- **Tagy:** [[@aj]] - [[Odborná angličtina - předmět UJEP]] - **Zdroje:** --- ## General rules of pronunciation = *obecná pravidla výslovnosti* - It is individual. - The shortest versions are preferred. - [ef eks] = $fx$, $f(x)$, $f_x$, FX, $\overline{FX}$ - The difference is usually made clear **by the context**: - $f$ multiplied by $x$ - the function of $x$ - $f$ sub $x$ - line FX - vector FX --- ## Fundamental symbols = *základní symboly* - $=$ - equals; is equal to - $\neq$ - is not equal to; does not equal - $\equiv$ - is equivalent to; is identical with; is always equal to - $\cong$ - is approximately equal to; approximately equals - gt;$ - is greater than - lt;$ - is less than - $\leq$ - is less than or equal; is not greater than - $\geq$ - is greater than or equal to; is not less than - $!$ - factorial (*a*! - *a* factorial; factorial *a*) - ~; $\propto$ - is (directly) proportional to; varies as - $m_a$ - *m*a; *m* sub (script) *a* - $x_{ij}$ - *x* *ij*; x with the indices *ij* - $x'$ - *x* prime; *x* dashed - $x''$ - *x* double-prime; *x* double-dashed - $x^*$ - *x* star; *x* asterisk - $\bar{a}$ - *a* bar - $\tilde{a}$ - *a* tilde - $\hat{a}$ - *a* hat; *a* roof - $\ddot{a}$ - *a* double dot - $|a|$ - the absolute value of *a*; modulus *a* - % - per cent - $\infty$ - infinity - ( ) - parentheses; round brackets - $[\,]$ - brackets; square brackets - { } - braces; curly brackets - $\langle \, \rangle$ - angle brackets - ( ] - hybrid brackets - $(a;b)$ - (the) ordered pair *x*, *y* --- ## Combinatorics = *kombinatorika* - $V_k(n)$ - *k* variations of *n* things/objects/entities - $C_k(n)$ - *k* combinations of *n* things/objects/entities - $P(n)$ - *n* permutations - $V_{k}^{'}(n)$ - *k* variations of *n* things/objects/entities with repetitions - $C_{k}^{'}(n)$ - *k* combinations of *n* things/objects/entities with repetitions - $P^{'}(k_1,k_2,\dots,k_n)$ - multiset permutation; multinomial coefficient - $\left( \begin{array}{x}n \\ k \end{array} \right)$ - *n* choose *k*; binomial *n* over *k*; the *k*th binomial coefficient of the *n*th degree ## Mathematical logic = *matematická logika* - $X \wedge Y$ - *X* and *Y* (conjunction of statements *X* and *Y*) - $X \vee Y$ - *X* or *Y* (alternative of statements *X* and *Y*) - $X \Rightarrow Y$ - *X* implies *Y* (implication) - *Y* follows from *X* - if *X* holds then *Y* also holds - *X* is the sufficient condition for *Y* - *Y* is the necessary condition for *X* - $X \Leftrightarrow Y$ - *X* is equivalent y *Y* (equivalence) - *X* holds if and only if *Y* holds - *X* is the necessary and sufficient condition for *Y* - $\forall$ - for all; the universal quantifier - $\forall x \in I: V(x)$ - for each $x \in I$ the statement $V(x)$ holds - $\exists$ - there exists; the existential quantifier - $\exists \, x \in I: V(x)$ - there exists $x \in I$ such that the statement $V(x)$ holds - $\therefore$ - therefore - $\because$ - bacause - $\neg X$ - (the) negation (of) *X* - $X^{'}$ - (the) negation (of) *X* - 1, 0 - truth value; logical value - 1 - true - $\top$ - true - 0 - false - $\perp$ - false --- ## Sets = *množiny* - $x \in A$ - *x* is an element of *A*; *x* lies in *A* - *x* belongs to *A* - *x* is a member of *A* - $x \notin A$ - *x* is not an element of *A*; *x* does not lie in *A* - *x* does not belong to *A* - *x* is not a member of *A* - $A = \{a,b,c\}$ - *A* is the set with the elements *a*, *b*, *c* - $A \subset B$ - *A* is included in *B* - *A* is contained in *B* - *A* is a (proper) subset of *B* - $A = \varnothing$ - *A* is an empty set - *A* is a null set - $A \cup B$ - the union of *A* and *B*; *A* union *B* - $A \cap B$ - the intersection of *A* and *B*; *A* intersection *B* - $A \subseteq B$ - *A* is a subset of *B* - $A \sim B$ - *A* and *B* are equivalent to each other - $(a,b)$ - the open interval *a b* with the end points *a*, *b* - $[a,b]$; $\langle a,b\rangle$ - the closed interval *a b* - $(a,\,b]$; $(a,\,b\rangle$ - half-open (semi-open) interval *a b*, open on the left and closed on the right - $X=(-\infty, +\infty)$ - capital *X* equals the open interval minus infinity, plus infinity - $\bigcup\limits_{\alpha \, \in \, A} S_a$ - (the) union of all sets *M* sub $\alpha$; $\alpha \in A$ - $\bigcap\limits_{\alpha \, \in \, A} S_a$ - (the) intersection of all sets *M* sub $\alpha$; $\alpha \in A$ - $A \times B$ - the Cartesian product of *A* and *B*; *A* cross *B* - $A'_B$ - the relative complement of (a set) *A* with respect to (a set) *B* - $A \setminus B$ - the (set-theoretic) difference of *A* and B --- ## Addition = *sčítání* - $5 + 15 = 20$ - $5$, $15$ - summands = *sčítance* - $20$ - sum = *součet* - five plus fifteen equals twenty - five and fifteen equals twenty - five plus fifteen is equal to twenty - five added to fifteen makes twenty - five and fifteen is/are twenty - twenty is the sum of five and fifteen - $a+b=c$ - $a$ plus $b$ equals $c$ - $a_1+a_2=c$ - $a$ one plus $a$ two equals $c$ --- ## Subtraction = *odčítání* - $20 - 5 = 15$ - $20$ - minuend = *menšenec* - $5$ - subtrahend = *menšitel* - $15$ - difference = *rozdíl* - twenty minus five equals fifteen - five from twenty leaves fifteen - twenty diminished by five is equal to fifteen - fifteen is the difference of twenty and five - $a-b=c$ - $a$ minus $b$ equals $c$ --- ## Multiplication = *násobení* - $3 \times 2 = 6$ - $2$, $3$ - factors = *činitelé* - $6$ - product = *součin* - three times two is six - twice three is six - three (multiplied) by two equals six - $ab=c$ - $ab$ equals $c$ - $a$ multiplied by $b$ is equal to $c$ --- ## Division = *dělení* - $20:5 = 4$ - $25$ - dividend = *dělenec* - $5$ - divisor = *dělitel* - $4$ - quotient = *podíl* - twenty divided by five equals four - $a\div b=c$ - $a$ divided by $b$ equals $c$ --- ## Fractions = *zlomky* - $\frac{a}{b}=c$ - $a$ - numerator = *čitatel* - $b$ - denominator = *jmenovatel* - $c$ - quotient = *podíl* - $\frac{1}{2}$ - one half; a half - $\frac{1}{3}$ - one third; a third - $\frac{4}{9}$ - four ninths - $2\frac{3}{8}$ - two and three eighths - $\frac{a}{b}$ - $a$ over $b$ - $\frac{a+b}{a-b} = \frac{c+d}{c-d}$ - $a$ plus $b$ over $a$ minus $b$ equals $c$ plus $d$ over $c$ minus $d$ *Pokud poslední vztah diktujeme, je třeba udělat pauzu vždy po přečtení čitatele, abychom se vyhnuli nedorozumění.