| Module name (EN): Mathematics 1 |
| Degree programme: Applied Informatics, Bachelor, ASPO 01.10.2011 |
| Module code: PIB125 |
| Hours per semester week / Teaching method: 4V+2U (6 hours per week) |
| ECTS credits: 7 |
| Semester: 1 |
| Mandatory course: yes |
| Language of instruction: German |
| Assessment: Written examination [updated 08.05.2008] |
| Applicability / Curricular relevance: PIB125 Applied Informatics, Bachelor, ASPO 01.10.2011, semester 1, mandatory course |
| Workload: 90 class hours (= 67.5 clock hours) over a 15-week period. The total student study time is 210 hours (equivalent to 7 ECTS credits). There are therefore 142.5 hours available for class preparation and follow-up work and exam preparation. |
| Recommended prerequisites (modules): None. |
| Recommended as prerequisite for: PIB215 Mathematics 2 PIB220 Graph Theory PIB330 Databases PIBWI19 Machine Learning PIBWI83 Computer Vision PIBWI92 Numerical Software [updated 02.03.2017] |
| Module coordinator: Prof. Dr. Rainer Lenz |
| Lecturer: Prof. Dr. Rainer Lenz Dipl.-Ing. Dirk Ammon (exercise) Dipl.-Math. Wolfgang Braun (exercise) [updated 01.06.2011] |
| Learning outcomes: Students will be taught basic skills in general mathematics, they will acquire a basic understanding of algebra and analysis and will become familiar with mathematical terminology. [updated 08.05.2008] |
| Module content: 1 Basic mathematical terminology Predicate logic, sets, relations, maps 2 Natural numbers, mathematical induction, recursion 2.1 The axioms of the natural numbers 2.2 Mathematical induction 2.3 Recursive definitions 2.4 Binomial coefficients and binomial formulae 2.5 Basic terminology of combinatorics 3 Elementary vector calculus in Euclidian vector space 3.1 Vector algebra, linear independence, dimension 3.2 Vectors in the Cartesian coordinate system, scalar product, vector product, mixed product 3.3 Geometrical applications 4 Vectors in n-dimensional space 4.1 Generating system, basis, subspaces 4.2 Linear maps, range, kernel 4.3 Matrix representation of linear maps 4.4 Geometrical applications: Projections, reflections, rotations 5 Matrices 5.1 Linear systems of equations, Gaussian algorithm 5.2 Matrix algebra 5.3 Quadratic matrices, determining the inverse matrix, determinants, Cramer’s rule, adjoint eigenvalue problems, basis transformation 6 Basic terminology of algebra 6.1 Semigroups, monoids 6.2 Groups, subgroups, normal subgroup, factor groups, homomorphism 6.3 Rings and fields 7 Sequences and series 7.1 Limits, limit theorems, Cauchy sequences 7.2 Series, conditional and absolute convergence, comparison test and ratio test, Cauchy product 7.3 Geometrical series, exponential series 8 Continuity 8.1 Limits of functions 8.2 Properties of continuous functionsInverse functions, logarithms, inverse hyperbolic and inverse trigonometric functions [updated 08.05.2008] |
| Recommended or required reading: Hartmann, P.: Mathematik für Informatiker, Vieweg, 3. Aufl. 2004 Meyberg, K. Vachenauer, P.: Höhere Mathematik 1, Springer [updated 08.05.2008] |
| Module offered in: WS 2016/17, WS 2015/16, WS 2014/15, WS 2013/14, WS 2012/13, ... |
[Sat May 21 00:54:30 CEST 2022, CKEY=pmathe1, BKEY=pi, CID=PIB125, LANGUAGE=en, DATE=21.05.2022]