de·gree / diˈgrē/ • n. 1. [in sing.] the amount, level, or extent to which something happens or is present: a degree of caution.2. a unit of measurement of angles, one three-hundred-and-sixtieth of the circumference of a circle. (Symbol: °) 3. a stage in a scale or series, in particular: ∎  a unit in any of various scales of temperature, intensity, or hardness: water boils at 100 degrees Celsius. (Symbol: °) ∎  [in comb.] each of a set of grades (usually three) used to classify burns according to their severity. See first-degree, second-degree, third-degree. ∎  [in comb.] a legal grade of crime or offense, esp. murder: second-degree murder. ∎  Mus. a position in a musical scale, counting upward from the tonic or fundamental note: the lowered third degree of the scale. ∎  Math. the class into which an equation falls according to the highest power of unknowns or variables present: an equation of the second degree. ∎  Gram. any of the three steps on the scale of comparison of gradable adjectives and adverbs, namely positive, comparative, and superlative. ∎ archaic a thing placed like a step in a series; a tier or row.4. an academic rank conferred by a college or university after examination or after completion of a course of study, or conferred as an honor on a distinguished person. ∎ archaic social or official rank: persons of unequal degree. ∎  a rank in an order of Freemasonry.PHRASES: by degrees a little at a time; gradually.to a degree to some extent: to a degree, it is possible to educate oneself.

Degree

The word “degree” has several distinct meanings in science and mathematics. First, in physics, it refers to a unit of temperature. Common units of temperature are degrees Celsius (°C) and degrees Fahrenheit (°F). Absolute temperature is measured in Kelvins (not “degrees Kelvin”).

Second, in geometry, a degree is a unit of angle. A right angle is 90 degrees, the interior angles of a triangle always add to 180 degrees, and so on. Alternative units of angle are grads and radians.

Third, in algebra, “degree” refers to a property of polynomials. The degree of a polynomial in one variable (a monomial), such as 5x³, is the exponent, 3, of the variable. The degree of a monomial involving more than one variable, such as 3x²y, is the sum of the exponents; in this case, 2 + 1 = 3. The degree of a polynomial with more than one term is the highest degree among its monomial terms. Thus the degree of 5 x²y + 7 x³y²z² + 8x⁴y is 3 + 2 + 2 = 7.

The degree of a polynomial equation is the highest degree among its terms. Thus the degree of the equation 5x³ –3x² = x + 1 is 3.

DEGREE.
1. A grammatical category for items of language used to express relative intensity: very much, of a verb in I admire them very much; highly, of an adjective in highly intelligent; very, of an adverb in very often; big, of a noun in a big fool; dead, of a preposition in They're dead against it. Such intensifiers or words of degree are used with other words that are gradable (that is, on a scale of intensity). They may indicate a relatively high or low point: slightly, somewhat, hardly, a bit.

2. Three types of comparison applied to gradable adjectives and adverbs: to a high degree (bigger, biggest); to the same degree (as big as), and with a preceding negative (not so big as); to a lower degree (less big, least big). Non-extreme forms may be followed by comparative clauses: ‘Jeremy is taller than his parents (are)’; ‘Naomi is less tall than Ruth (is)’; ‘Doreen is as tall as Leslie (is).’ Higher-degree comparisons may be expressed by inflections (the absolute or positive degree happy, the comparative degree happier, and the superlative degree happiest) or periphrastically, in combination with more for comparatives (more happy) and most for superlatives (most happy). Monosyllabic adjectives (young, sad, small) generally take inflections, polysyllabic adjectives (beautiful) periphrastic more/most. Many disyllabic adjectives take either form: commoner/more common, commonest/most common. Most adverbs allow only periphrastic comparison (happily/more happily/most happily), but a few are suppletive: badly/worse/worst; well/better/best. See PERIPHRASIS, SUPPLETION.

degree
1. of a vertex of a graph. The number of edges incident with the vertex, i.e. that emanate from that vertex. In a directed graph, the indegree is the number of edges entering a vertex while the outdegree is the number leaving a vertex.

2. of a node in a tree. The number of children of that node, i.e. the number of subtrees rooted at that node. More correctly, this is the outdegree of the node.

3. of a tree. The maximum degree of all the nodes in the tree.

4. of a polynomial. See polynomial.

Degree

The word "degree" as used in algebra refers to a property of polynomials . The degree of a polynomial in one variable (a monomial), such as 5x3, is the exponent , 3, of the variable. The degree of a monomial involving more than one variable, such as 3x2y, is the sum of the exponents; in this case, 2 + 1 = 3. The degree of a polynomial with more than one term is the highest degree among its monomial terms. Thus the degree of 5x2y + 7x3y2z2 + 8x4y is 3 + 2 + 2 = 7.

The degree of a polynomial equation is the highest degree among its terms. Thus the degree of the equation 5x3 - 3x2 = x + 1 is 3.