121. Perl Contains The Lambda-Calculus Explains why this computer program is well suited to apply to functional application. http://perl.plover.com/lambda/

Perl contains the -calculus -Calculus (pronounced `lambda calculus') is a model of computation invented by Alonzo Church in 1934. It's analogous to Turing machines, but it's both simpler and more practical. Where the Turing machine is something like a model of assembly language, the -calculus is a model of function application. Like Turing machines, it defines a simplified programming language that you can write real programs in. Writing Turing machine programs is like writing in assembly language, but writing -calculus programs is more like writing in a higher-level language, because it has functions. The two legal operations in the -calculus are to construct a function of one argument with a specified body, and to invoke one of these functions on an argument. What can be in the body of the function? Any legal expression, but expressions are limited to variables, function constructions, and function invocations. What can the argument be? It has to be another function; functions are all you have. With this tiny amount of machinery, we can construct a programming language that can express any computation that any other language can express. Unlike most popular programming languages, Perl is powerful enough to express the

122. Shreve Notes in probability theory prepared by Prasad Chalasani and Somesh Jha, with a strong bias towards financial modeling and option pricing. http://www.cs.cmu.edu/~chal/shreve.html

Steven Shreve 's Lectures on Stochastic Calculus and Finance Prepared by Prasad Chalasani and Somesh Jha New Risk Waters Course: Stochastic Calculus for Derivatives: Frankfurt/London/New York, March 2003 In the table of contents below, click on a chapter name to down-load that chapter (Postscript). You may also down-load/view the entire document (364 pages) in Postscript or PDF format. If the links don't work, try re-loading this page. PC/Mac Users: You may need to download a Postscript viewer or a PDF viewer to view these notes. FastCounter by LinkExchange Table of contents Probability Theory Binomial asset pricing Finite probability spaces Lebesgue measure, lebesgue integral General probability spaces Independence Conditional Expectation Binomial model for stock prices Information Conditional expectation Martingales Arbitrage Pricing Binomial pricing General one-step APT Risk-neutral probability measure, portfolio process Simple European derivative securities Completeness of binomial model Markov Property Binomial model pricing and hedging Computational issues Markov processes Showing that a process is Markov Applications to exotic options Stopping times, American Options

123. Page Of Yves Lafont University of Marseille II Linear logic, lambda calculus, proof theory, term rewriting. Lafont invented the theory of interaction nets, an elegant theory of graph rewriting. http://iml.univ-mrs.fr/~lafont/welcome.html

photo by M. Arovas Yves LAFONT professor at Aix-Marseille 2 research at (team : Logique de la Programmation teaching at Maths adress: office: - phone: - fax: - e-mail: lafont@iml.univ-mrs.fr Discipline maths Specialities logic algebra theoretical computer science; Papers More information on my french home page

124. [math/9906155] Lectures On Pseudo-differential Operators These lecture notes cover a first year graduate course that was given on pseudodifferential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem. http://arxiv.org/abs/math.AP/9906155

Mathematics, abstract math.AP/9906155 From: Mark S. Joshi [ view email ] Date: Wed, 23 Jun 1999 13:41:14 GMT (125kb,S) Lectures on Pseudo-differential Operators Authors: M. S. Joshi Subj-class: Analysis of PDEs MSC-class: This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem. Problems are included. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

125. Deep Inference And The Calculus Of Structures The calculus of structures is a new proof theoretical formalism. It exploits a topdown symmetry of derivations made possible by deep inference. http://alessio.guglielmi.name/res/cos/index.html

Alessio Guglielmi's Research / Deep Inference and the Calculus of Structures Deep Inference and the Calculus of Structures NEW The first book on deep inference and the calculus of structures appeared: it's un updated version of Kai's thesis. You can download it from here , but you can also BUY IT and make your library BUY IT here and here NEW I will teach deep inference at next ESSLLI 2004 and ICCL Summer School 2004 NEW There is a mailing list for the calculus of structures and related matters. Contents Frequently Asked Questions Papers, Lectures and Theses Classical Logic Linear Logic ... Acknowledgements The calculus of structures is a new proof theoretical formalism, introduced by myself in 1999 and mostly developed by members of my group in Dresden since 2000. It exploits a new top-down symmetry of derivations made possible by deep inference . We can present deductive systems in the calculus of structures and analyse their properties, as we do in the sequent calculus , natural deduction and proof nets. Typical properties of interest are normalisation and cut elimination The main purpose of our new formalism is to allow a richer combinatorial analysis structures , which are expressions intermediate between formulae and sequents.

