Workload: 390 hours (1 semester)
ECTS credits: 13 ECTS
Term: Summer (2^nd semester)
Repeatablity: not restricted in attempts

Final assessment: Assessment folder (GPA of 2 components of the module):
• component a: Data Analysis (5 ECTS points): solution of weekly exercises + 30-minutes oral discussion;
• component b: Parallel Algorithms (8 ECTS points): solution of weekly exercises + 30-minutes oral discussion.

Pre-requisites for the final exam: Knowledge of numerical mathematics and basic algorithms from Bachelor´s level is assumed.

Description of the module: Acquisition of the mathematical concepts and practical methods of data analysis strongly based on practical examples. The students shall be enabled to autonomously solve basic problems in data analysis. The students learn mastering of the requirements for algorithms specific to high performance computing. They are able to develop complex parallel algorithms, to analyze them and judge their efficiency.

Components of CSim2 module:

• CSim2-a. Data Analysis
  Teaching format: Lectures and exercises
  Weekly hours: 4 (150 hours in total)
  ECTS: 5 points
  Assessment: Solution of weekly exercises + 30-minutes oral discussion
  Contents: Probability, important distributions and their properties, expectation values, RMS, correlation, error propagation, tests, parameter estimation, max. likelihood, least squares, fits, optimisation, confidence intervals, detector unfolding, special methods (Bootstrap, Jacknife), parameterisation, profile likelihood method, marginalisation of systematic uncertainties, multivariate techniques.
   
• CSim2-b. Parallel Algorithms
  Teaching format: Lectures and exercises
  Weekly hours: 6 (240 hours in total)
  ECTS: 8 points
  Assessment: Solution of weekly exercises + 30-minutes oral discussion
  Contents: Parallel architectures and parallel programming models, speedup, efficiency, scalability, linear systems of equations, communication avoiding, sparse matrices and graphs, partitioning methods, iterative methods, colouring schemes, preconditioning using different methods (e.g., incomplete factorizations, domain decomposition and Schwarz iterative methods)

Workload: 360 hours (1 semester)
ECTS credits: 12 ECTS
Term: Winter (3^rd semester)
Repeatablity: restricted to 3 attempts

Final assessment: electronic module examination for 180 minutes (exam is counted as 10 ECTS)

Pre-requisites for the final exam:
• successfully completed CSim1 Module;
• successfully completed CS1 Module;
• ungraded exercises for Lab Course II (2 ECTS) with at least 50% of the exercise points and 50% of the project.
* Knowledge of numerical mathematics, basic algorithms and programming from bachelor are assumed.

Description of the module: Mastering the fundamental mathematical concepts underlying the master programme. Acquisition of basic knowledge of numerical algorithms and their applications in natural sciences and mathematics. Ability to write computer programs to implement the algorithms. The students are parallel able to use this knowledge independently and apply it to solve projects in a laboratory course.

Components of CSim3 module:

• CSim3-a.  Introduction to Computer Simulation II
  Teaching format: Lectures
  Weekly hours: 2 (120 hours in total)
  Contents: Physical and mathematical problems will be discussed together with the parallel algorithms used to solve them: Linear algebra (matrix product, Lanczos and CG algorithm and others); Differential equations; Many-body problems; Monte Carlo simulation of statistical systems.
   
• CSim3-b. Lab Course II
  Teaching format: Lectures and lab exercises
  Weekly hours: 4 (240 hours in total)
  ECTS: 2 points
  Assessment: Ungraded exercises with at least 50% of the exercise points and 50% of the project
  Contents: Introduction to MPI; An application: numerical integration; Collective communication; Fox's algorithm for parallel matrix multiplication; Strong/weak scaling, Amdahl's law; OpenMP; Hybrid programming with MPI & OpenMP; Monte Carlo simulations of a scalar field; GPU Parallel Programming with CUDA. Project work: e.g., Parallelizing the Poisson equation or Monte Carlo Simulation of a statistical system on a lattice (4d Ising model, q-state Potts models, 3d two-component scalar field theory); Many-Body Simulations (Lennard-Jones potential with systolic algorithm), Time-Dependent Schrödinger Equation; Electromagnetic Radiation; Computational Fluid Flow, etc.