**Directors of the specialization**: Antti Kupiainen and Jani Lukkarinen

**Mandatory core courses**, at least 15 cr

MAST30132 Introduction to Real and Fourier Analysis (5 cr)

MAST31002 Functional analysis (10 cr)

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)

**Specialization courses**, at least xx cr from the following list

MAST31302 Hamiltonian dynamics (10 cr)

TCM309 Kinetic theory (10 cr)

MAST31303 Quantum dynamics (10 cr)

MAST31301 Specialization course in mathematical physics (10 cr)

TCM310 Stochastic methods (10 cr)

MAST30130 Introduction to Mathematical physics A

MAST30131 Introduction to Mathematical physics B

MAST30001 **Master's thesis seminar (5 cr)**

MAST30000 **Master's thesis (30 cr) (the link includes grading scale and criteria)**

Other advanced courses from the list of core courses, mathematics, applied mathematics, statistic courses and/or courses from other programmes as approved in personal study plan.

Other requirements, such as possibly required bachelor's level mathematics courses (the module 0-35 cr other studies) are explained here:

Antti Kupiainen and Jani Lukkarinen

Antti Kupiainen and Jani Lukkarinen

Mandatory requirement for courses in Physics: At least 20 cr. from Physics courses, other than Mathematical Methods for Physicists I, II, and III (FYMM I-III). Suggested topics: Analytical Mechanics, Quantum Mechanics, Statistical Mechanics, Quantum Statistics.

Example 1

This example concerns a student interested in learning a solid background in mathematical methodology in analysis and probability, as well as in their applications in Physics. The student considered in the example did not do Vector analysis II in the candidate studies so these courses need to included in the master studies.

**Year 1, Autumn:**

Vector analysis II, 5 cr.

MAST30132 Introduction to Real and Fourier Analysis , 5 cr.

Functional Analysis, 10 cr.

Stochastic Methods (TCM 310), 10 cr.

or Probability theory I and II, 5 cr. + 5 cr.

**Year 1, Spring:**

Partial differential equations I, 10 cr.

or Complex Analysis I and II, 10 cr.

Fourier analysis I and II, 5 cr. + 5 cr.

Physics or numerics courses, in total 10 cr.,

or Introduction to mathematical physics, 10 cr.,

or Hamiltonian dynamics, 10 cr.,

or Quantum dynamics, 10 cr.,

or Kinetic Theory (TCM 309), 10 cr.,

or other courses taught by Mathematical Physics group members

**Year 2, Autumn:**

Physics courses,

and/or courses taught by Mathematical Physics group members,

and/or advanced Mathematics courses,

in total 15 cr.

Pro gradu work seminar starts

Pro gradu work starts

**Year 2, Spring:**

Pro gradu, 30 cr, completed + Pro gradu seminar 5 cr.

Introduction to mathematical physics, 10 cr.,

or Spectral theory, 10 cr.,

or Hamiltonian dynamics, 10 cr.,

or Quantum dynamics, 10 cr.,

or Kinetic Theory (TCM 309), 10 cr.,

or other courses taught by Mathematical Physics group members,

or other courses supporting the Pro Gradu -work,

in total 10 cr.

Example 2

This example concerns a student who is interested in Mathematical physics and who is interested in applying to graduate school after completing their master's degree. The example is based on the assumption that the student has chosen Vector analysis II courses in their candidate studies.

**Year 1, Autumn:**

Physics course or numerics course, 5 cr.

Introduction to Real and Fourier Analysis , 5 cr.

Functional Analysis, 10 cr.

Probability theory I and II, 5 cr. + 5 cr.

or Stochastic Methods (TCM 310), 10 cr.

**Year 1, Spring:**

Partial differential equations I, 10 cr.

or other supporting Mathematics courses

Fourier analysis I and II, 5 cr. + 5 cr.

Introduction to mathematical physics, 10 cr.,

or Hamiltonian dynamics, 10 cr.,

or Quantum dynamics, 10 cr.,

or Kinetic Theory (TCM 309), 10 cr.,

or other courses taught by Mathematical Physics group members,

or Physics or numerics courses, in total 10 cr

**Year 2, Autumn:**

Physics courses,

and/or courses taught by Mathematical Physics group members,

and/or advanced Mathematics courses,

in total 15 cr.

Pro gradu work seminar starts

Pro gradu work starts

**Year 2, Spring:**

Pro gradu, 30 cr, completed + Pro gradu seminar 5 cr.

Introduction to mathematical physics, 10 cr.,

or Spectral theory, 10 cr.,

or Hamiltonian dynamics, 10 cr.,

or Quantum dynamics, 10 cr.,

or Kinetic Theory (TCM 309), 10 cr.,

or other courses taught by Mathematical Physics group members,

or other courses supporting the Pro Gradu -work