Computational Sciences

Module:Computational Sciences

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students learn the main interdisciplinary features of scientific work in the computational sciences. They are able to describe problems in the quantitative natural sciences in theoretical terms and to understand the real-world significance of the equations involved. They can formulate the problem in algorithms and identify computer-aided solution methods. They can describe these computer-aided processes numerically and select stable solution methods. They can implement these algorithms, evaluate their time and memory efficiency and optimize them.

Content: The main focus of the module is on learning working methods. 1-3 problems of interdisciplinary relevance are selected and scientific theory, algorithmics, numerics and efficiency are rigorously practiced on these examples. In the computer exercises, students work in teams to develop, test and optimize implementations of the problems. Examples of suitable problems are e.g.:

• Wave phenomena and spectral analysis methods: Waves and oscillations in physics, the Fourier and Laplace transforms, discretization, DFT, FFT, implementation, stability analysis, duration analysis, code optimization, hardware acceleration
• Gravitation, electrostatics and computational procedures: gravitation problems and Coulomb‘s law, periodic systems and convergence, Ewald summation, error analysis, Particle Mesh Ewald, efficient implementation, hardware acceleration
• Thermal conductivity equation, Poisson’s equation and solution methods: thermal conductivity equation, Poisson’s equation, parabolic PDEs, PDEs, analytical solutions for special cases, domain decomposition / finite element approximation, solution using algebraic methods, implementation, convergence analysis, code optimization, hardware acceleration
• Data analysis and dimensional reduction: examples of correlated high-dimensional signals, Rayleigh quotient and optimality principle, eigenvalue problem, singular value decomposition and usual solution methods, Nyström approximation and sparse sampling, efficient implementation

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

Successful preparation of an efficient commented implementation in teams. Regular presentation of interim findings.

Successful completion of project-related tasks.

Lecture contact hours

Lecture preparation and follow-up

PS contact hours

PS preparation and follow-up

Preparation for examination

Examination

60

120

60

160

50

Project seminar

4

Module examination

Written examination (120 minutes)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One semester

Module offered

Every winter semester

Applicability

Master’s program Computational Sciences

Module: Introduction to Molecular Spectroscopy

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy

Responsible for the module: Module lecturers

Admission requirements: Successful completion of the module Atomic Structure and Chemical Bonding (8 CP) of the Bachelor program Chemistry of the Department of Biology, Chemistry, Pharmacy of the Freie Universität Berlin or equivalent knowledge of quantum mechanics

Qualification objectives: The students are able to apply rotational, vibrational, and electronic spectra as important aids in researching geometric structure, electronic structure and energetic and other properties of molecules up to the qualitative analysis of large molecules. Using current examples of optical spectroscopy, the students have gained a deeper knowledge of the relationships and understand the fundamental significance of spectroscopy in science and technology. They solve practice problems and discuss their solutions in groups.

Content: Physical principles of electromagnetic radiation, interaction of electromagnetic radiation with material with /without absorption and emissions of photons, experimental aspects, rotational spectroscopy, vibrational spectroscopy, electronic transitions

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination

30

30

30

30

30

Practice seminar

2

Work on practice tasks, contributions to discussion

Module examination

Written examination (120 Minutes) or oral examination (approx. 30 Minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Mandatory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module: Introduction to Theoretical Chemistry

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students are familiar with fundamental analytical and numerical concepts and methods of theoretical chemistry. They can apply time-independent and time-dependent quantum mechanical methods for selected model systems in chemistry and have the numerical skills to carry out the appropriate computer simulations. This gives them a deeper understanding of the properties of molecules and chemical reactions.

Content: In-depth mathematical representation of time-independent and time-dependent quantum mechanics, solving quantum mechanical one-particle problems (free particle, harmonic oscillator, hydrogen atom), dynamics of the nucleus (oscillation and rotation), nucleus oscillations of multi-atom molecules, time-dependent and time-independent calculation of perturbations, selected numerical solution methods for calculating time-dependent quantum mechanical model systems

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours
Supervised computer exercise
Independent computer work

Prac.S preparation and follow-up

Preparation for examination

30

30

15
15

30

30

Practice seminar

1

Contributions to discussion, Presentation of selected simulation findings

Module examination

Practical examination (approx. 30 minutes); the module examination is not evaluated in detail.

Module language

German

Mandatory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

Every winter semester

Applicability

Master’s program Computational Science

Module: Quantum Mechanical Description of Atoms and Chemical Bonding

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have a basic understanding of quantum mechanics and its application to simple chemically relevant examples. They can use mathematical tools to describe the electron structures of atoms and small molecules and are familiar with atomic models and the quantum mechanical principles of spectroscopic measurement. They know the connections of quantum theory with orbitals and chemical bonding. They can analytically examine simple issues on the quantum nature of chemical model systems independently and in groups using selected numerical methods, prepare them for teaching purposes and present them appropriately in gender-specific and diversity-specific ways.

