1. Boolean Algebra Theorem A Using it wisely will prevent you from writing overly complex if, else if conditional tests. http://www.kosmix.com/topic/boolean_algebra_theorem

2. Fundamental Theorem Of Algebra - Wikipedia, The Free Encyclopedia In mathematics, the fundamental theorem of algebra states that every non constant single-variable polynomial with complex coefficients has at least one http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , the fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root . Equivalently, the field of complex numbers is algebraically closed Sometimes, this theorem is stated as: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity . Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors. 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 in which algebra was mainly about solving polynomial equations with real or complex coefficients. Contents History Proofs Complex-analytic proofs Topological proofs ... edit History Peter Rothe (Petrus Roth), in his book

3. DeMorgan's Theorems : BOOLEAN ALGEBRA DeMorgan s Theorems. A mathematician named DeMorgan developed a pair of important rules regarding group complementation in Boolean algebra. http://www.allaboutcircuits.com/vol_4/chpt_7/8.html

Hilite.elementid = "main"; All About Circuits Vol. I - DC Vol. II - AC Vol. III - Semiconductors ... Blogs Search this site Table of Contents: Introduction Boolean arithmetic Boolean algebraic identities Boolean algebraic properties ... PDF var addthis_pub = 'GFYGCMPH6Z132X8G'; Volume IV - Digital BOOLEAN ALGEBRA DeMorgan's Theorems A mathematician named DeMorgan developed a pair of important rules regarding group complementation in Boolean algebra. By group complementation, I'm referring to the complement of a group of terms, represented by a long bar over more than one variable. You should recall from the chapter on logic gates that inverting all inputs to a gate reverses that gate's essential function from AND to OR, or vice versa, and also inverts the output. So, an OR gate with all inputs inverted (a Negative-OR gate) behaves the same as a NAND gate, and an AND gate with all inputs inverted (a Negative-AND gate) behaves the same as a NOR gate. DeMorgan's theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs: A long bar extending over the term AB acts as a grouping symbol, and as such is entirely different from the product of A and B independently inverted. In other words, (AB)' is not equal to A'B'. Because the "prime" symbol (') cannot be stretched over two variables like a bar can, we are forced to use parentheses to make it apply to the whole term AB in the previous sentence. A bar, however, acts as its own grouping symbol when stretched over more than one variable. This has profound impact on how Boolean expressions are evaluated and reduced, as we shall see.

4. PlanetMath: Fundamental Theorem Of Algebra proof of fundamental theorem of algebra (due to Cauchy) (Proof) by pahio This is version 11 of fundamental theorem of algebra, born on 200202-13, http://planetmath.org/encyclopedia/FundamentalTheoremOfAlgebra.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About fundamental theorem of algebra (Theorem) Theorem Let be a non-constant polynomial . Then there is a with $f(z)=0$ In other words, is algebraically closed As a corollary, a non-constant polynomial in factors completely into linear factors. "fundamental theorem of algebra" is owned by Mathprof full author list owner history view preamble ... get metadata View style: jsMath HTML HTML with images page images TeX source See Also: complex number complex topic entry on complex analysis GaussLucas theorem Attachments: proof of the fundamental theorem of algebra (Liouville's theorem) (Proof) by Evandar proof of fundamental theorem of algebra (Proof) by scanez fundamental theorem of algebra result (Theorem) by rspuzio proof of fundamental theorem of algebra (due to d'Alembert) (Proof) by rspuzio proof of fundamental theorem of algebra (argument principle) (Proof) by rspuzio proof of fundamental theorem of algebra (Rouché's theorem) (Proof) by Wkbj79 polynomial equation of odd degree (Theorem) by pahio proof of fundamental theorem of algebra (due to Cauchy) (Proof) by pahio Log in to rate this entry.

