Izbrana poglavja iz računalniške matematike

2025/2026

Program:

Doktorski študijski program 3. stopnje Matematika in fizika

Smer:

Matematika

Letnik:

1 ali 2 letnik

Semester:

prvi ali drugi

Vrsta:

izbirni

ECTS:

Jezik:

slovenski, angleški

Nosilec predmeta:

prof. dr. Andrej Bauer, prof. dr. Sergio Cabello Justo, izr. prof. dr. Matija Pretnar, prof. dr. Alexander Keith Simpson

Izvajalec (kontaktna oseba):

prof. dr. Alexander Keith Simpson, doc. Doctor of Philosophy Andrew Wakelin Swan

Ure na teden – 1. ali 2. semester:

Predavanja

Seminar

Vaje

Laboratorij

Pogojev za vključitev v delo ni.

Izbrane bodo nekatere standardne teme iz podiplomske računalniške matematike, kot so:
simbolno računanje, teorija izračunljivosti, računska geometrija, logika v računalništvu, teorija programskih jezikov, algoritmi in podatkovne strukture, kriptografija, analiza omrežij idr. Izbira je odvisna od interesov in raziskovalne usmeritve študentov.

T. H. Cormen ... [et al.]: Introduction to Algorithms, 2nd ed. - Cambridge (Mass.) : MIT Press ; Boston : McGraw-Hill, cop. 2001.
P. Doreian, V. Batagelj, A. Ferligoj: Generalized blockmodeling, Cambridge : Cambridge University Press, 2005.
M. Huth, M. Ryan: Logic in computer science : modelling and reasoning about systems, 2nd ed., Cambridge : Cambridge University Press, 2019.
J. Matoušek: Lectures on discrete geometry, New York : Springer, cop. 2002.
M. Petkovšek, H. S. Wilf, D. Zeilberger: A=B, Wellesley (Massachusetts) : A. K. Peters, cop. 1996.
B. C. Pierce: Types and programming languages, Cambridge (Massachusetts) : The MIT Press, cop. 2002.
H. Rogers: Theory of recursive functions and effective computability, New York : McGraw-Hill, cop. 1967.
D. R. Stinson: Cryptography : theory and practice, 3rd ed., Boca Raton : Chapman & Hall/CRC, cop. 2006.

Namen predmeta je seznaniti študente z nekaterimi pomembnimi temami računalniške matematike.

Znanje in razumevanje predstavljenih konceptov.
Sposobnost uporabe pridobljenega znanja in spretnosti.

Predavanja, konzultacije, reševanje problemov

Pisni izpit (domače naloge), ustni izpit
(ocene: 5 (negativno), 6-10 (pozitivno), ob upoštevanju Statuta UL)

BAUER, Andrej, CVETKO-VAH, Karin. Stone duality for skew Boolean algebras with intersections. Houston journal of mathematics, ISSN 0362-1588, 2013, vol. 39, no. 1, str. 73-109. [COBISS-SI-ID 16620377]
BAUER, Andrej, STONE, Christopher A. RZ: a tool for bringing constructive and computable mathematics closer to programming practice. Journal of logic and computation, ISSN 0955-792X, 2009, vol. 19, no. 1, str. 17-43. [COBISS-SI-ID 15325785]
AWODEY, Steve, BAUER, Andrej. Propositions as [Types]. Journal of logic and computation, ISSN 0955-792X, 2004, vol. 14, no. 4, str. 447-471. [COBISS-SI-ID 13374809]
BAUER, Andrej, PETKOVŠEK, Marko. Multibasic and mixed hypergeometric Gosper-type algorithms. Journal of symbolic computation, ISSN 0747-7171, 1999, let. 28, št. 4-5, str. 711-736. [COBISS-SI-ID 9210969]
CABELLO, Sergio, GIANNOPOULOS, Panos. The complexity of separating points in the plane. Algorithmica, ISSN 0178-4617, 2016, vol. 74, iss. 2, str. 643-663. [COBISS-SI-ID 17195097]
CABELLO, Sergio. Hardness of approximation for crossing number. Discrete & computational geometry, ISSN 0179-5376, 2013, vol. 49, iss. 2, str. 348-358. [COBISS-SI-ID 16340313]
CABELLO, Sergio. Many distances in planar graphs. Algorithmica, ISSN 0178-4617, 2012, vol. 62, no. 1-2, str. 361-381. [COBISS-SI-ID 15702873]
SIMPSON, Alex. A characterization of the least-fixed-point operator by dinaturality. Theoretical computer science, ISSN 0304-3975, 1993, vol. 118, iss. 2, str. 301-314. [COBISS-SI-ID 17181017]
SIMPSON, Alex. Computational adequacy for recursive types in models of intuitionistic set theory. Annals of pure and applied Logic, ISSN 0168-0072. [Print ed.], 2004, vol. 130, iss. 1-3, str. 207-275. [COBISS-SI-ID 17117017]
AWODEY, Steve, BUTZ, Carsten, SIMPSON, Alex, STREICHER, Thomas. Relating first-order set theories and elementary toposes. Bulletin of symbolic logic, ISSN 1079-8986, 2007, vol. 13, no. 3, str. 340-358. [COBISS-SI-ID 17096537]
Matija Pretnar:
BAUER, Andrej, PRETNAR, Matija. An effect system for algebraic effects and handlers. Logical methods in computer science, ISSN 1860-5974, 2014, vol. 10, iss. 4, paper 9 (str. 1-29). http://arxiv.org/pdf/1306.6316 [COBISS-SI-ID 17191001]
PRETNAR, Matija. Inferring algebraic effects. Logical methods in computer science, ISSN 1860-5974, 2014, vol. 10, iss. 3, paper 21 (str. 1-43) [COBISS-SI-ID 17190745]
PLOTKIN, Gordon, PRETNAR, Matija. Handling algebraic effects. Logical methods in computer science, ISSN 1860-5974, 2013, vol. 9, iss. 4, paper 23 (str. 1-36) [COBISS-SI-ID 16816729]