Content: Introduction to the quantum nature of matter and energy, principles of quantum theory, quantum mechanical solutions of the time-independent Schrödinger equation for chemically relevant model systems, quantum theory of orbital angular momentum and spin. Quantum mechanics of the hydrogen atom, multi-electron atoms, spin-orbit coupling, theory of chemical bonding, elementary quantum theory of simple molecules. Analytical and numerical solution methods for simple quantum mechanical problems.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination

Examination

60
70

30
70

70

Practice seminar

2

Work on practice tasks, Contributions to discussion

Developing and presenting a quantum theoretical topic using numerical methods

Module examination

Written examination (180 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

300 hours

10 CP

Duration of module

One semester

Module offered

Every semester

Applicability

Master’s program Computational Sciences

Module:Principles of Remote Sensing and Digital Image Analysis

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have basic skills and competences in digital remote sensing and digital image analysis in the earth sciences. They can work independently and in groups to examine issues in remote sensing and image analysis, using selected numerical methods, prepare the issues didactically and present them in a gender-specific and diversity-specific way.

Content: The module gives a theoretical introduction to the topic; selected aspects are studied in more detail and practiced in relation to practical examples, using current software packages. The topics include the principles of:

-          Introduction to radiation physics

-          Principles of photogrammetry

-          Digital and analog passive image recording systems

-          Visualization of multispectral data

-          Principles of image analysis

-          Special image extraction (e.g. indices, PCA)

-          Interpretation of remote sensing data

-          Time series analysis with raster data (change detection)

-          Multispectral classification method

-          Introduction to active remote sensing systems

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Contact hours S

Preparation and follow-up S

Preparation for examination Examination

30

20

30

25

45

Seminar

2

Practice tasks

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Mandatory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year, every winter semester

Applicability

Master’s program Computational Sciences

Module: Principles of Hydrogeography and Climate Geography

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered fundamental knowledge on climate geography and hydrogeography, in particular the specialist terminology, and can apply it in scientific discourse. They can describe global relationships of the climate system including the interaction with the oceans, the general circulation of the atmosphere and elements of the water cycle.

Content: The module presents the principles of climate geography and hydrogeography. This includes among other things the principles of the climate system; the radiation budget and thermal budget; general circulation of the atmosphere; climate classifications; role of the oceans in the climate system; elements of the water cycle and their space-time characteristics and metrological determination; water balance and water budget on various levels of scale. Students study selected content in more detail, working on practice tasks independently or in small groups. In addition, the module gives an introduction to scientific work, in particular using specialist literature, e.g. principles of literature preparation and correct references to scientific texts.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Preparation for examination Examination

30

15

30

30

45

Seminar

2

Practice tasks, presentation

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

Two semesters

Module offered

At least once per academic year, every winter semester

Applicability

Master’s program Computational Sciences

Module:Principles of Geographical Information Systems

University/Department: Freie Universität Berlin/ Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have gained the fundamental skills and competences of digital spatial information processing for work in earth sciences. They can examine issues relating to geographical information systems independently and in groups, using selected computer-aided methods, prepare them for teaching purposes and present them in a gender-specific and diversity-specific way.

Content: The module gives a theoretical introduction to the topic. Selected aspects are studied in more detail and practiced in relation to practical examples, using current software packages. It covers the principles of:

-       Structure and applications of geoinformation systems

-       Data models (raster data /vector data)

-       Methods and problems of imaging geospace (geodetic reference systems)

-       Georeferencing

-       Extracting and processing vector data

-       Processing spatial and attributive information

-       Geodatabases

-       Interpolation methods

-       Preparing and analyzing digital terrain models

-       Extracting hydrological parameters

Visualizing geodata

-       Interfaces of geodata processing

-       Developing and preparing maps

-       Principles of remote sensing

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Preparation for examination

Examination

30

20

30

25

45

Seminar

2

Practice tasks

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year every summer semester

Applicability

Master’s program Computational Sciences

Module:Synchronization Earth

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students gain a thorough understanding of the structure, composition and process of our planet and the earth’s uniqueness in comparison to other planets. They gain an insight into the physical and chemical processes which shape the surface and the driving forces behind them in the earth’s interior. They know the earth’s structure and its significance and have learnt the methods used by earth scientists to examine the earth’s interior. The students are familiar with geological cycles and their time frames. They are able to identify the most important rock-forming minerals and rocks and can classify them according to their formation conditions. The students have an advanced understanding of our planet‘s structure, composition and processes. They understand the principles of the interaction between the earth’s solid structure, the atmosphere, the hydrosphere and biosphere and of (mostly exogenic) processes in different time scales.

Content: The module covers the following topics: fundamental systems and processes of planet earth; space and time; material components; geoscientific cycles; interaction between hydrosphere, atmosphere, geosphere; relative and absolute age; sedimentary cycles (weathering, erosion, sedimentation); phenomenological geophysics; magmatism; metamorphism; structure; plate tectonics; processes and mutual interaction of tectonics, weathering, erosion, climate, transport processes and depositional environments depending on exogenic and endogenic variables; influence of organisms on these processes; carbon cycle; climate change; surface-shaping processes in the interplay of climate, atmospheric composition and tectonics; mass balances and flow behaviors in global systems. The students study the macroscopic identification of minerals and rocks.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Introductory course 1

