Courses
In the Master's Programme Theoretical and Computational Methods, you tailor according to your plans and existing knowledge a suitable combination of courses in physics, mathematics, chemistry and computer science.

Your personal study plan will ensure that your courses will form a sensible functional combination. See examples of TCM study paths.

The programme comprises 120 credits (ECTS) and it is possible to complete the degree in two academic years. The degree includes 90 credits of advanced studies (incl. the Master’s thesis of 30 credits) and 30 credits of other studies from your or other Master's programmes.

The preliminary syllabus for the academic year 2022-2023 can be found in the Studies service. Make sure that the correct programme is selected on the drop-down menu. The final syllabus will be published in Sisu. Please note, that some courses will not be lectured every academic year.

Ad­vanced stud­ies (90-120)

Com­puls­ory Stud­ies (35 cr)

TCM307 Seminar in Theoretical and Computational Methods (5 cr)
TCM350 Master's thesis (30 cr)
TCM399 Maturity test (0 cr)
Personal Study Plan (included in the Seminar)

Op­tional Course Pack­ages (55-85 cr)

You can select whole course packages or singular courses.

Quantum Physics

TCM302 Quantum mechanics IIa (5 cr)
TCM303 Quantum mechanics IIb (5 cr)
TCM304 Mathematical Methods of Physics IIIa (5 cr)
TCM305 Mathematical Methods of Physics IIIb (5 cr)
TCM322 Quantum Information A (5 cr)
TCM323 Quantum Information B (5 cr)

Statistical Physics

TCM306 Advanced statistical physics (5 cr)
TCM325 Kinetic Theory I (5 cr)
TCM326 Kinetic Theory II (5 cr)

Particle Physics and Cosmology

PAP325 Introduction to particle physics II (5 cr)
TCM327 Quantum Field Theory I (5 cr)
TCM328 Quantum Field Theory II (5 cr)
TCM329 Quantum Field Theory III (5 cr)
TCM332 Quantum Field Theory IV (5 cr)
PAP326 Cosmology II (5 cr)
PAP348 General relativity I (5 cr)
PAP349 General relativity II (5 cr)
TCM308 Lattice field theory (5 cr)
TCM313 Thermal field theory (5 cr)
TCM314 String theory (5 cr)

Condensed matter physics

MATR333 Modelling of biological systems (5 cr)
MATR318 Solid state continuum mechanics II (5 cr)
MATR3031 Solid state physics: crystal structure and atomic dynamics (5 cr)
MATR3032 Solid state physics: electronic structure and properties (5 cr)
TCM324 QM and hybrid QM/MM modeling of bio/chemical systems (5 cr)

Programming and numerical methods

PAP334 Statistical methods (5 cr)
MATR322 Numerical Methods in Scientific Computing (10 cr)
MATR323 Basics of Monte Carlo simulations (5 cr)
MATR324 Monte Carlo simulations in physics (5 cr)
MATR325 Molecular dynamics simulations (10 cr)
MATR326 Tools for high performance computing (5 cr)

Atmospheric sciences

ATM311 Simulations of Formation of Molecular Clusters (5 cr)
ATM312 Aerosol Modelling (5 cr)
ATM313 Biosphere-atmosphere process modelling I (5 cr)
ATM314 Chemical transport modelling II (5 cr)
ATM315 Numerical Meteorology I (5 cr)
ATM316 Numerical Meteorology II (5 cr)
ATM317 Laboratory Course in Numerical Meteorology (5 cr)
ATM377 Introduction to Earth System Modelling (5 cr)

Functional analysis and spectral theory

MAST31002 Advanced topics in Functional analysis (10 cr)
MAST31018 Spectral theory (10 cr)
MAST30172 Partial Differential Equations I (5 cr)
MAST30173 Partial Differential Equations II (5 cr)
MAST31403 Integral equations (10 cr)
MAST30132 Introduction to Real and Fourier Analysis (5 cr)
MAST30129 Fourier Analysis and Distributions (5 cr)

