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Studying Applied Mathematics Applied mathematics quantifies and explains observed physical, social or business phenomena, but also to predict possible outcomes.By using mathematical methods and models, applied and computational mathematics can solve real-world issues, such as materials analysis and processing, weather forecasting, financial services, network management or more about studying Applied Mathematics Is Applied Mathematics the right study option for you? Take the test! Studying in United States The U.
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It has an internationally renowned education system, and offers a huge variety of English-language courses and speciality more about studying in United States Are you sure you can handle the weather in United States? Take the country test! Testimonial Registration Module I call StudyPortals an engine for choice because you will virtually find universities and courses.It offers you any information you want in the course of your search for overseas studies SIAM Graduate Education for Computational Science and Engineering.It offers you any information you want in the course of your search for overseas studies.StudyPortals offers great information and listings SIAM Graduate Education for Computational Science and Engineering.
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That allowed me the ease of not only finding courses I was interested in, but also giving me contact information and much more.STUDENTSEducational Resources SIAM Working Group on CSE Education 1.Introduction Computation is now regarded as an equal and indispensable partner, along with theory and experiment, in the advance of scientific knowledge and engineering practice.Numerical simulation enables the study of complex systems and natural phenomena that would be too expensive or dangerous, or even impossible, to study by direct experimentation.
The quest for ever higher levels of detail and realism in such simulations requires enormous computational capacity, and has provided the impetus for dramatic breakthroughs in computer algorithms and architectures.
Due to these advances, computational scientists and engineers can now solve large-scale problems that were once thought intractable.Computational science and engineering (CSE) is a rapidly growing multidisciplinary area with connections to the sciences, engineering, mathematics and computer science.CSE focuses on the development of problem-solving methodologies and robust tools for the solution of scientific and engineering problems.We believe that CSE will play an important if not dominating role for the future of the scientific discovery process and engineering design.It is natural that SIAM, as the society whose aim is to foster the computational and applied mathematics which is at the core of CSE, should play a role in the growth and development of this new discipline.
The objectives of this report are to attempt to define the core areas and scope of CSE, to provide ideas, advice and information regarding curriculum and graduate programs in CSE, and to give recommendations regarding the potential for SIAM to contribute.What is it? CSE is a broad multidisciplinary area that encompasses applications in science/engineering, applied mathematics, numerical analysis, and computer science.
Computer models and computer simulations have become an important part of the research repertoire, supplementing (and in some cases replacing) experimentation.Going from application area to computational results requires domain expertise, mathematical modeling, numerical analysis, algorithm development, software implementation, program execution, analysis, validation and visualization of results.One point we would like to emphasize in this document is that CSE is a legitimate and important academic enterprise, even if it has yet to be formally recognized as such at some institutions.Although it includes elements from computer science, applied mathematics, engineering and science, CSE focuses on the integration of knowledge and methodologies from all of these disciplines, and as such is a subject which is distinct from any of them.
What is it not? CSE makes use of the techniques of applied mathematics and computer science for the development of problem-solving methodologies and robust tools which will be the building blocks for solutions to scientific and engineering problems of ever-increasing complexity.It differs from mathematics or computer science in that analysis and methodologies are directed specifically at the solution of problem classes from science and engineering, and will generally require a detailed knowledge or substantial collaboration from those disciplines.The computing and mathematical techniques used may be more domain specific, and the computer science and mathematics skills needed will be broader.
It is more than a scientist or engineer using a canned code to generate and visualize results (skipping all of the intermediate steps).Research in CSE Research in CSE involves the development of state of the art computer science, mathematical and computational tools directed at the effective solution of real-world problems from science and engineering.CSE in science and industry Although some researchers have been doing what might now be called CSE research for quite some time, for a number of reasons we appear to be at a critical juncture in terms of the role being played by simulation in science and industry.Historically, simulation has been used as a qualitative guide for design and control, but has often not been expected to provide accurate results for realistic physical systems.Increasingly, simulation is being used in a more quantitative way, as an integral part of the manufacturing, design and decision-making processes, and as a fundamental tool for scientific research.
Problems where CSE has played and is expected to continue to play a pivotal role include: Weather and climate prediction.Future energy and environmental strategies will require unprecedented accuracy and resolution for understanding how global changes are related to events on regional scales where the impact on people and the environment is the greatest.Achieving such accuracy means bringing the resolution used in weather forecasting to the global predictions, which is not practical currently because of the very large amounts of data storage and long computation times that are required.A major advance in computing power will enable scientists to incorporate knowledge about the interactions between the oceans, the atmosphere and living ecosystems, such as swamps, forests, grasslands and the tundra, into the models used to predict long-term change.Climate modeling at the global, regional and local levels can reduce uncertainties regarding long term climate change, provide input for the formulation of energy and environmental policy, and abate the impact of violent storms.
