                             Mathematics Main Site  Program Specializations Challenges New Curriculum 2015 Handbook 2014 Concept Requirements Study Plan Courses Faculty Career Admission FAQ Mathematics BSc Graduate Program Visiting Program Summer School  Program Contact: Marcel Oliver Professor of Mathematics m.oliver@jacobs-university.de Research I, 107 +49 421 200 3212     Print version # Courses

## Applied and Computational Mathematics

### 110101: General Mathematics and Computational Science I

 Short Name: GenMathCPS I Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: Yes

#### Course contents

General Mathematics and Computational Science I and II are the introductory first year courses for students in Mathematics and Applied and Computational Mathematics. In addition, these courses address anyone with an interest in mathematics and mathematical modeling. Each semester includes a selection of ``pure'' and ``applied'' topics which provide a solid foundation for further study, convey the pleasure of doing mathematics, and relate mathematical concepts to real-world applications.

Topics covered in the first semester are:

• Fundamental concepts: sets, relations, functions, equivalence classes.
• Numbers: Peano axioms, proof by induction, construction of integers and rational numbers.
• Discrete Mathematics: combinatorics, binomial coefficients, generating functions, applications to elementary discrete probability.
• Inequalities: Geometric-arithmetic mean inequalities, Cauchy inequality; Laplace's method and Stirling's approximation.
• Difference equations: linear first order difference equations, nonlinear first order difference equations, equilibrium points and their stability, linear second order difference equations; modeling with difference equations.

### 110102: General Mathematics and Computational Science II

 Short Name: GenMathCPS II Type: Lecture Credit Points: 5 Prerequisites: 110101 Corequisites: None Tutorial: Yes

#### Course contents

This course continues General Mathematics and Computational Science I with the following selection of topics:
• Groups: Basic properties and simple examples, Euclidean symmetries of the plane, symmetry groups of subsets of the plane, symmetry groups of polyhedra.
• Graph Theory: Graphs and parity, trees, Euler's formula and Euler characteristic, pairings, Eulerian graphs.
• Stochastic Modeling: Simple discrete stochastic systems, continuum limits, introduction to entropy.
• Linear Programming: graphical method, simplex method, duality.
• Fourier Transform: Discrete Fourier transform, fast Fourier transform, Fourier transform on groups.

### 110111: Natural Science Lab Unit - Symbolic Software

 Short Name: NatSciLab SymbSoft Type: Lab Credit Points: 2.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The Natural Science Lab Units in Mathematics and ACM will introduce the computer as a tool for the working mathematician, as well as for scientists in many other fields.

The Lab Unit Symbolic Software introduces Mathematica, a software package that can perform complex symbolic manipulations such as solving algebraic equations, finding integrals in closed form, or factoring mathematical expressions. Mathematica also has powerful and flexible graphing capabilities that are useful for illustrating concepts as well as numerical data. The computer will be used as a tool in this course so that you will also learn some mathematics alongside learning to use the computer program.

### 110112: Natural Science Lab Unit - Numerical Software

 Short Name: NatSciLab NumSoft Type: Lab Credit Points: 2.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The Natural Science Lab Units in Mathematics and ACM will introduce the computer as a tool for the working mathematician, as well as for scientists in many other fields.

The Lab Unit Numerical Software introduces Matlab and its free cousin Octave, software packages that allow easy and in many cases efficient implementations of matrix-based ``number crunching''. The software is ideal for numerical work such as solving differential equations or analyzing large amounts of laboratory data. The computer will be used as a tool in this course so that you will also learn some mathematics alongside learning to use the computer program.

This Lab Unit is particularly suited for students from both schools interested in experiments, as Matlab is used as a standard tool for analyzing and visualizing data in many fields of research. 1#1 10202

### 110231: Nonlinear Dynamics Lab

 Short Name: NLDLab Type: Lab Credit Points: 7.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The Nonlinear Dynamics Lab is an introduction to a variety of nonlinear phenomena and chaos through experiments. Most experiments will be done in a virtual laboratory, your laptop, but we will also include a few ``wet-lab'' experiments. Programming environments will be Scientific Python for number crunching and Mathematica for symbolic computing.

Topics include nonlinear electric oscillators, coupled pendula, and pattern formation in chemical reactions. A main focus of the lab is the development of standard tools for the numerical solution of differential equations, the application of automated tools for bifurcation analysis, and continuation methods. We will also implement simple agent-based models and pseudo-spectral PDE solvers for reaction-diffusion equations.

The lab is accessible to second and third year students in Physics, Mathematics, and EE/CS who have completed the recommended course load of these majors. Prerequisite is a willingness to learn about differential equations and the associated calculus.

### 110221: Derivatives Lab

 Short Name: DerivLab Type: Lab Credit Points: 7.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The lab gives a first practical introduction to stochastic processes and to the pricing of derivative assets in finance.

Topics include an introduction to finance (bonds, yields, immunization), binomial tree models, discrete Brownian paths, stochastic ODEs, Monte-Carlo methods, finite differences solutions for the Black-Scholes equation, and an introduction to time series analysis, parameter estimation, and calibration. Students will program and explore all basic techniques in a numerical programming environment and apply these algorithms to real data whenever possible.

### 110262: Applied Differential Equations and Modeling

 Short Name: ApplDEMod Type: Lecture Credit Points: 5 Prerequisites: 120101 Corequisites: None Tutorial: No

#### Course contents

This course offers an introduction to ordinary differential equations and their applications. Mathematical modeling of continuous-time dynamics has its origins in classical mechanics but is now prevalent in all areas of physical and life sciences. Attempting to solve such problems often leads to a differential equation. Consequently, a variety of analytical and numerical methods have been developed to deal with various classes of equations and initial value problems, the most important of which is the class of linear equations. Other methods (such as Laplace transform) for solving many differential equations of special form will also be discussed. The course underlines the importance of qualitative analysis of differential equations, with a discussion of simple models such as the Lotka-Volterra equation.

All students in the School of Engineering and Science with and interest in the application of Mathematics to real-life problems, and have a mathematical background equivalent to either Engineering and Science Mathematics 1B (Multivariable Calculus, ODE) or Analysis I/II should consider taking this course as a home school elective. Students of ACM can take this course as part of their second year major requirements.

### 110301: Introduction to parallel programming with MPI and OpenMP

 Short Name: MPI/Open MP Workshop Type: Lab Credit Points: 2.5 Prerequisites: 120202 Corequisites: None Tutorial: No

#### Course contents

This intersession workshop is a practical introduction to parallel programming. The focus is on the Message-Passing Interface (MPI) which is the standard programming method for parallel computers with distributed memory, in particular PC-clusters. The last day of the workshop is devoted to OpenMP which is used to program computers with shared memory.

