, and describe a simple way to prove that the world around us must be like this! Even better, we can use its inherent unpredictability to achieve perfect security in communications. We also describe the basics of a Quantum Computer which, when built, will be radically different in its computational capabilities to any computer ever built.

This course is only taught every other year (Spring term 2015, 2017...) and is administered via moodle, where you can find question sheets and lecture notes.

MT341 & 441 - Channels

The channels course, available to third and fourth years with no prerequisites, is really an introductory course to infomration theory. We study the basic concepts of things like information and how to quantify it. With these in place, it is possible to go forward and understand the central concepts of the field. This is illustrated with two of the cornerstone results of information theory - the noiseless and noisy channel coding theorems.

These theorems are vital to the way that our information driven society works. The first, the noiseless coding theorem, describes how much a data file (text, image, video) can be compressed without losing any of the information it conveys. On the other hand, the noisy coding theorem describes how efficiently you can communicate when there are errors getting in the way. This underpins technology that we now take for granted - how come a usb stick can store data without using any power; without needing to be regularly error corrected for the faults that are constantly occurring as it gets bashed around in your pocket?

The course is administered via moodle, where you can find question sheets and lecture notes. While there are no official prerequisites, a familiarity with probability theory is very helpful. This course, while not essential, provides an interesting contrast to some of the material found in the quantum information and computation course which is taught in alternate years.