Schaum´s Ouline Series, 2007. Matthews. Elementary linear algebra. Nolt,
Rohatyn &Varzi. Logic. Schaum´s Outline Series, 2011. Reynolds, Tymann.
Natural Sciences Department
The University of the Faroe Islands
Winter Semester 2012
Maths. 2 for Information Technology 5023.10
detailled description, 7.5 ECTS pts.
Lecturer Roland Kaschek
Natural Sciences Department calendar week
content
The University of the Faroe Islands source
chapter
pages
2
systems of linear equations, Gauss-Jordan algorithm, matrix computations, subspaces
Matthews
1–3
1 – 70
3
algebraic structures (semigroup, group, field, vector space), morphisms, congruences, quotient structures
Kolman et al.
9
344 – 384
Kolman et al.
10
Lipschutz & Lipson, Ziegenbalg et al.
13, 7.2, 5.7
4
5
6
languages, Chomsky hierarchy, grammars, BNF & syntax diagrams, finite state machines, machines & languages computable functions, Turing machine & while program, countable sets, real vs rationale numbers, diagonalization, computer numbers,“Halteproblem“, complexity classes P vs NP undirected trees, spanning trees, minimal spanning trees, Prim´s algorithm, Kruskal´s algorithm, Petri nets
7. 4 & 7.5, Kolman et al. experiment 6, 3.4
Winter Semester 2012
Learning outcomes (the successful student can:) solve systems of linear equations including disturbed ones, calculate with matrices, find nullity & rank of a matrix Define semigroup, group, field and vector space & give simple examples
Read & create grammars, rank languages, use BNF and syntax diagrams, define state machine & relate regular sets to Moore machines relate computable functions to Turing machines & while 323 – 336, programs, explain the differences between real, rational and 225 – 229, computer numbers and give related examples, know the 183 – 194 Halteproblem and its solution execute Kruskal´s and Prim´s algorithm, use Petri nets for 295 - 305, specifying simple concurrent processes, define elementary 267 – 269 discrete probability spaces and compute probabilities of probabilities of related events execute fleury´s algorithm and give sufficuent conditions for 305 – 329 the existence of Hamiltonian circuits, execute the Ford & Fulkerson algorithm 386 – 428
graphs, graph morphisms, quotient graphs, Euler paths & circuits, Hamiltonian paths & circuits, transport Kolman et al. 8.1 – 8.4 networks Kolman et al., 8.5 – 8.6, 329 – 343, apply Hall´s Marriage theorem, execute the Welch-Powell graph matchings, graph coloring,predicate logic, Lipschutz & 8 8.11, 168 – 170, algorithm, explain what a well-formed formula is and explain miscellaneous (recap) Lipson, 6.1 – 6.4 130 – 149 what the meaning of wff is Nolt et al. References: (textbooks are boldfaced) Kolman, Busby & Ross Discrete mathematical structures Pearson International, 2009 Lipschutz, Lipson Discrete mathematics Schaum´s Ouline Series, 2007 Matthews Elementary linear algebra http://www.numbertheory.org/book/ Nolt, Rohatyn &Varzi Logic Schaum´s Outline Series, 2011 Reynolds, Tymann Principles of Computer Science Schaum´s Ouline Series, 2008 Spiegel, Schiller, Srinivasan Probability and Statistics Schaum´s Ouline Series, 2009 Algorithmen von Hammurapi bis Ziegenbalg et al. Verlag Harri Deutsch, 2010 Gödel 7
Maths. 2 for Information Technology 5023.10
detailled description, 7.5 ECTS pts.
Lecturer Roland Kaschek