The workshop comprises lectures and hands-on MPI programming sessions.

### 110341: Numerical Analysis

 Short Name: NumAnal Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

This course an advanced introduction to Numerical Analysis. It complements ESM 4A - Numerical Methods, placing emphasis, on the one hand, on the analysis of numerical schemes, on the other hand, focusing on problems faced in large-scale computations. Topics include sparse matrix linear algebra, large scale and/or stiff systems of ordinary differential equations, and a first introduction to methods for partial differential equations.

### 110361: Mathematical Modeling in Biomedical Applications

 Short Name: MathMod BioMed Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

The course discusses the area of mathematical modeling in biomedical applications. It includes an introduction into the basic principles of mathematical modeling, and it covers a variety of models for growth and treatment of cancer with increasing complexity ranging from simple ordinary differential equations to more complicated free boundary problems and partial differential equations. Further models for the description of physiology in the human body like blood flow and breathing are briefly touched as well.

### 110391: Guided Research Applied and Computational Mathematics I

 Short Name: GR ACM I Type: Self Study Credit Points: 7.5 Prerequisites: Permission of instructor Corequisites: None Tutorial: No

#### Course contents

Guided Research allows study, typically in the form of a research project, in a particular area of specialization that is not offered by regularly scheduled courses. Each participant must find a member of the faculty as a supervisor, and arrange to work with him or her in a small study group or on a one-on-one basis.

Guided research has three major components: Literature study, research project, and seminar presentation. The relative weight of each will vary according to topic area, the level of preparedness of the participant(s), and the number of students in the study group. Possible research tasks include formulating and proving a conjecture, proving a known theorem in a novel way, investigating a mathematical problem by computer experiments, or studying a problem of practical importance using mathematical methods.

Third year students in Mathematics and ACM may take two semesters of Guided Research. The Guided Research report in the spring semester will typically be the Bachelor Thesis which is a graduation requirement for every undergraduate. Note that the Bachelor Thesis may also be written as part of any other course by arrangement with the respective instructor of record.

Students are responsible for finding a member of the faculty as a supervisor and report the name of the supervisor and the project title to the instructor of record no later than the end of Week 4. A semester plan is due by the end of Week 6.

### 110392: Guided Research and BSc Thesis in Applied and Computational Mathematics II

 Short Name: GR ACM II Type: Self Study Credit Points: 7.5 Prerequisites: Permission of instructor Corequisites: None Tutorial: No

#### Course contents

As for Guided Research Applied and Computational Mathematics I.

## Engineering and Science Mathematics

### 120101: ESM 1A - Single Variable Calculus

 Short Name: ESM 1A Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: Yes

#### Course contents

The courses from the Engineering and Science Mathematics 1 series provide the foundation for all other Engineering and Science Mathematics courses. Taking at least one of them is mandatory for all Engineering and Science majors. Emphasis is on the use of basic mathematical concepts and methods in the sciences, rather than on detailed proofs of the underlying mathematical theory.

The course ESM 1A covers basic differential and integral calculus of functions of one variable. It starts with a brief review of number systems and elementary functions, then introduces limits (for both sequences and functions) and continuity, and finally derivatives and differentiation with applications (tangent problem, error propagation, minima/maxima, zero-finding, curve sketching). A short chapter introduces complex numbers.

The second half of the semester is devoted to integration (anti-derivatives and Riemann integral) with applications, and concluded by brief introductions to scalar separable and linear first-order differential equations, and the convergence of sequences and power series.

Compared to ESM 1C which covers similar material, this course assumes a rigorous high school preparation in Mathematics and leaves more room for explaining mathematical concepts (as needed for the majority of SES majors).

### 120111: ESM 1B - Multivariable Calculus, ODE

 Short Name: ESM 1B Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: 120101 Tutorial: Yes

#### Course contents

Engineering and Science Mathematics 1B introduces multivariable calculus and ordinary differential equations, topics of particular importance to the physical sciences. Students of ACM, Physics, and Electrical Engineering are strongly encouraged to take this course in their first semester. The curriculum is designed so that ESM 1A and ESM 1B can be taken at the same time.

The course covers vector algebra (three-dimensional vectors, dot product, cross product), equations of lines, planes, and spheres, Euclidean distance, vector-valued functions, space curves, functions of several variables, partial derivatives, chain rule, gradient, directional derivative, extrema, Lagrange multipliers, double and triple integrals with applications, change of variables, vector fields, divergence, curl, cylindrical and spherical coordinates, line integrals, Green's theorem in the plane, surface and volume integrals, divergence theorem, Stokes' theorem, introduction to ordinary differential equations (direction field, the question of existence and uniqueness of solutions), separable and exact equations, integrating factors, and linear higher order ODEs with constant coefficients.

### 120102: ESM 2A - Linear Algebra, Probability, Statistics

 Short Name: ESM 2A Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: Yes

#### Course contents

Second semester Engineering and Science Mathematics is offered in two parallel classes that cover a common set of core topics at approximately the same level of difficulty. However, style of exposition and selection of additional material will vary slightly to meet the needs of different groups of majors.

ESM 2A is recommended for students majoring in Life Sciences or Chemistry. It covers the following topics: Linear Algebra (equations of lines and planes, matrix algebra, system of linear equations, matrix inverse, vector spaces, linear independence, basis, dimension, linear transformations, change of basis, eigenvalues and eigenvectors, diagonalization). Probability (basic notions of set theory, outcomes, events, sample space, probability, conditional probability, Bayes' rule, permutations and combinations, random variables, expected value, variance, binomial, Poisson, and normal distributions, central limit theorem). Statistics (one-sample hypothesis testing, two sample hypothesis testing, chi-square hypothesis testing, analysis of variance, bivariate association, simple linear regression, multiple regression and correlation).

### 120112: ESM 2B - Linear Algebra, Fourier, Probability

 Short Name: ESM 2B Type: Lecture Credit Points: 5 Prerequisites: 120101 or 120111 or 120121 Corequisites: None Tutorial: Yes

#### Course contents

Second semester Engineering and Science Mathematics is offered in two parallel classes that cover a common set of core topics at approximately the same level of difficulty. However, style of exposition and selection of additional material will vary slightly to meet the needs of different groups of majors.

