**Mathematics**- She served on the mathematics faculty of the University of British Columbia from 1957 till 1968, where she introduced numerical analysis and computer courses into the curriculum and was instrumental in the formation of the Computer Science Department. (wikipedia.org)
- Mathematics has been constantly developed into various theories, computations, algorithmic techniques, and computer software that have and will continue to assist in the solving problems in diverse topics including engineering, the sciences, physics, business, and economics. (mypursuit.com)
- Other vital and related topics include topology, discrete mathematics, numerical analysis, probability & statistics, mathematical analysis and mathematical logic. (mypursuit.com)
- In addition most colleges insist that students pursuing a major in mathematics take up a course in an affiliated area for example engineering, economics, physical sciences, or computer science etc. (mypursuit.com)
- Professor Andrew Odlyzko is a mathematician of world renown whose research interests cover large areas of pure and applied mathematics and computer science, including number heory, combinatorics, analysis, probability theory, computational complexity, cryptography, coding theory, electronic publishing, electronic commerce and economics of data networks. (umn.edu)
- Lecture Notes in Mathematics 1397: Numerical Analysis and Parallel Processing (Lancaster 1987) (P. R. Turner, ed. (nist.gov)
- It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit. (wikipedia.org)
- Mathematicians have always practised experimental mathematics. (wikipedia.org)
- Existing records of early mathematics, such as Babylonian mathematics, typically consist of lists of numerical examples illustrating algebraic identities. (wikipedia.org)
- Experimental mathematics as a separate area of study re-emerged in the twentieth century, when the invention of the electronic computer vastly increased the range of feasible calculations, with a speed and precision far greater than anything available to previous generations of mathematicians. (wikipedia.org)
- Experimental mathematics makes use of numerical methods to calculate approximate values for integrals and infinite series. (wikipedia.org)
- The use of computer tools in laboratory work, in information technology courses and in mathematics courses, enables students to learn specific skills and to greatly increase their capacity for experimenting the applied use of the knowledge that they have learned, whether under supervision or independently. (unipr.it)
- Numerical mathematics software and general explanations of methods used. (mathforum.org)
- Engineering,Computer Science and Mathematics are among the most popular majors at California Institute of Technology, located in sunny Pasadena, CA. Often compared to other well-known tech schools like MIT, Caltech stands out due to its small size and favorable student-to-faculty ratio, which students say allows for increased access to opportunities like research in top labs, access to professors, special funds and scholarships, and travel grants. (noodle.com)
- In fall of 1956, Sammet taught one of the earliest graduate-level courses in computer programming in the Applied Mathematics department of Adelphi College (now University) on Long Island. (wikipedia.org)
- The School's applied mathematics, biomedical engineering, computer science and the financial engineering program in operations research are very famous and ranked high. (wikipedia.org)
- Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. (wikipedia.org)

**women mathematicians**- In 1943 Vaughan started to work at NACA, which in 1935 had established a section of women mathematicians, who performed complex calculations. (wikipedia.org)
- She led a group composed entirely of African-American women mathematicians. (wikipedia.org)

**algebraic**- In 1887, mathematicians Heinrich Bruns and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals. (wikipedia.org)

**partial different**- Professor Arnold, the new IMA Director, is one of the world's leaders in numerical analysis of partial differential equations, particularly those dealing with mechanicsProfessor Maria-Carme Calderer. (umn.edu)
- Home of Numerica, a library of source codes for solving hyperbolic partial differential equations using a broad range of modern, high-resolution shock-capturing conservative and non-conservative numerical methods. (mathforum.org)

**engineers**- It had already ramped up airplane production, creating a great demand for engineers, mathematicians, craftsmen and skilled tradesmen. (wikipedia.org)
- Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems. (cambridge.org)
- Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. (nist.gov)
- The "open shop" consisted of programmers acting as consultants to the engineers and involved scientists who assisted them in writing and testing their routines. (wikipedia.org)

**1958**- Douglas Rayner Hartree PhD, FRS (27 March 1897 - 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of a differential analyser using Meccano. (wikipedia.org)
- From 1953 to 1958, Sammet was a mathematician for Sperry Gyroscope in New York. (wikipedia.org)

