• 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
Multiplying Polynomials
Multiplying Polynomials

Two proofs of the infinitude of primes Ben Chastek
Two proofs of the infinitude of primes Ben Chastek

(pdf)
(pdf)

... (b) If A is diagonalizable, what are the dimensions of the eigenspaces E−1 , E1 , E2 . ...
Sample homework solutions for 2.2 Jim Brown
Sample homework solutions for 2.2 Jim Brown

proof - Jim Hogan
proof - Jim Hogan

Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the
Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the

arXiv:math/0408107v1 [math.NT] 9 Aug 2004
arXiv:math/0408107v1 [math.NT] 9 Aug 2004

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

MAE 301 Notes for September 1, 2010 By Jillian Stark Properties of
MAE 301 Notes for September 1, 2010 By Jillian Stark Properties of

AN EMPIRICAL CENTRAL LIMIT THEOREM FOR INTERMITTENT
AN EMPIRICAL CENTRAL LIMIT THEOREM FOR INTERMITTENT

... limit theorem follows from Theorem 5 applied to Example 1.4 in Borovkova, Burton and Dehling (2001). Under the weaker assumption that there exist A > 0 and λ > 1 such that |(T n )0 | ≥ Aλn for any positive integer n on any interval of the partition associated to T n , the empirical central limit the ...
Midterm Exam 2 Solutions
Midterm Exam 2 Solutions

Help Examples for w10 First of all, let us set a few terms straight. For
Help Examples for w10 First of all, let us set a few terms straight. For

A Geometric Proof that e is Irrational and a New
A Geometric Proof that e is Irrational and a New

Full text
Full text

... In the first case, since x = φn , and n ≥ 2, it follows that x2 ≥ φ4 > 6.8. So, it suffices that the leading coefficient, multiplied by 6.8, be greater than the absolute value of the sum of the negative coefficients, which is 66488086. This is easily seen to be the case. The second case follows simi ...
Seiberg-Witten Theory and Z/2^ p actions on spin 4
Seiberg-Witten Theory and Z/2^ p actions on spin 4

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11
Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11

Fermat`s Last Theorem - UCLA Department of Mathematics
Fermat`s Last Theorem - UCLA Department of Mathematics

Algebra II Notes Polynomial Functions Unit 4.1 – 4.5 Introduction to
Algebra II Notes Polynomial Functions Unit 4.1 – 4.5 Introduction to

... Pascal’s Triangle – A triangular array of numbers in which each row starts and ends with 1 and each number in between is the sum of the pair of numbers above it. The number at the apex is 1. The numbers at the nth row of Pascal’s triangle are the same as the coefficients of x and y in the expansion ...
Homework for Chapter 1 and 2 scanned from the textbook (4th ed)
Homework for Chapter 1 and 2 scanned from the textbook (4th ed)

Bernoulli numbers and solitons
Bernoulli numbers and solitons

Complex Roots: A Graphical Solution
Complex Roots: A Graphical Solution

Proof
Proof

LHF - Maths, NUS
LHF - Maths, NUS

Linear recursions over all fields
Linear recursions over all fields

... How is {n3n−1 } found? If {λn } and {µn } satisfy the same linear recursion, so does any linear combination. If λ 6= µ a linear combination is (λn − µn )/(λ − µ), and as µ → λ this “becomes” {nλn−1 }, which up to scaling is {nλn }.2 This suggests that since 3 is a double root of x2 − x − 1 in charac ...
Invariant Measures
Invariant Measures

< 1 ... 349 350 351 352 353 354 355 356 357 ... 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