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The Discriminant
The Discriminant

1. Problems and Results in Number Theory
1. Problems and Results in Number Theory

Continued fractions and transcendental numbers Boris
Continued fractions and transcendental numbers Boris

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THE PRIME FACTORS OF CONSECUTIVE, INTEGERS II by P

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SECTION 1-6 Rational Exponents

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arXiv:math/0511682v1 [math.NT] 28 Nov 2005

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Functions - UCSD Mathematics

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Classical Logic and the Curry–Howard Correspondence
Classical Logic and the Curry–Howard Correspondence

Smoothness of the sum and Riemann summability of double
Smoothness of the sum and Riemann summability of double

... In the second part of the disertation we dene two new summation methods: the Riemann summability od double trigonometric series, and Lebesgue summability of double trigonometric integrals. In the third chapter we extend the concept of the Riemann summability from single to double trigonometric seri ...
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13.0 Central Limit Theorem

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On Subrecursive Representability of Irrational Numbers Lars Kristiansen

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Solution Set 1 - MIT Mathematics

Programming using the GeomLab language
Programming using the GeomLab language

... (c) Try computing quad(1,2,3). What happens? Why is this? From our definition of quad we can see that the expression b2 − 4ac, called the discriminant, is calculated twice. Question 1.4. Rewrite the definition of quad to put the discriminant in a let expression. So your new definition will look like ...
Important Properties of Polynomial Functions
Important Properties of Polynomial Functions

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Of course

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Elementary Number Theory Definitions and Theorems
Elementary Number Theory Definitions and Theorems

Full text
Full text

... teger value > p M and such that (19) is satisfied. The Lemma assures us that there are infinitely many values of p > p M such that ...
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Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century.""
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