Department of Computer Science DIKU > Study programmes > M.Sc. in Computer Science > Computational and math...

Competence profile and curriculum for Computational and mathematical modelling (CMM) (supplementing GCS):

• Mastering the Basic Tools of Modelling. Explain various methods, techniques and models. Explain the individual steps of the scientific work process of modelling. In general terms this corresponds to analyzing the problem and possibly available data, building ideal mathematical models, deriving computational models, analyzing or simulating results, and comparing them with previous steps, or unseen data for natural phenomena.
• Analysis and Syntheses of Sampled Data. Evaluate the usage of given sampled data, in particular in 2 and 3-dimensional images. This includes evaluating which models are suitable for the given data, and evaluating sampling errors, usefulness, and significance of the data.
  Analyze all aspects of the originating problem to be included in a model and evaluate which ones are appropriate to include. This involves data analysis, and a clear specification of the basic assumptions.
• Apply a modelling process in order to synthesize a mathematical model of a given problem.
  Effects of Mathematical Models. Understand and explain the degradation in the mathematical and computational models.
• Reflect over the impact of modelling choices in relation to the originating problem and implementation.
• Numerical Implementation. Implement a model on a computer and reflect over the implementation in relation to the mathematical model and the original problem.
  Apply and use mathematical and numerical methods. This involves recasting the mathematical model into a computationally feasible form.
• Experiments. Formulate hypotheses for experiments, perform experiments, compare and evaluate results of experiments. This involves quantifying how well the final solution actually solves the problem.

Curriculum:

Prerequisites for CMM-profile students

The real (as opposed to formal) expected prerequisites for studying under the CMM-profile at DIKU is as follows. We expect all students to be competent programmers, able to quickly learn new programming languages and programming methods. We expect students to have an operational and basic mathematical training with focus on calculus, linear algebra, numerical analysis, and statistics. We expect mature and independent students able to fill out gaps in their knowledge without being asked to, to work independently, to ask for help when needed, and to express the result of their study orally as well as in written form.

In more detail, the CMM-profile at DIKU covers scientific areas such as image analysis, machine learning, simulation, and graphics and animation. These are all disciplines requiring extensive use of math. Common for most courses are that they involve practical elements, often implementation. Typical languages used are MATLAB, C++, PYTHON etc. We expect you to be familiar with several of these languages and able to quickly learn new languages yourself. More specifically, we expect you to have passed courses in programming corresponding to at least 15 ECTS. Additional, we expect you to have extensive programming experience e.g. obtained by using programming in non-programming courses. The expected mathematical skills roughly correspond to what may be obtained studying mathematics for about 30-60 ECTS. Basic required disciplines are 1) Mathematical analysis (calculus) including complex numbers, functions of several variables, continuity, integration and differential calculus, series, Taylor series, simple differential equations; 2) Linear algebra including eigenvector analysis, change of basis, ortho-normalization etc. 3) Basic probability theory and statistics including normal distribution and how to compute mean, variance and covariance estimators as well as Bayes rule. The abovementioned disciplines are the bare minimum. Students will benefit from knowledge on: Calculus of variation, Multivariate statistics and Bayesian estimation, linear and non-linear regression, Geometry etc. Also, knowledge on discrete mathematics will be advantageous.