• Students are able to find their way around selected special areas of management within the scope of business management.
• Students are able to explain basic theories, categories, and models in selected special areas of business management.
• Students are able to interrelate technical and management knowledge.

• Students are able to apply basic methods in selected areas of business management.
• Students are able to explain and give reasons for decision proposals on practical issues in areas of business management.

• Students are able to communicate in small interdisciplinary groups and to jointly develop solutions for complex problems

Dual students …

… can describe and classify selected classic and current theories, concepts and methods 

• related to project management and
• change and transformation management

... and apply them to specific situations, processes and plans in a personal, professional context.

Dual students …

• ... anticipate typical difficulties, positive and negative effects, as well as success and failure factors in the engineering sector, evaluate them and consider promising strategies and courses of action.
• … develop specialised technical and conceptual skills to solve complex tasks and problems in their professional field of activity/work.

Dual students …

• … can responsibly lead interdisciplinary teams within the framework of complex tasks and problems.
• … engage in sector-specific and cross-sectoral discussions with experts, stakeholders and staff, representing their approaches, points of view and work results.

Dual students …

• … combine their knowledge of facts, principles, theories and methods gained from previous study content with acquired practical knowledge - in particular their knowledge of practical professional procedures and approaches, in the current field of activity in engineering. 
• … have a critical understanding of the practical applications of their engineering subject.
  

Dual students …

• … apply technical theoretical knowledge to complex, interdisciplinary problems within the company, and evaluate the associated work processes and results, taking into account different possible courses of action.
• … implement the university’s application recommendations with regard to their current tasks. 
• … develop solutions as well as procedures and approaches in their field of activity and area of responsibility.

Dual students …

• … work responsibly in project teams within their working area and proactively deal with problems within their team. 
• … represent complex engineering viewpoints, facts, problems and solution approaches in discussions with internal and external stakeholders.

Dual students …

• … combine their knowledge of facts, principles, theories and methods gained from previous study content with acquired practical knowledge - in particular their knowledge of practical professional procedures and approaches, in the current field of activity in engineering. 
• … have a critical understanding of the practical applications of their engineering subject.
  

Dual students …

• … apply technical theoretical knowledge to complex, interdisciplinary problems within the company, and evaluate the associated work processes and results, taking into account different possible courses of action.
• … implement the university’s application recommendations with regard to their current tasks. 
• … develop (new) solutions as well as procedures and approaches in their field of activity and area of responsibility - including in the case of frequently changing requirements (systemic skills).

Dual students …

• … work responsibly in cross-departmental and interdisciplinary project teams and proactively deal with problems within their team. 
• … represent complex engineering viewpoints, facts, problems and solution approaches in discussions with internal and external stakeholders and develop these further together.

Students are able to acquire advanced knowledge in a subfield of Computer Science and can independently acquire deeper knowledge in the field.

The students are able to formulate the scientific problems to be considered and to work out solutions in an independent manner and to realize them.

The students are able to discuss proposals for solutions of scientific problems within the team. They are able to present the results in a clear and well structured manner. 

Dual students …

• … combine their comprehensive and specialised engineering knowledge acquired from previous study contents with the strategy-oriented practical knowledge gained from their current field of work and area of responsibility. 
• … have a critical understanding of the practical applications of their engineering subject, as well as related fields when implementing innovations.

Dual students …

• … apply specialised and conceptual skills to solve complex, sometimes interdisciplinary problems within the company, and evaluate the associated work processes and results, taking into account different possible courses of action.
• … implement the university’s application recommendations with regard to their current tasks. 
• … develop new solutions as well as procedures and approaches to implement operational projects and assignments - even when facing frequently changing requirements and unpredictable changes (systemic skills).
• … can use academic methods to develop new ideas and procedures for operational problems and issues, and to assess these with regard to their usability.

Dual students …

• … work responsibly in cross-departmental and interdisciplinary project teams and proactively deal with problems within their team. 
• … can promote the professional development of others in a targeted manner.
• … represent complex and interdisciplinary engineering viewpoints, facts, problems and solution approaches in discussions with internal and external stakeholders and develop these further together.

Students apply the major verification techniques in model checking and deductive verification. They explain in formal terms syntax and semantics of the underlying logics, and assess the expressivity of different logics as well as their limitations. They classify formal properties of software systems. They find flaws in formal arguments, arising from modeling artifacts or underspecification. 