ESM 2B is recommended for students who do not intend to major in the Life Sciences or Chemistry. It covers the following topics:

• Linear Algebra (equations of lines and planes, matrix algebra, system of linear equations, matrix inverse, vector spaces, linear independence, basis, dimension, linear transformations, change of basis, eigenvalues and eigenvectors, diagonalization, inner products, orthonormalization)
• Fourier methods (expanding functions in terms of orthonormal function systems, Fourier series, Fourier transform, Dirac delta-function)
• Probability (basic notions of set theory, outcomes, events, sample space, probability, conditional probability, Bayes' rule, permutations and combinations, random variables, expected value, variance, binomial, Poisson, and normal distributions, central limit theorem).

### 120201: ESM 3A - Advanced Linear Algebra, Stochastic Processes

 Short Name: ESM 3A Type: Lecture Credit Points: 5 Prerequisites: 120102 or 120112 Corequisites: None Tutorial: No

#### Course contents

Engineering and Science Mathematics 3A is mandatory for students in Electrical Engineering and Computer Science, and is also recommended as a home school elective for students who would like to learn more advanced topics from Linear Algebra and Probability than were covered in second semester Engineering and Science Mathematics.

The course covers matrix factorizations such as Jordan normal form, QR, and SVD with their typical applications, for example, to least-squares and low-rank approximation problems. It deepens the understanding of discrete and continuous random variables and vectors (joint and conditional distributions and moments, correlation and covariance, generating functions), of sums of i.i.d. random variables and limit theorems, and introduces to the basic types of stochastic processes (Markov chains, Poisson process, Wiener process) and their properties.

### 120211: ESM 3B - Complex Variable Calculus, PDE

 Short Name: ESM 3B Type: Lecture Credit Points: 5 Prerequisites: 120102 or 120112 Corequisites: None Tutorial: No

#### Course contents

Engineering and Science Mathematics 3B is mandatory for students of Physics and for some students in Applied and Computational Mathematics (please consult program handbook).

The course covers the Cauchy-Riemann equations, singularities and zeros, branch cuts, potential theory, conformal transformations, complex integrals, Cauchy's theorem and integral formula, Taylor and Laurent series, residue theorem with applications; the basic linear PDEs (wave, heat, Laplace equation), linear first order PDEs, inhomogeneous and second order equations, characteristics, uniqueness, separation of variables, transform methods, an introduction to Green's functions, the Dirichlet and Neumann problems, and an outlook on nonlinear PDEs.

### 120202: ESM 4A - Numerical Methods

 Short Name: ESM 4A Type: Lecture Credit Points: 5 Prerequisites: 120112 or 100221 Corequisites: None Tutorial: No

#### Course contents

Engineering and Science Mathematics 4A is mandatory for students of Electrical Engineering, Computer Science, and Applied and Computational Mathematics. It is also recommended as a home school elective for students who would like to get a short, one-semester introduction to Numerical Methods.

This course is a hands-on introduction to numerical methods. It covers root finding methods, solving systems of linear equations, interpolation, numerical quadrature, solving ordinary differential equations, the fast Fourier transform, and optimization. These methods are crucial for anyone who wishes to apply mathematics to the real world, i.e. computer scientists, electrical engineers, physicists and, of course, mathematicians themselves.

## Mathematics

### 100211: Analysis I

 Short Name: Analysis I Type: Lecture Credit Points: 7.5 Prerequisites: None Corequisites: None Tutorial: Yes

#### Course contents

Analysis I/II is one of the fundamental courses in the mathematical education (together with Linear Algebra I/II). Its goal is to develop calculus in a rigorous manner and in sufficient generality to prepare the student for advanced work in mathematics. At the same time, the content is chosen so that students arrive quickly at central concepts which are used in essentially all mathematics courses, and which are needed in the exact sciences.

The Analysis sequence begins with a quick review of natural, rational and real numbers (which are assumed as known), and introduces the field of complex numbers. The axiom of completeness distinguishes the real numbers from the rationals and marks the beginning of Analysis. The complex exponential and trigonometric functions are defined.

Metric spaces are introduced and used to define continuity and convergence in a general framework. The Bolzano-Weierstraß and the Heine-Borel theorems are proved. The intermediate and maximal value theorems for functions on the real line are discussed as consequences of connectedness and compactness on metric spaces. Sequences of functions are discussed, in particular uniform convergence, as well as the continuity, differentiability, integrability of the limit function.

Differentiability of functions on the real line is introduced. The mean value theorem and Taylor's theorem is discussed.

The Riemann integral in one variable is introduced. The relation between the derivative and the integral, i.e., the fundamental theorem of calculus is proved.

This course has no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this class in their first semester. However, a familiarity with mathematical reasoning and proof (e.g. proof by induction or by contradiction), such as introduced in General Mathematics and Computational Science I, is required.

### 100212: Analysis II

 Short Name: Analysis II Type: Lecture Credit Points: 7.5 Prerequisites: 100211 Corequisites: 100221 or 120102 or 120112 (if not already taken) Tutorial: Yes

#### Course contents

This course is a continuation of Analysis I. Its main theme is to extend the concepts from Analysis I, in particular differentiation and integration, to functions of several variables. Taylor's theorem in several variables, the implicit function theorem and the inverse function theorem are proved. (Riemann) integration in several real variables is introduced, including the transformation formula for integrals in several variables.

### 100221: Linear Algebra I

 Short Name: LinAlg I Type: Lecture Credit Points: 7.5 Prerequisites: None Corequisites: None Tutorial: Yes

#### Course contents

Together with Analysis I, this is one of the basic mathematics courses. It introduces vector spaces and linear maps, which play an important role throughout mathematics and its applications.

The course begins by introducing the concept of a vector space over an arbitrary field (for example, the real or complex numbers) and the concept of linear independence, leading to the notion of ``dimension''. We proceed to define linear maps between vector spaces and discuss properties such as nullity and rank. Linear maps can be represented by matrices and we show how matrices can be used to compute ranks and kernels of linear maps or to solve linear systems of equations.

In order to study some geometric problems and talk about lengths and angles, we introduce an additional structure called the inner or scalar product on real vector spaces. Properties of Euclidean vector spaces and orthogonal maps are treated, including the Cauchy-Schwarz inequality, Gram-Schmidt orthonormalization and orthogonal and unitary groups.

An endomorphism is a linear map from a vector space to itself and is represented by a square matrix. We study the trace and determinant of endomorphisms and matrices and discuss eigenvalues and eigenvectors. We discuss the question whether a matrix is diagonalizable and state the theorem on Jordan Normal Form which provides a classification of endomorphisms.

This course has no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this class in their first semester. However, a familiarity with mathematical reasoning and proof (e.g. proof by induction or by contradiction), such as introduced in General Mathematics and Computational Science I, is required.

