Department of MathematicsProf Simon Salamon

Mathematics atKing’s College London

• Brief introduction to KCL• Why study mathematics at KCL?• What’s it like to be here?• University versus A-level maths

Mathematics at King’s College London

15,500 (UG) + 10,500 (PG) studentsMember of the Russell groupTwelve Nobel prize winnersMany nationalities Approx 50/50 gender balanceAround 200 undergraduate programmes

.

King’s is big & diverse

Organised in Faculties

Life Science & Medicine

Dental Institute

Psychiatry, Psychology & Neuroscience

Nursing & Midwifery

Arts & Humanities

Law

Social Science & Public Policy

Natural & Mathematical Sciences

Departments

MathematicsInformaticsPhysicsChemistry

Faculty of Natural & Mathematical Sciences

James Clerk Maxwell:

Theory of electromagnetism (1865)

Maurice Wilkins, Rosalind Franklin:

Helical structure of DNA (1953)

Professor Peter Higgs (2013)

Three further Nobel prizes in physics

King’s College has a long line of distinguished alumni.

Why King’s

• Distinguished history• High in international league tables • Central London location• Excellent library (in Chancery Lane)• East Wing of Somerset House• Expansion into Bush House

Bush House

“…the Bush House buildings will provide approximately 300,000 square feet of additional space for student study and social space, new teaching facilities…”

King’s is expanding

Why Maths at King’s?

• One of the oldest and most established mathematics departments in London and the UK

• All faculty members are internationally recognised• Two members of staff are FRS• 4th in UK for research output in REF 2014• Strong links with:

other maths departments in UK and abroad, the City's financial institutions, biomedical sciences ...

What’s it like to be here?

• Wide variety of courses and options• All have classes in addition to lectures• 'Drop-in' sessions and office hours• Friendly and approachable lecturers• Computer facilities for students• Dynamic student society: MathSoc

- runs various social events- annual weekend in Windsor Great Park

24 Junes 2015

24 June 2015

Our Undergraduate Programmes

Mathematics with Management & Finance BSc Mathematics BScMathematics MSciMathematics & Philosophy BA Mathematics & Physics BSc and MSciNEW Mathematics with Statistics BSc

Visit our website

www.kcl.ac.uk/nms/depts/mathematics

CoursesCourses typically include:FIRST YEARCalculus I Calculus II Linear Methods Numbers and Functions Introduction to Abstract Algebra Introduction to Dynamical Systems Probability and Statistics IGeometry I

SECOND YEARAnalysis I Linear Algebra Geometry of Surfaces

PDE's and Complex VariablesIntermediate Dynamics Groups and Symmetries Probability and Statistics IILinear Models and Regression Analysis Applied Analytic Methods Discrete Mathematics Elementary Number Theory

THIRD YEARIntroductory Quantum Theory Real Analysis IIQuantum Mechanics II Complex AnalysisSpecial Relativity and Electromagnetism Fourier AnalysisSpace-Time Geometry & GR TopologyNumerical Methods Rings and ModulesMathematical Finance I Representations of Finite GroupsMathematical Finance II Galois TheoryMathematical BiologyTheory of Complex Networks Mathematical Education Theory of Collective Behaviour

FOURTH YEARLie Groups and Lie Algebras Algebraic Number Theory Metrics and Banach Spaces Probability TheoryOperator Theory Fourier Analysis Foundations of Mathematical Physics Algebraic Geometry Quantum Mechanics IINonlinear analysisQuantum Field Theory Strings and Branes Advanced General Relativity Supersymmetry Equilibrium Analysis of SystemsDynamical Analysis of SystemsTheoretical Physics Project Elements of Statistical LearningMathematics ProjectRare Events and Large DeviationsComplex Systems Project

Our Research

Pure maths research groups:AnalysisGeometryNumber Theory

Applied maths research groups:Financial MathematicsStatisticsTheoretical PhysicsDisordered Systems

3 facts of university maths

1. It is not just an extension of A-level mathsMemorizing model solutions will no longer work

• At school you may have sat in the back seat • University teaches you to drive• Excellent A-level student may well be average at

University• Average A-level student may well be excellent at

University

3 facts of university maths

2. Everything is connected to everything else

• Deep problems in one field are usually connected to deep problems in another

• You must have an open mind and broad interests• For example: geometry is used in quantum theory, quantum theory is used in finance, number theory is used in cryptography...

3 facts of university maths

3. Maths at university is more abstract: you must be able to generalize and turn concepts upside down

• Infinite sums can give finite results• Dimensions need not be 1, 2 or 3 (nor integral nor finite)• Time is a fourth dimension but there may be others• XY is different from YX for many objects X and Y

Get used to asking 'what if ' all the time...

Thank you!