Students formulate provable properties of a software system in a formal language. They develop logic-based models that properly abstract from the software under verification and, where necessary, adapt model or property. They construct proofs and property checks by hand or using tools for model checking or deductive verification, and reflect on the scope of the results. Presented with a verification problem in natural language, they select the appropriate verification technique and justify their choice.   

Students discuss relevant topics in class. They defend their solutions orally. They communicate in English. 

Students can 

• name the main causes for security vulnerabilities in software 
• explain current methods for identifying and avoiding security vulnerabilities 
• explain the fundamental concepts of code-based access control 

Students are capable of 

• performing a software vulnerability analysis 
• developing secure code 

The students know and can explain 

- the threats posed by cyber attacks to cyber-physical systems (CPS)

- concrete attacks at a technical level, e.g. on bus systems

- security solutions specific to CPS with their capabilities and limitations

- examples of security architectures for CPS and the requirements they guarantee 

- standard security engineering processes for CPS

The students are able to

-  identify security threats and assess the risks for a given CPS

-  apply attack toolkits to analyse a networked control system, and detect attacks beyond those taught in class 

-  identify and apply security solutions suitable to the requirements

-  follow security engineering processes to develop a security architecture for a given CPS 

-  recognize challenges and limitations, e.g. posed by novel types of attack

The students are able to

- expertly discuss security risks and incidents of CPS and their mitigation in a solution-oriented fashion with experts and non-experts

- foster a security culture with respect to CPS and the corresponding critical infrastructures 

In the field of computer science we have only limited possibilities to influence the efficiency of the hardware directly, respectively we are dependent on the manufacturers (e.g. of microcontrollers). However, in order to exploit the full potential of the hardware we are given at the system level, we need a deeper understanding of the background, processes and mechanisms of power dissipation in embedded systems. Where does the power dissipation come from, what happens at the hardware level, what mechanisms can I use directly/indirectly, what is the tradeoff between flexibility and efficiency,.... are only a few questions, which will be elaborated and discussed in this event.

• Motivation and power dissipation on semiconductor level
• Power dissipation of digital circuits, inparticular CMOS
• Power Management in Hard- and Software (Sleep Modes, DVS, FS, Undervolting)
• Energy efficient system design (applications)
• Energy Harvesting and Transiently Powered Computing (TPC)

Upon completion of this module, students will have a deeper understanding of hardware and software mechanisms for evaluating and developing energy-efficient embedded systems

• They have a deeper understanding of the electrotechnical basics of power dissipation in digital systems
• They can analyze the power dissipation of systems at any level and apply appropriate methods to increase efficiency
• They can use a variety of standard techniques to achieve "Energy Efficiency by Design"
• They can model, evaluate as well as implement energy-autonomous systems

As part of the module, concepts learned in the lecture will be implemented on a hardware platform within small groups. Students learn to work in a team and to develop solutions together. Specific tasks are worked on within the group, whereby cross-group collaboration (exchange) also takes place. The second part is a challenge-based project in which the groups find the most energy-efficient solutions possible in healthy competition with each other. This strengthens the cohesion in the groups and reinforces mutual motivation, support and creativity.

In the following "dependable" summarizes the concepts Reliability, Availability, Maintainability, Safety and Security.

Knowledge about approaches for designing dependable systems, e.g.,

• Structural solutions like modular redundancy
• Algorithmic solutions like handling byzantine faults or checkpointing

Knowledge about methods for the analysis of dependable systems

Ability to implement dependable systems using the above approaches.

Ability to analyzs the dependability of systems using the above methods for analysis.

Students

• discuss relevant topics in class and
• present their solutions orally.

Students know

• algorithms and data structures for model checking,
• basics of Boolean reasoning engines and
• the impact of specification and modelling on the computational effort for model checking.
  

Students can

• explain and implement algorithms and data structures for model checking,
• decide whether a given problem can be solved using Boolean reasoning or model checking, and
• implement the respective algorithms.
  

Students

• discuss relevant topics in class and
• defend their solutions orally.

Students explain the different phases of testing, describe fundamental
techniques of different types of testing, and paraphrase the basic
principles of the corresponding test process. They give examples of
software development scenarios and the corresponding test type and
technique. They explain algorithms used for particular testing
techniques and describe possible advantages and limitations.