### 100313: Real Analysis

 Short Name: RealAna Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

Real Analysis is one of the core advanced courses in the Mathematics curriculum. It introduces measures, integration, elements from functional analysis, and the theory of function spaces. Knowledge of these topics, especially Lebesgue integration, is instrumental in many areas, in particular, for stochastic processes, partial differential equations, applied and harmonic analysis, and is a prerequisite for the graduate course in Functional Analysis.

The course is suitable for undergraduate students who have taken Analysis I/II, and Linear Algebra I; it should also be taken by incoming students of the Graduate Program in the Mathematical Sciences. Due to the central role of integration in the applied sciences, this course provides an excellent foundation for mathematically advanced students from physics and engineering.

### 100361: Ordinary Differential Equations and Dynamical Systems

 Short Name: DynSystems Type: Lecture Credit Points: 7.5 Prerequisites: 100212 and 100221 Corequisites: None Tutorial: Yes

#### Course contents

Dynamical systems is an topic which links pure mathematics with applications in physics, biology, electrical engineering, and others. The course will furnish a systematic introduction to ordinary differential equations in one and several variables, focusing more on qualitative aspects of solutions than on explicit solution formulas in those few cases where such exist. It will be shown how simple differential equations can lead to complicated and interesting, often ``chaotic'' dynamical behavior, and that such arise naturally in the ``real world''. We will also discuss time-discrete dynamical systems (iteration theory) with its relations and differences to differential equations.

### 100362: Introductory Partial Differential Equations

 Short Name: Intro PDE Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

This course is a rigorous, but elementary introduction to the theory of partial differential equations: classification of PDEs, linear prototypes (transport equation, Poisson equation, heat equation, wave equation); functional setting, function spaces, variational methods, weak and strong solutions; first order nonlinear PDEs, introduction to conservation laws; exact solution techniques, transform methods, power series solutions, asymptotics.

This course alternates with Partial Differential Equations which takes a functional analytic approach to partial differential equations.

### 100472: Partial Differential Equations

 Short Name: PDE Type: Lecture Credit Points: 7.5 Prerequisites: 100313 Corequisites: None Tutorial: No

#### Course contents

The course is an introduction to the theory of partial differential equations in a Sobolev space setting. Topics include Sobolev spaces, second order elliptic equations, parabolic equations, semi-groups, and a selection of nonlinear problems.

This course differs from the approach taken in Introductory Partial Differential Equations which focuses on solutions in classical function spaces via Greens functions. It may therefore be taken by students who have attended Introductory Partial Differential Equations, but we will again start from basic principles so that Introductory Partial Differential Equations is not a prerequisite.

### 100382: Stochastic Processes

 Short Name: StochProc Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

This course is an introduction to the theory of stochastic processes. The course will start with a brief review of probability theory including probability spaces, random variables, independence, conditional probability, and expectation.

The main part of the course is devoted to studying important classes of discrete and continuous time stochastic processes. In the discrete time case, topics include sequences of independent random variables, large deviation theory, Markov chains (in particular random walks on graphs), branching processes, and optimal stopping times. In the continuous time case, Poisson processes, Wiener processes (Brownian motion) and some related processes will be discussed.

This course alternates with Applied Stochastic Processes.

### 100383: Applied Stochastic Processes

 Short Name: ApplStochProc Type: Lecture Credit Points: 7.5 Prerequisites: 100212 Corequisites: None Tutorial: Yes

#### Course contents

This course aims at an introduction to the mathematical theory of financial markets that discusses important theoretical concepts from the theory of stochastic processes developed in parallel to their application to the mathematical finance.

The applied part of this course revolves around the central question of option pricing in markets without arbitrage which will be first posed and fully solved in the case of binomial model. Interestingly enough, many of the fundamental concepts of financial mathematics such as arbitrage, martingale measure, replication and hedging will manifest themselves, even in this simple model. After discussing conditional expectation and martingales, more sophisticated models will be introduced that involve multiple assets and several trading dates. After discussing the fundamental theorem of asset pricing in the discrete case, the course will turn to continuous processes. The Wiener process, Ito integrals, basic stochastic calculus, combined with the main applied counterpart, the Black-Scholes model, will conclude the course.

This course alternates with Stochastic Processes.

## Electrical Engineering and Computer Science

### 320101: General Computer Science I

 Short Name: GenCompSci I Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The course covers the fundamental concepts and techniques of computer science in a bottom-up manner. Based on clear mathematical foundations (which are developed as needed) the course discusses abstract and concrete notions of computing machines, information, and algorithms, focusing on the question of representation vs. meaning in Computer Science.
To have a theoretical notion of computation, we introduce inductively defined structures, term representations, abstract interpretation via equational substitution. This is contrasted with a first concrete model of computation: Standard ML, which will also act as the primary programming language for the course. We cover a basic subset of ML that includes types, recursion, termination, lists, strings, higher-order programming, effects, and exceptions. Back on the theoretical side, we cover string codes, formal languages, Boolean expressions (syntax) and Boolean Algebras (semantics). The course introduces elementary complexity theory (big-O), applying it to analyzing the gate-complexity of Boolean Expressions (prime implicants and Quine McCluskey's algorithm).

### 320102: General Computer Science II

 Short Name: GenCS II Type: Lecture Credit Points: 5 Prerequisites: 320101 Corequisites: None Tutorial: No

#### Course contents

The course continues the introduction of the fundamental concepts and techniques of Computer Science. Building on Boolean Algebra, it introduces Propositional Logic as a model for general logical systems (syntax, semantics, calculi). Based on elementary graph theory, combinatory circuits are introduced as basic logic computational devices. Interpreting sequences of Boolean values as representations of numbers (in positional number systems, twos-complement system), Boolean circuits are extended to numerical computational machines (presenting adders, subtracters, multipliers) and extended to basic ALUs. The course introduces very elementary computer architectures and assembly language concrete computational devices, and compares them to Turing machines to fathom the reach of computability.

In a final part of the course, two topics of general Computer Science are covered in depth, for instance ``search algorithms'' and ``programming as search'' to complement the rather horizontal (i.e.^Mmethods-oriented) organization of the course with vertically (i.e.^Mgoal-oriented) organized topics.

Topics: Propositional logic, calculi, soundness, completeness, automated theorem proving, combinatory circuits, assembler Turing machines, search, logic programming.

### 320111: NatSciLab Unit Computer Science I

 Short Name: NatSciLab CS I Type: Lab Credit Points: 2.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This lab unit is a first introduction to programming using the programming language C. The course covers fundamental procedural programming constructs and simple algorithms in a hands-on manner.