Accurate simulation of combustion systems offers the promise of developing the understanding needed to improve efficiency and reduce emissions as mandated by U.Combustion of fossil fuels accounts for 85% of the energy consumed annually in the U.
and will continue to do so for the foreseeable future.Achieving predictive simulation of combustion processes will require terascale computing and an unprecedented level of integration among disciplines including physics, chemistry, engineering, mathematics and computer science.While new weapon production has ceased, the ability to design nuclear weapons, analyze their performance, predict their safety and reliability, and certify their functionality as they age is essential for conscientious management of the enduring U.
Dramatic advances in computer technology have made virtual testing and prototyping viable alternatives to traditional nuclear and nonnuclear test-based methods for stockpile stewardship.Rudimentary versions of virtual testing and prototyping exist today.
However, to meet the needs of stockpile stewardship for the near future requires high-performance computing far beyond our current level of performance.
1 The ability to estimate and manage uncertainty in models and computations is critical for this application, and increasingly important for many others.Simulation, design and control of vehicles.It is now standard practice in the design of mechanical systems such as vehicles, machines or robots to use computer simulation to observe the dynamic response of the system being designed.Computer-aided design drastically reduces the need to construct and test prototypes.Simulation is used not only to improve performance, but also for safety and ergonomics.
Real-time simulation with operator in the loop and/or hardware in the loop presents substantial challenges for algorithms and software.Since the early days of computing, computational simulation has been used in the performance analysis and design of aircraft components, such as the analysis of lift and drag of airfoil designs.As computations become more sophisticated and computers more powerful, computational simulation is used as an essential tool in the complete design process.For example, the Boeing 777 was the first jetliner to be 100% digitally designed, using 3D solid modeling.
Throughout the design process, the airplane was preassembled on the computer, eliminating the need for a costly full-scale mark-up.CSE will play an increasing important role in the entire design and analysis process as capabilities improve for such things as numerical modeling of combustion for engine design.Electronic design automation and CSE have long had a symbiotic relationship.Modern electronic systems (most notably the microprocessors that have enabled CSE to achieve its current prominence) are extraordinarily complex.
The development of such systems is only possible with the aid of computational tools for simulation and verification of the systems as part of the design process.Computation plays an important role at all levels of electronic design, from simulating the processes used to fabricate semiconductor devices, to simulating and verifying the logic of a microprocessor system, to laying out the floor plan of VLSI circuitry.CSE tools are critical in the exploration of scientific areas such as astrophysics, quantum mechanics, relativity, chemistry and molecular biology, where experiments are difficult and expensive if not impossible 9 , and in analyzing the reams of experimental data and developing models in emerging areas such as: Biology.CSE technologies are rapidly becoming indispensable to the biological and medical sciences.Simulation plays a major role in the conceptual development of medical devices, both those used in diagnostic procedures (electromagnetic, ultrasonic, etc.
) and in design of artificial organs (hearts, kidneys, etc.Biomedical optics depend heavily on computational modeling in uses in detection and treatment in oncology, opthalmology, cardiology, and physiology.Computational modeling plays a fundamental role in the emerging efforts to combine mathematics and biology in the genomic sciences (genome sequencing, gene expression profiling, genotyping, etc.In this area one needs large scale simulations with complex computational models to develop new theoretical/conceptual models and understanding of molecular level interactions.Computational chemistry (CC) is widely used in academic and industrial research., very often are more reliable than experimentally determined ones.According to "Chemical & Engineering News," the newsletter of the American Chemical Society, Computational Chemistry has developed from a "nice to have"' to a "must-have"' tool 2 .The main incentive of CC is the prediction of chemical phenomena based on models which relate either to first principles theory ("rigorous models"), to statistical ensembles governed by the laws of classical physics or thermodynamics, or simply to empirical knowledge.In real problem solving situations, these models are often combined to form "hybrid models" where only the critical part of the problem is treated at the rigorous level of theory.Rigorous theory in the molecular context is synonymous with quantum mechanics, i.
, solving the Schr dinger equation for a molecular complex with or without the presence of external perturbation (photons, electric fields, etc.There are a number of methods available which provide approximate solutions to the Schr dinger equation (Hartree-Fock and Density Functional theory, e.Simulation is used to predict properties of large and complex entities such as a liquid, the folding of a protein in solution, or the elasticity of a polymer.Finally, empirical models most often try to establish correlations between the structure of a molecule and its (pharmaceutical) activity.Simulations and quantum chemical calculations, on the other hand, very often are extremely compute-intensive due to the number of degrees of freedom and the complexity of the terms to be evaluated.The high accuracy required in these calculations sets restrictions with regard to the method used to solve the partial differential equations (PDEs) involved.
