Mathematical Physics For Students

The aim of mathematical physics is to adapt concept and methods of pure mathematics to study physical problems. A student interested in mathematical physics may choose to have as a major for her/his Master Degree (FM-tutkinto) either Mathematics or Theoretical Physics. The Department of Mathematics and Statistics and the Department of Physics offer a wide range of courses pertaining to Mathematical Physics education. On the basis of such offer the interested student can compose a study plan with emphasis on the mathematical or on physical side according to her/his preferences.

Below a list of recommended courses (most courses are available in english if there is demand).

Basic and Intermediate courses (Perus-Ja Aineopinnot).

Mathematics:

Please refer also for updates to the dedicated web page hosted by the Mathematics and Statistics Department.

Vector Analysis (Vektorianalyysi)
Measure and Integration theory (Mitta ja integraali )
Topology I (Topologia I )
Real Analysis I (Reaalianalyysi I)
Introduction to Probability theory (Johdatus todennäköisyyslaskentaan)

Theoretical Physics:

Please refer also for updates to the dedicated web page hosted by the Physics department.

Mathematical Methods I (Matemaattiset apuneuvot I)
Mathematical Methods II (Matemaattiset apuneuvot II)
Mathematical Methods for Physics I (Fysiikan matemaattiset menetelmät Ia)
Mathematical Methods for Physics II (Fysiikan matemaattiset menetelmät IIa)
Statistical Physics I (Statistinen fysiikka I)

Advanced courses (Perus-ja Aineopinnot).

Mathematics:

Please refer also for updates to the dedicated web page hosted by the Mathematics and Statistics Department.

Introduction to Mathematical Physics (Johdatus matemaattiseen fysiikkaan)
Foundations of Functional Analysis (Funktionaalianalyysin peruskurssi )
Function theory I (Funktioteoria I )
Function theory I (Funktioteoria II )
Partial Differential Equations (Osittaisdifferentiaaliyhtälöt)
Differential Geometry (Johdatus differentiaaligeometriaan)
Riemannian Geometry (Riemannin geometria)
Theory of Probability (Todennäköisyysteoria)
Stochastic Processes (Stokastiset prosessit)
Algebraic Topology I (Algebrallinen Topologia I)
Topology II (Topologia II)
Linear Algebra and Matricial Calculus II (Lineaarialgebra ja matriisilaskenta II)
Algebra II (Algebra II)
Real Analysis II (Reaalianalyysi II)
Principal bundle and Yang-Mills theory (Pääsäiekimpuista ja Yang-Mills -teoriasta)

Theoretical Physics:

Please refer also for updates to the dedicated web page hosted by the Physics department.

Mathematical Methods for Physics III (Fysiikan matemaattiset menetelmät IIIa )
General Relativity (Yleinen suhteellisuusteoria)
Quantum Mechanics II (Kvanttimekaniikka)
Statistical Physics II (Statistinen fysiikka II)
Introduction to Quantum Field Theory
Path Integrals
Theoretical Particle Physics
Introduction to SUSY (Johdatus Supersymmetriaan)
String Theory I
Quantum Mechanics and Computing
Many Body Physics (Monen kappaleen ilmiöt)
Hydrodynamics (Hydrodynamiikka)

Courses taught by the Mathematical physics group personnel.

The topic of the course "Introduction to mathematical physics" may vary from semester to semester. It is often aimed at
providing an introduction to hot topics in contemporary mathematical physics.

Stochastic methods in physics and biology (spring 2012) (Paolo Muratore-Ginanneschi)
Introduction to mathematical physics, Fall 2011: Multiscale Methods (Paolo Muratore-Ginanneschi)
Introduction to mathematical physics, Spring 2011: Stochastic particle systems (Antti Kupiainen)
Introduction to Hopf algebras and representations, Spring 2011 (Kalle Kytölä)
Introduction to mathematical physics, fall 2010: Spectral theory (Jani Lukkarinen)
Introduction to Mathematical Physics, spring 2010: Quantum Probability (Antti Kupiainen)
Stochastic methods in physics and biology (spring 2010) (Paolo Muratore-Ginanneschi)
Mathematical modeling, fall 2009 (Stefan Geritz and Paolo Muratore-Ginanneschi)
Introduction to mathematical physics, spring 2008: Quantum Dynamics (Jani Lukkarinen)
Stochastic population models, fall 2008 (Stefan Geritz and Paolo Muratore-Ginanneschi)
Introduction to mathematical physics, spring 2007: Dynamical Systems and Chaos (Paolo Muratore-Ginanneschi)
Introduction to mathematical physics: Turbulence and Stochastic Differential Equations (Antti Kupiainen)
Introduction to mathematical physics, spring 2007: Dynamical Systems and Chaos (Alain Schenkel)
Introduction to mathematical physics, fall 2002: Conformal Field Theory (Antti Kupiainen)

Opportunities

Professor Kupiainen is willing to supervise

Master's Theses, Ph.D. Theses, and the like.

He may also assign

reading courses in diverse fields of mathematics and physics.

The latter include subjects such as Stochastics, Partial Differential Equations, Dynamical Systems, Turbulence, and Field Theory. If interested, please contact Kupiainen directly.

Other training activities

During each semester, the Mathematical Physics Group also has a

weekly seminar meeting.

Moreover, the students have organized informal "study groups" concentrating on a chosen subject.