https://mathwiki.cs.ut.ee/ 2026-04-15T18:03:33+00:00 https://mathwiki.cs.ut.ee/ https://mathwiki.cs.ut.ee/lib/exe/fetch.php?media=wiki:dokuwiki.svg text/html 2014-11-14T01:21:59+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=asymptotics&rev=1415928119&do=diff Asymptotics In this topic we will learn how to compare the performance of algorithms on large inputs using asymptotic notations — the Big Oh and the Big Omega. In our examples, we will mainly deal with running times of algorithms (so-called time complexity text/html 2014-01-31T09:50:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=divisibility_and_modular_arithmetics&rev=1391161854&do=diff Divisibility and modular arithmetics A lot of cryptography constructions are built on top of various algebraic structures. All this structures are ultimately built on top of integers $\{\dots, -3, -2, -1, 0, 1, 2, 3, 4, \dots\}$. In the following lessons we will recall and study some more important aspects of integers. text/html 2014-01-20T00:08:09+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=finite_fields&rev=1390176489&do=diff Finite fields This topic introduces the algebraic concept of field. We shall give the precise definition of this algebraic structure and study the properties of finite fields. We shall find that in addition to the (infinite) field of real numbers that every schoolchild is familiar with, there exist many more. In cryptography, e. g. in encryption and computation of error-correcting codes, some of these fields have turned out to be very useful. On our way we shall also meet the algebraic structur… text/html 2014-01-02T08:56:53+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=introduction&rev=1388653013&do=diff Introduction About Mathwiki Mathwiki is a self-study environment, which consist, at the moment, of six topics: asymptotics, divisibility and modular arithmetics, finite fields, linear algebra, number theory, probability theory. These topics are the ones which most often are needed by students of informatics in their studies. For example, asymtotics for comparing performances of algorithms or programs (time efficiency, memory efficiency). Or modular arithmetics and finite field theory … text/html 2014-01-30T22:36:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=linear_algebra&rev=1391121393&do=diff Linear algebra A system of linear equations, for example, $$ \begin{cases} 5 x_1 + 2 x_2 = 4\\ 3 x_1 + 6 x_2 = 7 \end{cases} $$ can be written down using matrix notation in the following way: $$ \begin{pmatrix} 5 & 2\\ 3 & 6 \end{pmatrix} \begin{pmatrix} x_1\\ x_2 \end{pmatrix} = \begin{pmatrix} 4\\ 7 \end{pmatrix} $$ Using such a matrix notation is a standard way of solving systems of linear equation by computer algebra systems both symbolically (e.g., Wolfram Mathematica, Sage) and numer… text/html 2014-01-30T22:35:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=probability_theory&rev=1391121347&do=diff Probability theory Quite often in life we do not know for sure, what will be the result of an experiment or a process. For example, some hacker tries to attacks a particular information system. Surely both, the attacker and the information system owner wants to know the risks. So how to describe, what is going to happen? The answer to this gives probability theory. text/html 2014-01-31T09:52:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=sidebar&rev=1391161949&do=diff * Asymptotics * The need for asymptotic notation: a case study * Big Oh * Big Omega * Multiple variables * Polynomial complexity * The negligible, the noticeable and the overwhelming * Divisibility and modular arithmetics * Divisibility * Primes and divisibility * Greatest common divisor and least common multiple * Euclidean algorithm * Extended Euclidean algorithm * Modular arithmetics * Finite fields * What are rings and fields? * Long division of polynomial… text/html 2022-02-06T15:54:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=start&rev=1644162867&do=diff Welcome Mathwiki is a self-study environment for students of computer science. It contains selection of math topics needed in their studies. The materials here include important definitions, general ideas of theory, lot of examples and different exercises with answers.