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IMPACT Program
Students in summer on north campus, red gears in background. © Roland Baege​/​TU Dortmund

Course Description

As a central component of the IMPACT program, six sessions per week are offered with subject-specific content for the preparation of studies. Four of these six sessions are dedicated to repeating the most important mathematical and statistical basics and are distributed over the eight-week long IMPACT program as described in the following:

Step 1

In the first two weeks, a brief repetition of the most important mathematical methods will take place, ensuring that everyone starts at the same level and knows all the important basics.
This includes:

  • Linear Algebra: Vector spaces, matrices and equation systems, linear maps, QR-, and singular value decomposition, numerical aspects, generalized inverses,
  • Differential Calculus with several variables: Derivatives, inverse and implicit  functions, Taylor expansion and extreme values,
  • Integral calculus with several variables, and
  • Proofing techniques.

Step 2

In the weeks three and four, a repetition of the concept of probability and its implications will take place. These two weeks prepare for the exam of the pre-requisite course “Probability”.
In detail, this includes:

  • Concepts of probability, distributions, conditional probability and independence, Bayes’ rule, sequences of events,
  • Sampling, Binomial distribution, Normal approximation, Poisson distribution,
  • Random variables, expectation and variance,
  • Probability densities, Exponential and Gamma distributions, substitutions, cumulative distribution functions,
  • Joint distributions, Uniform and Normal distributions, and
  • Dependence, conditional distributions, covariance and correlation.

Step 3

The remaining four weeks are dedicated to an exhaustive introduction to statistical inference. These four weeks prepare for the exam of the pre-requisite course “Inference”.
In detail, this includes:

  • Parametric point estimation: method of moments and maximum likelihood; consistency; sufficiency; error, bias and loss; completeness; Rao-Cramer-bound; invariance; Bayesian estimation,
  • Parametric interval estimation: confidence intervals, especially for Normal distribution parameters, finding methods, Bayesian estimation, and
  • Tests of hypotheses: simple and composite hypotheses, loss function, (uniformly) most powerful tests, unbiased tests, tests for (multivariate) Normal distribution parameters, Chi-square tests, relation to confidence intervals.

Step 4

During the entire 8 weeks of the program, the programming course "Introduction to R" will take place with one theoretical and one practical session per week.  It teaches the basics of the statistical language R, which will be used in most lectures of the Department of Statistics.
This includes:

  • Assignments, elementary operators, data types, data structures, input/output of data,
  • Programming constructs such as loops and case differentiation,
  • Creating your own functions, 
  • Dealing with stat. distributions incl. drawing random numbers and simulations, 
  • Object-oriented (S3, S4) programming and
  • efficient programming, scoping rules and parallel programming, computing with R.
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