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Months after its $80 million Series B fundraise, Course Hero has acquired Symbolab, an artificial intelligence-powered calculator that helps students answer and understand complex math questions.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series:. If or if the limit does not exist, then = diverges.. Many authors do not name this test or give it a shorter name.
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof that was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs). Another example of a program-assisted proof ...
This is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, to biology, [14] philosophy [15] and to cryptography (see P versus NP problem proof consequences). A common example of an NP problem not known to be in P is ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Notably, these series provide examples of infinite sums that converge or diverge arbitrarily slowly. For instance, in the case of k = 2 {\displaystyle k=2} and α = 1 {\displaystyle \alpha =1} , the partial sum exceeds 10 only after 10 10 100 {\displaystyle 10^{10^{100}}} (a googolplex ) terms; yet the series diverges nevertheless.