### 320112: NatSciLab Unit Computer Science II

 Short Name: NatSciLab CS II Type: Lab Credit Points: 2.5 Prerequisites: 320111 Corequisites: None Tutorial: No

#### Course contents

This lab unit is a continuation of the first year CS lab unit and deepens the basic programming skills from the first lab. It covers advanced topics of C programming such as data structures, file handling, libraries, and debugging techniques.

### 320201: Fundamental Computer Science I (Algorithms and Data Structures)

 Short Name: Fund CS I Type: Lecture Credit Points: 5 Prerequisites: 320102, 120112 Corequisites: None Tutorial: No

#### Course contents

This course introduces a basic set of data structures and algorithms that form the basis of almost all computer programs. The data structures and algorithms are analyzed in respect to their computational complexity with techniques such as worst case and amortized analysis.

Topics: Fundamental data structures (lists, stacks, trees, hash tables), fundamental algorithms (sorting, searching, graph traversal).

### 300301: Dynamical Systems and Control

 Short Name: DynSys+Control Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

Dynamical systems in nature and technology often behave in a counter-intuitive fashion and are thus difficult to predict and to regulate. The counter-intuitive behavior comes from nonlinear interactions between the system components and the nonlinear processing of incoming information. This course is an introduction to nonlinear dynamics and control with a focus on a broad range of applications. Topics include:

1. Low dimensional autonomous dynamical systems: formulation as differential equation, flow, fixed points, stability, stability criteria, potentials and Lyapunov functionals, simple local bifurcations (saddle-node, pitchfork, transcritical, cusp, Hopf), simple numerical schemes, time-discrete maps (fixed points, stability), introduction to chaos.

2. Control for linear systems: general matrix-based solution for driven linear ODEs, reachability, controllability, observability, Gram-matrix for determining control laws and for reconstruction, linear-state feedback controller, stable-state estimation, introduction to optimal control.

3. Reaction-diffusion partial differential equations (activator-inhibitor, relations to control), stability of stationary solutions, Turing instability.

### 320322: Graphics and Visualization

 Short Name: CSGV Type: Lecture Credit Points: 5 Prerequisites: Please check on Campus Net Corequisites: Please check on Campus Net Tutorial: No

#### Course contents

Course topics: input and output devices, 2D and 3D graphic algorithms, transformations, projections, hidden line/surface removal, shading algorithms, color reduction. Role of the course in the curriculum: This course introduces the basic algorithms and techniques in computer graphics and data visualization. Students taking this course will develop an understanding how computer graphics are created and which algorithms are implemented by graphic processors. This course is recommended for all EECS students with an interest in data visualization and computer graphics.

### 300491: Convex Optimization

 Short Name: ConOpt Type: Lecture Credit Points: 5 Prerequisites: Please Check Campus Net Corequisites: Please Check Campus Net Tutorial: No

#### Course contents

Convex optimization is an important part of optimization in general. It deals with convex functions on convex domains. Convex problems are more general than linear ones but although convex optimization is about non-linear problems, optimum solutions are still globally optimal. The course is an introduction to the theory and application of convex optimization. It provides a wide variety of examples and discusses different optimization algorithms.

### 300493: Optimization Lab

 Short Name: OptLab Type: Lab Credit Points: 5 Prerequisites: Please Check Campus Net Corequisites: Please Check Campus Net Tutorial: No

#### Course contents

This is a hands-on extension to the optimization lecture. Based on solving several optimization problems, students develop broad practical experience concerning implementation and application of optimization techniques. Topics covered include standard optimization tools but also genetic algorithms and learning algorithms. A large part of the lab focuses on algorithms for games (like reversi).

### 300501: Computational Electromagnetics

 Short Name: CompElectromagnetics Type: Lecture Credit Points: 5 Prerequisites: Please Check Campus Net Corequisites: Please Check Campus Net Tutorial: No

#### Course contents

Recent advances in diverse engineering and scientific disciplines, such as optical and wireless communications, electronic computing, medical imaging, radar, and remote sensing, have been enabled by high-frequency electronic devices operating in the radiofrequency, microwave, and optical regimes. Although the behavior of such devices is completely described by Maxwell's equations, direct analytical solutions are only possible for very simple structures. With the advent of powerful computers, however, exact numerical solutions of Maxwell's equations have been developed, allowing highly accurate characterization of nearly arbitrary structures. Inclusion of these computational electromagnetic (CEM) techniques in powerful computer assisted design (CAD) packages allows the engineer to test and modify potential high-frequency designs conveniently on a computer, shortening the design cycle and saving valuable resources.

This course covers the most important developments in CEM, allowing students to visualize the behavior of complex devices, to understand the benefits/limitations of commercial packages, and to develop new CEM codes when needed. Although the target application is electromagnetics, the same methods for obtaining numerical solutions to partial differential equations can be applied to general problems in physics and engineering. This lecture stresses an analytical treatment of the various CEM techniques, where the lecture is complimented by a number of short assignments requiring derivations or closed-form analysis. Students interested in gaining practical experience writing and applying CEM codes are encouraged to take the Computational Electromagnetics Lab in parallel.

Concepts Covered:

• Basic numerical techniques: numerical integration, Monte-Carlo analysis, solutions of simultaneous equations
• Finite-difference techniques: Laplace equation, the wave equation, finite-difference time-domain (FDTD), absorbing boundary conditions (ABC), eigenvalue problems and mode solutions
• Method-of-moments: Green's functions, expansion and weighting functions, surface and volume methods
• Variational methods: variational calculus, functionals, weighted residual method
• Finite-element method (FEM): element equations, mesh generation, solutions
• Introduction to modern developments: multipole techniques, ray-tracing, domain decomposition, hybrid methods

## Physics

### 200101: General Physics I

 Short Name: GenPhys I Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This course is an introduction to physics and its basic principles, covering classical mechanics and thermodynamics. It is a mandatory course for physics majors but can also serve as a general introduction to physics for all other majors.

It is neither the traditional experimental physics lecture, nor a pure theoretical physics course. Both aspects are combined and special emphasis is laid on general principles, not on extensive mathematical derivations. Nevertheless, the course teaches calculus based physics so that some basic mathematical knowledge will be required. Experiments are integrated into the lectures.

The course consists of the following two parts:

• Mechanics including: motion and coordinate systems; forces and Newton laws; work and energy; collisions and momentum; rotations, torque, angular momentum; Kepler laws and gravitation; continuum mechanics and elasticity; fluid mechanics; harmonic oscillator, damping, resonance; waves.
• Thermodynamics including: temperature, heat, heat capacity; transport phenomena; ideal gas, kinetic gas theory; MB distribution; Brownian motion; 1st law, energy, heat and work; 2nd law, cyclic processes, engines; entropy and statistical interpretation; thermodynamic potentials.