5. Boolean Algebra : Worksheet Learning to analyze digital circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against http://www.allaboutcircuits.com/worksheets/boolean.html

Hilite.elementid = "main"; All About Circuits Vol. I - DC Vol. II - AC Vol. III - Semiconductors ... Blogs Search this site Print PDF var addthis_pub = 'GFYGCMPH6Z132X8G'; Worksheets Boolean algebra Boolean algebra Question 1: Don't just sit there! Build something!! Learning to analyze digital circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way. You will learn much more by actually building and analyzing real circuits Draw the schematic diagram for the digital circuit to be analyzed. Carefully build this circuit on a breadboard or other convenient medium. Check the accuracy of the circuit's construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram. Analyze the circuit, determining all output logic states for given input conditions. Carefully measure those logic states, to verify the accuracy of your analysis. If there are any errors, carefully check your circuit's construction against the diagram, then carefully re-analyze the circuit and re-measure.

6. The Fundamental Theorem Of Algebra What does The Fundamental Theorem of Algebra not tell us? It is not constructive , that is, it does not tell us how to factor a polynomial completely! http://www.sosmath.com/algebra/factor/fac04/fac04.html

The Fundamental Theorem of Algebra The multiplicity of roots. Let's factor the polynomial . We can "pull out" a term Can we do anything else? No, we're done, we have factored the polynomial completely; indeed we have found the four linear (=degree 1) polynomials, which make up f x It just happens that the linear factor x shows up three times. What are the roots of f x )? There are two distinct roots: x =0 and x =-1. It is convenient to say in this situation that the root x =0 has multiplicity 3 , since the term x x -0) shows up three times in the factorization of f x ). Of course, the other root x =-1 is said to have multiplicity 1. We will from now on always count roots according to their multiplicity. So we will say that the polynomial has FOUR roots. Here is another example: How many roots does the polynomial have? The root x =1 has multiplicity 2, the root has multiplicity 3, and the root x =-2 has multiplicity 4. All in all, the polynomial has 9 real roots! Irreducible quadratic polynomials. A degree 2 polynomial is called a quadratic polynomial. In factoring quadratic polynomials, we naturally encounter three different cases:

7. Algebra Theorem | TutorVista * Talk to a Live Tutor * 24/7 Tutor Availability * Homework Help * Get help in Math, English, Science, Physics, Chemistry, Biology and Statistics http://www.tutorvista.com/topic/algebra-theorem

8. The Fundamental Theorem Of Algebra (Undergraduate Texts In Mathematics) By Benja Powell's Books is the largest independent used and new bookstore in the world. We carry an extensive collection of out of print rare, and technical titles as well as many other new http://www.powells.com/biblio/4-9780387946573-4

9. Fundamental Theorem Of Algebra: Statement And Significance Fundamental Theorem of Algebra Statement and Significance. Any nonconstant polynomial with complex coefficients has a root. http://www.cut-the-knot.org/do_you_know/fundamental2.shtml

10. Algebra Theorem | TutorVista | Web Stone's representation theorem for Boolean algebras In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a http://www.tutorvista.com/ks/algebra-theorem

11. Rational Root Theorem (mathematics) -- Britannica Online Encyclopedia rational root theorem (mathematics), in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational http://www.britannica.com/EBchecked/topic/960307/rational-root-theorem

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. rational-root-theorem My Britannica CREATE MY rational roo... NEW ARTICLE ... SAVE rational root theorem Table of Contents: rational root theorem Article Article Citations Article Citations ARTICLE from the rational root theorem also called rational root test , in algebra theorem that for a polynomial equation in one variable with integer coefficients to have a solution ( root ) that is a rational number , the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator. In algebraic notation the canonical form for a polynomial equation in one variable ( x ) is a n x n a n x n a x a where a a a n are ordinary integers. Thus, for a polynomial equation to have a rational solution

12. ABSTRACT ALGEBRA ON LINE: Theorems List of Theorems. This page contains a list of the major results in the following books. Abstract Algebra, Second Edition, by John A. Beachy and William D. http://www.math.niu.edu/~beachy/aaol/theorems.html

