Zulassung zum Masterstudium (Medien-)Informatik (externer Abschluss)

/

• Technical Foundations of Computer Science

  • Integer arithmetic
  • Boolean algebra
  • CMOS technology
  • Logic gates
  • Storage technologies
  • Caching
  • Scalar and superscalar computer architectures
  • Basics of quantum computing

   
  Literature for reference:  John L. Hennessy, David A. Patterson: Computer Architecture: A Quantitative Approach. Elsevier.
• Theoretical Computer Science

  • Propositional logic: Syntax: variables, logical connectives, formulas, conjunctive and disjunctive normal forms. Semantic: truth table, satisfiability of a formula, consistency of a set of formulas, tautology, logical implication (logical consequence). Proof of consistency of a set of formulas. Proof of correctness of logical consequence.
  • First order predicate logic: Syntax: function and predicate symbols, terms, atomic formulas, free and bound variables, formulas, prenex normal form. Semantic: structures, models, satisfiability and validity of a first order formula.
  • Formal grammars: regular grammar, context-free grammar, context-sensitive grammar, unrestricted grammar.
  • Automata theory: finite-state automaton, pushdown automaton, Turing machine, deterministic and nondeterministic automata.
  • Chomsky hierarchy: relationship languages/grammars/automata.
  • Computability theory. Computable functions, decidable sets and problems. Undecidable problems. Halting problem.
  • Complexity theory. Complexity classes P and NP. SAT problem.

   
  Literature for reference: John E. Hopcroft, Rajeev Motwani, Jeffrey Ullman: Introduction to Automata Theory, Languages and Computation. Addison-Wesley.
• Mathematical Foundations

  • Power set, operations with sets, cartesian product of sets, proof by mathematical induction
  • N-ary, equivalence, and partial order relations
  • Mappings and functions: injective, surjective, bijective
  • Groups and rings as algebraic structures and their properties
  • Vectors and matrices: basic operations, unit matrix, inverse matrix, rank
  • Linear independence of vectors, basis and dimension of a vector space, coordinates in a vector space
  • Linear systems of equations, Gauss algorithm and various uses of it
  • Determinants, eigenvalues/vectors, characteristic polynomial of a matrix, similar matrices
  • Scalar product, orthogonal vectors, orthogonal matrices, vector norms
  • Graphs: directed, undirected, complete, planar, adjacency matrix, degree of a node, paths in graphs
  • Trees and their characterization, properties of (regular) binary trees, Huffman codes 
  • Fundamentals: complex numbers, fundamental theorem of algebra, linear factors, Euler's formula, properties of different types of functions, exponential function incl. complex exponential
  • Differentiation: limits, derivative, sign of derivative, critical points, implicit differentiation, logarithmic differentiation
  • Integration: fundamental theorem of calculus, antiderivative, Riemann integral, integration by substitution incl. trigonometric substitution, integration by parts, improper integrals
  • Sequences of Functions: uniform convergence, power series, Taylor series, Taylor series in several variables
  • Differentiation in Higher Dimensions: vector-valued functions, Frenet–Serret formulas, partial derivative, tangent planes, directional derivative, total derivative, Jacobian, gradient, divergence, curl, Hessian matrix, definite quadratic forms, critical points
  • Integration in Higher Dimensions: multiple integral, substitution for multiple variables, Jacobian determinant, polar coordinate system, cylindrical coordinate system, spherical coordinate system

   
  Literature for reference: Kenneth L Kuttler: Calculus of One and Many Variables https://klkuttler.com/
• Programming

  • Programming Language Paradigms
  • Imperative Programming, Variables, Assignment, Selection, Iteration, Sequence
  • Algorithm Definition (Unambiguous, Effective, Deterministic, Finite, Complete, Correct)
  • Recursion
  • Object Oriented Programming, Data Hiding, Polymorphism, Inheritance
  • Generic Programming, Templates (C++), Generics (Java)
  • Lambda Expressions
  • STL, Container, Algorithms (C++), Collections (Java)

