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	[No title]
		Lecture 13 Sigma - Summation Notation "Sigma notation" is a compact method of writing an expression that involves a large number of terms which are to be added together.
		The "i=1" at the bottom of the sigma tells us that the index which is used in the summation is named "i", and that the starting value (or lower bound) for i will be 1.
		2 i=1 The "i" is an index (as in sigma notation), with lower bound 1 and upper bound 10.
	www.unf.edu /public/cot3100/jgiles/lecture13 (1387 words)

	PlanetMath: summation
		Sigma notation is often used to write complicated sums in a concise and compact way.
		symbol (capital sigma) means sum and the expression (1) is equivalent to the sum
		I have always (in 44 years) seen only such a practice, that the summing operator, similarly as the deriving and integral operators, affects only the first term (or addend) on its right side.
	www.planetmath.org /encyclopedia/Summation.html (1061 words)

	Sigma notation (Site not responding. Last check: 2007-10-30)
		Thus, the sum of all the natural numbers from 1 to 100 is 1 + 2 +...
		Alternatively, the sum can be represented by the summation symbol, which is the capital Sigma.
		These degenerate cases are usually only used when the summation notation gives a degenerateresult in a special case.
	www.therfcc.org /sigma-notation-210610.html (707 words)

	MAT 200 Lecture Notes -- Summation and Matrix Notation (Site not responding. Last check: 2007-10-30)
		In describing general theorems some notation is needed for sums of a variable number of terms.
		The notation puts more of a burden on the reader, who is now expected to know that the range of values for k runs from 1 to n.
		A consequence of these notations is that when I write two tables of number next to each other there is an implied sum over the columns of the first and rows of the second.
	www.math.princeton.edu /~stalker/200s00/notation.html (538 words)

	Calculus - Mathematics Essay \| Essay Essay Essay (Site not responding. Last check: 2007-10-30)
		To understand the concept of area of a plane region, it is necessary to first understand sigma notation.
		Sigma notation uses the uppercase Greek letter sigma: Σ.
		The Greek letter sigma is closely associated with the word "sum." The letter sigma is a signal that summation notation is being used.
	essayessayessay.com /calculus-mathematics-essay (439 words)

	Sigma Notation
		The Greek letter, sigma, shown above, is very often used in mathematics to represent the sum of a series.
		This allows you to either multiply each term by c then add the series, or first add the series and then multipy the result by c.
		Your job in this section, is to learn to write sigma notation in expanded form and vice versa.
	home.alltel.net /okrebs/page136.html (493 words)

	unit01-sect01-les02-lessona (Site not responding. Last check: 2007-10-30)
		There is a shorthand notation we can use to represent this sum.
		It is called "sigma notation" and involves the use of the symbol sigma,
		What is important however, is that you realize the variable name appears below the sigma symbol and usually also within the expression to the right of the sigma.
	www.cdli.ca /courses/math3207/unit01/section01/lesson02/3-lesson-a.htm (270 words)

	Sigma Chess 6.1.3 - MacUpdate (Site not responding. Last check: 2007-10-30)
		Sigma Chess is a master strength Macintosh chess program for both OS X and Classic Mac OS.
		Sigma Chess Lite, which is freeware and can be downloaded here.
		Sigma Chess Pro, which is not freeware, but a full featured commercial product.
	www.macupdate.com /info.php/id/2325 (576 words)

	Truth Tables Help (Site not responding. Last check: 2007-10-30)
		Most likely, the sigma notation is a compact form of writing a Boolean
		form of question two and is similar to the sigma notation except the pi
		notation is commonly used when working with karnaugh maps, or k-maps for
	www.electrical-engineering-forum.net /ee/Truth_Tables_Help_126298.html (805 words)

	Proof that T(n)=n(n+1)/2
		The first uses "..." notation and the second introduces you to the Sigma notation which makes the proof more precise.
		For this reason, in summing a series, the sigma notation is used.
		In fact, the formula after the sigma can be written in terms of any variable not just i, for instance k, but then we must indicate which is the letter that varies in the sum under the sigma.
	www.mcs.surrey.ac.uk /Personal/R.Knott/runsums/triNbProof.html (708 words)

	Summation notation (1 of 4) (Site not responding. Last check: 2007-10-30)
		The Greek letter Σ (a capital sigma) is used to designate summation.
		This notation is read as follows: Sum the values of X from X
		The index i (shown just under the Σsign) indicates which values of X are to be summed.
	www.davidmlane.com /hyperstat/A46748.html (146 words)

