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 2021-2022 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.

**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)**

*Quantum Physics*

TCM302 Quantum mechanics IIa (5 cr)

TCM303 Quantum mechanics IIb (5 cr)

KEM341 Quantum chemistry (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)

(Required background knowledge: FYS2018 Quantum mechanics I, FYS2019 Quantum statistics and FYS2015 Statistical mechanics)

*Statistical Physics*

TCM306 Advanced statistical physics (5 cr)

TCM309 Kinetic Theory (10 cr)

(Required background knowledge: FYS2019 Quantum statistics)

*Particle Physics and Cosmology*

PAP325 Introduction to particle physics II (5 cr)

TCM311 Quantum field theory I (10 cr)

TCM312 Quantum field theory II (10 cr)

PAP326 Cosmology II (5 cr)

PAP335 General relativity (10 cr)

TCM308 Lattice field theory (5 cr)

TCM313 Thermal field theory (5 cr)

TCM314 String theory (5 cr)

Special courses in particle physics, 5-20 cr

Special courses in cosmology, 10-20 cr

*Condensed matter physics*

MATR333 Modelling of biological systems (5 cr)

MATR318 Solid state continuum mechanics II (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)

MATR327 Computational nanoscience (10 cr)

Specialized courses in computational methods, 5-15 cr

(Required background knowledge: FYS1013 Scientific computing I + FYS2085 Scientific computing II, programming skills)

*Atmospheric sciences*

ATM311 Simulations of Formation of Molecular Clusters (5 cr)

ATM312 Aerosol Modelling (5 cr) (Required background knowledge: FYS2071 Aerosol physics I + ATM304 Aerosol physics II)

ATM313 Biosphere-atmosphere process modelling I (5 cr)

ATM314 Biosphere-atmosphere process 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 Functional analysis (10 cr)

MAST31018 Spectral theory (10 cr)

MAST31010 Partial Differential Equations I (10 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*

MAST31010 Partial Differential Equations I (10 cr)

MAST31403 Integral equations (10 cr)

MAST31011 Partial Differential Equations II (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 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*

TCM315 Open Quantum Systems (10 cr)

MAST30130 Introduction to mathematical physics A (5 cr)

MAST31131 Introduction to mathematical physics B (5 cr)

MAST31302 Hamiltonian dynamics (10 cr)

MAST31303 Quantum dynamics (10 cr)

TCM309 Kinetic Theory (10 cr)

*Mathematics courses in the Applied mathematics*

MAST31010 Partial differential equations I (10 cr)

MAST31403 Integral equations (10 cr)

MAST31402 Bayesian inversion (10 cr)

MAST31401 Inverse Problems (10 cr)

*Mathematics of imaging*

MAST31002 Functional analysis (10 cr)

MAST31402 Bayesian inversion (10 cr)

MAST31401 Inverse Problems 1: convolution and deconvolution (10 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 Compinatorial 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*

KEM341 Quantum Chemistry (5 cr)

KEM367 Mathematical and Numerical Methods in Theoretical Chemistry (5 cr)

KEM368 Density Functional Theory (5 cr)

KEM343 Spectroscopy (5 cr)

KEM342 Molecular Modelling (5 cr)

KEM345 Molecular Properties (5 cr)

KEM365 Laser Spectroscopy (5 cr)

KEM369 Molecular electronic structure (5 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.

P.O. Box 4
(Yliopistonkatu 3)
00014 University of Helsinki
Switchboard:
+358 (0) 2941 911 (mobile call charge / local network charge)