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Further information is available at the website for the International Union of Pure and Applied Chemistry 7 .The challenge in materials research is to invent new materials and to perfect existing ones by fabrication and processing so that they have the desired performance and environmental response 8 .For example, there are many new and important applications for thin films, including silicon-based microelectronics, compound semiconductors, opto-electronics devices, high-temperature superconductors and photovoltaic systems Study an MSc in Applied Mathematical Sciences at the multi-award-winning University of Strathclyde. Join over 22000 students from 100+ countries..
For example, there are many new and important applications for thin films, including silicon-based microelectronics, compound semiconductors, opto-electronics devices, high-temperature superconductors and photovoltaic systems.
The growth of such thin films, which can be accomplished via processes such as chemical vapor deposition (CVD), is sensitive to many factors in the manufacturing process.
Simulation is an essential tool for understanding this process, and requires the development of mathematical models and computational techniques.Process control, which is an order of magnitude more computationally complex than simulation, is emerging as an essential tool in fabrication 4 .Recently, large scale complex computational modeling has been used to design high pressure, high throughput CVD reactors to be used as enabling devices in the production of new and exotic materials.Historically, engineers have used chemistry, thermodynamics, and transport to design chemical processes.
Now these fundamental processes are applied to the understanding of complex biological phenomena that are governed by the same physical laws.Computer models are being used to understand and to develop treatments for glaucoma, to understand and to fabricate bioartificial materials for example bioartificial arteries, and for studying the normal and pathologic response of soft hydrated tissues in the human musculoskeletal system 11, 10 .Enabling technologies for CSE Growth in the expectations for and applications of CSE methodology has been fueled by rapid and sustained advances over the past twenty years of computing power and algorithm speed and reliability (see diagram below), and the emergence of software tools for the development and integration of complex software systems and the visualization of results.
In many areas of science and engineering, the boundary has been crossed where simulation, or simulation in combination with experiment is more effective (in some combination of time/cost/accuracy) than experiment alone for real needs.Educational Objectives In addition to a background in mathematics and computer science, a CSE graduate must have a thorough education in an application area (engineering discipline or science).
The CSE graduate's mathematical knowledge will be sufficient to model technological and scientific problems.Knowledge of computer science, and in particular numerical algorithms, software design and visualization, enable the CSE graduate to make efficient use of computers.A graduate knows how to find and exploit software (-packages) for a certain task.A CSE student performs interdisciplinary work in mathematics, computer science and an application area.A CSE graduate is trained to communicate with and team with an engineer or physicist and/or a computer scientist or mathematician to solve difficult practical problems.
Relevant background We describe below the background that a well-prepared undergraduate will have had before entering a CSE program.It is expected that many students will be strong in several of the areas but may need to acquire expertise in other areas during the initial stages of graduate study.Mathematics and computer science Calculus Data structures and algorithms Physics Fluid dynamics 1.Mathematics and computer science Numerical analysis (linear algebra and optimization, ordinary and partial differential equations) Applied mathematics (ordinary differential equations, dynamical systems, partial differential equations, mathematical modeling) Computing (languauges/operating systems/networking; parallel/distributed) Data Analysis (visualization, statistical methods) We note that in many institutions there is much redundancy and overlap between courses for example in numerical analysis or applied mathematics being taught in various engineering departments and mathematics.
It may be advantageous to have a single core track, perhaps adding special sections for discipline-specific material if that is deemed to be necessary.This has the obvious advantage of cost-effectiveness, enabling even relatively small institutions to start a CSE program.Perhaps even more importantly, it gives the students a common educational foundation for the more advanced courses, and exposes them to other students and faculty with a wide variety of interests in computer science, mathematics, science and engineering.It is absolutely essential that interdisciplinary collaboration be an integral part of the curriculum and the thesis research.Courses should include projects and presentations whenever possible.A CSE graduate should have working knowledge in an application area like Computational physics Astronomy Semiconductor simulation Interdisciplinary collaboration can be accomplished via participation in a multidisciplinary research team and/or internship at a National Laboratory or in industry.Graduate Degree Programs and Models Two general models for the organization of CSE graduate degree programs have emerged.In the first model, a graduate degree is awarded in the new discipline of CSE.Often in this model the CSE program resides within an existing department, usually mathematics or computer science.In the second model, graduate degrees are awarded in the traditional disciplines of mathematics, computer science, science and engineering, with an area of specialization of CSE.The CSE programs residing in different departments usually share a core curriculum and a basic set of standards for graduation with the CSE specialization.
Here we describe several existing programs which illustrate the two models.MS/PhD in CSE CSE at Stanford University.
The Scientific Computing and Computational Mathematics Program at Stanford University was established in 1987 and is a graduate degree (M.) awarding unit comprised of faculty from a variety of departments, including Mathematics, Computer Science, Operations Research, Statistics, Chemical Engineering, Mechanical Engineering and Electrical Engineering.