List of Theorems This page contains a list of the major results in the following books. Abstract Algebra Second Edition , by John A. Beachy and William D. Blair Waveland Press , P.O. Box 400, Prospect Heights, Illinois, 60070, Tel. 847 / 634-0081 Abstract Algebra II , by John A. Beachy About this document Back to the Table of Contents List of Theorems Division algorithm for integers Existence of greatest common divisors (for integers) Euclidean algorithm for integers Euclid's lemma characterizing primes ... Euclidean algorithm for polynomials (Example 4.2.3) Partial fractions (Example 4.2.4) Existence of greatest common divisors (for polynomials) Unique factorization of polynomials Rational roots Gauss's lemma ... DeMoivre's theorem (A.5.2) Irreducible polynomials over R (A.5.7) Back to the Table of Contents About this document

13. Pauls Online Notes : Linear Algebra - Fundamental Subspaces You can navigate through this EBook using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and http://tutorial.math.lamar.edu/Classes/LinAlg/FundamentalSubspaces.aspx

MPBodyInit('FundamentalSubspaces_files') Paul's Online Math Notes Online Notes / Linear Algebra / Vector Spaces / Fundamental Subspaces Linear Algebra You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material. Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book Chapter , and/or the Section link provided below. For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it. Change Of Basis E-Book Chapter Section Inner Product Spaces Fundamental Subspaces In this section we want to take a look at some important subspaces that are associated with matrices.  In fact they are so important that they are often called the fundamental subspaces of a matrix.  We’ve actually already seen one of the fundamental subspaces, the null space

14. Fundamental Theorem Of Algebra -- From Wolfram MathWorld Oct 11, 2010 Courant, R. and Robbins, H. The Fundamental Theorem of Algebra. §2.5.4 in What Is Mathematics? An Elementary Approach to Ideas and http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Fundamental Theorem of Algebra Every polynomial equation having complex coefficients and degree has at least one complex root . This theorem was first proven by Gauss. It is equivalent to the statement that a polynomial of degree has values (some of them possibly degenerate) for which . Such values are called polynomial roots . An example of a polynomial with a single root of multiplicity is , which has as a root of multiplicity 2. SEE ALSO: Degenerate Frivolous Theorem of Arithmetic Polynomial Polynomial Factorization ... Principal Ring REFERENCES: Courant, R. and Robbins, H. "The Fundamental Theorem of Algebra." §2.5.4 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 101-103, 1996. Krantz, S. G. "The Fundamental Theorem of Algebra." §1.1.7 and 3.1.4 in Handbook of Complex Variables. Smithies, F. "A Forgotten Paper on the Fundamental Theorem of Algebra." Notes Rec. Roy. Soc. London

15. Computer Algebra, Theorem Proving, And Types Computer Algebra, Theorem Proving, and Types Todd Wilson October 4, 1994 Abstract. Many computations a mathematician performs can be described in algebraic terms, that is, as http://www.cs.cornell.edu/NuPrl/PRLSeminar/PRLSeminar94_95/Wilson/Oct4.html

PRL Seminars Computer Algebra, Theorem Proving, and Types Todd Wilson October 4, 1994 Abstract Many computations a mathematician performs can be described in "algebraic" terms, that is, as dealing with various symbolic entities that are combined in restricted ways and are subject to laws (e.g., equations) specifying which combinations are equivalent. The term "computer algebra", as it appears in my title, has this general sense (as opposed to the more restrictive sense of "computational commutative algebra"), and my talk will discuss this subject and its relation to automatic theorem proving and type theory. In more detail, the talk will consist of the following: A survey of examples of computer algebra drawn from several areas of mathematics, including commutative algebra and algebraic geometry, invariant theory, (algebraic) number theory, group theory, Lie algebra, combinatorics, algebraic topology, and analysis (scientific computation). A discussion of the roles automatic theorem proving might have in these fields. A discussion of types, including

16. Boolean Algebra Calculator | TutorNext.com boolean algebra theorem. (Uniqueness of complement) Let a be any element in a Boolean algebra B. Then http://www.tutornext.com/help/boolean-algebra-calculator

17. Complex Numbers: The Fundamental Theorem Of Algebra Also, the part of the Fundamental Theorem of Algebra which stated there actually are n solutions of an nth degree equation was yet to be proved, pending, http://www.clarku.edu/~djoyce/complex/fta.html