	Sigma notation (Site not responding. Last check: 2007-10-30)
		It uses material from the Wiktionary page "Sigma".
		If you are planning to come, make sure and register.
		Collection of Widgets and UI elements from various websites, with notation of their sterling or plate metal qualities
	www.serebella.com /encyclopedia/article-Sigma_notation.html (1061 words)

	Sigma Chess - Macintosh Chess Software
		Sigma Chess can also be used as an engine from within ExaChess.
		Sigma Chess 6.1 Lite, which is freeware and can be downloaded here.
		Sigma Chess 6.1 was written by Ole K. Christensen.
	www.sigmachess.com (438 words)

	Karl's Calculus Tutor - Math Notation
		using the more traditional notation of just leaving out the multiply symbol and letting it be understood (that is when no operator symbol is shown between two expressions you should assume that the two expressions are multiplied).
		SIGMA, PI When letters are used to represent sets or vectors, I shall render them in bold type:
		This notation can be extended to any number of dimensions.
	www.karlscalculus.org /notation.html (1310 words)

	Algebra II: Probability - Math for Morons Like Us
		Sigma notation is especially useful to know because you use it a lot in calculus when you find area under curves.
		Σ, the Greek letter sigma (if you have an old browser that can't display Sigma, it looks like a mix between an E and a Z), can be used to simplify sequences of numbers.
		The sum of terms in the sequence is found using sigma notation (also called summations).
	library.thinkquest.org /20991/alg2/prob.html (903 words)

	Thomas Pyzdek and Six Sigma--Quality Digest Columnist
		But this should come as no surprise, as projects are the means by which Six Sigma converts knowledge into bottom-line results.
		In addition to telling us where to conduct Six Sigma projects, knowing the process constraints also helps us determine what the focus of the project should be.
		Applying the TOC strategy described in the June column, we know that Six Sigma projects that affect step C should be given priority, those affecting steps D and E second priority, and those affecting A and B third priority.
	www.qualitydigest.com /sept00/html/sixsigma.html (506 words)

	[No title]
		(The quantity $\sigma$ itself is the standard deviation.) This process is known as the {\em Ornstein-Uhlenbeck process}.
		(ref.\ ?) We note that the correlation function (\ref{eq:1}) of the random walk is not defined, since $\sigma \rightarrow \infty$ as $\alpha \rightarrow 0$.
		We again have Eq.\ (\ref{eq:27}) but with \begin{eqnarray}\label{eq:28.1} {\bar x} &=& {(t_{m+1}-t_{m})x_{m-1} + (t_{m}-t_{m-1})x_{m+1} \over t_{m+1}-t_{m-1}} \nonumber\\ {\bar \sigma} &=& {D(t_{m+1}-t_{m})(t_{m}-t_{m-1}) \over t_{m+1}-t_{m-1}} \end{eqnarray} Thus the mean ${\bar x}$ is given simply by linear interpolation between the bounding values.
	www.lanl.gov /DLDSTP/fast/OU_process.tex.txt (1450 words)

	Glossary of Signed and Gain Graphs and Allied Areas
		The sign function of Sigma is sigma, the gain function of Phi is phi; that is, I use upper and lower case consistently for the graph and its edge labelling.
		Notation: {+, -}, {+1, -1}, or {0, 1} (mod 2)
		Notation: Lambda(B) » L(B), bidirected so that each edge end has the same character (pointing into or out of its vertex) as does the corresponding end in B. This is a bidirected graph.
	www.math.binghamton.edu /zaslav/Bsg/glossary.html (10726 words)

	Summation notation (Site not responding. Last check: 2007-10-30)
		The upper case Greek Sigma is used to denote that the following expression is to be added to itself or summed over the specified range of values of the index.
		We shall use it to calculate the mean and variance (hence standard deviation).
		Leonhard Euler introduced the notation Sigma for summation in 1755 (he also introduced e for the base of the natural logarithm, pi for the ratio of the circumference to diameter of a circle, and i for the square root of -1).
	www.math.uni.edu /~campbell/stat/Sigma.html (235 words)

	Calculus Table of Contents (Site not responding. Last check: 2007-10-30)
		This lesson covers the mathematical definition of the word "function", the function notation, graphing of functions, and some simple examples of functions and their graphs.
		The sigma notation for summation is reviewed; examples are worked showing how to compute sums expressed in sigma notation.
		The concept of dummy index is discussed and examples are worked showing how to change indices in the sigma notation via substitution.
	www.sieducation.com /schools/CalcTOC.html (1908 words)