2

-

IC 1 contact hours

IC 1 preparation and follow-up

P contact hours

P preparation and follow-up

IC2 contact hours

IC2 preparation and follow-up

Preparation for examination Examination

30

45

30

60

30

45

60

Practical

2

Successful completion of practice tasks

Introductory course 2

2

-

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

300 hours

10 CP

Duration of module

Two semesters

Module offered

At least once per academic year (IC1 und P in the winter semester, IC2 in the summer semester)

Applicability

Master’s program Computational Sciences

Module:Complex Algorithms A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered the principles of the current design techniques for algorithms and can use them to design algorithms. They can analyze algorithms in relation to their time and memory requirements, applying advanced analytical methods. They understand the principles of the theory of NP completeness. They know the most common complexity classes and can classify simple problems according to their complexity. They further develop these skills independently in a selected topic area of higher computer science. The students can apply complex algorithms to one of the following topics: distributed systems, pattern recognition, database technology or artificial intelligence.

Content: The module covers aspects of the following topics: path and flow problems in graphs; string matching; randomized algorithms; amortized analysis; the ‘master theorem’ for the analysis of divide-and-conquer recursion equations; NP completeness; approximation algorithms for difficult problems; number-theoretic algorithms (including RSA cryptosystems); arithmetic algorithms and circuits and Fast Fourier Transform. These topics are subsequently examined in more depth, using examples. The following topics are offered:

-       Distributed systems, distributed algorithms, distributed data management, search methods for solving combinatorial tasks

-       First-order logic and its mechanization, resolution and theorem proofs, knowledge-based and expert systems, fuzzy logic

-       Bayesian pattern recognition, clustering, expectation maximization, neural networks and learning algorithms, associative networks, recurrent networks. Computer vision with neural networks

-       Database access technologies and query optimization; realization of transactions, particularly synchronization methods; technological measures to make database systems fault-tolerant. Methods of efficient management of different types of large data sets, in particular of XML documents; correct implementation of transactional guarantees in data management systems

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a research topic

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computer Science and Data Structures A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students possess basic skills in developing object-oriented software: they can deal with data abstraction, inheritance, and polymorphic type systems and are able to specify and implement abstract data types, to carry out soundness proofs for the implementation of abstract data types, and to take decisions on selecting the data representation method in each case, taking efficiency analyses into account. They are familiar with the main abstract data types and their current implementations and the relevant interfaces and classes from the libraries of the programming language used.

Content: The module’s starting point is information hiding and its significance for structuring programs and constructing data objects using modules and classes. The term data abstraction, linked with the distinction between specification and implementation of abstract data objects and data types, plays a crucial part in data modeling. Sequences, sets, relations, trees, graphs and geometrical objects are introduces as abstract types. Finally, efficiently manipulatable representations of these types are studied and the complexity of the related algorithms examined.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module: Computer Science and Functional Programming A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students are able to functionally design elementary algorithms, to formally specify demands on functional programs, to develop well-structured functional programs, to examine the complexity of functional programs and to formally prove the properties of functional programs. They understand the principles of computability.

Content: Principles of computability (Lambda calculus, primitive recursion, μ-recursion). Introduction to functional programming (syntax, primitive data types, lists, tuples, strings, expressions, function definitions, recursion and iteration, higher order functions, polymorphism, type systems, type inference and type checking, algebraic and abstract data types, input and output, search and sorting algorithms). Proofs of program properties (rewriting, structural induction, scheduling). Implementation and programming technique (evaluation strategies for functional programs, modular program design)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computer Science and Object-Oriented Programming A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can specify algorithms in relation to their condition, develop well-structured imperative programs, analyze the complexity of imperative programs and formally prove the properties of imperative programs.

Content: Principles of computability (universal register machines, syntax and operational semantics of imperative programming languages); formal methods for specification and verification of imperative programs: (conditions of the state-space, Hoare logic, partial soundness, termination); concepts of imperative and object-oriented programming (primitive and combined data types, methods, parameter passing, overloading, modules, classes, objects, class hierarchies, inheritance, abstract classes, interfaces); programming methodology (incremental correct program development, divide-and-conquer, backtracking, analysis of time and memory requirements, big O notation, transformation of recursion into iteration, analysis of search and sorting algorithms)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

one or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Introduction to Numerical Mathematics A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered basic numerical solution methods for elementary algebra problems and ordinary differential equations. They have developed a sense for the mathematical structure of these problems and can select and develop reliable and efficient solution algorithms. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Solution methods for linear equation systems; Cholesky decomposition and QR decomposition; eigenvalue problems; best approximations; polynomial and spline interpolation; Gaussian quadrature and adaptive quadrature; initial value problems for ordinary differential equations

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Numerics of ODEs and numerical linear algebra A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered basic numerical solution methods for ordinary differential equations and have a basic knowledge of numerical linear algebra and can deal these topics confidently. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Selection from the following topics:

-      Initial value problems for stiff differential equations (stability and asymptotic stability of fixed points, test equations)

-      implicit Runge-Kutta methods (inheritance methods, stability fields, A- and B-stability, Gaussian method)

-      differential algebraic equations (basic terminology, index)

-      Hamiltonian systems (energy conservation, symplecticism, symplectic Rung-Kutta method)

-      Iterative methods for solving large linear equation systems (linear iterative method, preconditioning, method of steepest descent, conjugate gradient method)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German or English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Numerics of partial differential equations A