Students identify the appropriate testing type and technique for a given
problem. They adapt and execute respective algorithms to execute a
concrete test technique properly. They interpret testing results and
execute corresponding steps for proper re-test scenarios. They write and
analyze test specifications. They apply bug finding techniques for
non-trivial problems.

Students discuss relevant topics in class. They defend their solutions orally.
They communicate in English.

• Students can name the basic concepts in algorithmic game theory and mechanism design. They are able to explain them using appropriate examples.
• Students can discuss logical connections between these concepts.  They are capable of illustrating these connections with the help of examples.
• They know game and mechanism design strategies and can reproduce them.
  

• Students can model strategic interaction systems of agents with the help of the concepts studied in this course. Moreover, they are capable of analyzing their efficiency and equilibria, by applying established methods.
• Students are able to discover and verify further logical connections between the concepts studied in the course.
• For a given problem, the students can develop and execute a suitable approach, and are able to critically evaluate the results.

• Students are able to work together in teams. They are capable to use mathematics as a common language.
• In doing so, they can communicate new concepts according to the needs of their cooperating partners. Moreover, they can design examples to check and deepen the understanding of their peers.

Students can:

• Elicit security requirements in a software project
• Model and document security measures in a software design
• Use threat and risk analysis techniques
• Understand how security code reviews are performed
• Understand the core definitions of concepts related to privacy
• Understand privacy enhancing technologies

The relevance of embedded systems increases from year to year. Within such systems, the amount of software to be executed on embedded processors grows continuously due to its lower costs and higher flexibility. Because of the particular application areas of embedded systems, highly optimized and application-specific processors are deployed. Such highly specialized processors impose high demands on compilers which have to generate code of highest quality. After the successful attendance of this course, the students are able

• to illustrate the structure and organization of such compilers,
• to distinguish and explain intermediate representations of various abstraction levels, and
• to assess optimizations and their underlying problems in all compiler phases.

The high demands on compilers for embedded systems make effective code optimizations mandatory. The students learn in particular,

• which kinds of optimizations are applicable at the source code level,
• how the translation from source code to assembly code is performed,
• which kinds of optimizations are applicable at the assembly code level,
• how register allocation is performed, and
• how memory hierarchies can be exploited effectively.
  

Since compilers for embedded systems often have to optimize for multiple objectives (e.g., average- or worst-case execution time, energy dissipation, code size), the students learn to evaluate the influence of optimizations on these different criteria.

After successful completion of the course, students shall be able to translate high-level program code into machine code. They will be enabled to assess which kind of code optimization should be applied most effectively at which abstraction level (e.g., source or assembly code) within a compiler.

While attending the labs, the students will learn to implement a fully functional compiler including optimizations.

Students are able to solve similar problems alone or in a group and to present the results accordingly.

Students who have successfully completed the module:

• explain the start-up process of a computing system using an IA32 PC as an example.
• describe the specific challenges in software development for "bare metal".
• describe the sequence of an interrupt handling from hardware to (system) software.
• outline specifics and strategies of interrupt handling in hardware for multi-core systems using the IA32 APIC as an example.
• distinguish the different types of control flows in an operating system using the level model.
• distinguish hard, multi-level, and soft methods for interrupt synchronization in operating systems.
• analyze the interaction of scheduling and interrupt synchronization.
• distinguish basic ways of coordinating and synchronizing threads (active/passive waiting, non-displaceable critical sections).
• know basic synchronization problems (lost update, lost wakeup) and propose appropriate countermeasures.
• can distinguish between different driver models.
• compare basic OS architectures (library, monolith, microkernel, exokernel, hypervisor) based on fundamental characteristics (robustness, performance, portability) and mechanisms.
• describe the basic paradigms for interprocess communication in operating systems (memory-based vs. message-based).
• can describe the challenges of implementing a multi-core operating system
• distinguish between inter-process, inter-core, and interrupt synchronization and can differentiate between them
• can recognize race conditions between concurrent and preemptable threads
  

Students who have successfully completed the module:

• discuss the division of tasks between hardware and system software in interrupt handling.
• can implement multi-stage interrupt synchronization for use in a multi-core operating system.
• classify concrete concurrent situations and derive appropriate synchronization measures.
• develop the coroutine switch for a given architecture.
• can implement preemptive scheduling in an multi-core operating system.
• develop mechanisms for thread-level synchronization.
• can integrate device drivers into an operating system architecture.
• outline how higher-level synchronization constructs are implemented from basic synchronization primitives (monitors, reader/writer lock).
• can implement and use primitives for interprocess communication.
• can proactively detect and remove race conditions between truly parallel activities

Students who have successfully completed the module:

• can work cooperatively in small groups.
• can present and argue their design and implementation decisions in a compact manner.