**differential equations**- Because bounding the error in Hermite interpolation in terms of the derivative which kills the interpolating space is of interest in numerical analysis and in the analysis of ordinary differential equations, there is an extensive literature on the subject. (mathforum.org)
- He joined a group working on anti-aircraft ballistics under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper. (wikipedia.org)
- With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. (wikipedia.org)

**arithmetic**- Fourth---and here we are looking further into the future---the use of systems of computer arithmetic other than floating-point should be considered. (nist.gov)
- While earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry. (wikipedia.org)

**linear algebra**- This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. (cambridge.org)
- Books include: Spectral Methods in Matlab, Finite Difference and Spectral Methods, Numerical Linear Algebra, and Spectra and Pseudospectra. (mathforum.org)

**antiquity**- The study of mechanical or "formal" reasoning began with philosophers and mathematicians in antiquity. (wikipedia.org)

**algebra**- Computer Algebra System, actually a set of tools that uses the A# language. (scriptol.com)
- The Unix and Linux versions do not contain a computer algebra subsystem. (wikipedia.org)
- In 2007, Euler was married with the Maxima computer algebra system. (wikipedia.org)

**approximations**- The general case of the three body problem does not have a known solution, and is addressed by numerical analysis approximations. (wikipedia.org)
- The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. (nist.gov)

**computational**- In recent years he has been working in the area of computational relativity, which seeks numerical solutions of Einstein's field equations. (umn.edu)
- August 15, 2009 - July 31, 2013 "A Hybrid of Theoretical and Computational Methods for Bifurcation Analysis" (co-PI) NSF Grant Number DMS-0907818, $105,000. (gmu.edu)
- It also includes period-doubling cascades during the onset of complex behavior, numerical methods for studying quasiperiodicity, and rigorous computational methods for bifurcation theory. (gmu.edu)
- Some of the most common are Computational expense: Sensitivity analysis is almost always performed by running the model a (possibly large) number of times, i.e. a sampling-based approach. (wikipedia.org)
- Computational expense is a problem in many practical sensitivity analyses. (wikipedia.org)

**proofs**- The use of computers in formal proofs, exemplified by the computer-assisted. (psu.edu)
- In the 10th century CE, the Iraqi mathematician Al-Hashimi provided general proofs for numbers (rather than geometric demonstrations) as he considered multiplication, division, etc. for "lines. (wikipedia.org)

**equations**- Analysis of Fluids and Related Topics: Well-posedness for Stochastic Continuity Equations with Rough Coefficients. (princeton.edu)
- However, I came to believe that the lack of well-posed governing equations was the major obstacle to progress in the field, and I believe that finding appropriate constitutive relations is a task better suited for physicsts than mathematicians, so I reluctantly moved on. (duke.edu)

**Computation**- she later headed the programming section of the Analysis and Computation Division (ACD) at Langley. (wikipedia.org)
- We describe a paradigm for numerical computing, based on exact computation. (psu.edu)
- 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original mass-produced computers were pocket calculators. (psu.edu)
- Indeed, Maxima is used in various Euler functions (e.g. the Newton method) to assist in the computation of derivatives, Taylor expansions and integrals. (wikipedia.org)

**mainly**- Mathematicians find employment mainly in the research and development departments of various firms. (mypursuit.com)
- Once a human-only endeavor based mainly upon changes in barometric pressure, current weather conditions, and sky condition, weather forecasting now relies on computer-based models that take many atmospheric factors into account. (wikipedia.org)
- Since then, knowledge of the subject, still fragmentary, has had to be built up by painstaking analysis of deciphered texts, mainly in numerical form, on tablets from Babylon and Uruk (no trace has yet been found of anything from the third school mentioned by Pliny). (wikipedia.org)

**algorithms**- Third, the potential offered by the ongoing increase in power of computers should be exploited with a view to reducing the number and complexity of algorithms to be used. (nist.gov)
- The main aim of the program was to create a tool for testing numerical algorithms, to visualize results, and to demonstrate mathematical content in the classroom. (wikipedia.org)