* - 0.123 - nought point one two three - zero point one two three - point one two three - oh [∂u] point one two three - 10.12 - ten point one two - 0.003 - oh point oh oh three - point two ohs three - point double-o-three - point nought nought three - 3.7777777777777 - three point seven recurring - 6.321321321 - six point three two one recurring --- ## Powers = *mocniny* - $a^n = b$ - *a* - base = *základ* - *n* - power exponent = *mocnitel* - *b* - value of a power = *výsledek mocnění* - *a* to the *n* equals *b* - *a* to the *n*th equals *b* - *a* to the *n*th (or *n*-th) power of *n* is equal to *b* - *a* (raised) to the power (of) *n* is equal to *b* - the *n*th power of *a* is equal to *b* - $5^2$ - five squared (square) - five (raised) to the second power - five to the power two - the second power of five - $2^3$ - two cubed (cube) - the cube of two - two (raised) to the third power - two to the power of three - the third power of two - $10^6$ - ten to the six - ten to the sixth power - $10^{-6}$ - ten to the minus six - $a^{-10}$ - *a* to the minus tenth; to the power minu ten - $a^2$ - *a* squared - the square of *a* - $a^n$ - *a* to the (power) *n*; to the *n*th (power) - the *n*th power of *a* - $(x+y)^2$ - *x* + *y* all squared ## Roots = *odmocniny* - $\surd$ - root sign (radical sign) = *odmocnítko* - $\sqrt[n]{c}$ - radical = *odmocnina* - $\sqrt{9} = 3$ - the (square) root (of) nine is three - $\sqrt{a}$ - root *a* - the square root (of) *a* - $\sqrt[3]{a}$ - the cube root (of) *a* - $\sqrt[4]{256}$ - the fourth root (of) 256 - $\sqrt[5]{a^6}$ - the fifth root out of *a* to the power six - $\sqrt[n]{a}$ - the *n*th root of *a* - $\sqrt[r]{x^s}$ - the *r*th root of *x* to the *s*th ## Logarithms = *logaritmy* - $\log_b{c}=n$ - logarithmic expression = *logaritmický výraz* - the logarithm to the base *b* of *c* is equal to *n* - the logarithm (of) *c* to/with the base *b* is equal to *n* - $\ln{c}$ - the natural logarithm of *c* - $\log{c}$ - the (common) logarithm of *c* - log-ten *c* - $\log_2{a}$ - the logarithm (of) *a* to the base two - $\log{x_1 x_2}$ - the logarithm (of) *x* one *x* two - $\log{x^n}$ - the logarithm (of) *x* to the power *n* ## Matrices and determinants = *matice a determinanty* - $A_{m,n}$ - *m* by *n* matrix - $A_{[m,n]}$ - *m* by *n* matrix - $A^\top$ - the transpose of a matrix *A* - $\left(\begin{array}{cc}a & b \\ c & d \end{array}\right)$ - a two-by-two matrix, the first row ia *a*, *b*, the second row is *c*, *d* - $\left(\begin{array}{cc|r}a & b & c \\ d & e & f \end{array}\right)$ - a two-by-three matrix - $A = \left(\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right)$ - *A* is an upper-triangular three-by-three matrix - $|A| = 1$ - the determinant of *A* equals 1 - $M_{12} = \begin{array}{|cc|}0 & 1 \\ 0 & 1 \end{array}$ - the minor of the entry $a_{12}$ - $A_{12} = (-1)^{1+2}M_{12}$ - the cofactor of the entry $a_{12}$ - the (*i*, *j*)th cofactor of *A* ## Calculus = *diferenciální a integrální počet; matematická analýza* - $D_{f}$ - the definition domain of (the function) *f* - $R_{f}$ - the range domain of (the function) *f* - $g(f(x))$ - the composition of (the functions) *g* and *f* - *g* composed with *f* - $g \circ f$ - the composition of (the functions) *g* and *f* - *g* composed with *f* - $x \rightarrow a+$ - f *x* approaches *a* from the right - $U_\delta (x_0)$ - the $\delta$ neighborhood of *x* sub 0 - $U_\delta^+ (x_0)$ - the right-hand $\delta$ neighborhood of *x* sub 0 - $P_\delta^+ (x_0)$ - the reduced right-hand $\delta$ neighborhood