It was established in recognition of the need for graduate-level training at the intersection of the disciplines of mathematics and computer science, which at the same time draws on applications of fundamental scientific or technological importance.students must complete, are two year-long sequences, one in Numerical Analysis the other in Methods of Mathematical Physics.student must complete a year of courses in a focused application area, a year of courses in Computer Science (Parallel Computing or Data Structures and Algorithms are common choices) and further courses in Applied Mathematics and Numerical Analysis.The choice outside the core sequences is very broad, allowing the flexibility desirable in a Program of this scope, while the core sequences ensure a sound intellectual basis for the Program and a commonality among the students.work falls into two broad categories: theoretical studies of computational algorithms for the solution of problems in applied and computational mathematics, and the development and application of novel software for the solution of problems of scientific or engineering significance.
Students in the former category typically work with faculty from Computer Science, Mathematics, Operational Rerearch or Statistics while those in the second category work with advisors rooted in specific application domains; occasional joint supervision of research also occurs and is encouraged.graduates of the Program a significant proportion (roughly 45%) have moved on to academic positions, typically in applied and computational mathematics environments.The remainder are distributed throughout government labs and industry.
At the University of Texas at Austin, CSE is known as CAM (Computational and Applied Mathematics) but all six departments of the College of Engineering are strong contributors to the program.There are a number of special features of the CAM program at Texas that are noteworthy: CSE is an independent academic program leading to the Ph.in CAM, which reports directly to the Graduate School.
It has its own curriculum, although at present all courses are jointly listed, with some offered by participating departments, each with its own oversight committee that is involved in management of the program and its graduate students.Fourteen academic departments participate in the CAM program, including Mathematics, Computer Sciences, Aerospace Engineering and Engineering Mechanics, Chemical Engineering, Petroleum and Geophysical Engineering, Electrical Engineering, and Physics.Each member of the CAM Graduate Studies Committee is a faculty member from one of the participating departments.There is an organized research center associated with the program called TICAM---The Texas Institute for Computational and Applied Mathematics.The mission of TICAM is to develop, organize, and administer programs in basic and applied research in areas of applied mathematics and computational sciences that deal with mathematical modeling and computer simulation.
Each student is expected to demonstrate a graduate level proficiency in three areas.This has traditionally included functional analysis, partial differential equations, and mathematical physics but could include mathematics or other areas of applicable mathematics.Area B is Numerical Analysis in Scientific Computation, including a significant block of course work in computer sciences, architecture, parallel computing, etc.Area C is Mathematical Modeling and Applications.
This is an intellectually rich area in which course work may be selected from one or more participating departments.Typical Area C options are acoustics, computational fluid mechanics, electromagnetics, quantum mechanics, kinetic theory, solid mechanics, materials science, and, most recently, computational finance).Students take written exams in all of these areas except Area B where traditionally an oral exam is given.Each student's dissertation is expected to reflect components of all three areas.Advisory Committees must have representatives from all three areas, as does the Graduate Studies Committee that manages the overall program.Faculty in the program hold tenure in one of the participating departments.There is a written document, signed by the Deans of the Colleges of the participating departments, that guarantees that all participants in the program will be judged in matters of promotion, merit raises and tenure on the basis of their contribution to the CAM program independently of their contributions to their individual departments.
MS/PhD in traditional area, with specialization in CSE CSE at University of Illinois.The purpose of the CSE Option at the University of Illinois is to foster interdisciplinary, computationally oriented research among all fields of science and engineering, and to prepare students to work effectively in such an environment.Students electing the CSE Option become proficient in computing technology, including numerical computation and the practical use of advanced computer architectures, as well as in one or more applied disciplines.
Such proficiency is gained, in part, through courses that are designed to reduce the usual barriers to interdisciplinary work.Thesis research by CSE students is expected to be computationally oriented and actively advised by faculty members from multiple departments.CSE is administered by a Steering Committee composed of one representative from each participating department and chaired by the Director of CSE.All faculty members affiliated with CSE have regular faculty appointments in one of the participating departments.CSE is sponsored by the College of Engineering, but it is not limited to academic departments within the College.
Departments involved include Aeronautical and Astronautical Engineering, Atmospheric Sciences, Chemical Engineering, Civil Engineering, Computer Science, Electrical and Computer Engineering, Materials Science and Engineering, Mathematics, Mechanical and Industrial Engineering, Nuclear Engineering, Physics and Theoretical and Applied Mechanics.CSE is a cooperative effort among the participating departments.Each participating department has its own specific requirements for its CSE option, but all are similar and share the common goals of the program.Details are available by accessing the CSE website.3 Upon satisfying the degree requirements of the student's graduate department and the CSE requirements, the student is awarded a CSE Certificate signifying successful completion of the CSE Option.