After successful completion of the course, students are able to:

• Describe basic concepts of Cloud Computing, the Internet of Things (IoT), and blockchain technologies
• Discuss and assess critical aspects of Cloud Computing, the IoT, and blockchain technologies
• Select and apply cloud and IoT technologies for particular application areas
• Design and develop practical solutions for the integration of smart objects in IoT, Cloud, and blockchain software
• Implement IoT services

The students acquire the ability to model Internet-based distributed systems and to work with these systems. This comprises especially the ability to select and utilize fitting technologies for different application areas. Furthermore, students are able to critically assess the chosen technologies. 

Students can work on complex problems both independently and in teams. They can exchange ideas with each other and use their individual strengths to solve the problem.

Students can:

• Apply data science methods to the resolution of complex cybersecurity problems.
• Use of data science methods to quantify risks and optimize cybersecurity operations.
• Identify strengths and limitations of state-of-the-art methods
• Select the performance indicators of data-oriented cybersecurity solutions.
• Understand cybersecurity threats in data science methods.
  

Implement and evaluate data-driven models for the identification, treatment, and mitigation of cybersecurity risks

• Students know the basic principles and procedures of software engineering for embedded systems.
• They are able to describe the usage and advantages of event-based programming using interrupts.
• They know the components and functions of a concrete microcontroller.
• The participants explain requirements of real time systems.
• They know at least three scheduling algorithms for real time operating systems including their pros and cons.

• Students design and write hardware-oriented software modules for an embedded system based on a specific microcontroller.
• They learn to interact with peripherals (timer, ADC, EEPROM), including interrupt-based processing and program flow.
• They build and use a (preemptive) scheduler for an embedded system.
• They learn to write independent, reusable software components.
  

• Students are able to work goal-oriented in small mixed groups.
• They learn and broaden their teamwork abilities.
• They learn to define and split tasks within the team.

Cyber-Physical Systems form the basis for many modern control tasks in automation and for methods for monitoring the environment, infrastructure, etc. Essential aspects in the implementation of such systems are their networking, especially based on wireless technologies, and their autonomous operation, especially on the basis of regenerative energy sources. After successfully attending this event, the students are able to

• to present the special features of cyber-physical systems and the associated challenges and concepts,
• describe and evaluate wired and wireless communication on different layers of the ISO/OSI model,
• explain and compare methods of regenerative energy production,
• discuss and evaluate procedures for the autonomous and self-sufficient operation of such systems.

Students will be able to

• to implement programs for cyber-physical systems in high-level languages ​​and using existing libraries,
• to assess which communication and networking protocols can be used most sensibly in which application and to use them in real scenarios,
• select and implement suitable methods for adapting the tasks based on the energy consumption and the future expected energy yield,
• plan and evaluate scientific experiments.

After completing the module, the students are able to work on similar tasks alone or in a group and to present the results in a suitable way.

• Students can describe basic concepts from the theory of constraint satisfaction such as primitive positive formulas, interpretations, polymorphisms, clones
• Students can discuss the connections between these concepts
• Students know proofs strategies and can reproduce them
  
  

• Students can use CSPs to model problems from complexity theory and decide their complexity using methods from the course.

Students are able to describe methods for planning, optimisation and performance evaluation of communication networks.

Students are able to solve typical planning and optimisation tasks for communication networks. Furthermore they are able to evaluate the network performance using queuing theory.

Students are able to apply independently what they have learned to other and new problems. They can present their results in front of experts and discuss them.

