Some transcendence results from a harmless irrationality theorem
Some transcendence results from a harmless irrationality theorem

Polar Form of Complex Numbers
Polar Form of Complex Numbers

Polar Form of Complex Numbers
Polar Form of Complex Numbers

Hybrid Elementary Algebra 5.3 – 5.5 Introduction Factoring
Hybrid Elementary Algebra 5.3 – 5.5 Introduction Factoring

... Factoring trinomials of the form ax + bx + c, a ≠ 1 . Steps to factor a polynomial of the form ax 2 + bx + c . 1. Find the GCF of all terms in the polynomial. If it is something other than 1, factor it out. 2. If the trinomial can be factored, it will be the product of two binomials (remember factor ...
REVIEW OF FACTORING
REVIEW OF FACTORING

§ 3.3 Proof by Contradiction
§ 3.3 Proof by Contradiction

MORE ON THE SYLOW THEOREMS 1. Introduction
MORE ON THE SYLOW THEOREMS 1. Introduction

Fields and vector spaces
Fields and vector spaces

Lesson5
Lesson5

ERGODIC.PDF
ERGODIC.PDF

On condition numbers of polynomial eigenvalue problems
On condition numbers of polynomial eigenvalue problems

Full text
Full text

... to the Fibonacci cube Tn which is the graph defined as 2J, except for the fact that the vertices are binary strings of length n without two consecutive ones. The Fibonacci cube has been introduced as a new topology for the interconnection of parallel multicomputers alternative to the classical one g ...
1 On the lines passing through two conjugates of a Salem number
1 On the lines passing through two conjugates of a Salem number

Department of Economics | Maths Revision Notes 2: Algebra
Department of Economics | Maths Revision Notes 2: Algebra

[Michel Waldschmidt] Continued fractions
[Michel Waldschmidt] Continued fractions

Isotriviality and the Space of Morphisms on Projective Varieties
Isotriviality and the Space of Morphisms on Projective Varieties

... is reductive. Then φ is isotrivial if and only if φ has potential good reduction at all places v of K. Proof. The only if direction is clear. For the if direction, we imitate the proof in [12] to create a morphism from the complete curve C to the affine variety Md (X, L), which must be constant. Spe ...
Cellular Resolutions of Monomial Modules
Cellular Resolutions of Monomial Modules

Use synthetic division to find rational zero
Use synthetic division to find rational zero

*7. Polynomials
*7. Polynomials

Inductive reasoning
Inductive reasoning

Classification of complex projective towers up to dimension 8 and
Classification of complex projective towers up to dimension 8 and

1-2 - helinski
1-2 - helinski

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000–000
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000–000

Solutions for Review problems (Chpt. 1 and 2) (pdf file)
Solutions for Review problems (Chpt. 1 and 2) (pdf file)

Equations solvable by radicals in a uniquely divisible
Equations solvable by radicals in a uniquely divisible

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.