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have gained a fundamental knowledge of numerical solutions for partial differential equations and numerical linear algebra and can deal with them confidently. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Selection from the following topics:

-          Mathematical modeling with partial differential equations

-      Classification (elliptic, parabolic, hyperbolic) and well-posedness

-      Classical solutions and finite differences (maximum principle, consistency, convergence)

-      Weak solutions and finite elements (Sobolev spaces, error estimates, partial volume correction methods)

-      Parabolic differential equations (method of lines, Rothe’s method)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German or English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module: Synchronization Mathematics

University/Department: Freie Universität Berlin/Physics, Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have gained an overview of the structure and aims of mathematics and their working methods. They also have a grasp of the core structures and clause-sets of linear algebra and of computation with matrices and vectors. They can map algebraic problems on the computer and solve them using numerical methods.

Content:

-       Linear algebra: Working methods and aims of mathematics, logic, sets and maps, algebraic structures, fields, real numbers, complex numbers, linear maps, linear equation systems, matrices, representations and changes of basis, determinants, eigenvalues and eigenvectors, scalar products, orthogonal systems

-       Computer-oriented mathematics: Using computers to solve mathematical problems. Number description, round-off errors, condition, stability, complexity and efficiency

-       Computer algebra systems: Principles of use and script-based programming

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

90

150

60

60

60

30

Practice seminar

2

Successful completion of practice tasks

Lecture

2

-

Practice seminar

2

Successful completion of practice tasks

Module examination

Written examination (90 minutes) or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Atmospheric Dynamics

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have a grasp of hydrodynamics and thermodynamics specific to the specialization area Atmospheric Sciences, which form the theoretical basis for practical weather prediction in the synoptic scale area. They can understand in physical terms the most important formation mechanisms of mid-latitude high-pressure and low-pressure areas and can analyze them independently.

Content: The module covers topics such as introduction to derived values of divergence, vorticity and deformation; comprehensive evaluation of the basic equations for gaining meteorological statements on the synoptic scale with the aid of derived values; discussion of the quasi-geostrophic baroclinic model of the atmosphere; introduction to basic large-scale vorticity and the concept of potential vorticity; land-sea wind circulation; planetary waves and the main instability processes in the atmosphere; theory of general atmospheric circulation.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination

Examination

60

50

30

50

50

Practice seminar

2

Successful completion of practice tasks

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

240 hours

8 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module: Introduction to Atmospheric Dynamics

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have a grasp of applied hydrodynamics and thermodynamics in meteorology. They are familiar with the basic meteorological equation system and can apply the terminology of the scales, conserved quantities and wind approximation in the meteorological context.

Content: The module covers topics such as atmospheric thermodynamics; changes to atmospheric air conditions; atmospheric structure; polytropic atmospheres; water vapor and latent heat; principles of kinematics; derivation of the prognostic basic meteorological equations from classical hydrodynamics and thermodynamics; scale terminology in meteorology; Lagrangian and Eulerian representations; natural coordinates; basic balances (geostrophic wind, cyclostrophic wind, gradient wind) and thermal wind.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

Successful completion of practice tasks

Lecture contact hours

Lecture preparation and follow-up

60

150

Module examination

none

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

210 hours

7 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Principles of Synoptic Meteorology

University/Department: Freie Universität Berlin/Earth Sciences

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students understand the three-dimensional spatial and temporal structures, processes and interactions that determine the weather conditions on the synoptic, global and convective scales in the mid-latitudes. They can analyze, classify, present and evaluate the current weather situation on the basis of weather maps.

Content: The module covers topics such as the introduction of three-dimensional diagnosis of mid-latitude synoptic-scale weather systems: air masses and fronts, cyclones and anti-cyclones, jet streams and waves of the west wind zone, their temporal development and relation to weather phenomena. Practical work on the DWD’s (graphic) system Niño is introduced and carried out independently. This includes analyzing current global examples related to the content of each lecture. Solving practical tasks helps the students to develop a basic understanding of the lecture content. Analysis and discussion of the current weather situation in the European-Atlantic sector by means of meteorological fields and satellite images.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

30

65

30

85

Practice seminar

2

Successful completion of practice tasks,

lecture

Module examination

none

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

210 hours

7 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computational Statistical Physics I A

University/Department: Freie Universität Berlin/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students are able to name and describe the principle concepts and theorems of statistical physics and thermodynamics. They are also capable of applying the methods they have learnt to given problems and to solve them. The students have also mastered the computation methods necessary for dealing with statistical physics and thermodynamics and are able to apply them. They can apply their knowledge of methodology and computation methods in the field of statistical physics to complex issues.

Content: Elementary statistics and the laws of large numbers, equilibrium ensembles, the principle of maximum entropy, main theorems of thermodynamics, thermodynamic potentials, thermodynamic processes, phase transition, ideal quantum gases, interactive systems.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computational Statistical Physics II A

University/Department: Freie Universität Berlin/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have a grasp of the fundamental concepts and theorems of statistical physics. They can name, describe and apply them and apply the methods they have learnt to existing problems to solve them. The students have extended their knowledge of methods and calculation methods in the field of statistical physics and are now able to apply these to complex issues. Using the methods they have learnt, they are also able to derive and analyze microscopic physical processes / laws at the macroscopic level.