	Math Jams
		Second, sigma notation often expresses math in a way that is in fact easier to manipulate.
		While this notation may look intimidating at first, a little experience makes it look more and more natural and once we get used to it it becomes very very useful.
		Once we are comfortable with the sigma notation we can skip this step and think of such a series as its own variable that we are solving for.
	www.artofproblemsolving.com /Community/AoPS_Y_MJ_Transcripts.php?mj_id=35 (3983 words)

	Sigma Notation
		For instance, the above sum can be written using sigma notation as shown below:
		The upper case Greek letter sigma, written as
		Write each of the following using sigma notation.
	www.saskschools.ca /curr_content/mathb30/seq_series/les3/notes.htm (184 words)

	Previous Questions (Site not responding. Last check: 2007-10-30)
		Sigma Notation: (n + 5)^2 where n = 1 to 8
		Bracket Notation: {104 - 8n} and n = 1 to 16
		Sigma Notation: (48 - 3n) where n = 1 to n = 13
	www.gomath.com /Questions/question.php?question=1611 (445 words)

	Calculus II (Math 2414) - Series & Sequences - Series - The Basics (Site not responding. Last check: 2007-10-30)
		The series notation (or summation notation or sigma notation, which ever you prefer) tells us to add all the items from the sequence starting at the value of the index that is below the sigma. Also note that the letter that we use for the index is not important. The following two series are identical.
		Okay, now that the notational stuff is out of the way, let’s think about these facts a little. The first fact should make some sense. We can always factor a constant out of a series. We know that we can do this with a finite sum,
		This is a convenient notation when we are stripping out a large number of terms or if we need to strip out an undetermined number of terms. In general, we can write a series as follows,
	tutorial.math.lamar.edu /AllBrowsers/2414/Series_Basics.asp (1089 words)

	Earliest Uses of Symbols in Probability and Statistics (Site not responding. Last check: 2007-10-30)
		It occurs in a paper "On Algebraic Notation" that was printed in 1830 in the Transactions of the Cambridge Philosophical Society and it appears in 1831 in An Essay on Algebraic Development containing the Principal Expansions in Common Algebra, in the Differential and Integral Calculus and in the Calculus of Finite Differences (Cajori vol.
		The notational highpoint of the correlation/regression development was Yule’s "On the Theory of Correlation for any Number of Variables, Treated by a New System of Notation," Proc.
		Yule’s regression notation is used sometimes in multivariate analysis but the most familiar modern regression notation dates from the 1920s when R. Fisher drew the Gauss and Pearson lines together.
	members.aol.com /jeff570/stat.html (4234 words)

	SMC's Mathematics Department
		Use interval notation to express the solution to a linear, quadratic or rational inequality.
		Use the language and standard mathematical notation of the algebra of functions.
		Use the language and notation of sequences and series.
	www.smc.edu /math/course_info_math_02.htm (392 words)

	Comparison
		A separate section is provided on general rate interpretations with delta notation after the calculus but before trigonometry.
		The Leibniz notation is used extensively with delta notation.
		Limit concepts are developed slowly with notation for limits developed first as a short hand for concepts related to the derivative.
	www.humboldt.edu /%7Emef2/book/comparison.html (570 words)

	Some special sums
		In this course, we will be considering lots of different sums and it will be useful to have some notation for representing them compactly.
		What follows the sigma tells us what we are going to add.
		Summation notation can be confusing at first, but after getting used to it, it will become familiar.
	www.ugrad.math.ubc.ca /coursedoc/math101/notes/integration/sums.htmx (992 words)

	Previous Questions (Site not responding. Last check: 2007-10-30)
		Sigma notation (n = 0 to positive infinity) [(-1)^n](1 / n!)
		Sigma notation (n = 1 to positive infinity) [(inverse tan n)^2] / (n^2 + 1)
		Sigma notation (n = 1 to positive infinity) 1 / (n^2 + 1)
	www.gomath.com /Questions/question.php?question=6181 (697 words)

	SMC's Mathematics Department
		Solve linear or quadratic equations/inequalities involving one variable and express the answer in interval notation.
		Use the language and notation of the algebra of functions.
		Use interval and set builder notation to state the domain and range of functions.
	www.smc.edu /math/course_info_math_22.htm (333 words)

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		Sigma Chess 6.1 supports third party piece set and board plug-ins.
		Installation: After download, copy the library to the Sigma Chess 6.1 folder, start the Sigma Chess application and open the library from the File/Open menu.
	www.sigmachess.com /_download/download.html (628 words)

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