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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
2. Equivalence class: given an equivalence relation, [] often denotes the equivalence class of the element x. 3. Integral part: if x is a real number, [] often denotes the integral part or truncation of x, that is, the integer obtained by removing all digits after the decimal mark.
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. Much of analysis happens in some metric space; the most commonly used are the real line , the complex plane , Euclidean space , other vector spaces , and the integers .
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, an orange, or an ...
A 2006 article in The Harvard Crimson reported that only 17 women completed the class between 1990 and 2006, [3] and a 2017 article said that enrollment had been less than 7% female in the previous five years. [30] Math 25 has more women: in 1994–95, Math 55 had no women, while Math 25 had about 10 women in the 55-person course. [7]
A branch of mathematics that studies change and has two major sub-fields: differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). These two branches are related to each other by the fundamental theorem of calculus.