Content: A selection of the following advanced topics of statistical physics: non-equilibrium thermodynamics (entropy production, Onsager relations), linear response theory and fluctuation-dissipation theorem, stochastic processes (Markov processes, master equation, Langevin equation and Fokker-Planck equation), kinetic theory, phase transition (Landau theory, Gaussian fluctuations, correlation functions, renormalization groups), theory of liquids, hydrodynamics and elasticity, statistical quantum mechanics, exactly solvable models.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages); the module examination is not evaluated in detail.

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module: Introduction to Quantum Mechanics

University/Department: Freie Universität Berlin/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students learn the basic mathematical and methodological concepts of the quantum mechanics of particles. They can apply this knowledge to given problems and solve them. The students can express the new way of thinking in their own words and describe the fundamental differences to classical mechanics. They can also assess which problems are suitable for the application of quantum mechanical methods and what effects the application has on the validity of classical mechanics. Students have gained an overview of the history of quantum mechanics and some fundamental experiments. They are familiar with the content of quantum mechanics and its significance. They have also mastered the necessary mathematical formalism for the representation and computation of quantum theory problems and can apply them.

Content: Mathematical principles and formalism, Schrödinger equation, one-dimensional problems, harmonic oscillators, uncertainty principle, angular momentum, hydrogen atom, potential scattering, density matrix, perturbation theory, basic experiments (e.g. wave-particle duality, diffraction and interference effects, black body radiation, photoelectric effect, Stern-Gerlach experiment)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

5

Successful completion of practice tasks

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

75

60

15

30

120

Practice seminar

1

Module examination

none

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

300 hours

10 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Complex Algorithms B

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered the principles of the current design techniques for algorithms and can use them to design algorithms. They can analyze algorithms in relation to their time and memory requirements, applying advanced analysis methods. They understand the principles of the theory of NP completeness. They know the most common complexity classes and can classify simple problems according to their complexity. They further develop these skills independently in a selected topic area of higher computing science. The students can apply complex algorithms to one of the following topics: distributed systems, pattern recognition, database technology or artificial intelligence.

Content: The module covers aspects of the following topics: path and flow problems in graphs; string matching; randomized algorithms; amortized analysis; the ‘master theorem’ for the analysis of divide-and-conquer recursion equations; NP completeness; approximation algorithms for difficult problems; number-theoretic algorithms (including RSA cryptosystems); arithmetic algorithms and circuits and Fast Fourier Transform. These topics are subsequently examined in more depth. The following topics may also be covered:

-       Distributed systems, distributed algorithms, distributed data management, search methods for solving combinatorial tasks

-       First-order logic and its mechanization, resolution and theorem proofs, knowledge-based and expert systems, fuzzy logic

-       Bayesian pattern recognition, clustering, expectation maximization, neural networks and learning algorithms, associative networks, recurrent networks. Computer vision with neural networks

-       Database access technologies and query optimization; realization of transactions, particularly synchronization methods; technological measures to make database systems fault-tolerant. Methods of efficient management of different types of large data sets, in particular of XML documents; correct implementation of transactional guarantees in data management systems

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a research topic

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computer Science and Data Structures B

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can develop object-oriented software: they can deal with data abstraction, inheritance, and polymorphic type systems and are able to specify and implement abstract data types, to carry out soundness proofs for the implementation of abstract data types, and to take decisions on selecting the most suitable data representation taking efficiency analyses into account. They are familiar with the main abstract data types and their current implementations and the relevant interfaces and classes from the libraries of the programming language used.

Content: The module’s starting point is information hiding and its significance for structuring programs and constructing data objects using modules and classes. The term data abstraction, linked with the distinction between specification and implementation of abstract data objects and data types, plays a crucial part in data modeling. Sequences, sets, relations, trees, graphs and geometrical objects are introduces as abstract types. Finally, efficiently manipulatable representations of these types are studied and the related algorithms examined for their complexity.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computer Science and Functional Programming B

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students are able to functionally design elementary algorithms, to formally specify demands on functional programs, to develop well-structured functional programs, to examine the complexity of functional programs and to formally prove the properties of functional programs. They understand the principles of computability.

Content: Principles of computability (Lambda calculus, primitive recursion, μ-recursion). Introduction to functional programming (syntax, primitive data types, lists, tuples, strings, expressions, function definitions, recursion and iteration, higher order functions, polymorphism, type systems, type inference and type checking, algebraic and abstract data types, input and output, search and sorting algorithms). Proving program properties (rewriting, structural induction, scheduling). Implementation and programming technique (evaluation strategies for functional programs, modular program design).

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computer Science and Object-oriented Programming B

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can specify algorithms in relation to their condition, develop well-structured imperative programs, analyze the complexity of imperative programs and formally prove the properties of imperative programs.

Content: Principles of computability (universal register machines, syntax and operational semantics of imperative programming languages); formal methods for specification and verification of imperative programs: (conditions of the state-space, Hoare logic, partial soundness, termination); concepts of imperative and object-oriented programming (primitive and combined data types, methods, parameter passing, overloading, modules, classes, objects, class hierarchies, inheritance, abstract classes, interfaces); programming methodology (incremental correct program development, divide-and-conquer, backtracking, analyzing time and memory requirements, big O notation, transforming recursion into iteration, analyzing search and sorting algorithms).