Applied analysis and partial differential equations

MAST30172 Partial Differential Equations I (5 cr)
MAST30173 Partial Differential Equations II (5 cr)
MAST31403 Integral equations (10 cr)
MAST31011 Advanced topics in partial differential equations (10 cr)
MAST31002 Functional analysis (10 cr)
MAST30132 Introduction to Real and Fourier Analysis (5 cr)
MAST30129 Fourier Analysis and Distributions (5 cr)
MAST30127 Advanced Course in Real Analysis (10 cr)

Stochastic analysis

TCM320 Stochastic Methods A (5 cr)
TCM321 Stochastic Methods B (5 cr)
MAST31701 Probability theory I (5 cr)
MAST31702 Probability theory II (5 cr)
MAST31002 Advanced topics in Functional analysis (10 cr)
MAST30132 Introduction to Real and Fourier Analysis (5 cr)

Algebraic and topological methods

MAST31003 Topology II (10 cr)
MAST31005 Algebra II (10 cr)
MAST31026 Riemannian geometry (10 cr)

Courses in Mathematical physics

TCM333 Open Quantum Systems I (5 cr)
TCM334 Open Quantum Systems II (5 cr)
MAST30130 Introduction to mathematical physics A (5 cr)
MAST30131 Introduction to mathematical physics B (5 cr)
TCM325 Kinetic Theory I (5 cr)
TCM326 Kinetic Theory II (5 cr)

Mathematics courses in the Applied mathematics

MAST30172 Partial Differential Equations I (5 cr)
MAST30173 Partial Differential Equations I (5 cr)
MAST31403 Integral equations (10 cr)
MAST31402 Bayesian inversion (10 cr)
MAST31401 Inverse problems 1: convolution and deconvolution (5 cr)

Mathematics of imaging

MAST31002 Advanced topics in Functional analysis (10 cr)
MAST31402 Bayesian inversion (10 cr)
MAST31401 Inverse Problems 1: convolution and deconvolution (5 cr)
MAST31405 Inverse problems project work (5 cr)

Computer science

CSM12101 Design and Analysis of Algorithms (5 cr)
CSM12106 Approximation algorithms (5 cr)
CSM12104 Randomized Algorithms I (5 cr)
CSM12105 Randomized Algorithms II (5 cr)
CSM12107 Combinatorial Optimization (5 cr)
LSI31007 Algorithms in Genome Analysis (5 cr)

Data science

DATA11001 Introduction to Data Science (5 cr)
DATA11002 Introduction to Machine Learning (5 cr)
DATA12001 Advanced Course in Machine Learning (5 cr)
DATA16001 Network Analysis (5 cr)
MAST32001 Computational Statistics I (5 cr)
LSI35002 Bayesian Data Analysis (5 cr)

Chemistry

KEM342 Molecular Modelling (5 cr)
KEM345 Molecular Properties (5 cr)
KEM365 Laser Spectroscopy (5 cr)
KEM369 Molecular electronic structure (5 cr)
KEM384 Electronic excited state dynamic of molecules (5 cr)
KEM505 Computational Chemistry II: Surface calculations (5 cr)
KEM381 Programming projects in molecular modelling (5 cr)
KEM378 Molecular symmetry and group theory (5 cr)
KEM347 Quantum chemistry and spectroscopy (5 cr)

Elective courses offered by Aalto University

TCM370 Advanced Quantum Mechanics (5 cr)
TCM371 Low Temperature Physics (5 cr)
TCM372 Quantum Many-body Physics (5 cr)
TCM373 Solid State Physics (5 cr)
TCM374 Modern Optics (5 cr)
TCM375 Laser Physics (5 cr)
TCM376 Microscopy of Nanomaterials (5 cr)
TCM377 Machine Learning for Materials Science (5 cr)
TCM378 Computational Physics (5 cr)
TCM379 Nanotechnology (5 cr)
TCM380 Electromagnetic Fields (5 cr)
TCM381 Semiconductor Physics (5 cr)
TCM382 Semiconductor Devices (5 cr)
TCM383 Photonics (5 cr)
TCM384 Metamaterials and Nanophotonics (5 cr)

Other stud­ies (0-30 cr)

Other studies can include study modules or individual courses from other programmes or courses from the programme Theoretical and Computational Methods as agreed in the student's personal study plan. Also practical training (e.g. an internship at a company) and language studies can be included.