PDF containing two proofs that √2 is irrational
PDF containing two proofs that √2 is irrational

Notes on Linear Recurrence Sequences
Notes on Linear Recurrence Sequences

Nth Term - MathsBedwas
Nth Term - MathsBedwas

1. The proof follows easily by induction on n. For
1. The proof follows easily by induction on n. For

Two Special Right Triangle
Two Special Right Triangle

of odd perfect numbers - American Mathematical Society
of odd perfect numbers - American Mathematical Society

Tutorial 4 solutions. File
Tutorial 4 solutions. File

NUMBER THEORY 1. Divisor Counting Theorem 1. A number is a
NUMBER THEORY 1. Divisor Counting Theorem 1. A number is a

Polynomial and Synthetic Division 2.3
Polynomial and Synthetic Division 2.3

Full text
Full text

Worked Problems
Worked Problems

Sols - Tufts Math Multi
Sols - Tufts Math Multi

Normal numbers without measure theory - Research Online
Normal numbers without measure theory - Research Online

... quite accesible to undergraduate students, except at one point, where it is necessary to invoke the Beppo Levi Theorem to interchange the order of summation and integration in a series of non-negative functions. The Beppo Levi Theorem is similarly invoked by Goodman [1], in his extension of Kac’s ap ...
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let

Simplifying Radicals
Simplifying Radicals

x - HCC Learning Web
x - HCC Learning Web

... You know that an nth-degree polynomial function can have at most n real zeros. Of course, many nth-degree polynomials do not have that many real zeros. For instance f(x) = x2 + 1, has no real zeros, and f(x) = x3 + 1 has only one real zero. The following theorem, called Descartes’s Rule of Signs, sh ...
Chapter Summary
Chapter Summary

Lecture 4: Cauchy sequences, Bolzano
Lecture 4: Cauchy sequences, Bolzano

I. BASIC PERRON FROBENIUS THEORY AND INVERSE
I. BASIC PERRON FROBENIUS THEORY AND INVERSE

Mathematics - Renton School District
Mathematics - Renton School District

Riemann`s Zeta Function and the Prime Number
Riemann`s Zeta Function and the Prime Number

On the Reciprocal of the Binary Generating Function for the Sum of
On the Reciprocal of the Binary Generating Function for the Sum of

MATH 225A PROBLEMS OCTOBER 2, 2012 (1)
MATH 225A PROBLEMS OCTOBER 2, 2012 (1)

Full text
Full text

Generalization of Numerical Series and its Relationship with the
Generalization of Numerical Series and its Relationship with the

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.