Konzultacije

ponedjeljak 14-16


Science – Znanost

I am interested in topology geometry, mathematical physics and fundamenta.

I was at IHÉS for three months this academic year as an invited researcher, from Oct 1 to Dec 31, 2019. ♬

Doctoral disertation
Upotpunjeni Hopfovi algebroidi, in Croatian language, defended on October 20, 2017 ♫♪♬♫ mentor: Zoran Škoda
Completed Hopf algebroids, Doctoral presentation, English translation of the doctoral presentation in Croatian language

Publications
– S. Meljanac, Z. Škoda, M. Stojić, Lie algebra type noncommutative phase spaces are Hopf algebroids, Letters in Mathematical Physics, 107:3, 475-503 (2017)
– Z. Škoda, M. Stojić, A two-sided ideal trick in Hopf algebroid axiomatics, preprint
Lists of publications: arXiv, google scholar, bib.irb.hr

Projects
Quantum Current Algebras and Their Representation Theory, Croatian Science Foundation installation research project
I am the topologist entrusted with completions of algebraic structures.

Conferences
Noordung forum: Building European Blockchain Infrastructure, Center Noordung - Center vesoljskih tehnologij Hermana Potočnika Noordunga, Vitanje, Slovenia, Apr 23, 2019
39th Winter School Geometry and Physics, Srni, Czech Republic, January 12-19, 2019
   Contributed talk: Completed Hopf algebroid over U(g) of formal differential operators on a Lie group G
Dubrovnik VIII – Geometric Topology, Geometric Group Theory & Dynamical Systems, Dubrovnik, Croatia, June 22-26, 2015
Manifolds, K-theory, and Related Topics, Dubrovnik, Croatia, June 23-27, 2014
Dubrovnik VII – Geometric Topology, Dubrovnik, Croatia, June 26 - July 3, 2011

Other talks
The symmetric monoidal category indprofinVect of ind-pro-finite-dimensional vector spaces, Topology Seminar Ljubljana-Maribor-Zagreb, University of Maribor, Slovenia, 2019
The category indproVect of filtered-cofiltered vector spaces, short series of talks at Topology Seminar, PMF-MO, Zagreb, 2017
Automorphic sets and quandles in geometry and topology, short series of talks from literature at Topology Seminar, PMF-MO, Zagreb, 2014
From Maxwell equations to Gauge theory, short series of talks from literature at Topology Seminar, PMF-MO, Zagreb, 2012
Alexander polynomial, short series of talks from diploma thesis at Topology Seminar, PMF-MO, Zagreb, 2010

Diploma thesis
Alexanderov polinom, mentor: profesor Šime Ungar
siječanj 2010. diplomirana inženjerka matematike, smjer: teorijska matematika

mono no aware.


Teaching – Nastava

Kompleksna analiza – srijeda 11-13
Materijali za vježbe, 38 stranica
    1. Kompleksni brojevi i funkcije
        1.1. Kompleksni brojevi
        1.2. Geometrija kompleksne ravnine
        1.3. Derivacija kompleksne funkcije
        1.4. Elementarne funkcije
    2. Nizovi i redovi kompleksnih funkcija
        2.1. Nizovi i redovi kompleksnih brojeva
        2.2. Redovi potencija
        2.3. Integral kompleksne funkcije
        2.4. Taylorov red
        2.5. Laurentov red
        2.6. Singulariteti
    3. Teorem o reziduumima i primjene
        3.1. Reziduumi
        3.2. Teorem o reziduumima
        3.3. Rouchéov teorem
        3.4. Računanje integrala funkcija realne varijable pomoću reziduuma
Zanimljivosti
– Daniel, Viallet, The geometrical setting of gauge theories of the Yang-Mills type, Reviews of Modern Physics, Vol. 52, No. 1, January 1980
Non-technical introduction to Gauge theory
– Richard Feynman, QED: The Strange Theory of Light and Matter, wikipedia
– Frederic P. Schuller, A thorough introduction to the theory of general relativity, WE-Heraeus International Winter School on Gravity and Light ♡ 24 predavanja
Circle Packing: A Mathematical Tale, AMS Notices
– Alexandru Scorpan, The Wild World of Four Manifolds, AMS, 2005.
– LaTeX online editor and documentation: www.overleaf.com