126. A Calculus Of Risk Article by Gary Stix. http://www.ge.infm.it/~ecph/bibliography/stix98.html

A Calculus of Risk Financial engineering can lessen exposure to the perils of running a multibillion-dollar business or a small household. But mathematical models used by this discipline may present a new set of hazards by Gary Stix, staff writer SUBTOPICS: Einstein and Options Physicists on Wall Street Physics Versus Finance Financial Hydrogen Bombs Weather derivatives mark an example of the growing reach of a discipline called financial engineering. This bailiwick of high-speed computing and the intricate mathematical modeling of mathematicians, physicists and economists can help mitigate the vagaries of running a global business. It entails the custom packaging of securities to provide price insurance against a drop in either the yen or the thermometer. The uncertainties of a market crash or the next monsoon can be priced, divided into marketable chunks and sold to someone who is willing to bear that riskin exchange for a fee or a future stream of payments. "The technology will effectively allow you to completely manage the risks of an entire organization," says Robert A. Jarrow, a professor of finance at Cornell University. The engineering of financial instruments has emerged in response to turbulence during recent decades in ever more interconnected world markets: a result of floating exchange rates, oil crises, interest-rate shocks and stock-market collapses. The creative unleashing of new products continues with increasingly sophisticated forms of securities and derivativesoptions, futures and other contracts derived from an underlying asset, financial index, interest or currency exchange rate. New derivatives will help electric utilities protect against price and capacity swings in newly deregulated markets. Credit derivatives let banks pass off to other parties the risk of default on a loan. Securities that would help a business cope with the year 2000 bug have even been contemplated.

127. Introduction To Translation Of Grassmann's Ausdehnungslehre Explains the published paper called Ausdehnungslehre, which translates to Theory of Extension . The purpose is to create a universal type of geometric calculus. This development is used in linear and nonlinear algebra, today. http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannTranslation/node3.html

NEXT PAGE CONTENTS PREVIOUS PAGE Introduction Hermann Grassmann's 1862 Ausdehnungslehre (literally, ``Theory of Extension'') is one of the great mathematical works of the nineteenth century. In it the foundations of linear and multilinear algebra are laid and much of the superstructure too is constructed. It is regrettable that such a book on such a subject should, from the moment of publication, have been not much read. Indeed, Grassmann's reputation for impenetrability has persisted to this day. Yet one may suspect that a writer who is, in many respects, a century ahead of his time will be somewhat more readable when that century has elapsed than he was to his contemporaries. It is my hope that this translation and commentary will make it easy for today's mathematically educated reader to appreciate Grassmann's presentation of the theory of basis and dimension - it does not differ much from the initial chapter of a modern linear algebra text. The work called simply Die Ausdehnungslehre , though its title page bears the date 1862, actually appeared in the latter half of 1861. It was Grassmann's second attempt to present his theory and was totally different in conception from

128. Quantum Logic And Probability Theory How quantum mechanics can be regarded as a nonclassical probabilistic calculus; by Alexander Wilce. http://plato.stanford.edu/entries/qt-quantlog/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change FEB Quantum Logic and Probability Theory At its core, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form "the value of physical quantity A lies in the range B " is represented by a projection operator on a Hilbert space H . These form a non-Boolean in particular, non-distributive orthocomplemented lattice. Quantum-mechanical states correspond exactly to probability measures (suitably defined) on this lattice. What are we to make of this? Some have argued that the empirical success of quantum mechanics calls for a revolution in logic itself. This view is associated with the demand for a realistic interpretation of quantum mechanics, i.e., one not grounded in any primitive notion of measurement. Against this, there is a long tradition of interpreting quantum mechanics operationally, that is, as being precisely a theory of measurement. On this latter view, it is not surprising that a "logic" of measurement-outcomes, in a setting where not all measurements are compatible, should prove not to be Boolean. Rather, the mystery is why it should have the particular non-Boolean structure that it does in quantum mechanics. A substantial literature has grown up around the programme of giving some independent motivation for this structure ideally, by deriving it from more primitive and plausible axioms governing a generalized probability theory.

