SUMMER 2019
\nMATH 503\/503G: APPLIED DISCRETE MATHEMATICS (3 credit hours)
\nThis course is entirely online and will run from 6\/3\/19 through 7\/26\/19.
\nPrerequisites: MT200 (introduction to writing mathematical proofs) or equivalent and MT357 (proof-based introduction
\nto linear algebra) or equivalent. Previous coursework in discrete mathematics would be helpful but is not required.
\nNote: When taken as MT503, this course will count as a list B elective in the mathematics major.
\nCOURSE DESCRIPTION:
\nAn introduction to topics that frequently arise in applications of discrete mathematics in bioinformatics, computer science, and
\ndigital communications technology. The course will be divided into four modules described below: Enumeration, Recurrence
\nRelations, Graph Theory, and Coding Theory. Each module will start with a short video introduction, a description of the
\nlearning objectives, reading assignments, and link to a blog where online discussions will take place. The reading assignments
\nwill come from lecture notes that I post and from the text. Online discussion will center around questions posed in the lecture
\nnotes. Each module will conclude with a set of problems that you work on individually and submit to me for grading. Your
\nparticipation in the group discussion will count for 50% of your grade and the individual homework assignments will count
\nfor 50% of your grade.
\nText: Combinatorics: Topics, Techniques, Algorithms, Peter J. Cameron, Cambridge Univ. Press. Additional course notes
\nwill be made available via Blackboard.
\nEnumeration
\n\u2022 Permutations, combinations, inclusion\/exclusion, Pigeonhole Principle, binomial identities, multinomial coefficients,
\nand generalized binomial coefficients.
\n\u2022 Derangements, partitions, Catalan and Bell numbers, Stirling numbers of the first and second kind.
\n\u2022 Counting selections, ordered or unordered, with or without replacement, from multi-sets.
\nRecurrence Relations
\n\u2022 Linear and nonlinear recurrence relations.
\n\u2022 Solution of homogeneous, linear recurrence relations with constant coefficients using eigenvalues and eigenvectors of
\nlinear transformations.
\n\u2022 Solution of recurrence relations using ordinary and exponential generating functions.
\nGraph Theory
\n\u2022 Directed and undirected graphs, basic definitions\/results.
\n\u2022 Eulerian and Hamiltonian cycles, trees, graph coloring.
\n\u2022 The mathematics of Google\u2019s page ranking algorithm.
\nCoding Theory
\n\u2022 Linear and nonlinear block codes, basic definitions\/results.
\n\u2022 Bounds on the size of a code.
\n\u2022 Erasure codes. (Used in internet and cell-phone communications.)
\nFor more information, see Prof. Michael Adams, VH2148, mjadams@truman.edu.<\/p>\n","protected":false},"excerpt":{"rendered":"
SUMMER 2019 MATH 503\/503G: APPLIED DISCRETE MATHEMATICS (3 credit hours) This course is entirely online and will run from 6\/3\/19 through 7\/26\/19. Prerequisites: MT200 (introduction to writing mathematical proofs) or equivalent and MT357 (proof-based introduction to linear algebra) or equivalent. Previous coursework in discrete mathematics would be helpful but is not required. Note: When taken […]<\/p>\n","protected":false},"author":357,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1384","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"yoast_head":"\n