**methods**- Unlike two-body problems, there is no general closed-form solution for every condition and numerical methods are needed to solve these problems. (wikipedia.org)
- An extensive list of centers (including online services and search engines), individual libraries, other sites (general and specific), journals, books, online publications, and other resources for numerical methods. (mathforum.org)
- A prototype site funded by the National Science Foundation to bring numerical methods holistically to undergraduate students through customization of the engineering major and mathematical package of choice. (mathforum.org)
- Seeing the potential for further exploiting his numerical methods using the machine, he persuaded Sir Robert McDougall to fund a more robust machine, which was built in collaboration with Metropolitan-Vickers. (wikipedia.org)
- My research is on numerical and theoretical methods of dynamical systems. (gmu.edu)
- Since the development of rotor cipher machines in World War I and the advent of computers in World War II, the methods used to carry out cryptology have become increasingly complex and its application more widespread. (wikipedia.org)
- He also covered methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic. (wikipedia.org)

**calculations**- She specialized in calculations for flight paths, the Scout Project, and FORTRAN computer programming. (wikipedia.org)
- Charlotte Froese Fischer (born 1929) is a Canadian-American applied mathematician and computer scientist who gained world recognition for the development and implementation of the Multi-Configurational Hartree-Fock (MCHF) approach to atomic-structure calculations and for her theoretical prediction concerning the existence of the negative calcium ion. (wikipedia.org)
- She worked under the supervision of Douglas Hartree, whom she assisted in programming the Electronic Delay Storage Automatic Calculator (EDSAC) for atomic-structure calculations. (wikipedia.org)
- If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers. (wikipedia.org)

**working on mathematical**- She spent time working on mathematical analysis problems for clients and ran an analog computer. (wikipedia.org)

**discrete**- originally in mechanical controllers, and then using discrete electronics and latterly in industrial process computers. (wikipedia.org)

**2017**- Jean E. Sammet (March 23, 1928 - May 20, 2017) was an American computer scientist who developed the FORMAC programming language in 1962. (wikipedia.org)

**typically**- The choice of method of sensitivity analysis is typically dictated by a number of problem constraints or settings. (wikipedia.org)
- Other gear not typically shown on screen are an ion generator, a device that charges the air with electricity and is theorized to help spirits manifest, and the white noise generator, an audio device that makes a static background noise and is theorized to act as a catalyst for assisting entities in making EVPs. (wikipedia.org)

**science**- She is currently an emerita research professor of computer science at Vanderbilt University and a guest scientist of the Atomic Spectroscopy Laboratory at NIST. (wikipedia.org)
- ACM's special interest group on advanced multimedia applications will now be headed by Klara Nahrstedt, a computer science professor at the University of Illinois at Urbana-Champaign (UICU). (acm.org)
- In computer science AI research is defined as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of success at some goal. (wikipedia.org)
- and AI techniques have become an essential part of the technology industry, helping to solve many challenging problems in computer science. (wikipedia.org)

**practice**- The NA Digest is a collection of articles on topics related to numerical analysis and those who practice it. (mathforum.org)

**1987**- The early version of the MCHF program, published in the first volume of Computer Physics Communications received two Citation Classics Awards in 1987. (wikipedia.org)

**programmer**- In 1943, Vaughan began what developed as a 28-year-career as a mathematician and programmer at Langley Research Center. (wikipedia.org)
- Sperry Gyroscope was working on a digital computer, the Sperry Electronic Digital Automatic Computer (SPEEDAC) and asked Sammet to be their programmer. (wikipedia.org)

**system**- Finding serendipitous numerical patterns Edward Lorenz found the Lorenz attractor, an early example of a chaotic dynamical system, by investigating anomalous behaviours in a numerical weather model. (wikipedia.org)
- Sample topics include analysis of spring-mass system and numerical integration. (jointmathematicsmeetings.org)
- The Euler core is a numerical system written in C/C++. (wikipedia.org)
- Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs. (wikipedia.org)
- The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes, including: Testing the robustness of the results of a model or system in the presence of uncertainty. (wikipedia.org)

**Maxima**- Symbolic expressions and other functions were added to communicate with Maxima, and to reach a good degree of integration into the numerical Euler core. (wikipedia.org)

**FORTRAN**- Vaughan became proficient in computer programming, teaching herself FORTRAN and teaching it to her coworkers to prepare them for the transition. (wikipedia.org)

**software**- Information about MicroWorlds Logo (Windows 95) computer programming software for kids, from satisfied customer and dealer Don Sleeth. (mathforum.org)
- Euler (now Euler Mathematical Toolbox or EuMathT) is a free and open-source numerical software package. (wikipedia.org)