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Students must first be admitted to one of the participating departments before enrolling in the CSE Option.All CSE courses are cross-listed with several of the participating departments.CSE instruction includes both core and advanced courses Overview. This course offers excellent training in advanced pure and applied mathematics, together with a range of more specialised options, equipping students with a range of mathematical skills in problem solving, project work and presentation. The very broad choice of courses, covering all areas of applied mathematics .CSE instruction includes both core and advanced courses.
A sampling of CSE courses includes numerical methods, parallel programming, computer architecture, combinatorial algorithms, data structures, software design, computer methods in civil engineering, computational solid and fluid mechanics, finite element analysis, computational aerodynamics, computer simulation of materials, parallel numerical algorithms, scientific visualization and grid generation.The CSE Program at Purdue University is an interdisciplinary graduate program that started in Fall 1995.It offers specializations in Computational Science and Computational Engineering in 17 departments across the schools of Purdue .It offers specializations in Computational Science and Computational Engineering in 17 departments across the schools of Purdue.Specializations are offered at both M.The CSE Program at Purdue provides students with the opportunity to study a specific science or engineering discipline along with computing in a multidisciplinary environment.The aim of the program is not to produce a student with parts of two degrees, but rather a student who has leaned how to integrate computing with another scientific or engineering discipline and is able to make original contributions in both disciplines.The expected course load and examinations for students in this program are roughly the same as for M.D degrees in other disciplines at Purdue, with approximately one third of the course load and examinations from computing and two thirds in the student's home department.For students whose home department is Computer Science or Computer Engineering, one third of the course load will be from outside department application areas.level are offered by Agricultural Economics, Agronomy, Biological Sciences, Chemistry, Computer Sciences, Earth and Atmospheric Sciences, Electrical Engineering, Food Science, Industrial and Physical Pharmacy, Mathematics, Mechanical Engineering, Medicinal Chemistry and Pharmacology, Nuclear Engineering, Pharmacy Practice, Physics, Psychological Sciences, and Statistics.Students must be admitted both to one of these departments and to the CSE program.The degree is awarded in the home department with the specialization Computational Engineering or Computational Science indicated on the transcript.
The program is administered by the CSE Graduate Committee with representation from participating departments.CSE requirements are tailored to the home department's requirements.Students are expected to have a strong interest in computation and its application to science and engineering.Their undergraduate training is expected to have given them a strong foundation in several areas of science, engineering and computing 12 .CSE programs in Europe We discuss CSE programs in Europe separately from those in North America because of the differences in structure of the educational systems, although there is also much in common.In Europe there are strong activities in CSE.
For example, a curriculum was started in 1997, at the Royal Institute of Technology in Stockholm, Sweden.
Interdisciplinary application oriented and problem solving curricula that take into account computer simulation have been introduced into the U.in recent years under the label Computational Science and Engineering (CSE).Related curricula called "Industrial Mathematics" or "Technical Mathematics" have been introduced earlier at various places, e.Jeltsch (Mathematics) took up the discussion on CSE in 1995.They were supported by the Executive Board of the ETH Zurich which nominated a committee with two more members, W.In April 1996 this committee worked out a curriculum relying on existing courses at ETH, a cost neutral approach without a need for additional personnel.The concept for the curriculum CSE was accepted by the Executive Board ETH in July 1997 and the program began in October 1997.5 years (9 semesters) of diploma studies at ETH, the CSE curriculum takes only 2.
5 years and builds upon knowledge acquired in the first two years of a classical discipline.Candidates for the CSE curriculum must take two years of basic studies in Mechanical or Electrical Engineering, Computer Science, Chemistry, Mathematics, and Physics at ETH, or elsewhere.Depending on their first studies the students have to close the "gaps" between those first two years of studies and the model undergraduate studies for the CSE curriculum.CSE graduates are able to work on interdisciplinary problem solving in an application area making use of knowledge in mathematics and computer science.Outline of the Curriculum The core courses are mandatory.
One field of specialization is to be chosen.The core courses are: theory and numerical techniques of differential equations, optimization, parallel computing, computational quantum mechanics, computational statistical mechanics, software engineering, and visualization/graphics.The specialization fields are: physics of the atmosphere, computational chemistry, computational fluid dynamics, control theory, robotics and computational physics.Further information is available at the ETH CSE website 6 .International Master Program in Scientific Computing at the Department of Numerical Analysis and Computing Science, Royal Institute of Technology (KTH), Stockholm, Sweden.
KTH, founded in 1827 and the largest of Sweden's six universities of technology, has extensive international cooperation both in research and education.About 30% of the regular students spend one year of their studies at some university abroad and the KTH Master Programs were started to strengthen internationalization.The programs are given in English with tuition free of charge.A limited number of grants from the Swedish Institute is available to cover living expenses.The International Master Program in Scientific Computing, hosted by the Department of Numerical Analysis and Computing Science, was initiated in 1996.
