Algebra

Algebra is a branch of mathematics that uses letters or symbols as a place holder for unknown values or numbers.  These variables are used to represent relationships and to solve equations.  For other math terms see Geometry and Trigonometry.

Math Symbols

Nomenclature & Symbols for Engineering, Mathematics, & Science

Algebra Terms

A

  • Absolute value - Makes a negative number positive  \(\large{ \left\vert -x \right\vert = x }\)  and positive numbers and  \(\large{ 0 }\)  are not changed.
  • Axiom - A statement accepted as true without proof.

B

  • Base - The term  \(\large{13a^2 }\)  has a base  \(\large{ a }\) .
  • Binary numbers - Use only the digits \(\large{ 0 }\) and \(\large{ 1 }\) .
  • Binomial - A polynomial with only two term  \(\large{ 13a^2+7x }\) .

C

  • Coefficient - A number  \(\large{13a^2+7x-21=19 }\)  multiplied by a variable having the coefficients  \(\large{13, 7 }\) .
  • Common demoninator - Two or more fractions  \(\large{ \frac{3}{8} + \frac{7}{8}}\)  that have the same denominator  \(\large{ 8 }\) .
  • Common difference - \(\large{ 3 }\)  is the difference between each number  \(\large{ 3, 6, 9, 12, ... }\)  in a sequence  \(\large{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ... }\) .
  • Common factor - The factors of two or more numbers that have some factors that are the same (common) in each.
  • Common fraction - A fraction where both numbers  \(\large{ \frac{3}{4}, \frac{7}{8} }\)  top and bottom are integers.
  • Common multiple - Two or more numbers that have the same multiple.
  • Complex number - A combination of a real  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  number and imaginary  \(\large{\sqrt{-1} = i }\)  number for a result of  \(\large{x + y\;i }\) .   \(\large{ x }\)  is the real part and  \(\large{ y }\)  is the imaginary part.
  • Composite number - A positive integer number  \(\large{ 4, 6, 8, 9,... }\)  that has factors other than  \(\large{ 1 }\)  and the number itself.
  • Compute - To compute  \(\large{ 3-2 }\)  is to figuring out the answer  \(\large{ 1 }\) .
  • Conjugate - Is when you change the sign.  from  \(\large{ a+b }\)  to  \(\large{ a-b }\),  from  \(\large{ 3a-4b }\)  to  \(\large{ 3a+4b }\)  \(\large{ ,... }\)
  • Counting Number - Any number used to count things  \(\large{ 1, 2, 3, 4, 5, 6,... }\)  excluding  \(\large{ 0 }\) , negative numbers, fractions or decimals.
  • Cube number - \(\large{ 5 \;x\; 5 \;x\; 5 = 125 }\) ,  \(\large{ 125 }\) is the cube number.
  • Cube root - \(\large{ ^3\sqrt{125} = 5 }\) ,  \(\large{ 5 }\) is the cube root.

D

  • Decimal number - Based on 10 digits.  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }\)
  • Denominator - The number of equal parts of the whole is  \(\large{ 8 }\) , fraction is  \(\large{ \frac{3}{8} }\) .
  • Digit - A numeral  \(\large{ 2119 }\)  has digits  \(\large{ 2, 1, 1, }\)  and  \(\large{ 9 }\)
  • Disjoint event (mutually exclusive) - Events that have no outcomes in common.
  • Distribution - Multiply the parts of an expression  \(\large{ a \left(b-c \right) }\)  into another expression  \(\large{ a\;b-a\;c }\) .
  • Domain of a function - A set of values for the independent variable that makes the function work.

E

  • Equation - \(\large{ 13a^2+7x-21=19 }\)
  • Exponent (also called index or power) - Is how mant times you multiply the number.  Term is \(\large{ 13a^2 }\), the exponent is \(\large{ 2 }\)
  • Expression - A group  \(\large{ 13a^2+7x-23 }\)  of terms, coefficients, constants and variables separate by an operation.

F

  • Factor number - Numbers \(\large{ 3 }\) and \(\large{ 8 }\) are factors that can be multiplied to get another number \(\large{ 24 }\) .  Equation \(\large{ 3\;x\;8=24 }\)
  • Factoring - Factor \(\large{ 7 \left(x-3\right) }\) expand to  \(\large{ 7x-21 }\)  or expressed as  \(\large{ 7 \left(x-3\right) = 7x-21 }\)
  • Factorial - The symbol is  \(\large{ ! }\) .  Multiply all whole numbers from the chosen number down to 1.  \(\large{ 5!=5\;x\;4\;x\;3\;x\;2\;x\;1=120 }\)  or  \(\large{ n!=\left(n+3\right) 2y\;x\;2\;x\;1=n }\)
  • Fraction - A part  \(\large{ \frac{3}{8} }\)  of the whole.
  • Function - A relationship where a set of inputs (domain) determine a set of possible outputs (range).  The function of  \(\large{ f \left( x \right) = 5\;x }\)  is  \(\large{ f \left( x \right) }\) , the function name is  \(\large{ f }\) , the input value is  \(\large{ \left( x \right) }\) , and the output is  \(\large{ 5\;x }\) .