  
  Literature for reference: Bjarne Stroustrup: Programming Principles and Practice Using C++,  Addison-Wesley.
• Database Systems

  • Relational Model (Definition of Relation, Key, Superkey, Data Definition Language of SQL)
  • Normal Forms (Functional and Multivalued Dependencies, 1.-4. Normal Form, Boyce-Codd-Normal Form, Decomposition- and Synthesis Algorithm)
  • Relational Algebra (select, project, cartesian product, union, difference, intersection, division, join including inner, outer, equi-, and natural join)
  • Tuple and Domain Calculus (formulas and expressions, quantors)
  • SQL (select, from, where, set operations, aggregation, grouping, ordering, views)
  • Transactions, (Concurrency and Recovery including schedules, locking, logging)
  • Index Structures (B-trees and hashing methods)
  • Relational Query Optimization (push projection, push selection, cost estimation)

   
  Literature for reference: Ramez Elmasri, Shamkant B. Navathe: Fundamentals of Database Systems. Pearson.
• Algorithms and Data Structures

  • Algorithm Paradigms, Greedy, Divide and Conquer, Dynamic Programming
  • Asymptotic Computational Complexity (O, Omega, Theta, o, omega, ~)
  • Data Structures (List, Trees, Graphs)
  • Sorting Algorithm Properties (Insitu, Exsitu, Stable, Unstable, O(n ln n) Limit for Comparison Sort)
  • Sorting Algorithms (Selection Sort, Insertion Sort, Bubble Sort, Quicksort, Mergesort, Heapsort)
  • Linear Time Sorting Algorithms (Counting Sort, Radix Sort, Bucket Sort)
  • Hashing Principles (Hash Function, Static, Dynamic, Collision Resolution)
  • Hashing Methods (Double Hashing, Separate Chaining, Linear Hashing, Extendible Hashing, BISEH, Coalesced Hashing, Cuckoo Hashing)
  • Search Trees (BST, Multiway Trees, B+ Tree)
  • Graphs (Internal Representation, Traversal, Shortest Paths Algorithms)

  
  Literature for reference: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest: Introduction to Algorithms. MIT Press and McGraw-Hill.
• Software Engineering

  • Software Requirements Specification
  • Software Verification and Validation
  • Software Rollout and Maintenance
  • Software Quality and Code Quality
  • Software Design and Architecture
  • Design Patterns

   
  Literature for reference: Ian Sommerville: Software Engineering. Pearson.
• Modelling

  • UML: Unified Modelling Language (UseCase, Class, Object, Activitiy, State, Sequence, Package, Component, and Deployment Diagrams)
  • Entity Relationship Model
  • BPMN: Business Process Model and Notation
  • DMN: Decision Model and Notation
  • Petri Nets
  • Event-driven process Chain (EPC)

  
  Literature for reference: Martin Fowler: UML Distilled: A Brief Guide to the Standard Object Modelling Language. Addison Wesley.
• Computer Networks

  • Physical Layer: Guided Transmission Media, Wireless Transmission, Spectra and Waveforms
  • Data Link Layer: Framing, Error Control, Flow Control, Media Access Control, Ethernet, WLAN
  • Network Layer: Internet Protocol, Routing Algorithms and Protocols, Traffic Management and Quality of Service
  • Transport Layer: UDP and TCP
  • Application Layer: Domain Name System, Electronic Mail, World Wide Web
  • Fundamentals of Network Security: Attacks, Symmetric-Key and Public-Key Cryptography, Digital Signatures

  
  Literature for reference: James F. Kurose, Keith W. Ross: Computer Networking. A Top-Down Approach. Pearson.
• Human Computer Interaction

  • Human-Centered Design (User research)
  • Usability and User Experience
  • Interaction Design Principles
  • Accessibility and Inclusive Design
  • Emerging Technologies in HCI (GenAI)
  • Perception and Cognition
  • Prototyping

  
  Literature for reference: Alan Dix, Janet Finlay, Gregory Abowd, Russell Beale: Human-Computer Interaction. Prentice Hall.