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

- written completion of the work sheets

- two oral presentations, each showing the solution of one practice task in the practice seminar

Seminar

2

Preparation and presentation of a programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Introduction to Numerical Mathematics B

University/Department: Freie Universität Berlin/ Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have mastered advanced numerical solution methods for elementary algebra problems and ordinary differential equations. They have developed a sense for the mathematical structure of these problems and can select and develop reliable and efficient solution algorithms. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Solution methods for linear equation systems, Cholesky decomposition and QR decomposition, eigenvalue problems, best approximations, polynomial and spline interpolation, Gaussian quadrature and adaptive quadrature. Initial value problems for ordinary differential equations

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Numerics of ODEs and numerical linear algebra B

University/Department: Freie Universität Berlin/ Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have in-depth knowledge of numerical solution methods for ordinary differential equations and numerical linear algebra and can deal with them confidently. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Selection from the following topics:

-      Initial value problems for stiff differential equations (stability and asymptotic stability of fixed points, test equations)

-      Implicit Runge-Kutta methods (inheritance methods, stability fields, A- and B-stability, Gaussian method)

-      Differential algebraic equations (basic terminology, index)

-      Hamiltonian systems (energy conservation, symplecticism, symplectic Rung-Kutta method)

-      Iterative methods for solving large linear equation systems (linear iterative methods, preconditioning, method of steepest descent, conjugate gradient method)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

German or English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Numerics of partial differential equations B

University/Department: Freie Universität Berlin/ Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have in-depth knowledge of numerical solutions for partial differential equations and numerical linear algebra and can deal with them confidently. During the seminars, the students have applied what they have learnt to practical problems of scientific computation and gained an insight into the mathematical modeling of this type of problem.

Content: Selection from the following topics:

-          Mathematical modeling with partial differential equations

-      Classification (elliptic, parabolic, hyperbolic) and well-posedness

-      Classical solutions and finite differences (maximum principle, consistency, convergence)

-      Weak solutions and finite elements (Sobolev spaces, error estimates, partial volume correction methods)

-      parabolic differential equations (method of lines, Rothe’s method)

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 Pages).

Module language

German or English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computational Statistical Physics I B

University/Department: Freie Universität Berlin/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students are able to name and describe the principle concepts and theorems of statistical physics and thermodynamics. They are also capable of applying the methods they have learnt to existing problems and to solve them.

The students have also mastered the computation methods necessary for dealing with statistical physics and thermodynamics and are able to apply them. They can apply their knowledge of methodology and computation methods in the field of statistical physics to complex issues.

Content: Elementary statistics and the laws of large numbers, equilibrium ensembles, the principle of maximum entropy, main theorems of thermodynamics, thermodynamic potentials, thermodynamic processes, phase transition, ideal quantum gases, interactive systems.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Computational Statistical Physics II B

University/Department: Freie Universität Berlin/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students have in-depth knowledge of the fundamental concepts and theorems of statistical physics. They can name, describe and apply them and apply the methods they have learnt to given problems to solve them. The students have extended their knowledge of methods and calculation methods in the field of statistical physics and are now able to apply these to complex issues. Using the methods they have learnt, they are also able to derive and analyze microscopic physical processes / laws at the macroscopic level.

Content: A selection of the following advanced topics of statistical physics: non-equilibrium thermodynamics (entropy production, Onsager relations), linear response theory and fluctuation-dissipation theorem, stochastic processes (Markov processes, master equation, Langevin equation and Fokker-Planck equation), kinetic theory, phase transitions (Landau theory, Gaussian fluctuations, correlation functions, renormalization groups), theory of liquids, hydrodynamics and elasticity, statistical quantum mechanics, exactly solvable models.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

4

-

Lecture contact hours

Lecture preparation and follow-up

S contact hours

S preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Written practice tasks

Preparation for examination Examination

60

80

30

60

30

60

60

70

Practice seminar

2

Successful completion of practice tasks

Seminar

2

Preparation and presentation of a research topic or programming project

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

450 hours

15 CP

Duration of module

One or two semesters

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Molecular Simulation I

University/Department: Freie Universität Berlin/Mathematics and Computer Science, Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students learn the theoretical principles and simulation techniques for simple stochastic systems (e.g. molecule models, Ising models, diffusion in model potentials). They understand the physical principles and relations between stochastic trajectories and ensembles, can generate simulation data and estimate expectation values. They can apply what they have learnt confidently.

Content: Thermostatics: Principles and derivations for the most important ensembles. Boltzmann distribution, partition functions, expectation values

-          Monte-Carlo method: Theory, construction, convergence and implementation of the Monte-Carlo method for calculating stationary expectation values

-          Kinetics: Theory of rates, time correlations and other time-dependent expectation values

-          Molecular dynamic simulation: Theory, construction, convergence and implementation of molecular dynamic simulations to calculate time-dependent expectation values

This module complements Molecular Simulation II. We recommend taking first Molecular Simulation I followed by Molecular Simulation II, but this is not strictly necessary.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination

Examination

30

30

30

30

30

Practice seminar

2

Successful completion of practice worksheets and oral presentation of solutions

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Research Project A

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy/Earth Sciences/ Mathematics and Computer Science/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can apply their knowledge, skills and abilities in scientific computing in a current research project, as far as possible industry-related. They can work in teams and communicate appropriately about their work. They are willing to offer assistance within the team if necessary; they can select and evaluate the appropriate aids and offer factual criticism.

