MA021 Concrete Mathematics

Faculty of Informatics
Autumn 2009
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Karel Zikan, PhD. (lecturer)
Guaranteed by
prof. Ing. Jiří Sochor, CSc.
Department of Visual Computing – Faculty of Informatics
Contact Person: prof. Ing. Jiří Sochor, CSc.
Timetable
Thu 14:00–15:50 B204
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 25 student(s).
Current registration and enrolment status: enrolled: 0/25, only registered: 0/25, only registered with preference (fields directly associated with the programme): 0/25
fields of study / plans the course is directly associated with
there are 23 fields of study the course is directly associated with, display
Course objectives
This set of lectures concerns primarily the area of deterministic linear, near-linear, and mainly-linear recurrences and related topics. The course is demanding in that it teaches as well as requires concrete computations, concrete derivations of equations, identities, and relationships. For his or her efforts, the student learns to command several powerful mathematical machines. Our course is built mainly around the text: Graham, Knuth, Patashnik, "Concrete Mathematics -- A Foundation for Computer Science". In turn, "Concrete Mathematics" is an elaboration of the introductory chapter "1.2 Mathematical Preliminaries" of the classic 'bible' of Computer Science: Donald E. Knuth, "The Art of Computer Programming, Vol.1". An excellent exposition of several themes (e.g., generating functions) can be found in George Polya: "Mathematics and Plausible Reasoning; Vol. I. Induction and Analogy in Mathematics; Vol. II. Patterns of Plausible Inference." Extensive background of monotropic functions can be found in R.T Rockafellar, "Network Flows and Monotropic Optimization"; and "all about conjugate duality“ can be found in R.T. Rockafellar, "Convex Analysis".
Syllabus
  • (1) Deterministic recurrences -- introduction and examples (3) Sums (3) Monotropic functions, conjugate duality, optimization (4) Integer functions and number theory (5) Binomial coefficients (6) Additional systems of special numbers (7) Generating functions (8) Discrete probability (9) Asymptotic analysis
Language of instruction
Czech
Further Comments
Study Materials
The course is taught only once.
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