121. 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

122. 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

123. [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

124. 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.

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

126. 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

127. 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.

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

129. 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.

130. Teaching Calculus Resources At Questia - The Online Library Of Teaching calculus. Questia. The World s Largest Online Library. QuestiaSubscribers Say Primary Content. Teaching calculus. Welcome http://www.questia.com/popularSearches/teaching_calculus.jsp

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. 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

136. Lambda Calculus 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/

Lambda Calculus (interpreters) LA home FP Lambda Introduction Examples Also see: Semantics There are lazy and strict versions of the toy lambda-calculus interpreter. They both share the same input syntax and can be used on the same example lambda-calculus programs, although some programs will not work (i.e. will loop) when using the strict interpreter of course. Introduction: Lambda-calculus and the lazy interpreter Syntax - quick guide Example lambda-calculus programs Lazy Interpreter Strict Interpreter main programs Lazy.p Strict.p declarations define values lazy.type.P interpreters proper lazy.exec.P strict.exec.P output lazy.show.P (evaluation is print driven) strict.show.P expressions lazy.eval.p (by-need evaluation) strict.eval.P (strict evaluation) apply functions lazy.apply.P strict.apply.P process declarations lazy.D.P strict.D.P binary operators lazy.O.P unary operators lazy.U.P strict.U.P manipulate environments lazy.env.P strict.env.P form basic values lazy.mkval.P It is a useful exercise to compare the strict and lazy versions of the above files, particularly *.eval.P General routines common to both interpreters: lexical syntax lex.type.P

137. 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.

138. 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

139. Lee Lady: Topics In Calculus A set of downloadable lectures. http://www.math.hawaii.edu/~lee/calculus/#Series-Sol

Topics in Calculus Professor Lee Lady University of Hawaii A Conceptual Approach to Applications of Integration The Derivatives of the Sine and Cosine Functions ... Review Problems for Differential Equations In my opinion, calculus is one of the major intellectual achievements of Western civilization - in fact of world civilization. Certainly it has had much more impact in shaping our world today than most of the works commonly included in a Western Civilization course books such as Descartes's Discourse on Method or The Prince by Machiavelli. But at most universities, we have taken this magnificent accomplishment of the human intellect and turned it into a boring course. Sawyer's little book What Is Calculus About? (Another book in the same vein, but more recent, is The Hitchhiker's Guide to Calculus by Michael Spivak.) For many of us mathematicians, calculus is far removed from what we see as interesting and important mathematics. It certainly has no obvious relevance to any of my own research, and if it weren't for the fact that I teach it, I would long ago have forgotten all the calculus I ever learned. But we should remember that calculus is not a mere ``service course.'' For students, calculus is the gateway to further mathematics. And aside from our obligation as faculty to make all our courses interesting, we should remember that if calculus doesn't seem like an interesting and worthwhile subject to students, then they are unlikely to see mathematics as an attractive subject to pursue further.

140. Q - Equational Programming Language An extensible functional programming language based on the term rewriting calculus. http://www.musikwissenschaft.uni-mainz.de/~ag/q/q.php

Q - Equational Programming Language Q is open source software , which means that the sources of all programs and software modules included in the Q programming system are freely available. Q is also free software which is distributed under the GNU General Public License; see the file COPYING for details. NOTE: You're looking at the new Q website on SourceForge. The old website (Q versions up to 4.5) is still available here Latest News: 15+16 May 2004: Q-Midi 1.15 and Q-Synth 1.0 have been released. 15 April 2004: Q 5.3 has been released. This is another minor update with some bug fixes and a new built-in function composition operator; see the NEWS file for details. 7 March 2004: Kari Pahula has provided Debian packages for Q 5.2 on mentors.debian.net . Thanks! Contents: About Q Add-Ons Q Multimedia Library Download ... Links About Q As a practical programming language, Q comes with batteries included : A core set of Q scripts, collectively called the "standard library", implements a lot of useful Q types and functions, such as complex numbers, additional list processing functions, "streams" (a "lazy" variant of lists), container data structures (sets, dictionaries, etc.), the lambda calculus, and even a PostScript interface. Q has its own system module, "clib", which provides access to important system functions, like binary and C-style formatted I/O, Berkeley sockets, process manipulation and regular expression routines. Moreover, the distribution also includes add-on modules for interfacing to various third-party tools and libraries, which makes Q a powerful tool for scientific programming, computer music, multimedia, and other advanced applications. A Q module for the Apache web server is now also available, which enables you to run Q scripts "on the web", too.

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