Uvod u diferencijalnu geometriju – četvrtak 13-15 -->

Linearna algebra 1 (nastavnički smjer) – petak 15-18


Nastava prijašnjih godina

Konstruktivne metode u geometriji
Materijali za vježbe, 13 stranica
Algebarska metoda, zadaci s rješenjima i dodatnim uputama
        Interaktivni html s konstrukcijom & ggb:
            1. KMG-2-1-geometrijska-sredina.html & ggb
            2. KMG-2-Zadatak-2.2.html & ggb
Dodatni materijali
– Dvije konstrukcije: EG-konstrukcije.pdf
– D. Palman, Geometrijske konstrukcije, Element, Zagreb 1996.
Popis zadataka s vježbi, 2014/15, 4 stranice

Elementarna geometrija
– How to relax with geometry: breathe-in-and-out.gif
– Stereometrija, neki zadaci s vježbi: EG-stereometrija-4-8-9-10-11-15-16.pdf, EG-stereometrija-14-17-18-19.pdf

Analitička geometrija

Vektorski prostori
Materijali za vježbe, 25 stranica
    1. Ponavljanje linearne algebre
    2. Jordanova forma
    3. Funkcije operatora
    4. Unitarni prostori

Strukture podataka i algoritmi
Materijali za vježbe, 44 stranice, po knjizi: Aho, Hopcroft, Ullman, Data Structures and Algorithms, 2nd Edition, Addison-Wesley, Reading MA, 1987.
    1. Uvod
    2. Općenita lista (List)
    3. Stog (Stack)
    4. Red (Queue)
    5. Uređeno stablo (Tree)
    6. Binarno stablo (BinaryTree)
    7. Općeniti skup (Set)
    8. Rječnik (Dictionary)
    9. Prioritetni red (PriorityQueue)
    10. Preslikavanje (Mapping)
    11. Binarna relacija (Relation)
    12. Oblikovanje algoritama
Computer programming
– Kernighan, Ritchie, C Programming Language, 2 ed.
– Pointers: Pointer uses, Making pointers safer, Dangling pointer
Undefined behaviour
Technical debt
Design / metodology
Poka-yoke, Toyota Production System, Lean Software Development, Kanban, Scrum, Kanban vs. Scrum, REST
Abstract Data Types, OOP
– Sedgewick, Algorithms in C, Part 2, 1990
. Ch.3 Elementary Data Structures, Ch.4 Abstract Data Types, Ch.5 Recursion and Trees – dobar uvodni opis kako graditi ADT
– Hanson, C Interfaces and Implementations: Techniques for Creating Reusable Software, 1996. – detaljnije o ADT
Abstract Data Types, Java (Software Construction, MIT)
Problem Solving with Algorithms and Data Structures, Python

Elementarna matematika I
shu ha ri: wikipedia entry, Alistair Cockburn on Shu Ha Ri
– How To Count Past Infinity: youtube
– Teorija skupova, skripta profesora Vukovića: Hilbertov hotel, kardinalni brojevi, ordinalni brojevi, hipoteza kontinuuma
EM-indukcija-neki-zadaci-scan.pdf
Relacije.pdf
– Grothendieck: wikipedia entry, Grothendieck describes two styles in mathematics: opening the nut and the rising sea is one
Kongruencije.pdf
EM-Rastav-na-parcijalne-razlomke.pdf

Elementarna matematika II

Proteklih godina ukupno: Elementarna geometrija (8 godina), Konstruktivne metode u geometriji (7 godina), Strukture podataka i algoritmi (5 godina), Elementarna matematika I (4 godine), Elementarna matematika II (5 godina), Diskretna matematika, Uvod u matematiku, Vektorski prostori (2 godine), Analitička geometrija, Mjera i integral


Sada gledam-čitam-pohađam:
– Frederic P. Schuller, A thorough introduction to the theory of general relativity, WE-Heraeus International Winter School on Gravity and Light ♡ 24 predavanja
Titled "A thorough introduction to the theory of general relativity", the lectures introduce the mathematical and physical foundations of the theory in 24 self-contained lectures. The material is developed step by step from first principles and aims at an audience ranging from ambitious undergraduate students to beginning PhD students in mathematics and physics. Satellite Lectures (see other videos on this channel) by Bernard F Schutz (Gravitational Waves), Domenico Giulini (Canonical Formulation of Gravity), Marcus C Werner (Gravitational Lensing) and Valeria Pettorino (Cosmic Microwave Background) expand on the topics of this central lecture course and take students to the research frontier. Access to further material on www.gravity-and-light.org/lectures and www.gravity-and-light.org/tutorials
– Chan Hong-Mo, Tsou Sheung Tsun, Some Elementary Gauge Theory Concepts, Lecture Notes in Physics, World Scientific, 1993

Zadnja promjena: Martina Stojić,