It is open for students from all over the world with a BSc/BEng or equivalent with a very good background in mathematics and knowledge in numerical methods.Applicants are also required to be experienced in programming and to have good overview of at least one application area relevant to scientific computing, such as fluid dynamics, solid mechanics, or electromagnetics.The duration of the Program is one and a half years, with one year of courses and projects and half a year of thesis work.The first class was enrolled in 1997 with eight students.The program now attracts more than 100 applications, and 20 students from more than 10 countries were accepted to enroll autumn 1999.
In the first week at KTH, the last before the official term starts, the students are given an intensive course in the computer environment and MATLAB and C programming.After this immersion the term proper starts with lectures, labs, and project work.The regular courses are: First semester Applied numerical methods The finite element method High performance computing The thesis work is started at the end of the second semester and completed during the third semester.Throughout the entire program there are projects within the courses and projects running through several of the courses.Requirements for Graduation: To obtain a Master Degree in Scientific Computing at KTH the students must pass written exams on the six compulsory courses and at least three eligible courses.
All labs and projects shall be completed and the thesis shall be presented orally in a seminar and as a written technical report.More information about the program can be found on the web page 5 .Impact of educational structure for CSE education in Europe vs.In North America every child goes to high school and graduates at the age of 18.
After that most continue with a college education, and some continue their studies at a university.Selections are done by the colleges and universities themselves.In Europe the selection of university students is often done at an earlier stage.Though there are great differences in the evaluation process, in principle schools of different intellectual level exist in parallel.To enter a school of higher level, an entrance exam has to be passed.
As an example we consider Switzerland.We distinguish three levels: Level 1.Primary School: Nine school-years from age 7-16.Children who remain in this school will typically become factory workers or do some other less intellectually challenging work.
Secondary School: The entrance exam takes place after the first four or five years of primary school.The school also terminates at the age of 16.Typically a graduate of secondary school will continue with a 3-4 year apprenticeship and become a craftsman like a car mechanic, an optician or a bookkeeper.Gymnasium: In secondary school (at the age of about 13) another exam can be taken to pass into the Gymnasium.This school takes another six years and finishes with an exam, called Matura, at the age of 19.Passing the Matura means being mature for an university and every university in Switzerland will accept the person as a student.The Matura level differs from country to country in Europe.Only about 18% of the children in Switzerland pass the Matura.
The European mean is about 30% with exceptions like France with about 50% doing the "Baccalaureat.
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This title is roughly equivalent to a M.Persons who have completed secondary school and an apprenticeship have the possibility to take an entrance exam to one of the "Fachhochschulen" ("Universities of Applied Sciences").These institutions may be best compared with colleges and their diploma after three years of studies is generally accepted to be equivalent to a North American B Study Applied Mathematics at universities or colleges in United States - find 136 Master Applied Mathematics degrees to study abroad. The Department of Mathematics, Applied Mathematics, and Statistics at Case Western Reserve University is an active center for mathematical research. Faculty members conduct .These institutions may be best compared with colleges and their diploma after three years of studies is generally accepted to be equivalent to a North American B.
Discussion: structure of CSE graduate programs It is clear that two major models for structuring graduate programs in CSE have emerged, and that both have proven to be successful at various universities.When considering the creation of a new program, the model to be chosen and its chances for success will be highly dependent on local academic strengths and political considerations The Mathematics Department at UCL is an internationally renowned department which carries out excellent individual and group research applying modelling techniques The standard entry requirement for the masters course in Mathematical Modelling is a very good undergraduate degree (certainly more than 60%) in a .
When considering the creation of a new program, the model to be chosen and its chances for success will be highly dependent on local academic strengths and political considerations.
There is much in common in terms of basic academic content between the two models.Comparing the two models directly is difficult.The degree in CSE may allow a more focused and cohesive program, since this program is often implemented within a single department such as mathematics or computer science, or within a separate academic unit.On the other hand it may be difficult to achieve depth within this type of program, especially for the application areas, or to distinguish this program from applied mathematics.
Since CSE is an emerging area, employment possibilities for students with the CSE degree are not well documented.There is a strong feeling that the current climate is highly favorable toward interdisciplinary work in science and engineering.One argument in favor of the degree in traditional disciplines, with specialization in CSE, is that employers and in particular universities and industry may be more open to this more traditional degree structure.Broadening the CSE Student Experience It is absolutely essential that interdisciplinary collaboration be an integral part of the curriculum and the thesis research.
There are a number of ways in which this can be achieved.Courses should include multidisciplinary projects and presentations whenever possible.Participation in a multidisciplinary research team.Internship at a National Laboratory or in industry.