H

  • Hexadecimal number - Based on the number 16.  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }\)

I

  • Imaginary number - A number  \(\large{ i }\)  (imaginary symbol) when squared gives a negative number  \(\large{ i^2 = -1}\)  or  \(\large{\sqrt{-1} = i }\) .
  • Improper fraction - A fraction  \(\large{ \frac{21}{7} }\)  that has a larger numerator than denominator.
  • Integer number - A whole numbers that can be either positive or negative  \(\large{ ... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }\)  with no fractions.
  • Inverse (reciprocal) - Reverses the effect of another number.  \(\large{ 3\;x\;7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • Irrational number - A number that cannot be written as a fraction.

L

  • Like terms - These are terms where the variables are the same.  The terms are  \(\large{ 13a^2, 3a^2, -3a^2 }\), the like terms are \(\large{ a^2 }\)  or the terms are  \(\large{ 13a^2 + 3a^2 + -3a^2 }\) , the like terms are  \(\large{ 13a^2 }\)

M

  • Matrix - A rectangular or square array of numbers using either brackets  \({ [\;] }\)  or parentheses  \({ (\;) }\) .                                        \({  \begin{bmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 \\ 13 & 1.2 & -9 \end{bmatrix} }\)   or   \({ \begin{pmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 & \\ 13 & 1.2 & -9 \end{pmatrix}  }\)
  • Matrix addition - Matrices can be added term by term.                                                                                                                             \({  \begin{bmatrix} 4 & 7 & 2 \\ -9 & 3 & 3 \\ 13 & 1 & -9 \end{bmatrix} }\) \({\;+\;}\) \({ \begin{bmatrix} 5 & 3 & -2 \\ -4 & 6 & 2 \\ 11 & -1 & 14 \end{bmatrix}  }\) \({\;=\;}\) \({ \begin{bmatrix} 9 & 10 & 0 \\ -13 & 9 & 5 \\ 24 & 0 & 5 \end{bmatrix}  }\)
  • Matrix subtraction - Matrices can be subtracted term by term.                                                                                                                 \({  \begin{bmatrix} 4 & 7 & 2 \\ -9 & 3 & 3 \\ 13 & 1 & -9 \end{bmatrix} }\) \({\;-\;}\) \({ \begin{bmatrix} 5 & 3 & -2 \\ -4 & 6 & 2 \\ 11 & -1 & 14 \end{bmatrix}  }\) \({\;=\;}\) \({ \begin{bmatrix} -1 & 4 & 4 \\ -5 & -3 & 1 \\ 2 & 2 & -23 \end{bmatrix}  }\)
  • Mixed number - A number written as  \(\large{13 \frac{3}{8} }\)  a whole number  \(\large{13 }\) and a fraction  \(\large{ \frac{3}{8} }\) .
  • Monomial  - A polynomial with only one term  \(\large{ 13a^2 }\) .
  • Mutually Exclusive (disjoint event) - Events that have no outcomes in common.

N                                                   

  • Natural number - Can be either counting numbers  \(\large{ 1, 2, 3, 4, 5, 6, ... }\)  or whole numbers  \(\large{ 0, 1, 2, 3, 4, 5, 6, ... }\) .
  • Negative number - It is the oposite of a whole number  \(\large{ ... , -5, -4, -3, -2, -1 }\)  or decimal number excluding  \(\large{ 0 }\) .
  • nth root - Some number  \(\large{ n }\)  used as  \(\large{ ^n\sqrt{a} }\) .
  • Number line - Every point on a line represents a real number.
  • Numeral - A single symbol to make a numeral like  \(\large{ 2119 }\) .
  • Numerator - The number of parts is  \(\large{ 3 }\), fraction is  \(\large{ \frac{3}{8} }\) .

O

  • Octal number -  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7 }\)
  • Operator - A symbol such as  \(\large{ +, -, ... }\)
  • Ordered pair - Two numbers  \(\large{ \left(7, 21\right) }\)  or  \(\large{ \left(x, y\right) }\)  written in a certain order.
  • Ordered triple - Three numbers  \(\large{ \left(7, 21, 19\right) }\)  or  \(\large{ \left(x, y, z\right) }\)  written in a certain order.
  • Ordered n - Multiple numbers  \(\large{ \left(7, 14, 21, ..., x_n\right) }\)  or  \(\large{ \left(x_1, x_2, x_3, ...,x_n\right) }\)  written in a certain order.