### 200102: General Physics IIA (Electromagnetism, Optics)

 Short Name: GenPhys IIA Type: Lecture Credit Points: 5 Prerequisites: 200101 Corequisites: None Tutorial: No

#### Course contents

This course is a continuation of General Physics I (200101). It is mandatory for physics majors, but also interesting for e.g. life science or electrical engineering majors. It is an introduction to physics, covering electromagnetism and optics. It is neither the traditional experimental physics lecture, nor a pure theoretical physics course. Both aspects are combined, special emphasis is laid on general principles, not on mathematical derivations. Nevertheless, the course teaches calculus based physics so that some basic mathematical knowledge will be required. Experiments are integrated into the lectures.

The course consists of the following two parts:

• Electromagnetism: electric charge, field and potential, capacitance and dielectrics; resistance and current; magnetic force and field; magnetization and induction; AC/DC circuits; Maxwell equations and electromagnetic waves.
• Optics: waves and acoustics; refractive index, reflection, dispersion, polarization, scattering; lenses, geometrical optics, optical instruments; interference, interferometers, diffraction, resolving power.

### 200103: General Physics IIB (Modern Physics)

 Short Name: GenPhys IIB Type: Lecture Credit Points: 5 Prerequisites: 200101 Corequisites: None Tutorial: No

#### Course contents

This course is a continuation of General Physics I (200101). It is mandatory for physics majors but also interesting for all other majors. It is also an introduction to physics, covering all aspects of modern physics such as quantum physics, atomic and nuclear physics, particle physics and relativity. It is neither the traditional experimental physics lecture, nor a pure theoretical physics course. Both aspects are combined, special emphasis is laid on general principles, not on mathematical derivations. Nevertheless, the course teaches calculus based physics and some mathematical knowledge will be required. Experiments are integrated into the lectures.

The course introduces the following topics:

• Special relativity: Lorentz transformation, rest mass.
• Quantum physics: photons, electrons, wave nature of particles; Schroedinger equation, Heisenberg uncertainty principle.
• Atomic physics: X-ray and atomic structure, periodic systems, spin electronic excitations, atomic spectra.
• Molecules and condensed matter: molecular bonds and vibrations; crystals and semiconductors.
• Nuclear and particle physics: elementary particles, accelerators and detectors, quarks, standard model, decay of nuclei, nuclear reactions, nuclear fusion and fission.

### 200111: NatSciLab Unit Physics I

 Short Name: NatSciLab Phys I Type: Lab Credit Points: 2.5 Prerequisites: None Corequisites: 200101 Tutorial: No

#### Course contents

The Natural Science Laboratory Course Module in Physics forms an integral part of first-year physics education at Jacobs University. The physics module occupies 8 of the 24 afternoon sessions of the first year Natural Science Laboratory Course. For students planning to major in the School of Engineering and Science, participation in the Natural Science Lab Course is mandatory (lectures and lab course modules have to correspond). For all other students wishing to enroll in the physics lab module, attendance of the General Physics lecture is co-requisite, since the lab course is taught in close coordination with the lecture. In the physics module, participants carry out 7 experiments in total covering topics of mechanics, thermodynamics and optics. Aims of the lab course are: (1) to gain hands on experience of the material taught in General Physics, (2) to learn how scientific experiments are planned, carried out, analysed, and reported, (3) learn about technical aspects of measuring and measuring devices.

### 200112: NatSciLab Unit Physics II

 Short Name: NatSciLab Physics II Type: Lab Credit Points: 2.5 Prerequisites: Please check on Campus Net Corequisites: Please check on Campus Net Tutorial: No

#### Course contents

The Natural Science Laboratory Course Module in Physics forms an integral part of first-year physics education at Jacobs University. The physics unit occupies 8 of the 24 afternoon sessions of the first year Natural Science Laboratory Course. For students planning to major in the School of Engineering and Science, participation in the Natural Science Lab Course in mandatory (lectures and lab course units have to correspond). For all other students wishing to enroll in the physics lab unit, attendance of the General Physics lecture is a co-requisite, since the lab course is taught in coordination with the lecture. In the physics unit, participants carry out 8 experiments in total covering topics in Electromagnetism and Quantum Physics. Aims of the lab course are: (1) to gain hands on experience of material taught in General Physics, (2) to learn how scientific experiments are planned, carried out, analyzed, and reported, (3) to learn about technical aspects of measuring and measuring devices.

## Life Sciences

### 520101: General Biochemistry and Cell Biology I

 Short Name: GenBCCB I Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This is a unique course that gives, over the first year of studies at Jacobs University, a comprehensive introduction to biochemistry and cell biology. At the end of the course, students will have gained knowledge of the foundations and the scope of the subject and of the specific scientific reasoning that underlies research in this field. Topics covered will be the biochemistry and biophysics of DNA, proteins (especially enzymes), carbohydrates, and lipids; the buildup and the breakdown of these substances; the (animal, plant, and bacterial) cell, its substructure, and its organelles; an introduction to the most common chemical reactions in living cells and the underlying thermodynamic, chemical, and kinetic principles, including metabolism and its regulation; and introductory overviews of specialized fields such as biophysics, structural biology, molecular machines, molecular neurobiology, immunology, molecular genetics, developmental biology, and cancer. Information about the techniques and strategies to obtain knowledge and to ask questions in molecular life science, as well as historical outlines, will accompany each topic.

This course requires solid High School knowledge of both biology and chemistry, or the willingness to acquire it at Jacobs University. Depending on their previous training, prospective Biochemistry and Cell Biology major students are advised to take General Chemistry or General Biology or both in addition to this course. General Biochemical Engineering is also a very useful complement.

### 520102: General Biochemistry and Cell Biology II

 Short Name: GenBCCB II Type: Lecture Credit Points: 5 Prerequisites: 520101 Corequisites: None Tutorial: No

#### Course contents

This is the second part of the comprehensive introduction to biochemistry and cell biology with special emphasis on the connections to the related fields chemistry and biology. In the spring semester, the emphasis of the course will be on more complex cell biological topics, such as the synthesis, topogenesis and breakdown of cellular components in the context of the cellular environment, and introductory overviews of specialized fields such as biophysics, structural biology, cell cycle, molecular neurobiology, immunology, DNA technology, developmental biology, and cancer. Information about the techniques and strategies to obtain knowledge and to ask questions in molecular life science, as well as historical outlines, will accompany each topic.

Good High School knowledge of both biology and chemistry, or the willingness to acquire it in self-study, is assumed. Prospective Biochemistry and Cell Biology major students are advised to take General Chemistry or General Biology or both in addition to this course.

