• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
I CHAPTER 3 Counting
I CHAPTER 3 Counting

Technology Exercises Critical Thinking Exercises
Technology Exercises Critical Thinking Exercises

... Factoring is the process of writing a polynomial as the product of two or more polynomials. The factors of 6x2 - x - 2 are 2x + 1 and 3x - 2. In this section, we will be factoring over the set of integers, meaning that the coefficients in the factors are integers. Polynomials that cannot be factored ...
COMPUTING THE SMITH FORMS OF INTEGER MATRICES AND
COMPUTING THE SMITH FORMS OF INTEGER MATRICES AND

EQUIVALENCE CLOSURE IN THE TWO
EQUIVALENCE CLOSURE IN THE TWO

9.1 The Square Root Function
9.1 The Square Root Function

course notes
course notes

SYMMETRIC SPACES OF THE NON
SYMMETRIC SPACES OF THE NON

Online preprint - Villanova Computer Science
Online preprint - Villanova Computer Science

On some classes of nearly open sets
On some classes of nearly open sets

The Classification of Three-dimensional Lie Algebras
The Classification of Three-dimensional Lie Algebras

Abelian Varieties
Abelian Varieties

The space of sections of a sphere-bundle I
The space of sections of a sphere-bundle I

... viewpoint. We shall be doing homotopy theory over the base space X; [9] is a good textbook reference for the basic theory. First we must fix some notation. Let Q0->B,Qi->B be locally trivial bundles of pointed finite CW-complexes over a fixed finite CW-complex B. (This is sufficiently general for ou ...
Differential Calculus of Several Variables
Differential Calculus of Several Variables

Categorical and Kripke Semantics for Constructive S4 Modal Logic
Categorical and Kripke Semantics for Constructive S4 Modal Logic

Classification of Semisimple Lie Algebras
Classification of Semisimple Lie Algebras

... spread over hundreds of articles written by many individual authors. This fragmentation raised considerable doubts about the validity of the proof, since there is no way any one person could check the proof from beginning to end. Since then, considerable effort has been devoted to the simplification ...
Math 215 HW #9 Solutions
Math 215 HW #9 Solutions

A Computational Introduction to Number Theory and
A Computational Introduction to Number Theory and

On Star Coloring of Graphs - Membres du Departement d
On Star Coloring of Graphs - Membres du Departement d

Algebra Cheat Sheets
Algebra Cheat Sheets

x - cloudfront.net
x - cloudfront.net

MONOTONE METRIC SPACES 1. Introduction The following notions
MONOTONE METRIC SPACES 1. Introduction The following notions

Topological realizations of absolute Galois groups
Topological realizations of absolute Galois groups

16 • Real numbers
16 • Real numbers

RELATIVE KAZHDAN PROPERTY
RELATIVE KAZHDAN PROPERTY

... 1967. Since then, many consequences and characterizations have been given by various authors. The notion of relative Property for a pair (G, N ), where N is a normal subgroup in G was implicit in Kazhdan’s paper, and later made explicit by Margulis [Mar1]. The case when H is an abelian normal subgro ...
IDEAL FACTORIZATION 1. Introduction
IDEAL FACTORIZATION 1. Introduction

... has no prime factorization then let n > 1 be minimal without a prime factorization. Of course n is not prime, so n = ab with a, b > 1. Then a, b < n, so a and b are products of primes. Hence n = ab is a product of primes, which is a contradiction. Uniqueness of the prime factorization requires more ...
< 1 ... 24 25 26 27 28 29 30 31 32 ... 480 >

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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report