Content: In this module, the students work on application-oriented problems supported by scientific computing methods.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Project seminar

2

Contributions to discussion

PS contact hours

PS preparation and follow-up

Preparation for examination Examination

30

100

20

Module examination

Lecture (approx. 15 minutes) with written paper on the student’s individual project contribution (approx. 5 pages)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Scientific Computing

Module:Research project E

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy / Earth Sciences / Mathematics and Computer Science / Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can apply their knowledge, skills and abilities in scientific computing in a current research project, as far as possible industry-related. They can work in teams and communicate appropriately about their work. They are willing to offer assistance within the team if necessary; they can select and evaluate the appropriate aids and offer factual criticism.

Content: In this module, the students work on application-oriented problems supported by scientific computing methods.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Project seminar

4

Regular contributions to discussion

PS contact hours

PS preparation and follow-up

Preparation for examination Examination

60

210

30

Module examination

Lecture (approx. 30 minutes) with written paper on the student’s individual project contribution (approx. 10 pages)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

300 hours

10 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Scientific Computing

Module:Research Seminar Computational Sciences

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy / Earth Sciences / Mathematics and Computer Science / Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can work independently to familiarize themselves with current topics by reading specialist literature, prepare a topic for presentation and acquire supplementary background information. They can present even difficult topics in comprehensible form in lectures. They can highlight essential elements among less important elements and pay particular attention to the selection of appropriate media. They are willing to ask questions when an issues is unclear; they can take part in discussions on scientific issues and offer factual criticism.

Content: Current research topics are examined in this seminar, giving students the opportunity to prepare themselves for their Master’s thesis.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Seminar

2

Regular contributions to discussion

S contact hours

S preparation and follow-up

Preparation for examination Examination

30

30

90

Module examination

Presentation of a research project or a topic from specialist literature (approx. 45 minutes)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

Not offered regularly

Applicability

Master’s program Scientific Computing

Module:Markov modeling

University/Department: Freie Universität Berlin/Mathematics and Computer Science

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students learn the theoretical principles of conformational dynamics and the discrete description of continuous-state-space Markov processes. They can apply what they have learnt confidently using selected numerical and computer-supported methods. They are willing to ask questions when an issue is unclear; they can take part in discussions on scientific issues and offer factual criticism.

Content:

-          Markov chains: Theory on space-time-discrete Markov chains. Irreducibility, ergodicity, reversibility. Algorithms for calculating these properties.

-          Model estimation and error estimation: Methods for estimation of reversible and non-reversible models. Bayes theorem. Sampling method for estimating reversible and non-reversible models. Linear error perturbation

-          Simulation and convergence: Convergence of estimated values and improving the convergence

-          Ensemble analysis: Eigenvalues and eigenvectors of the transition matrix; correlation functions. Measurement values for molecular experiments

-          Trajectory analysis: Mean first passage times, committor functions, transition path theory

-          Discretization: Approximation of continuous Markov processes by Markov chains. Approximation errors. Variational principle

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination Examination

30

30

30

30

30

Practice seminar

2

Successful completion of practice worksheets and oral presentation of solutions

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Computational Sciences

Module:Molecular simulation II

University/Department: Freie Universität Berlin/ Mathematics and Computer Science, Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students learn classical (not quantum-mechanical) models for molecules, in particular macromolecules and biomolecules. They can apply what they have learnt confidently.

Content:

• Energy function: Structure, importance and parametrization of empirical energy functions in classical molecular dynamics
• Algorithms and data structures: Periodic boundary conditions, cut-off, efficient neighbor search
• Long-range interactions: Coulomb summation, convergence, Poisson‘s equation, Ewald summation, Particle Mesh methods
• Solvation methods: Explicit, Poisson-Boltzmann, Generalized Born
• Dynamics: Integrators, discretization errors
• Sampling methods: Metastability, replica exchange, umbrella sampling
• Expectation values: Calculating expectation values from molecular simulations

This module complements Molecular Simulation I. We recommend taking first Molecular Simulation I followed by Molecular Simulation II, but this is not strictly necessary.

Practical skills are taught in a simulation practical. This is usually a block unit and takes place in the lecture-free phase.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

Active participation and discussion

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination Examination

30

30

30

30

30

Practice seminar

(Block)

2

Successful completion of simulation and programming tasks

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester / block

Module offered

Not offered regularly

Applicability

Master’s program Computational Sciences

Module:Selected topics in theoretical computational sciences

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy/Earth Sciences/ Mathematics and Computer Science/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students know the principles of a selected research field in scientific computing and understand the relevant terminology. They can apply what they have learnt confidently. They are willing to ask questions when an issues is unclear; they can participate in discussions on scientific issues and offer factual criticism.

