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Date tag: January 18 2010 8:41:34
Taylor Polynomial of degree n centered at X.
Date tag: January 18 2010 8:19:22
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Date tag: January 18 2010 8:16:23
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Date tag: January 18 2010 8:13:28
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Date tag: January 18 2010 8:13:16
The unique factorization theorem says that every integer greater than one can be expressed as a product of primes, AND this expression is unique appart from order of the factor.
Date tag: January 18 2010 8:6:16
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Date tag: January 18 2010 8:6:4
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Date tag: January 18 2010 8:1:51
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Date tag: January 18 2010 7:53:48
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Date tag: January 18 2010 7:50:38
Euclids theorem says that there are infinitely many primes. Proof: Assume for a contradiction that there are finitely many primes. p1,p2,p3,...,pn Let N p1p2p3...pn 1 Claim: N is not prime because it is larger than each of p1, p2,...,pn.
Date tag: January 18 2010 7:47:30
r, s are elements of integers, and 1 r,s N Since 1 r,s N, both r and s can be expressed as products of primes. But then N rs is a product of primes, contradicting our choice of N. Thus our assumption is false, and every integer 1 is a product of primes
Date tag: January 18 2010 7:43:0
Assume for a contradiction that there exists an integer greater than one that is NOT a product of primes. Let N be the smallest such integer. If N is prime, then N is a product of one prime. So N cant be prime, thus N is composite ie N equals rs where...
Date tag: January 18 2010 7:38:5
Every integer greater than 1 can be expressed as a product of primes. Proof tip number 5: To prove a statement you may assume the statement is FALSE and derive a contradiction.
Date tag: January 18 2010 6:21:37
The usual high school algebra is that of a fields. On the other hand in a field every element has an additive inverse, and every nonzero element x has a multiplicative inverse x prime
Date tag: January 18 2010 6:18:10
For every element x in B its complement x prime is in B. There exists at least 2 element x not equal to y in B. For example let X be a set and P of X its power set, the set of all subsets, Then P of X together with union, intersection and set complement Y prime equals X minus Y is a boolean algebra.
Date tag: January 18 2010 6:12:1
The plus and times operations are commutative. Plus and times are distributive over each other.
Date tag: January 18 2010 6:11:40
1 The set B is closed with respect to these operations. Applying the operations to elements of B yields elements of B. 2a There exists an element 0 in B that is an identity element for addition. 2b there is an element 1 in B that is an identity element for multiplication
Date tag: January 18 2010 6:11:23
A boolean algebra is a set B equipped with two binary operators plus and times, and one unary operator not, such taht the following axioms are satisfied.
Date tag: January 18 2010 6:3:16
Shannon formulated this logical approach in terms of boolean algebra.
Date tag: January 18 2010 5:53:57
Gates are often called logic gates, and the resulting circuits are called logic circuits.
Date tag: January 18 2010 5:53:28
This is why we don t need more parentheses in out formula. We will assume that we have circuit components that implement these basic functions called gates.
Date tag: January 18 2010 5:49:7
To be more precise, by AND OR and NOT we mean the following functions. It can be easily checked that AND and OR are associative.
Date tag: January 18 2010 5:42:53
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Date tag: January 18 2010 5:39:43
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Date tag: January 18 2010 5:39:27
Think of 0 as false and 1 as true.
Date tag: January 18 2010 5:37:18
Boolean algebra and logic gates. To begin we will look at combinations circuits. These are circuits that depend only on the current input value to decide output.
Date tag: January 15 2010 9:15:17
Taylors inequality.
Date tag: January 15 2010 9:12:29
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Date tag: January 15 2010 9:9:31
The resulting integral cannot be solved. Can we bound
Date tag: January 15 2010 9:4:48
Taylors remainder theorem
Date tag: January 15 2010 9:1:41
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Date tag: January 15 2010 8:55:50
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Date tag: January 15 2010 8:52:23
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Date tag: January 15 2010 8:52:13
Taylor Polynomial of degree n centered at x
Date tag: January 15 2010 8:44:56
Apply inequality to a Riemann Sum
Date tag: January 15 2010 8:39:37
Recall the Triangle Inequality can be extended.
Date tag: January 15 2010 8:39:19
Taylors Remainder Theorem. How good are Taylor Polynomials at approximating. Note that we cannot possibly know the error of our approximation. We can have an upper bound on the error.
Date tag: January 15 2010 8:22:1
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Date tag: January 15 2010 8:19:30
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Date tag: January 15 2010 8:18:53
Composite numbers
Date tag: January 15 2010 8:15:11
Prime Numbers
Date tag: January 15 2010 8:6:4
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Date tag: January 15 2010 8:5:55
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Date tag: January 15 2010 8:2:52
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Date tag: January 15 2010 7:54:41
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Date tag: January 15 2010 7:54:30
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Date tag: January 15 2010 7:50:22
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Date tag: January 15 2010 7:44:36
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Date tag: January 15 2010 7:43:16
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Date tag: January 15 2010 7:39:45
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