    Close Help Print  Course module: 202001360  202001360Algorithmic Discrete Mathematics Course info   Course module 202001360
Credits (ECTS) 5
Course type Study Unit
Language of instruction English
Contact person dr.ir. R. Langerak
E-mail r.langerak@utwente.nl
Lecturer(s) Previous 1-5 of 86-8 of 8 Next 3 Examiner dr. A. Antoniadis   Examiner dr.ir. P. van 't Hof   Examiner dr. J. de Jong   Examiner dr.ir. R. Langerak   Contactperson for the course dr.ir. R. Langerak  Starting block
 2A RemarksMinor students: register for the minor!
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes Aims
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } At the end of the course the student is able to: use and explain elementary data structures like lists, heaps, binary trees, and priority queues use and explain elementary algorithms like sorting, traversing and updating data structures, and basic optimization problems analyse the time complexity of algorithms and operations on data structures, e.g. using the Master Theorem or recursions, and use dynamic programming use and understand the Euclidean algorithm, in fact the “grand daddy of all algorithms” (Knuth), in particular its computational efficiency, and its relevance in applications such as, e.g., RSA public key encryption use, explain and design algorithms on graphs and networks, such as computation of shortest paths, spanning trees and maximum flows solve second order linear recurrence relations using characteristic polynomials or generating functions solve complex combinatorial counting problems using the method of (linear or exponential) generating functions Content
 body { font-size: 9pt; font-family: Arial } table { font-size: 9pt; font-family: Arial } The first two weeks of the study unit “Algorithmic Discrete Mathematics” are devoted to the understanding of elementary data structures, and their use in the design and theoretical analysis of classic discrete algorithms. This includes basic principles and techniques to analyse the time and space complexity of algorithms, worst-case and average-case. The data structures include heaps, binary trees, as well as priority queues. Algorithms that are dealt with are for sorting, computational problems with permutations, the Euclidean algorithm to compute the greatest common divisor, the computation of shortest paths, and minimum spanning trees. General algorithmic techniques that are introduced are divide and conquer, as well as dynamic programming. (Some of these algorithms are implemented using the Python programming language, as part of the graph isomorphism implementation project.) The third and fourth weeks are devoted to structural, algorithmic, and combinatorial problems that lie in the core of discrete and combinatorial mathematics: Students understand the algorithmic power of duality on the example of maximum flows and minimum cuts, the characterization of graph classes by means of forbidden minors on the example of planarity, and learn how to solve advanced combinatorial counting problems using two different techniques, namely solving (second-order, linear) recurrence relations using the characteristic polynomial, as well as generating functions.  Module Module 7     Participating study Bachelor Applied Mathematics     Participating study   Required materials
Book
 Discrete and Combinatorial Mathematics: An Applied Introduction, Ralph P. Grimaldi, Pearson, 2003 (5th ed.). ISBN: 978-0201726343  Recommended materials
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