Students who have successfully completed the module:

• explain and implement design principles for system calls and discuss their specific advantages/disadvantages.
• classify protection, management, and virtualization techniques for memory (paging, segementation, language-based, capabilities) and implement them on the IA-32 architecture.
• compare basic OS architectures (monolith, microkernel, macrokernel, exokernel) on the basis of fundamental characteristics (robustness, performance, portability) and their influence on the implementation of mechanisms (system calls, address space protection).
• discuss address space models (multi-address space model, single-address space model, multi-level and inverse page mappings, sharing) and their implementability on common hardware architectures.
• discuss principles of code and data sharing with respect to operating system and address space architecture.
• can distinguish logical, virtual, and physical memory.
• can derive the cost advantages of zero-copy interfaces
• can distinguish technical and conceptual views of process generation by fork().

Students who have successfully completed the module:

• explain and implement design principles for system calls and discuss their specific advantages/disadvantages.
• can implement basic mechanisms for memory management
• understand typical problems (concurrency, compiler behavior, debugging without dedicated tools) and sources of errors in low-level software development.
• are able to design basic abstractions for address space virtualization.
• can name the necessary prerequisites for privilege separation and also implement these technically 
• implement techniques for lazy decoupling of memory operations (Copy-On Write)
• implement mechanisms and abstractions for interprocess communication.

Students who have successfully completed the module:

• can work cooperatively in small groups.
• can present and argue their design and implementation decisions in a compact manner.

The course starts with parallel computers classification, multithreading, and covers the architecture of centralized and distributed shared-memory parallel systems, multiprocessor cache coherence, snooping / directory-based cache coherence protocols, implementation, and limitations. Next, students study interconnection networks and routing in parallel systems. To ensure the correctness of shared-memory multithreaded programs, independent of the speed of execution of their individual threads, the important topics of memory consistency and synchronization will be covered in detail. As a case study, the architecture of a few accelerators such as GPUs will also be discussed in detail. Besides understanding the architecture and organization of parallel systems, programming them is also very challenging. The course will also cover how to program massively parallel systems using API/libraries such as CUDA/OpenCL/MPI/OpenMP.

After completing this course, students will be able to understand the architecture and organization of parallel systems. They will be able to evaluate different design choices and make decisions while designing a parallel system. In addition, they will be able to program parallel systems (ranging from an embedded system to a supercomputer) using CUDA/OpenCL/MPI/OpenMP. 

The students can evaluate and assess discrete event systems. They can evaluate properties of processes and explain methods for process analysis. The students can compare methods for process modelling and select an appropriate method for actual problems. They can discuss scheduling methods in the context of actual problems and give a detailed explanation of advantages and disadvantages of different programming methods. The students can relate process automation to methods from robotics and sensor systems as well as to recent topics like 'cyberphysical systems' and 'industry 4.0'.

The students are able to develop and model processes and evaluate them accordingly. This involves taking into account optimal scheduling, understanding algorithmic complexity, and implementation using PLCs.

The students can independently define work processes within their groups, distribute tasks within the group and develop solutions collaboratively.

Students can explain the agent abstraction, define intelligence in terms of rational behavior, and give details about agent design (goals, utilities, environments). They can describe the main features of environments. The notion of adversarial agent cooperation can be discussed in terms of decision problems and algorithms for solving these problems. For dealing with uncertainty in real-world scenarios, students can summarize how Bayesian networks can be employed as a knowledge representation and reasoning formalism in static and dynamic settings. In addition, students can define decision making procedures in simple and sequential settings, with and with complete access to the state of the environment. In this context, students can describe techniques for solving (partially observable) Markov decision problems, and they can recall techniques for measuring the value of information. Students can identify techniques for simultaneous localization and mapping, and can explain planning techniques for achieving desired states. Students can explain coordination problems and decision making in a multi-agent setting in term of different types of equilibria, social choice functions, voting protocol, and mechanism design techniques.

Students can select an appropriate agent architecture for concrete agent application scenarios. For simplified agent application students can derive decision trees and apply basic optimization techniques. For those applications they can also create Bayesian networks/dynamic Bayesian networks and apply bayesian reasoning for simple queries. Students can also name and apply different sampling techniques for simplified agent scenarios. For simple and complex decision making students can compute the best action or policies for concrete settings. In multi-agent situations students will apply techniques for finding different equilibria states,e.g., Nash equilibria. For multi-agent decision making students will apply different voting protocols and compare and explain the results.

Students are able to discuss their solutions to problems with others. They communicate in English

The students can explain kinematics and tracking systems in clinical contexts and illustrate systems and their components in detail. Systems can be evaluated with respect to collision detection and  safety and regulations. Students can assess typical systems regarding design and  limitations.