### 520111: NatSciLab Unit Biochemistry and Cell Biology I

 Short Name: NatSciLab BCCB I Type: Lab Credit Points: 2.5 Prerequisites: Please check on Campus Net Corequisites: Please check on Campus Net Tutorial: No

#### Course contents

This course trains basic laboratory skills and gives an introduction to biochemical and cell biological work in the laboratory. The course parallels the general biochemistry and cell biology lecture. An introduction is given to substance classes on one hand and methods on the other. Course days include e.g., the handling of glass and micropipettes, balances, spectrophotometers and light microscopes. Experiments include gel filtration, thin layer chromatography of plant pigments, titration, pH-dependence of enzymes, identification of carbohydrates, microscopy of sperms and muscle etc. For each course day, a lab report is handed in.

### 520112: NatSciLab Unit Biochemistry and Cell Biology II

 Short Name: NatSciLab BCCB II Type: Lab Credit Points: 2.5 Prerequisites: Please check on Campus Net Corequisites: Please check on Campus Net Tutorial: No

#### Course contents

This course trains basic laboratory skills and gives an introduction to biochemical and cell biological work in the laboratory. The course parallels the general biochemistry and cell biology lecture. An introduction is given to substance classes on one hand and methods on the other.

As a continuation of the fall course, this time the focus lies on DNA and RNA. Course days include e.g., the handling of glass and micropipettes, balances, spectrophotometers and light microscopes. Experiments include isolation of DNA and RNA from pea seedlings, isolation of DNA from stressed C6 glioma cells and detection of an apoptotic DNA ladder by means of agarose gel electrophoresis, sterile cultivation of yeast cells, determination of cytotoxicity, fixation, staining and microscopic investigation of M phase cells.

### 520201: Advanced Biochemistry and Molecular Biology I

 Short Name: AdvBCMB I Type: Lecture Credit Points: 5 Prerequisites: 520101, 520102 Corequisites: None Tutorial: No

#### Course contents

The course intends to give a detailed understanding of the chemical reactions that underlie life. In the first part the structures, dynamics and chemistry of important biomolecules will be described. The thermodynamics and kinetics of ligand binding to proteins and enzyme catalysis will be explained and enzymatic catalysis explored at the molecular and atomic level. The second part focuses on metabolism and describes how energy is produced by living organisms and how the molecules of life are synthesised and degraded. A special focus will be set on common principles and the integration of the metabolism. The third part of the course explains how the genetic information stored in the DNA sequence is maintained and expressed. In addition the mechanism of DNA binding and modification by proteins and enzymes will be presented. The techniques of modern molecular biology will be described and the results of the human genome project discussed.

### 520202: Advanced Biochemistry and Molecular Biology II

 Short Name: AdvBCMB II Type: Lecture Credit Points: 5 Prerequisites: 520201 Corequisites: None Tutorial: No

#### Course contents

The course intends to give a detailed understanding of the chemical reactions that underlie life. In the first part the structures, dynamics and chemistry of important biomolecules will be described. The thermodynamics and kinetics of ligand binding to proteins and enzyme catalysis will be explained and enzymatic catalysis explored at the molecular and atomic level. The second part focuses on metabolism and describes how energy is produced by living organisms and how the molecules of life are synthesised and degraded. A special focus will be set on common principles and the integration of the metabolism. The third part of the course explains how the genetic information stored in the DNA sequence is maintained and expressed. In addition the mechanism of DNA binding and modification by proteins and enzymes will be presented. The techniques of modern molecular biology will be described and the results of the human genome project discussed.

### 550201: Bioinformatics and Computational Biology

 Short Name: BICB Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

Intention of the course is to provide an overview over current bioinformatic approaches in sequence and genome analysis by a direct linkage of the biological problem with the computational approaches to solve them. An important task of bioinformatics is to put data into a larger context by identifying statistical similarities between the data. Finding genes in DNA sequences, identifying common structural features in (evolutionarily) related protein sequences and extracting functional properties from the architecture of cellular networks are examples of this general strategy of bioinformatics, which will be highlighted throughout the course.

Major topics will be: Biological data, acquisition and storage, Similarity and Alignment, Pairwise and Multiple Sequence comparisons, Sequence patterns and motifs, Genome analysis, Genome signatures, Hidden Markov models, Networks.

### 550221: Bioinformatics Lab Course

 Short Name: BICB Lab Type: Lab Credit Points: 7.5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

Part 1: Sequence analysis. The increasing amount of biological data in particular of protein and DNA sequences requires students to gain practical experience with algorithms and computational tools for sequence analysis. The lab course intends to train students in the application of computational approaches to nucleic acid and protein sequence analysis and secondary structure prediction. The script language Perl will be introduced and students will be trained to write own applications and to program bioinformatics algorithms and methods. It will give a practical introduction and an overview on available and frequently applied sequence analysis methods including the software to align and compare sequences and to predict coding and non-coding regions. Multiple alignment methods will be used to align several sequences and to identify conserved elements. In addition, computational methods for the prediction of protein and RNA secondary structure will be introduced and applied to selected examples. The generation of a SQL data base in combination with a script language will be introduced.

Part 2: Genomics. In the second part of the lab course (Genomics) hands on in genome analysis will be obtained. Starting with a students seminar on a special topic related to genome research every week, several tools will be tested and used for sequence analysis. We will use web-bases systems as well as standalone tools installed on a local server. Complete genomes as well as genomic fragments will be analysed. The genomic fragments will serve as the template for in depth annotation using an open source annotation system (GenDB). A local installation of the phylogenetic software package ARB will be used for phylogenetic inference and tree reconstruction of selected functional genes.

### 550321: Computational Systems Biology

 Short Name: SysBio Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

Systems Biology aims at understanding the functioning of a cell due to the concerted action of its constituents. At the same time, however, many spatial and temporal scales contribute to cellular organization and turn it into a complex interplay of regulatory processes. It seems, therefore, futile addressing this problem of system understanding without the appropriate toolbox. This course provides the toolbox for ''doing Systems Biology''.

In the first part we will look at general principles of systems modeling. We will discuss elementary models of dynamic processes, which help understand large classes of biological systems and then see, how an increase in complexity changes properties of the model.

The second part covers system biologic models of specific cellular processes: metabolism, signal transduction and gene regulation.

In the last segment we will discuss the integration of theoretical approaches: How can data sets on different levels of a biological systems been related and put into a wider context? How can specific models be interlinked, in order to pass from a minimal model (the domain of theoretical biology) to a realistic ``in-silico'' description (the realm of systems biology)?

