| Title | Primjena kongruencija |
| Author | Irena Užar |
| Mentor(s) | Ivan Matić (thesis advisor)
|
| Abstract | U diplomskom radu pokazat ćemo kako se kongruencija može primjeniti na različite načine.
Prvo ćemo definirati kongruenciju i navesti njezina svojstva koja ćemo koristiti u radu. Zatim
ćemo prikazati neke od njezinih primjena. Prvo neke od jednostavnjih poput testa djeljivosti
za brojeve 10, 5, 2^{i}, 3 , 9 i 11 koje se dokazuju primjenom kongruencija, zatim metoda
odbacivanja devetki i digitalni korijen. Nakon toga ćemo vidjeti kako se kongruencija koristi
za modeliranje dizajna, preko zvijezde s m vrhova, (m, n) dizajna ostataka do quilt dizajna.
Zatim slijede primjene koje omugućavaju otkrivanje grešaka u identifikacijskim brojevima
(UPC, EAN-13, ISBN,...).
I na kraju ćemo prikazati kako se primjenom kongruencija može rješiti problem p-kraljica,
raspored timova po skupinama (round-robin turnir) te odredivanje dana u tjednu za bilo
koji datum i bilo koju godinu (Perpetual kalendar). |
| Keywords | Congruence Congruence Applications divisibility test casting out nines digital roots modular designs check digit p-Queens Puzzle Round-Robin tournament Perpetual calendar |
| Parallel title (English) | Congruence Applications |
| Granter | Josip Juraj Strossmayer University of Osijek
Department of Mathematics |
| Lower level organizational units | Chair of Pure Mathematics
Algebra and Calculus Research Group |
| Place | Osijek |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics |
| Study specialization | Financial and Statistical Mathematics |
| Academic title abbreviation | mag.math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2016-11 |
| Parallel abstract (English) | In this work we will show how congruence has applications on many different ways.
First we will define congruence and show it properties that we will use in work. Then we
will show some simple applications like divisibility test for numbers 10, 5, 2^{i}, 3 , 9 and 11,
prove them with congruence. Then we will show method casting out nines and digital roots.
After that we will see how congruence is applied on design modular designs, from m-pointed
star, (m, n) residue design to quilt design.
In third part we will show how congruence is used to detect mistakes in identification numbers
(UPC, EAN-13, ISBN,...)
In the final three parts we will show how congruence applications can help to solve the pQueens
Puzzle, Round-Robin tournaments and to determinate the day of the week for any
date and any year. |
| Parallel keywords (Croatian) | kongruencija primjena kongruencija testovi djeljivosti odbacivanje devetke digitalni korijen modularni dizajni znamenka provjere problem p-kraljica roundrobin turnir Perpetual kalendar |
| Resource type | text |
| Access condition | Open access |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:126:114640 |
