FI:MA021 Concrete Mathematics - Course Information

MA021 Concrete Mathematics

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

• Applied Informatics (programme FI, N-AP)
• Information Technology Security (programme FI, N-IN)
• Bioinformatics (programme FI, N-AP)
• Information Systems (programme FI, N-IN)
• Informatics (eng.) (programme FI, D-IN4)
• Informatics (programme FI, D-IN4)
• Informatics (programme FI, N-IN)
• Mathematical Informatics (programme FI, B-IN)
• Parallel and Distributed Systems (programme FI, N-IN)
• Computer Graphics (programme FI, N-IN)
• Computer Networks and Communication (programme FI, N-IN)
• Computer Systems and Technologies (eng.) (programme FI, D-IN4)
• Computer Systems and Technologies (programme FI, D-IN4)
• Computer Systems (programme FI, N-IN)
• Embedded Systems (eng.) (programme FI, N-IN)
• Embedded Systems (programme FI, N-IN)
• Service Science, Management and Engineering (eng.) (programme FI, N-AP)
• Service Science, Management and Engineering (programme FI, N-AP)
• Theoretical Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)
• Artificial Intelligence and Natural Language Processing (programme FI, N-IN)
• Image Processing (programme FI, N-AP)

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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• Permalink: https://is.muni.cz/course/fi/autumn2009/MA021