1. 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.

2. [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://xxx.lanl.gov/abs/math.AP/9906155

Mathematics, abstract math.AP/9906155 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) Links to: arXiv math find abs

3. Awesome Library - Mathematics Large resource for students of middle schools. Includes algebra, calculus, graphing, and data analysis by subject and standard. http://www.awesomelibrary.org/Classroom/Mathematics/Middle-High_School_Math/Midd

Awesome Talking Library Examples ... Keystone Family Protection Here: Home Classroom Mathematics > Middle-High School Math Middle-High School Math Sub-Topics Algebra By Subject and Standard Calculus Data Analysis ... Trigonometry Also Try Assessment Information Math Lessons Problem Solving Standards Discussions Ask Dr. Math (Math Forum) Provides organized structure for gaining answers. Award-winning site. Questions for Discussion (Droujkov and Droujkova) Provides questions for students designed to turn a boring arthmetic exercise into an exciting research adventure. 5-00 Games Math Games (FunBrain.com) Provides almost two dozen games to help teens in junior high or high school learn basic math. 7-02 Math Puzzles (Bogomolny) Provides games and puzzles that require math to solve. 9-99 Lesson Plans By Grade Level (Learning Network - TeacherVision.com) Provides dozens of math lesson plans by grade level. 5-01 By Grade Level (PBS) 8-00 By Grade Level and Topic (8-10) (British Columbia Ministry of Education) Provides math outcomes and activities by topic and grade level (8-10). 5-00 By Topic (Thinkquest Team 20991) Provides math tutorials by topic. 5-00

4. 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

5. 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 content revised 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.

6. 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.

7. Ricci-Curbastro The mathematician who developed much of tensor calculus before Einstein found a use for it. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ricci-Curbastro.html

Gregorio Ricci-Curbastro Born: 12 Jan 1853 in Lugo, Papal States (now Italy) Died: 6 Aug 1925 in Bologna, Italy Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Gregorio Ricci-Curbastro 's father was Antonio Ricci-Curbastro and his mother was Livia Vecchi. It was a family of high status known throughout the province of Ravenna. Antonio Ricci-Curbastro, although certainly never achieving anything close to the fame achieved by his son Gregorio, nevertheless was himself well known as an engineer. Neither Gregorio nor his brother Domenico attended school. All their education prior to entering university was carried out at home where their parents employed private tutors. In 1869 Ricci-Curbastro entered the University of Rome with the intention of studying mathematics and philosophy. He was only sixteen years old at the time and, although he had not attended school, he was well prepared academically. Political events, however, conspired to make Rome a somewhat unfortunate choice, although a very natural one given his place of birth. When Ricci-Curbastro began his studies in Rome, although the Kingdom of Italy had been created a few years earlier, Rome was not part of that Kingdom being part of the Papal States in which Ricci was born and brought up. Rome had been attacked by Italian troops in 1867 but France had defended the city and employed its troops against the attack. In 1870, however, Italian troops captured Rome and it became the capital of the Kingdom of Italy. Ricci-Curbastro studied at Rome for one year from 1869 to 1870 and then returned to his parents home where he remained for two years before beginning a second university career.

8. Guided Readings In Elementary Quantum Mechanics Contains guided readings in Advanced Physical Chemistry and Theoretical Chemistry, specifically, Quantum Mechanics and Statistical Mechanics, with an emphasis on chemical applications. Notice that Guided Reading means what it says, you can not simply read the material contained in this site, you must answer questions about the material as you proceed. These notes allow persons to review/carry out the algebra and calculus for standard quantum mechanical problems. http://www.sp.uconn.edu/~ch351vc/

Physical Chemistry 351 at the University of Connecticut This site contains readings in Advanced Physical Chemistry and Theoretical Chemistry, specifically, Quantum Mechanics and Statistical Mechanics, with an emphasis on chemical applications. Notice that Guided Reading means what it says, you can not simply read the material contained in this site, you must answer questions about the material as you proceed. Be forewarned that I monitor your reading progress. To use the site, please sign in (below). Note, Guests are Welcome sign in HERE! Students enrolled in this class should not use this page to access the material, but instead should sign in properly, since their work is monitored. Others can choose to log in or not, as they see fit, but I would prefer that you log in and register, so that I can keep track of who is using these materials. Thanks. Here is an interesting primer on quantum mechanics which is worth looking at: Primer These are a dsp orbital (hybrid) shown in CountourPlot3D format and Countour form.; Advanced Physical Chemistry (including Quantum Mechanics and Statistical Mechanics, with pointers to Elementary Physical Chemistry (Main Menu)

9. R. K. Shyamasundar's Home Page Tata Institute of Fundamental Research, Mumbai Real-Time and Reactive Programming, Logic Programming, Pi-calculus and Mobile Computing, Parallel Programs, Programming Languages. http://www.tcs.tifr.res.in/~shyam/