Dave's Short Course on The Fundamental Theorem of Algebra As remarked before, in the 16th century Cardano noted that the sum of the three solutions to a cubic equation x bx cx d b , the negation of the coefficient of x . By the 17th century the theory of equations had developed so far as to allow Girard (1595-1632) to state a principle of algebra, what we call now "the fundamental theorem of algebra". His formulation, which he didn't prove, also gives a general relation between the n solutions to an n th degree equation and its n coefficients. An n th degree equation can be written in modern notation as x n a x n a n x a n x a n where the coefficients a a n a n , and a n are all constants. Girard said that an n th degree equation admits of n solutions, if you allow all roots and count roots with multiplicity. So, for example, the equation x x x + 1 = has the two solutions 1 and 1. Girard wasn't particularly clear what form his solutions were to have, just that there be n of them: x x x n , and x n Girard gave the relation between the n roots x x x n , and x n and the n coefficients a a n a n , and a n that extends Cardano's remark. First, the sum of the roots

18. Linear Algebra WebNotes. Part 1. Linear Algebra. Index . List of concepts and their definitions; Chapter 1. Systems of linear equations; Systems of linear equations; The geometric meaning of systems of linear equations http://www.sftw.umac.mo/~fstitl/linweb/jan10.html

Linear Algebra Index List of concepts and their definitions Chapter 1. Systems of linear equations Systems of linear equations The geometric meaning of systems of linear equations Augmented matrices The Gauss-Jordan elimination algorithm ... The theorem about solutions of homogeneous systems of equations. Chapter 2. Matrices Matrix operations Properties of matrix operations Properties that do not hold Transpose, trace, inverse ... The theorem about skew-symmetric matrices Chapter 3. Determinants Determinants. The theorem about the sign of a permutation. The first theorem about determinants. The second theorem about determinants. ... Cramer's rule. Chapter 4. Linear and Euclidean vector spaces Linear and Euclidean Spaces. Theorem about norms. Theorem about distances. Pythagoras theorem. Chapter 5. Linear transformations Linear transformations from R n to ... The theorem about linear transformations of arbitrary vector spaces. Chapter 6. Subspaces Subspaces of vector spaces. The theorem about subspaces. Sources of subspaces: kernels and ranges of linear transformations" Theorem: kernels and ranges are subspaces. ... How to find eigenvectors and eigenvalues Systems of linear equations A linear equation is an equation of the form a x +a x +...+a

19. The Fundamental Theorem Of Algebra Imaginary and complex numbers were not widely accepted at that time, but today this proposition – traditionally called the fundamental theorem of algebra http://www.mathpages.com/home/kmath056/kmath056.htm

The Fundamental Theorem of Algebra There is a Russian emissary here whose two young and intellectually gifted daughters I was supposed to instruct in mathematics and astronomy. I was, however, too late, and a French émigré obtained the position.                   C. F. Gauss, 1798 Gauss’s doctoral dissertation, published in 1799, provided the first genuine proof of the fact that every polynomial (in one variable) with real coefficients can be factored into linear and/or quadratic factors. Imaginary and complex numbers were not widely accepted at that time, but today this proposition – traditionally called the fundamental theorem of algebra - is usually expressed by saying that every polynomial of degree n possesses n complex roots, counting multiplicities. Although Gauss’s 1799 proof focused on polynomials with real coefficients, it isn’t difficult to extend the result to polynomials with complex coefficients as well. By modern standards, Gauss’s proof was not rigorously complete, since he relied on the continuity of certain curves, but it was a major improvement over all previous attempts at a proof. Only about a third of Gauss’s dissertation was actually taken up by the proof. The rest consisted of a rather frank assessment of the previously claimed proofs of this proposition by D’Alembert, Euler, Legendre, Lagrange, and others. Gauss explained that all their attempts were fallacious, and indeed that they didn’t even address the real problem. They all implicitly assumed the existence of the roots, and just sought to determine the form of those roots. Gauss pointed out that the real task was to prove the

20. Looking For A Proof Of Linear Algebra Theorem..? Everything about Looking for a proof of linear algebra theorem..? i'm looking for the proof of a famous theorem http://www.edaboard.com/ftopic121428.html

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