of *x* sub 0 - $|x|$ - the entire part of *x* - $\textrm{sgn}\,{x}$ - the sign of *x* - $f(A)$ - the image of *A* under *f* - $f_{-1}(A)$ - the inverse image of *A* under *f* - $f\,:\, X \rightarrow Y$ - *f* is mapping of *X* into *Y* - *f* maps *X* into *Y* - $f\,:\, X \xrightarrow{\text{onto}} Y$ - *f* is mapping of *X* onto *Y* - *f* maps *X* onto *Y* - $x \rightarrow x_0$ - *x* approaches *x* nought - *x* tends to *x* nought - $\lim_{x \rightarrow x_1} f(x) = L$ - as *x* tends to *x* one, *f* of *x* tends to *L* - the limit of *f* of *x* as *x* tends to *x* one is capital L - $\lim_{x \rightarrow \infty} a_n = 0$ - the limit of *a* sub *n* is zero as *a* tends to/approaches infinity - $\sum_{i = 1}^{n}$ - the sum from *i* equals one to *n* - $y = \sum_{i = 0}^{3}a_i x^i$ - *y* equals the sum of *a* (sub) *i*, *x* to the power of *i*, (taken) from (or over) (*k equal to*) zero to (*k* equal to) four - $\int$ - the (indefinite) integral - $\iint$ - the double integral - $\iiint$ - the triple integral - $\int_a^b$ - the integral from *a* to *b* - the (definite) integral between the values *a* and *b* - $\int f(x)\textrm{d}x$ - the integral of (function) *f* of *x* d*x* - $\textrm{d}$ - the differential - $\textrm{d}f$ - the differential of function *f* - $y = f(x)$ - *y* is equal to (the function) *f* of *x* - *y* is equal to *fx* - $f'(x)$ - *f* prime of *x* - the (first) derivative of (function) *f* with respect to *x* - $f''(x)$ - *f* double-prime of *x* - the second derivative of (function) *f* with respect to *x* - $f'''(x)$ - *f* triple-prime of *x* - *f* treble-dash *x* - the third derivative of (function) *f* with respect to *x* - $f^{(4)}(x)$ - *f* four of *x* - the derivative of the fourth order of function *f* - the fourth derivative of *f* with respect to *x* - $\frac{\partial y}{\partial x}$ - the partial derivative of *y* with respect to *x* - $\frac{\partial^2 y}{\partial x^2}$ - d two *y* by d *x* squared - the second partial derivative of *y* with respect to *x* squared ## Trigonometric functions = *goniometrické funkce* - $y = \sin{x}$ - *y* equals sine *x* - *y* equals the sine of *x* - $y = \cos{x}$ - *y* equals cos *x* - *y* equals the cosine of *x* - $y = \tan{x}$ - *y* equals tan *x* - *y* equals the tangent of *x* - $y = \cot{x}$ - *y* equals cot *x* - *y* equals the cotangent of *x* - $y = \arcsin{x}$ - *y* equals the inverse sine of *x* - *y* equals the arc sine of *x* - *y* equals the angle whose sine is *x* ## Equations = *rovnice* - $x + 7 = 3 - x$ - a linear equation - $x$ - unknown - $x = 5$ - the solution/the root of the equation - $ax^2 + bx + c = 0$ - a quadratic equation - the standard form of the quadratic equation - $D = b^2 - 4ac$ - a discriminant - $ax^3 + bx^2 + cx + d = 0$ - a cubic equation - $x + y = 3$; $x - 2y = 6$ - a system of two (linear) equations - $2 < \pi$ - an inequality - $x - 3 \leq 3x + 5$ - an inequality for unknown *x*/involving the unknown *x* - $x + y = 3$ - $x + y = 5$ - inconsistent system of two linear equations in two unknowns - $x + y = 2$ - $x + 2y = 4$ - consistent system of two linear equations in two unknowns - $x + y = 2$ - $x + 2y = 4$ - $2x + y = 1$ - overdetermined system of linear equations - $x + y + z = 3$ - $x + y + z = 6$ - undetermined system of linear equations