The students are able to design and evaluate navigation systems and robotic systems for medical applications.

The students are able to grasp practical tasks in groups, develop solution strategies independently, define work processes and work on them collaboratively.
The students are able to collaboratively organize their work processes and software solutions using virtual communication and software management tools.
The students can critically reflect on the results of other groups, make constructive suggestions for improvement, and also incorporate them into their own work.

Content: The module focuses primarily on discussing established imaging techniques including (a) optical and infrared imaging, (b) magnetic resonance imaging, (c) X-ray imaging and tomography, and (d) ultrasound imaging but also covers a range of more recent imaging modalities. The students will learn:

1. what these imaging techniques can measure (such as sample density or concentration, material transport, chemical composition, temperature),
2. how the measurements work (physical measurement principles, hardware requirements, image reconstruction), and
3. how to determine the most suited imaging methods for a given problem.

Learning goals: After the successful completion of the course, the students shall:

1. understand the physical principles and practical aspects of the most common imaging methods,
2. be able to assess the pros and cons of these methods with regard to cost, complexity, expected contrasts, spatial and temporal resolution, and based on this assessment
3. be able to identify the most suited imaging modality for any specific engineering challenge in the field of chemical and bioprocess engineering.

Students can explain the difference between instance-based and model-based learning approaches, and they can enumerate basic machine learning technique for each of the two basic approaches, either on the basis of static data, or on the basis of incrementally incoming data . For dealing with uncertainty, students can describe suitable representation formalisms, and they explain how axioms, features, parameters, or structures used in these formalisms can be learned automatically with different algorithms. Students are also able to sketch different clustering techniques. They depict how the performance of learned classifiers can be improved by ensemble learning, and they can summarize how this influences computational learning theory. Algorithms for reinforcement learning can also be explained by students.

Student derive decision trees and, in turn, propositional rule sets from simple and static data tables and are able to name and explain basic optimization techniques. They present and apply the basic idea of first-order inductive leaning. Students apply the BME, MAP, ML, and EM algorithms for learning parameters of Bayesian networks and compare the different algorithms. They also know how to carry out Gaussian mixture learning. They can contrast kNN classifiers, neural networks, and support vector machines, and name their basic application areas and algorithmic properties. Students can describe basic clustering techniques and explain the basic components of those techniques. Students compare related machine learning techniques, e.g., k-means clustering and nearest neighbor classification. They can distinguish various ensemble learning techniques and compare the different goals of those techniques.

• Students can explain humanoid robots.
• Students can explain the basic concepts, relationships and methods of forward- and inverse kinematics
• Students learn to apply basic control concepts for different tasks in humanoid robotics.

• Students can implement models for humanoid robotic systems in Matlab and C++, and use these models for robot motion or other tasks.
• They are capable of using models in Matlab for simulation and testing these models if necessary with C++ code on the real robot system.
• They are capable of selecting methods for solving abstract problems, for which no standard methods are available, and apply it successfully.

• Students can develop joint solutions in mixed teams and present these.
• They can provide appropriate feedback to others, and  constructively handle feedback on their own results

After successful completion of the module, students are able to describe reconstruction methods for different tomographic imaging modalities such as computed tomography and magnetic resonance imaging. They know the necessary basics from the fields of signal processing and inverse problems and are familiar with both analytical and iterative image reconstruction methods. The students have a deepened knowledge of the imaging operators of computed tomography and magnetic resonance imaging.

The students are able to implement reconstruction methods and test them using tomographic measurement data. They can visualize the reconstructed images and evaluate the quality of their data and results. In addition, students can estimate the temporal complexity of imaging algorithms.

Students can work on complex problems both independently and in teams. They can exchange ideas with each other and use their individual strengths to solve the problem.

The students are able to analyze and solve clinical treatment planning and decision support problems using methods for search, optimization, and planning. They are able to explain methods for classification and their respective advantages and disadvantages in clinical contexts. The students can compare  different methods for representing medical knowledge. They can evaluate methods in the context of clinical data  and explain challenges due to the clinical nature of the data and its acquisition and due to privacy and safety requirements.

The students can give reasons for selecting and adapting methods for classification, regression, and prediction. They can assess the methods based on actual patient data and evaluate the implemented methods.