Content: The module gives an introduction to a selected research area of scientific computing. Current research issues are also examined.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

-

Lecture contact hours

Lecture preparation and follow-up

Prac.S contact hours

Prac.S preparation and follow-up

Preparation for examination Examination

30

30

30

30

30

Practice seminar

2

Successful completion of practice worksheets and oral presentation of solutions

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Practice seminar: yes; Lecture: Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

Not offered regularly

Applicability

Master’s program Scientific Computing

Module:Selected topics in applied computational sciences

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy/Earth Sciences/ Mathematics and Computer Science/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students know the principles of a selected field in scientific computing and can work independently to develop solutions to selected problems. They are willing to ask questions when an issue is unclear; they can participate in discussions on scientific issues and offer factual criticism.

Content: The module gives insight into a selected area of scientific computing. Current research issues and areas of application are also examined.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Lecture

2

Active participation and where applicable, discussion

Lecture contact hours

Lecture preparation and follow-up

SPC contact hours

SPC preparation and follow-up

Preparation for examination Examination

30

30

15

15

60

Seminar on the computer

1

Successful completion of computer practice tasks

Module examination

Written examination (90 minutes), which may also be carried out as an electronic examination, or oral examination (approx. 30 minutes) or term paper (approx. 15 pages).

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

150 hours

5 CP

Duration of module

One semester

Module offered

Not offered regularly

Applicability

Master’s program Scientific Computing

Module:Research Project C

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmac / Earth Sciences / Mathematics and Computer Science / Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can apply their knowledge, skills and abilities in scientific computing in a current research project, as far as possible industry-related. They can work in teams and communicate appropriately about their work. They are willing to offer assistance within the team if necessary; they can select and evaluate the appropriate aids and offer factual criticism.

Content: In this module, the students work on application-oriented problems supported by scientific computing methods.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Project seminar

2

Regular contributions to discussion

PS contact hours

PS preparation and follow-up

Preparation for examination Examination

30

120

60

Module examination

Lecture (approx. 15 minutes) with written paper on the student’s individual project contribution (approx. 5 pages)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

210 hours

7 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Scientific Computing

Module:Research project B

University/Department: Freie Universität Berlin/Biology, Chemistry, Pharmacy/Earth Sciences/ Mathematics and Computer Science/Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can apply their knowledge, skills and abilities in scientific computing in a current research project, as far as possible industry-related. They can work in teams and communicate appropriately about their work. They are willing to offer assistance within the team if necessary; they can select and evaluate the appropriate aids and offer factual criticism.

Content: In this module, the students work on application-oriented problems supported by scientific computing methods.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Project seminar

2

Regular contributions to discussion

PS contact hours

PS preparation and follow-up

Preparation for examination Examination

30

130

20

Module examination

Lecture (approx. 15 minutes) with written paper on the student’s individual project contribution (approx. 5 pages)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

180 hours

6 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Scientific Computing

Supplementary module: Research project D

University/Department: Freie Universität Berlin/ Biology, Chemistry, Pharmacy / Earth Sciences / Mathematics and Computer Science / Physics

Responsible for the module: Module lecturers

Admission requirements: none

Qualification objectives: The students can apply their knowledge, skills and abilities in scientific computing in a current research project, as far as possible industry-related. They can work in teams and communicate appropriately about their work. They are willing to offer assistance within the team if necessary; they can select and evaluate the appropriate aids and offer factual criticism.

Content: In this module, the students work on application-oriented problems supported by scientific computing methods.

Teaching and learning units

Contact hours

(Semester hours per week = SH)

Forms of active participation

Workload

(hours)

Project seminar

4

Regular contributions to discussion

PS contact hours

PS preparation and follow-up

Preparation for examination Examination

60

180

30

Module examination

Lecture (approx. 20 minutes) with written paper on the student’s individual project contribution (approx. 5 pages)

Module language

English

Compulsory regular attendance

Attendance recommended

Workload, total hours

270 hours

9 CP

Duration of module

One semester

Module offered

At least once per academic year

Applicability

Master’s program Scientific Computing

1st Semester

2nd Semester

3rd Semester

4th Semester

Synchronization area

Required Module

Computational Sciences

(15 CP)

Scientific Computing area

Module A

(15 CP)

Specialization area

30 CP

Master’s thesis with accompanying colloquium

30 CP

Synchronization area

Elective module/s totaling

15 CP

Scientific Computing area

Module B

(15 CP)

Total: 30 CP

Total: 30 CP

Total: 30 CP

Total: 30 CP

1st Semester

2nd Semester

3rd Semester

4th Semester

Synchronization area

Required Module

Computational Sciences

(15 CP)

Scientific Computing area

Module A

(15 CP)

Specialization area

30 CP

Master’s thesis with accompanying colloquium

30 CP

Scientific Computing area

Module B

(15 CP)

Synchronization area

Elective module/s totaling

15 CP

Total: 30 CP

Total: 30 CP

Total: 30 CP

Total: 30 CP

Areas of study

Credit points

Grade

Synchronization area

30 (15)

n.n

Scientific Computing area

30 (15)

n.n

Specialization area [XX]

30 (30)

n.n

Master’s thesis

30 (30)

n.n