Fermat`s Last Theorem - Math @ McMaster University
... This proof makes use of a technique, called the method of infinite descent, introduced by Fermat. We start with the assumption that x, y , and w are positive integers that satisfy the equation such that w is as small as possible amongst all of the positive integer solutions to the equation. We then ...
... This proof makes use of a technique, called the method of infinite descent, introduced by Fermat. We start with the assumption that x, y , and w are positive integers that satisfy the equation such that w is as small as possible amongst all of the positive integer solutions to the equation. We then ...
ON THE DIVISIBILITY OF THE CLASS NUMBER OF
... Thus we have shown that m >_ g; but as 3# = x + d9 m = g. Hence, there exists in R(y/~d) a prime ideal ? ! whose gth power but none lower is a principal ideal. This immediately implies g | h. 3. Application. To show that there exist infinitely many fields each with class number divisible by g, we pr ...
... Thus we have shown that m >_ g; but as 3# = x + d9 m = g. Hence, there exists in R(y/~d) a prime ideal ? ! whose gth power but none lower is a principal ideal. This immediately implies g | h. 3. Application. To show that there exist infinitely many fields each with class number divisible by g, we pr ...
Chapter 3 – Solving Linear Equations
... Write the equation 2x – y = 9 so that x is a function of y. Use the result to find x when y = -2, -1, 0, and 1. ...
... Write the equation 2x – y = 9 so that x is a function of y. Use the result to find x when y = -2, -1, 0, and 1. ...
Lecture 10: What is a Function, definition, piecewise defined
... Lecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises when one quantity depends on another. Many everyday relationships between variables can be expressed in this form. Example 1 We have already seen examples of functions ...
... Lecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises when one quantity depends on another. Many everyday relationships between variables can be expressed in this form. Example 1 We have already seen examples of functions ...
Csorgo, Sandor and Simon, Gordon; (1994).A Strong Law of Large Numbers for Trimmed Sums, with Applications to Generalized St. Petersburg Games."
... The prototypical example, when light trimming is definitely needed for a strong law, is provided by the classical St. Petersburg game, a generalized version of which is discussed in Section 3. Feller (1945, cf. also Section XA of 1968a) used this game to illustrate a weak law in the spirit of (1.12) ...
... The prototypical example, when light trimming is definitely needed for a strong law, is provided by the classical St. Petersburg game, a generalized version of which is discussed in Section 3. Feller (1945, cf. also Section XA of 1968a) used this game to illustrate a weak law in the spirit of (1.12) ...
Section 8.2 Markov and Chebyshev Inequalities and the Weak Law
... EXAMPLE: An astronomer is measuring the distance to a star. Because of different errors, each measurement will not be precisely correct, but merely an estimate. He will therefore make a series of measurements and use the average as his estimate of the distance. He believes his measurements are indep ...
... EXAMPLE: An astronomer is measuring the distance to a star. Because of different errors, each measurement will not be precisely correct, but merely an estimate. He will therefore make a series of measurements and use the average as his estimate of the distance. He believes his measurements are indep ...
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.