129. Untitled Document Mathematica package for doing tensor and exterior calculus on differentiable manifolds. http://baldufa.upc.es/ttc/

130. Index The emphasis of the conference is on categorical decomposition techniques, especially calculus of functors and homology decompositions of classifying spaces, but the conference is intended to have a broad scope with talks on a variety of topics of current interest in topology. Isle of Skye, Scotland; 24 30 June 2001. http://maths.abdn.ac.uk/~stc2001/

International Conference in Algebraic Topology Isle of Skye - Scotland 24- 30 June 2001 Research Centre in Topology and Related Areas Department of Mathematical Sciences University of Aberdeen An international Algebraic Topology conference is planned for the last week of June 2001 (June 24 - 30, 2001). The conference will take place on the Isle of Skye - a scenic island off the west coast of Scotland. The emphasis of the conference is on categorical decomposition techniques, especially calculus of functors and homology decompositions of classifying spaces. But the conference is intended to have a broad scope, with talks on a variety of topics of current interest in topology. A London Mathematical Society invited lecture series will take place in Aberdeen the week before the conference (June 18 - 23, 2001). Prof. T. Goodwillie will give a series of ten lectures on calculus of functors. Participants who wish to attend both meetings are encouraged to do so and will enjoy reduced registration fees. The following mathematicians have agreed to attend and give a plenary talk.

131. Lemon Functional language with inductive and coinductive types. Based on simplytyped lambda calculus augmented with sums, products, and mu and nu constructors for least (inductive) and greatest (coinductive) solutions to recursive type equations. http://www.cis.ksu.edu/~bhoward/lemon.html

Lemon A Functional Language with Inductive and Coinductive Types The functional language lemon is based on the simply-typed lambda calculus augmented with sums, products, and the mu and nu constructors for least ( inductive ) and greatest ( coinductive ) solutions to recursive type equations. The term constructors of the language strictly follow the introduction and elimination rules for the corresponding types; in particular, the elimination for mu is iteration and the introduction for nu is coiteration (also called generation ). It includes a small amount of polymorphism and type inference; lambda-bound variables do not need type annotations, but iteration and coiteration need to have their corresponding recursive types specified (this is a problem with the language rather than the implementation). For example, the following program generates the stream of Fibonacci numbers starting with 1,1: Using iteration we may define a function which picks off the first n elements of a stream and returns them as a list: We may combine these terms as follows (currently there is syntactic sugar for natural numbers but not for lists; formatting inserted by hand for clarity):

132. Calculus On The Web An internet tutoring utility for learning and practicing calculus. C.O.W. gives the student or interested user the opportunity to learn and practice problems. Instant feedback for the correctness of answers. http://www.math.temple.edu/~cow/

Welcome to Calculus on the Web The COW Library Click on a button below to open a book General information desk. Contents of the COW library If you wish to log in for a recorded session, click on the Login button. Calculus on the Web is partially supported by the National Science Foundation A project of Gerardo Mendoza and Dan Reich Temple University

133. Transferring You To The Math Resource Pages A mathematics reference collection of K through 14 math tables, facts, definitions, formulas and explanations from general math through college calculus. http://www.hoxie.org/math/title.htm

Transferring you to the new math site location ... www.colbycc.org click here if you are not automatically transferred to the Math Pages http://www.colbycc.org/www/math/math.htm the Math Pages are now located at: http://www.colbycc.org/www/math/math.htm

134. S.O.S. Math Contains tutorials covering algebra, trigonometry, calculus, differential equations, matrices, and complex variables. Reviews the most important results, techniques and formulas. Presented in worksheet format and require active participation. Includes practice quizzes and forum board. http://www.sosmath.com/

Algebra Trigonometry Calculus Differential Equations ... CyberBoard Search our site! S.O.S. Math on CD Sale! Only $19.95. Works for PCs, Macs and Linux. Tell a Friend about S.O.S. Books We Like Math Sites on the WWW S.O.S. Math Awards ... Privacy Concerns? var version = 1.0; var version = 1.1; var version = 1.2; var version = 1.3; S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations! The perfect study site for high school, college students and adult learners. Get help to do your homework, refresh your memory, prepare for a test, .... Browse our more than 2,500 Math pages filled with short and easy-to-understand explanations - from simplifying fractions to the cubic formula , from the quadratic equation to Fourier series , from the sine function to systems of differential equations - this is the one stop site for your math needs. You want more? Check out our CyberExams to prepare for a test, or ask a question on our popular CyberBoard ! You can buy a personal copy of our site on CD, or browse our recommended book list Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

135. ENC Online: Web Links: Math Topics: Precalculus Cost Free ENC 029291 This Internet site offers lessons and interactive examples designed to prepare students for calculus by providing them with a solid http://www.enc.org/weblinks/math/0,1544,1-Precalculus,00.shtm