P

  • Perfect number - A whole number that is equal to the sum of its positive factors except the number itself.  \(\large{1+2+4+7=14}\) ,  \(\large{14}\) is a perfect number because the positive factors are  \(\large{1, 2, 4, 7,14}\) .
  • Polynomial - The sum of two or more terms.  A term can have constants, exponents and variables, such as  \(\large{ 13a^2 }\) .  Put them together and you get a polynomial.
    • Monomial - 1 term  \(\large{ 13a^2 }\)
    • Binomial - 2 terms  \(\large{ 13a^2+7x }\)
    • Trinomial - 3 terms  \(\large{ 13a^2+7x-21 }\)
  • Porportional - When the ratio of two variables are constant.
  • Positive number - A counting number  \(\large{ 1, 2, 3, 4, 5, 6,... }\)  or decimal number excluding  \(\large{ 0 }\) .
  • Prime factor - A factor  \(\large{13, 7 }\)  are prime numbers.  \(\large{13\;x\;7 =91 }\)
  • Prime number - A number that can be divided evenly only by  \(\large{1}\) , or itself and it must be a whole number greater than \(\large{1}\) .
  • Product - When two or more values are multiplied togeather  \(\large{13a^2\;x\;7x \;x\;21=19 }\) , the product is  \(\large{19 }\) .
  • Proper factor - Any of the factors of a number, except \(\large{1}\) or the number itself.

R

  • Radical - An expression  \(\large{ 13a^2+7x-23 }\)  that is a root  \(\large{ \sqrt{13a^2+7x-23} }\) .  The length of the bar  \(\large{ \sqrt{13a^2}+7x-23 }\)  tells how much of the expression is used.
  • Radicand - The number under the symbol \(\large{ \sqrt{x} }\)
  • Rational number - Numbers expressed as a ratio of two numbers like  \(\large{ \frac{3}{4} }\)  or  \(\large{ -\frac{1}{8} }\) .
  • Real number - Any number  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  that is normally used.
  • Reciprocal (inverse) - Reverses the effect of another number.  \(\large{ 3\;x\;7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • Rounding - Replacing a number  \(\large{ 3.1415926535 ... }\)  with another number having less digits  \(\large{ 3.1415 }\) .

S

  • Scalar number - Any single real number  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  used to measure.
  • Scientific notation - A way of writing large numbers  \(\large{ 1 2 3 4 5 6 7 8 . 9 }\)  into two part  \(\large{ 1 2 3 4 5 . 6 7 8 9 \;x\; 10^3 }\) .
  • Series - The sum of the terms of a sequence.  \(\large{ 1, 2, 3, 4, 5, 6, ... }\) or \(\large{ 1 + 2 + 3 + ... +\; n }\)
  • Set - A group of numbers, variables, or really anything written using \(\large{ (\; ) }\) or \(\large{ [\; ] }\) .
  • Significant digits - \(\large{ 1 2 3 0 }\)  Digits that are meaningful.  \(\large{ 0 . 0 1 2 3 0 }\)
  • Square number - \(\large{ 5 \;x\; 5 = 25 }\) ,  \(\large{ 25 }\) is the square number.
  • Square root - \(\large{ \sqrt{25} = 5 }\) ,  \(\large{ 5 }\) is the square root.
  • Subscript - A small letter or number lower than the normal text  \(\large{13_a^2 }\) .
  • Subset - A  \(\large{\left( 3, 4, 5 \right) }\)  is a subset of B  \(\large{\left( 1, 2, 3, 4, 5, 6, 7, 8, 9 \right) }\) .
    • Empty Set - \(\large{ (\; ) }\)  is a  subset of B
  • Superscript - A small letter or number higher than the normal text  \(\large{13_a^2 }\) .

T

  • Terms - Either a single number, a variable, or numbers and variables  \(\large{ 13a^2, 7x, 21 }\)  of an expression  \(\large{ 13a^2+7x-23 }\) .
  • Theorem - A true statement that can be proven.
  • Trinomial - A polynomial with only three term  \(\large{ 13a^2+7x-21 }\) .

V

  • Variable - Letters or symbols that are used to represent unknown values that can change depending in the infomation.  The variables are \(\large{ a }\) and \(\large{ x }\)

W

  • Whole number - Just positive numbers  \(\large{ 0, 1, 2, 3, 4, 5, 6, ... }\)  with no fractions.
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