
Induction 4 Solutions
... Mathematics studies many sequences of numbers—the evens, odds, primes, squares, powers of two, and so on. Some of the sequences studied are defined by referring back to previous numbers. This is called a recursive definition. One famous sequence that is defined like this is the Fibonacci numbers. Th ...
... Mathematics studies many sequences of numbers—the evens, odds, primes, squares, powers of two, and so on. Some of the sequences studied are defined by referring back to previous numbers. This is called a recursive definition. One famous sequence that is defined like this is the Fibonacci numbers. Th ...
Fermat`s Little Theorem
... 1799 . It doesn’t seem too useful to multiply 17 by itself 99 times, mod 101. Isn’t it better to solve the congruence 17x ≡ 1 mod 101? Perhaps so. But with large numbers, a computer can crunch out a power of a number mod another number in a very short time. For example, the program in the lab which ...
... 1799 . It doesn’t seem too useful to multiply 17 by itself 99 times, mod 101. Isn’t it better to solve the congruence 17x ≡ 1 mod 101? Perhaps so. But with large numbers, a computer can crunch out a power of a number mod another number in a very short time. For example, the program in the lab which ...
some applications of probability generating function based methods
... The PGF fully characterizes the law of its associated random variable. In fact, two random variables will have the same distribution if and only if the correspondent PGF coincide in a neighborhood of 1. We also have for PGF a result similar to Lévy theorem for characteristic functions. If for a seq ...
... The PGF fully characterizes the law of its associated random variable. In fact, two random variables will have the same distribution if and only if the correspondent PGF coincide in a neighborhood of 1. We also have for PGF a result similar to Lévy theorem for characteristic functions. If for a seq ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.