The NSF National Partnership for Advanced Computational Infrastructure (NPACIs) in the U.
has programs in place to assist in CSE education.Two excellent online news magazines provide up-to-date summaries of the activities of the NPACIs: /npaci/online/ and the National Computational Science Alliance (NCSA) /.The focused education programs are summarized through the cooperative EOT-PACI (Education, Outreach and Training) Web Site for both PACIs /.There are Research Experience for Undergraduates (REU) opportunities coordinated through the EOT-PACI and details for applying are provided.
Define the core areas and scope of this field.Examine SIAM's existing journals and determine whether there is a place for CSE research as we have defined it.Establish a special interest group (SIAG) on CSE.Create an electronic CSE Bulletin Board that would include the following: discussion forum; pointers to graduate degree programs; infrastructure for universities, government and industry to post internship opportunities and for students to post resumes; infrastructure for universities, government and industry to post job opportunities and for job seekers to post resumes 7.Publish information of use for CSE education, for example articles specifically oriented to teaching in CSE programs or courses.Acknowledgments We would like to thank our colleagues, Andrew Stuart and Gene Golub of Stanford University, Lennart Edsberg of KTH, Peter Arbenz and Kaspar Nipp of ETH Zurich, the SIAM Education Comittee and the SIAM Council and Board for their input and advice, and Laura Helfrich of the SIAM office for her assistance in creating this report.The SIAM Working Group on CSE Education The SIAM Working Group on CSE Education was formed in November 1998 to study the recent developments in CSE Education and to give recommendations regarding SIAM's potential role.The Working Group was comprised of: Prof.
Linda Petzold (University of California Santa Barbara, Chair); Prof.Uri Ascher, University of British Columbia; Prof.Thomas Banks, North Carolina State University; Dr.Leslie Greengard, Courant Institute of Mathematical Sciences, New York University; Prof.Michael Heath, University of Illinois at Urbana-Champaign; Prof.Andrew Lumsdaine, Notre Dame University; Dr.Tinsley Oden, University of Texas Austin; Prof.Robert Schnabel, University of Colorado Boulder; Prof.Kris Stewart, San Diego State University; and Dr.Anne Trefethen, Numerical Algorithms Group (NAG).
References 2 Chemical and Engineering News, May 1997.Program goals and structure The Master's Degree Program in Applied Mathematics is specially designed to prepare graduates for a successful career in today's industrial/business world.Accordingly, the program is structured into the following three components: a core of graduate courses in applied subjects within the Department of Mathematics and Statistics; a selection of advanced courses in other departments including, but not limited to, these; a group project in which an applied scientific problem is undertaken in a colloborative effort.The graduate courses in the Department concentrate on Analytical Methods, Numerical Methods, and Probability/Statistics.These two-semester courses sequences give the student a thorough background in advanced applied mathematics.
The elective courses outside the Department are determined depending on each student's interests and preparation.In recent years, they have been chosen from Computer Science, Engineering (Industrial, Mechanical, Electrical), Physics, and Management Science.These courses expose the student to the use of practical mathematical tools by scientists and engineers.The group project is the most novel component of this program.
It is intended to emulate industrial teamwork on a large, technical problem.
Through the combined efforts and diverse talents of the group members, a mathematical model is developed, a computer code is implemented, and a final report is written.In the process, the students learn how to start solving a new and hard problem, how to make a professional presentation of their work, and how to collaborate effectively with their coworkers.Student experiences and employment How is student life in the program? A comradery develops naturally among the students through their common coursework and the group project class, which meets weekly as a seminar and requires joint work outside class.There are around ten students in the program in any given year.This size allows the students and the faculty to interact easily and frequently.
Also, the second-year students often share their experiences and contacts with the first-year students.Where do the graduates go? While a few find the program useful for developing their mathematics prior to pursuing other advanced degrees, most graduates find jobs in industry.Typically, these jobs are in high-technology firms, often falling under the label of software development.Some recent graduates are employed by large, well-known companies: DEC, GTE, Hewlett-Packard, MIT Lincoln Labs, Pfizer.Others work for smaller, local firms, such as Artios (Ludlow, MA) and Amherst Process Instruments (Hadley, MA).
How do the graduates fare on the job market? It appears that many employers prefer to hire candidates having strong mathematical training together with good programming skills, rather than those with other, more specialized, degrees.And, indeed, all the recent graduates from the program have secured good jobs upon completion of the program.Many have received several attractive offers.What do the recent graduates have to say? Feedback from our graduates underscores the value of program, and the group project in particular, as preparation for the workplace.Here are a few examples of their comments: A 1993 grad now at Lincoln Labs writes, "One thing I would like to mention is that even though I may be using more computer skills than math, I feel that my math background has helped a lot.