R.K. Shyamasundar Picture Address Tata Institute of Fundamental Research Bombay 400 005 India Fax: +91 22 2215 2181 Fax: +91 22 2215 2110 Tel: +91 22 2215 2971 X 2288 e-mail: TCS Group shyam[AT]tcs.tifr.res.in shyam[AT]tifr.res.in shyam[AT]acm.org Secretary, John Barretto (X 2531) TCS john[AT]tcs.tifr.res.in Research Interests and Publications Real-Time and Reactive Programming Logic Programming Pi-Calculus and Mobile Computing Parallel Programs and Scheduling ... Papers on Systems for Ecommerce Computer and Network Security Indian Association for Research in Computing Science IARCS- Charter and Membership Conferences Nineteenth International Conference on Logic Programming ICLP'03 9-13 Dec, 2003 Mumbai (Bombay), INDIA ... ASIAN' 99 Asian Computing Science Conference ISCES FSCTTCS 99 Workshop On Cluster Computing 99 Collaborators Basant Rajan N. Raja M.R.K. Krishna Rao P. Pandya ... Eric Rutten Academies Fellow, Indian Academy of Sciences Fellow, Indian National Science Academy Fellow, Indian National Academy of Engineering Fellow, The National Academy of Sciences, India Fellow, IEEE

10. Simone Martini University of Bologna, Italy Type systems for programming languages, logic in computer science, lambda-calculus. http://www.cs.unibo.it/~martini/

home contact teaching publications ... Dipartimento di Scienze dell'Informazione Simone Martini Simone Martini Professor of Computer Science Simone Martini received the Laurea degree in Scienze dell'Informazione and the Dottorato di Ricerca in Informatica (Ph.D. in Computer Science) from . He has been visitor at Digital Equipment Corporation, Systems Research Center in Palo Alto, at Stanford University , Department of Computer Science, and at His research interests are in the logical foundations of programming languages. He has written papers in lambda-calculus, type theory, linear and resource logics.

11. CyberCalc Index A detailed differential calculus tutorial. Definitions, graphs and precalculus review. http://www.npac.syr.edu/REU/reu94/williams/calc-index.html

Chapter 1: Review of Needed Topics 1.1 Graphing with Coordinates in the Plane 1.2 Slope and Line Equations 1.3 Functions and Graphs ... 3.6 Implicit Differentiation Michele Williams, Saint Michael's College, mx_williams@smcvax.smcvt.edu, also williams@npac.syr.edu T. J. Willis, twillis@npac.syr.edu Ed Bogucz, bogucz@npac.syr.edu

12. 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

13. Calculus History The main ideas of calculus developed over a very long period of time. Read about some of the mathematicians who contributed to this field of mathematics. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

A history of the calculus Analysis index History Topics Index The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians. To the Greeks numbers were ratios of integers so the number line had "holes" in it. They got round this difficulty by using lengths, areas and volumes in addition to numbers for, to the Greeks, not all lengths were numbers. Zeno of Elea , about 450 BC, gave a number of problems which were based on the infinite. For example he argued that motion is impossible:- If a body moves from A to B then before it reaches B it passes through the mid-point, say B of AB . Now to move to B it must first reach the mid-point B of AB . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Leucippus Democritus and Antiphon all made contributions to the Greek method of exhaustion which was put on a scientific basis by Eudoxus about 370 BC. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area.

14. On The Pi-Calculus And Linear Logic - Bellin, Scott (ResearchIndex) (CiteSeer) Article by Bellin and Scott showing how classical linear logic may be interpreted in the pi calculus, thus supporting Abramksy's `Proofs as Processes' thesis. http://citeseer.nj.nec.com/bellin92calculus.html

On the pi-Calculus and Linear Logic (1994) (Make Corrections) (4 citations) G. Bellin, P.J. Scott Theoretical Computer Science Home/Search Context Related View or download: profs.sci.univr.it/~be PICALCPAPER.ps Cached: PS.gz PS PDF DjVu ... Help From: profs.sci.univr.it/~bell papers (more) Homepages: G.Bellin P.Scott HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: We detail Abramsky's "proofs-as-processes" paradigm for interpreting classical linear logic (CLL) [13] into a "synchronous" version of the -calculus recently proposed by Milner [27, 28]. The translation is given at the abstract level of proof structures. We give a detailed treatment of information flow in proof-nets and show how to mirror various evaluation strategies for proof normalization. We also give Soundness and Completeness results for the process-calculus translations of various... (Update) Context of citations to this paper: More called proof nets, and the dynamics of their normalization can be used to express some aspects of concurrency [Abramsky 1993, Bellin Scott 1992 , Lafont 1989, Lafont 1990] The Curry Howard Isomorphism also states that the types of programs can be seen as formulas, and the ...of) LL into stark relief.

