MathWiki

Welcome - [Welcome]

swen (swen@undisclosed.example.com) — 2022-02-06T15:54:27+00:00

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.

PlayGround

mirjam (mirjam@undisclosed.example.com) — 2015-03-20T12:04:34+00:00

PlayGround

Residue classes - imported from previous wiki

aleksei (aleksei@undisclosed.example.com) — 2015-03-19T18:00:27+00:00

Residue classes Modular arithmetics as a way of calculating modulo some number $n$ is a powerful tool. However, it can be made simpler, and thus even more effective. First, recall that numbers having the same remainder when divided by $n$ behave in exactly the same way in such a calculation and yield exactly the same results. $8 * 4 + 11 \equiv 3*(-1) + 6 \equiv 3 (\mod 5)$$n$$n$$n$$n$$a \in \mathbb Z$$n \in \mathbb N$$\overline a = \{b \in \mathbb Z \mid a \equiv b \ (\mod n)\} = \{a + kn \mi…

Modular arithmetics - imported from previous wiki

aleksei (aleksei@undisclosed.example.com) — 2015-03-19T17:57:08+00:00

Modular arithmetics $\renewcommand{\mod}{\operatorname{mod}}$ Sometimes when you want to calculate something you might only require the remainder of the answer when divided by some natural number $n$. With help of modular arithmetics finding the required remainder usually happens to be much easier than evaluating the original expression.$a, b$$n$$a \equiv b \ (\mod n)$$a$$b$$n$$a \mod n = b \mod n$$5638 \times 7891 + 2731 \times 3124$$17$$5638 \times 7891 + 2731 \times 3124 = 44489458 + 853164…

Mathematical induction - created

mirjam (mirjam@undisclosed.example.com) — 2015-01-27T12:22:07+00:00

Mathematical induction Some smartness about mathematical induction

Limit - [Some properties of limit]

jaan (jaan@undisclosed.example.com) — 2014-12-12T19:37:58+00:00

Limit Let $f$ be a real-valued function defined on some subset of the real line $\mathbb R$. Informally speaking, a number $c$ is said to be the limit of $f$ in the process $x \to \infty$ if $f(x)$ comes arbitrarily close to $c$ as $x$ gets larger and larger. The precise definition of limit is as follows:$c \in \mathbb R$$\epsilon$$N$$x > N$$|f(x)-c| < \epsilon$$x$$\lim_{x \to \infty} f(x) = c$$c$$f$$x \to \infty$$M$$N$$x > N$$f(x) > M$$x \to \infty$$\lim_{x \to \infty} f(x) = \infty$$M$$N$$x >…

gcd_primes.png - created

marje (marje@undisclosed.example.com) — 2014-01-31T08:53:51+00:00

gcd.png - created

marje (marje@undisclosed.example.com) — 2014-01-31T07:59:58+00:00

common_divisor.png - created

marje (marje@undisclosed.example.com) — 2014-01-31T07:42:45+00:00

prime_divisibility.png - created

marje (marje@undisclosed.example.com) — 2014-01-30T22:29:26+00:00

divisibility-lattice.svg - created

swen (swen@undisclosed.example.com) — 2014-01-30T12:13:52+00:00

transitivity.png - created

marje (marje@undisclosed.example.com) — 2014-01-30T11:05:03+00:00

lattice_divisibility.png

marje (marje@undisclosed.example.com) — 2014-01-29T23:22:32+00:00

divides.png

marje (marje@undisclosed.example.com) — 2014-01-29T23:15:55+00:00

quotient_remainder.png - created

marje (marje@undisclosed.example.com) — 2014-01-29T20:14:18+00:00

jensen_v1.png - created

marje (marje@undisclosed.example.com) — 2014-01-22T13:10:04+00:00

markov_5.png - created

marje (marje@undisclosed.example.com) — 2014-01-22T13:09:10+00:00

markov_4.png - created

marje (marje@undisclosed.example.com) — 2014-01-22T13:08:58+00:00

markov_3.png - created

marje (marje@undisclosed.example.com) — 2014-01-22T13:08:45+00:00

markov_2.png - created

marje (marje@undisclosed.example.com) — 2014-01-22T13:08:12+00:00