The students are able to grasp practical tasks in groups, develop solution strategies independently, define work processes and work on them collaboratively.
The students can critically reflect on the results of other groups, make constructive suggestions for improvement and also incorporate them into their own work.

Students can discuss logical connections between the following concepts and explain them by means of examples: Smith normal form, Chinese remainder theorem, grid point sets, integer solution of inequality systems.

Students are able to access independently further logical connections between the concepts with which they have become familiar and are able to verify them.

Students are able to develop a suitable solution approach to given problems, to pursue it and to evaluate the results critically, such as in solving multivariate equation systems and in grid point theory.

• Students can name the basic concepts in linear and non-linear optimization. They are able to explain them using appropriate examples.
• Students can discuss logical connections between these concepts.  They are capable of illustrating these connections with the help of examples.
• They know proof strategies and can reproduce them.

• Students can model problems in linear and non-linear optimization with the help of the concepts studied in this course. Moreover, they are capable of solving them by applying established methods.
• Students are able to discover and verify further logical connections between the concepts studied in the course.
• For a given problem, the students can develop and execute a suitable approach, and are able to critically evaluate the results.

• Students are able to work together in teams. They are capable to use mathematics as a common language.
• In doing so, they can communicate new concepts according to the needs of their cooperating partners. Moreover, they can design examples to check and deepen the understanding of their peers.

Students are able to

• name representatives of hierarchical algorithms and list their characteristics,
• explain construction techniques for hierarchical algorithms,
• discuss aspects regarding the efficient implementation of hierarchical algorithms.
  

Students are able to

• implement the hierarchical algorithms discussed in the lecture,
• analyse the storage and computational complexities of the algorithms,
• adapt algorithms to problem settings of various applications and thus develop problem adapted variants.
  

Students are able to

• work together in heterogeneously composed teams (i.e., teams from different study programs and background knowledge), explain theoretical foundations and support each other with practical aspects regarding the implementation of algorithms.
  

• Students can describe basic concepts in the area of Randomized Algorithms and Random Graphs such as random walks, tail bounds, fingerprinting and algebraic techniques, first and second moment methods, and various random graph models. They are able to explain them using appropriate examples.
• Students can discuss logical connections between these concepts.  They are capable of illustrating these connections with the help of examples.
• They know proof strategies and can apply them.
  
  

• Students can model problems with the help of the concepts studied in this course. Moreover, they are capable of solving them by applying established methods.
• Students are able to explore and verify further logical connections between the concepts studied in the course.
• For a given problem, the students can develop and execute a suitable technique, and are able to critically evaluate the results.

• Students are able to work together in teams. They are capable to establish a common language.
• In doing so, they can communicate new concepts according to the needs of their cooperating partners. Moreover, they can design examples to check and deepen the understanding of their peers.

Students are able to

• name numerical methods for the solution of ordinary differential equations and explain their core ideas,
• formulate convergence statements for the taught numerical methods (including the necessary assumptions about the solved problem),
• explain aspects regarding the practical realisation of a method,
• select the appropriate numerical method for specific problems, implement the numerical algorithms efficiently and interpret the numerical results.
  

Students are able to

• implement, apply and compare numerical methods for the solution of ordinary differential equations,
• explain the convergence behaviour of numerical methods, taking into consideration the solved problem and selected algorithm,
• develop a suitable solution approach for a given problem, if necessary by combining multiple algorithms, realise this approach and critically evaluate results.
  
  

Students are able to

• work together in heterogeneous teams (i.e., teams from different study programs and with different background knowledge), explain theoretical foundations and support each other with practical aspects regarding the implementation of algorithms.

• Students can name the basic concepts in probability theory. They are able to explain them using appropriate examples.
• Students can discuss logical connections between these concepts.  They are capable of illustrating these connections with the help of examples.
• They know proof strategies and can reproduce them.

• Students can model problems from probability theory with the help of the concepts studied in this course. Moreover, they are capable of solving them by applying established methods.
• Students are able to explore and verify further logical connections between the concepts studied in the course.
• For a given problem, the students can develop and execute a suitable technique, and are able to critically evaluate the results.

• Students are able to work together (e.g. on their regular home work) and to present their results appropriately (e.g. during exercise class).
• In doing so, they can communicate new concepts according to the needs of their cooperating partners. Moreover, they can design examples to check and deepen the understanding of their peers.