15. Graphing Software For Data, Algebra, Calculus And Trigonometry And Solutions Of Enter first and second order nonlinear ordinary differential in analytical form. The program will generate a numerical solution to the equations and graph multiple curves on a single graph. Can also be used for algebra and calculus formulas. Includes illustrations and free demo. http://www.hanleyinnovations.com/sgstandard.html

Software Airfoil Analysis VisualFoil VisualFoil NACA VisualFoil Lite ... Lite Sailboat Sailing- Aerodynamics Graphing Tools Graph Paper Science Graphs Smocking SmockSoft Perpetual Paper Calculators The Center of Gravity Calculator. eBooks Aerodynamics in Plain English. Services Workshops Consulting Purchase OnLine Mail Order Contact Dr. P. Hanley Tel:(352) 687-4466 PO Box 831514 Ocala, FL 34483 Dr. Hanley's Science Graphs Written by Patrick Hanley, Ph.D. Version: 2.0 Standard Standard Price Download Size: 2.73 MB Requirements Windows 95, 98, NT or 2000 Download Now!: Purchase OnLine. Order Toll Free Mail Order: Order Form. Technical: E-mail or (352) 687-4466 Qwerks, Inc . Secure On-line Purchase. Dr. Hanley's Science Graphs tm is an easy to use software package for graphing equations and data using your PC. The new version of Science Graphs can be used to generate numerical solutions of first and second order non-linear ordinary differential equations. This feature is Ideal for checking your analytical solutions against Science Graph's Numerical Answers. However, it can be used to solve problems that are too difficult to obtain by hand calculations. The software is useful for algebra trigonometry calculus , physics, differential equations and engineering . Science Graphs can also be used to graph up to 1,000 x-y data points from an ASCII file.

16. Advanced Calculus And Analysis MA1002 Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs. http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html

Next: Foreword Up: MA2001 Home Page Contents Index Advanced Calculus and Analysis Ian Craw Foreword These Notes Acknowledgements Contents ... The probability integral e d x The number e is irrational Differentiation of Functions of Several Variables Functions of Several Variables Graphing functions of Several Variables Continuity ... About this document ... Ian Craw 2002-01-07

17. 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. Online Bookshelf A number of useful probability textbooks have recently become available online. Meyn, S. and Tweedie, R., Markov Chains and Stochastic Stability Kelly, F., Reversibility and Stochastic Networks Publications Modelling the Performance of In-Call Probing for Multi-Level Adaptive Applications with Peter Key, Microsoft Research MSR Technical Report , MSR-TR-2002-06. Modelling the Performance of Distributed Admission Control for Adaptive Applications with Peter Key, Microsoft Research MAMA Workshop , June 2001 Stochastic Calculus Notes These notes provide a fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales (not just with respect to a Brownian Motion). They certainly contain all the theory usually needed for basic mathematical finance (Girsanov's theorem etc.). They do lack the martingale representation theorem. They may be downloaded and print out at about eighty pages. If you find any errors, or feel that there are serious omissions, or even just have some suggestions for improvements, please contact me by email and I shall endeavour to improve them! Contents The notes are available in various forms, but I have had reports of people experiencing trouble with the postscript versions. The idea of producing a PDF version was suggested to me by Noel Vaillant.

18. 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

Yves LAFONT professor at research at IML ) in the LDP group ( Logique de la programmation teaching at in the address : office : - phone : - fax : - e-mail : lafont@iml.univ-mrs.fr Research areas : proof theory and applications geometry of computation Papers Home page in french (with more information)

19. 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 Max-min Problems ... 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.

20. FreeMathHelp.com - Get Free Math Help In Subjects Like Algebra, Geometry, Calcul Provides games, activities, lessons, calculators for students studying algebra, geometry, calculus, or trigonometry including a daily problem. http://www.freemathhelp.com/

Math Subjects: algebra calculus geometry trigonometry ... other More Resources: ask an expert calculators competitions everyday math ... worksheets Featured Lesson: Popular Calculators: Combining Like Terms Graph Any Equation At a local highschool, 355 students are enrolled in Spanish. When the teacher decides to take a field trip, 2/3 of the boys signup and 4/7 of the girls do as well. If there are 180 boys taking Spanish, how many students are going on the trip? Featured Link: Jiskha Homework Help - Offers a message board, lessons, and many other resources in lots of different subjects, like English, foreign languages, math, and science. Forum Login: Username: Password: I forgot my password Register What is your favorite subject? Math English Science History Lunch Other recommend this site to your friends help contact suggest a site ... link to us

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