We also look at the current computational infrastructure of systems biology: data bases for mathematical models, standards for data formats. Beyond ACM, this course may also be of interest to biochemistry and computer science majors.

### 560302: Design of Biological Molecules and Systems

 Short Name: DBMS Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The course is intended to give an overview on theoretical/computational as well as experimental aspects of biological molecule and system design. It will include state of the art genetic engineering methods for directed protein evolution, molecular breeding and practical approached of rational, combinatorial and evolutionary molecule design. On the theoretical side the course covers computational approaches of bio-molecular modelling, structure prediction and mathematical models of evolution. This includes energetic and entropic contributions to ligand-receptor interactions and biomolecule stability. It covers also the prediction of the effect of mutations on biomolecular structure and function, prediction of ligand-receptor binding and an introduction to computational drug design and virtual screening methods.

## Courses from the School of Humanities and Social Science

### 032101: Microeconomics

 Short Name: Microeconomics Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

The study of economics concerns itself with the allocation of scarce resources and the associated implications for efficiency, equity, and human welfare. This course introduces the field of microeconomics, focusing specifically on the role of markets in facilitating exchange between the individual households, firms, and government institutions that make up the economy. Topics addressed include consumer theory, the behavior of firms, competition, and monopoly. The course applies the theoretical concepts covered to contemporary policy questions, such as when government intervention is justified to correct market imperfections.

Students who successfully complete this course will not receive credits towards the 180 ECTS-credits required for their BA degree from the course Introduction to Economics. These courses are mutually exclusive due to comparable content.

### 032102: Macroeconomics

 Short Name: Macroeconomics Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This course provides an introduction to the analysis of aggregate output, employment and economic growth and their relationship to the policy issues of unemployment, inflation and the balance of payments. Other topics include: national accounting; aggregate income and expenditure analysis; macroeconomic models of income determination; consumption, saving and investment functions; the role of money and banks; interactions between goods and money markets in equilibrium and disequilibrium situations.

Students who successfully complete this course will not receive credits towards the 180 ECTS-credits required for their BA degree from the course Introduction to Economics. These courses are mutually exclusive due to comparable content.

### 930201: Introduction to Economics

 Short Name: Intro.Economics Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This lecture introduces students to the institution of the market. It reconstructs the micro-logic of market exchanges at the level of individual market participants (microeconomics), analyzes the resulting macro-patterns at the level of market aggregates (macroeconomics), and looks into the role that governments play in defining, shaping, and destroying market relations.

Students who successfully complete this course will not receive credits towards the 180 ECTS-credits required for their BA degree from the courses Microeconomics and Macroeconomics. These courses are mutually exclusive due to comparable content.

### 930221: Managerial & Financial Accounting

 Short Name: Accounting MLM Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: no

#### Course contents

Physical movements of goods leave a financial trail. Accounting is the art of capturing this trail and transforming it into meaningful information for management and other stakeholders. This course provides an introduction to accounting principles. It focuses on measuring the financial position and performance of a firm, on reporting cash flows and on analyzing financial 20statements. It consists of modules on strategic and operative planning as well as on controlling (target setting, feed-back and feed-forward control, balanced scorecard). Cost allocation, full costing and cost-volume-profit analysis are the focus of managerial accounting.

### 930241: Finance

 Short Name: Finance Type: Seminar Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

Corporate Finance is crucial to the growth of all firms. This is even more so in a global environment that is characterized by liquidity shortages and turmoil in capital markets.

This course will provide students with the basics of corporate finance. It will introduce to the analytical tools and the necessary techniques for the financial management of a firm. Students will discuss these techniques in various contexts: the modern theories of corporate finance, corporate governance, value and capital budgeting, risk and return, capital structure and dividend policy, finance decisions as well as long term and short term financial planning.

### 930312: Firms and Markets

 Short Name: Firms/Markets Type: Seminar Credit Points: 5 Prerequisites: Please check on Campus Net Corequisites: Please check on Campus Net Tutorial: No

#### Course contents

This seminar continues the analysis of the market. It asks why in market economies, not all economic transactions take place within the market. Why are some transactions moved outside of the market and coordinated hierarchically within business firms? The seminar examines both the internal organization and management of business firms and their external behavior. The topics covered include the economics of transaction costs, agency theory, elementary game theory, competitive advantage, strategy formation, and strategic pricing.

### 990121: Statistical Concepts and Data Analysis

 Short Name: Stats_Concepts Type: Lecture/Lab Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: No

#### Course contents

This course aims to provide an introduction to fundamental statistical concepts and tools for data analysis. It is intended as a one-semester course that combines selected topics from both the mandatory statistical methods courses for SHSS students (Statistical Methods I: Exploring Relationships and Comparing Groups and Statistical Methods II: Classification, Modelling and Prediction) to offer the more relevant topics for logistics and SES major students. The course will focus on the understanding of statistical concepts and the application of statistical techniques. While some formulae might be used, no stringent mathematical derivation will be provided. The general objective is to become an intelligent user of the various univariate and multivariate statistical techniques and to acquire the knowledge for deciding which procedure is most suitable for the given business situation. We will discuss the theoretical aspects of the statistical methods, discuss the assumptions for their use, reflect on their limitations and the controversies they create. In practical sessions we will learn how to run the particular procedures using SPSS and/or R, how to interpret the computer output and how to skillfully communicate the results of statistical analyses.

### 990222: Econometrics

 Short Name: Econometrics Type: Lecture Credit Points: 5 Prerequisites: None Corequisites: None Tutorial: no

#### Course contents

This course focuses on the analysis of secondary data in the business world. Thus, one focus of the course consists of quantitative methods used in economy and business. We will expand on the knowledge acquired in the statistics class and intensify discussion of multiple regression analysis, in particular with an emphasis on longitudinal/time dependent data. The second focus of the course is on the analysis of large data sets that are created during the regular business process, such as billing data, customer information, etc.; data, that is more and more analysed by computer-intensive methods to find structures and patterns.

The general objective is to become familiar with classic and contemporary methods that are used in econometric and business analyses and to become a critical reader of case studies in this field. We will take a practical approach to learn how to run the particular procedures in state of the art software. To foster the practical approach homework and projects will be assigned. By the end of this course, students will know the rules for being competent practitioners of econometrics. This involves: Understanding how data should be organized for undertaking econometric modeling and the steps required for preparing data for analysis; Recognizing what technique to select from the econometric toolkit given the pattern of values in the data; Being able to interpret results with respect to both their statistical and economic/social significance; Be able to cast a skeptical eye on econometric results in the literature; Have fun working with social science data.