**1949**- In 1949, she became acting supervisor of the West Area Computers, the first African-American woman to supervise a group of staff at the center. (wikipedia.org)
- In 1949, Vaughan was assigned as the acting head of the West Area Computers, taking over from a white woman who had died. (wikipedia.org)
- When Sammet first encountered a computer, in 1949 at the University of Illinois, she was not impressed, considering it an obscene piece of hardware. (wikipedia.org)

**symbolic**- She joined IBM in 1961 where she developed FORMAC, the first widely used computer language for symbolic manipulation of mathematical formulas. (wikipedia.org)

**include**- His major honors and recognitions include the first Giovanni Sacchi Landriani Prize of the Milan Academy of Arts and Letters and an invitation to give a Plenary Lecture at the International Congress of Mathematicians in Beijing in August 2002. (umn.edu)
- Professor Maria-Carme Calderer is a well known applied mathematician whose research interests include mathematical studies of liquid crystals. (umn.edu)
- His major honors include an invited one-hour address at the annual AMS meeting, Pittsburgh 1981, as well as an invited lecture at the International Congress of Mathematicians, Berkeley 1986. (umn.edu)

**application**- Although one's first exposure to computers today is likely to be some non-numerical application, numeri. (psu.edu)
- The discovery and application, early on, of frequency analysis to the reading of encrypted communications has, on occasion, altered the course of history. (wikipedia.org)

**formal**- This insight, that digital computers can simulate any process of formal reasoning, is known as the Church-Turing thesis. (wikipedia.org)

**Berkeley**- Upon his return to Berkeley, he made plans for building the California Digital Computer (CALDIC) with Paul Morton and Leland Cunningham. (wikipedia.org)

**American**- Dorothy Johnson Vaughan (September 20, 1910 - November 10, 2008) was an African American mathematician and human computer who worked for the National Advisory Committee for Aeronautics (NACA), and NASA, at Langley Research Center in Hampton, Virginia. (wikipedia.org)
- Derrick Henry "Dick" Lehmer (February 23, 1905 - May 22, 1991) was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas-Lehmer test for Mersenne primes. (wikipedia.org)

**mechanical**- Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day. (wikipedia.org)

**cryptography**- Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which he described the first cryptanalytic techniques, including some for polyalphabetic ciphers, cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis. (wikipedia.org)

**scientist**- She is the widow of Patrick C. Fischer, himself a noted computer scientist and former professor at Vanderbilt. (wikipedia.org)

**general**- The numerical examples that may have led a mathematician to originally formulate a general theorem were not published, and were generally forgotten. (wikipedia.org)

**1961**- Vaughan moved into the area of electronic computing in 1961, after NACA introduced the first digital (non-human) computers to the center. (wikipedia.org)

**skills**- In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 - his advisor was Ernest Rutherford. (wikipedia.org)

**group**- Mathematician Katherine Johnson was initially assigned to Vaughan's group, before being transferred to Langley's Flight Mechanics Division. (wikipedia.org)
- Links to books and recent papers by the head of the Numerical Analysis Group at Oxford University. (mathforum.org)

**digital**- During investigations, the TAPS ghost hunters team use various equipment, including digital thermometers, EMF meters, thermographic and night vision cameras, handheld and static digital video cameras, digital audio recorders, and laptop computers. (wikipedia.org)

**invention**- The invention of the frequency-analysis technique for breaking monoalphabetic substitution ciphers, by Al-Kindi, a Arab mathematician sometime around AD 800 proved to be the single most significant cryptanalytic advance until World War II. (wikipedia.org)

**instead**- Starting around the third season, the team has used the K-2 (or K-II) meter, a type of EMF meter that uses a series of LEDs to measure the strength of an energy field instead of a numerical LCD screen. (wikipedia.org)

**tool**- An interactive tool designed to assist farm managers in assessing the strength of their management position. (mathforum.org)
- Based on the techniques of Dr. David Kohl, this tool will analyze responses from several key areas and provide recommendations and benchmark analysis. (mathforum.org)

**models**- then, a setting reveals the mathematicians of an desired models, or a t topics contacts. (ecombinatii.ro)
- In models involving many input variables, sensitivity analysis is an essential ingredient of model building and quality assurance. (wikipedia.org)

**comprehensive**- The book contains the source code of a comprehensive numerical library in Java. (mathforum.org)

**students**- Created to enable students at the Darmount College to use computers, it became widespread with personal computers. (scriptol.com)