Skip Navigation You Are Here ENC Home Web Links Math Topics Search the Site More Options Classroom Calendar Digital Dozen ENC Focus ... Frequently Asked Questions Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Math Topics Lists of web sites categorized by subject areas within mathematics. Precalculus Exploring precalculus ENC Digital Dozen Site Date: Grade(s): 10 - Post-Sec. Cost: Free ENC#: This Internet site offers lessons and interactive examples designed to prepare students for calculus by providing them with a solid understanding of functions. The web site introduces precalculus as a metaphorical bridge that connects the more familiar branches of mathematics, such as algebra and geometry to the study of calculus, and uses everyday analogies to reduce students' anxieties about learning precalculus. (For more details, see ENC Record Jim Loy's mathematics page ENC Digital Dozen Site Date: Grade(s): 6 - Post-Sec.

136. The Yacas Computer Algebra System Acronym for Yet Another Computer Algebra System, an opensource software package. Supports arbitrary precision arithmetic, matrices, and differential and integral calculus. http://www.xs4all.nl/~apinkus/yacas.html

Yacas is a general purpose easy to use Computer Algebra System (a CAS is a program that can be used to do symbolic manipulation of mathematical expressions). It is built on top of its own programming language designed for this purpose, in which new algorithms can easily be implemented. In addition, it comes with extensive documentation on the functionality implemented and methods used to implement them. This entire site (including the documentation) can also be found in the source code distribution

137. Lambda An online introduction to the lambda calculus by Lloyd Allison, complete with a web form that will evaluate lambda expressions. http://www.csse.monash.edu.au/~lloyd/tildeFP/Lambda/

138. Alan Bain These notes by Alan Bain provide a complete elementary introduction to stochastic integration with respect to continuous semimartingales. http://www.statslab.cam.ac.uk/~afrb2/

Alan Bain E-mail address: afrb2@cam.ac.uk Research Interests I am interested in the application of probability theory techniques to problems arising from communications networks, in particular the Internet. My recent work has focussed on using fluid limits to model the behaviour of various congestion control schemes similar to TCP (Transmission Control Protocol). I have submitted a thesis with the following abstract: Fluid Limits for Congestion Control in Networks In the Internet, congestion control mechanisms such as TCP are required in order to provide useful services. Propagation delays in the network affect any congestion control scheme, by causing a delay between an action and the controller's reaction, which can lead to undesirable instabilities. This problem is fundamental since, despite the steady increase in speed of networking technologies, the delays imposed by the finite speed of light provide a lower bound on the delays. We should like to understand the dynamical behaviour of the congestion control, for example to determine whether it is stable or not. Working with a model of a network carrying packet traffic, we consider the limit of a sequence of such networks, suitably rescaled, as the bandwidth tends to infinity.

139. Luke Ong Merton College, Oxford Categorical logic, game semantics, type theory, lambda calculus, semantics of programming languages, and sequentiality. http://web.comlab.ox.ac.uk/oucl/people/luke.ong.html

Luke Ong Reader in Computer Science Tutorial Fellow in Computation, Merton College Address Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford, OX1 3QD, England. Telephone Direct: +44 (0)1865 283522 Department: +44 (0)1865 273838 Fax: +44 (0)1865 273839 EMail Luke.Ong@comlab.ox.ac.uk WWW Work-related information (OUCL) Personal Information (Personal page, content is not the responsibility of OUCL) oucl people Updated April 2004 Home Search SiteMap Feedback ... News

140. Math 1710: Precalculus I This course is a study of the algebra necessary to prepare for calculus.......Precalculus MATH 1710 3 Credit Hours. Course Information. Course http://www.tn.regentsdegrees.org/courses/syllabi/math1710.htm

Precalculus MATH 1710 3 Credit Hours Course Information Course Description: This course is a study of the algebra necessary to prepare for calculus. Topics covered will include polynomial, rational, exponential, logarithmic, and trigonometric functions; systems of equations and inequalities; matrices; sequences and series; and conics including parametric and polar equations. Course Objectives: to understand the concept of function; and to use polynomial, rational, exponential, and logarithmic functions to represent data graphically and symbolically; to solve polynomial, rational, exponential, and logarithmic equations; to solve systems of equations by graphing and by use of matrices; to understand arithmetic and geometric sequences and series and apply these techniques in mathematical induction; to understand and apply the concepts of conics in rectangular, parametric, and polar form; to understand the appropriate use of technology in visually describing mathematical models and in finding numerical solutions to mathematical problems.

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