When I was hired, my boss told me that she preferred someone with a math background who could program than a computer science major.Also, the applied math group project is a great idea because it teaches you to work as a group and prepares you for the "real world"." One of our 1994 alumni, who worked for a while at Fuji Capital Markets Corporation before returning to school, recalls, "Well I remember some words from my boss at FCMC : He told me that, 'A good background in mathematics and programming makes you a very valuable person for an Investment bank or a Capital Markets firm like Fuji Capital Markets.Usually people are either one or the other.
If you combine both and have good conversational skills, that's exactly what employers are looking for.' And that is exactly what we tried to learn in the Master's Program : get a thorough math background, learn to program and communicate." An alumna from 1995, now working at GTE, states, "I think the best selling point is the project.Not so much in terms of what the project is about, but rather the fact that you're working in a group where you have to deal with people not getting their portion of the project done, and project management issues.The team aspect is emphasized a lot at GTE and also I think in other companies.
The C coding is also very important; even little things like the RCS configuration management tool are good things to talk about (We're using one now called ClearCase, and tho' I didn't know exactly how to use it, at least I knew the principles behind why we needed such a thing." A 1994 graduate reports, "I am currently a Statistician/Quality Engineer for the Hewlett-Packard Company.The Applied Math Program at UMASS was great for me.
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I was able to choose many classes that built on my previous engineering degree.The faculty at UMASS are also very supportive and are available for the students.I never had a problem trying to get advice on any matter The Oxford Centre for Industrial and Applied Mathematics (OCIAM) is a research centre within the Mathematical Institute of the University of Oxford. OCIAM was established in 1989 to foster collaborative research with both industry and other disciplines, aiming to promote a wider use of mathematics and mathematical .I never had a problem trying to get advice on any matter.
In addition, the faculty realizes that students will be looking for a job after the program and they give the students many opportunities to make contacts and explore various professional paths." A 1990 alumna who later received her PhD in meteorology writes, "The best thing about the applied math program is the solid theoretical background it gave me and the 'hands-on' application of that knowledge in a project.
I also enjoyed enormously the course I took outside the department in fluid dynamics, which set the foundation of my current research work informatics/computer science (be aware that CSE is not computer science); applied mathematics; an equivalent subject In contrast to the standard application documents for master's programs in the Informatics department, an essay is not mandatory to apply for CSE, but you have to provide a letter of motivation..I also enjoyed enormously the course I took outside the department in fluid dynamics, which set the foundation of my current research work." Group projects Each year a group project is completed by all of the current students.In a sense, this project class is the organizing experience for the students in the degree program ethics.In a sense, this project class is the organizing experience for the students in the degree program.In addition, it serves as the thesis component of the M.The second-year students are expected to take a leadership role in the project, along with the two faculty members who guide it.The first-year students gradually acquire the skills (as modelers, coders and communicators) that they will use during the next year, when they lead the project.The class meets as a weekly seminar throughout the academic year, although most of the real work occurs outside the classroom.The projects from recent years are described briefly below.
More details can be found at our Department Newsletters 2015-16: Non-transitive Systems in Grasslands This year’s Applied Math Master's Project modeled the non-transitive interactions between three plant species in a prairie and explored the effects that urban development would have on species survival and co-existence.We began by studying non-transitive systems.In a transitive system, if A defeats B and B defeats C then A defeats C; a non-transitive system is one that does not follow these rules.The prototypical example is the game of Rock-Paper-Scissors (RPS), where Paper covers Rock, Rock crushes Scissors, and Scissors cuts Paper.
Mathematically, non-transitive systems (often called RPS games) have been examined using discrete and continuous techniques and applied to model multi-player interactions in fields such as biology, economics, and social networking.
2014-15: Uncertainty Quantification: The Story Begins This year’s Applied Math Masters project utilized the emerging field of uncertainty quantification to focus on a topic of concern to human health: developing a Susceptible-Infected-Removed model (SIR) for forecasting the spread of dengue hemorrhagic fever (DHF).2013-14: From Atomic Physics and Materials Science to Financial Mathematics and Beyond This year the Applied Mathematics Masters’ Program tackled a diverse variety of themes in the context of its yearly project: Bose-Einstein condensates in atomic physics; granular crystals in materials science; and deterministic (and potentially chaotic) models of supply-demand-pricing and inflation in financial markets.2012-13: Multi-Agent Models This year the Masters students in the Applied Mathematics program undertook a multi-faceted project related to the broad theme of Multi-Agent Models.First, it offered an opportunity to model the collective behavior of complex systems arising in a range of different disciplines.
In particular, three subgroups of the students studied dynamical systems from physical chemistry, biology, and finance.Second, this theme demanded a computationally intensive approach, and the students themselves expressed a desire to use the project to push the limits of their abilities as computational modelers.2011-12: Power Grids and Energy Transmission Energy has become an important issue across the whole spectrum of our society.Overall electricity production, one of the most important forms of energy, is often used as an indicator whether a country is industrialized or non-industrialized.The power grids used to transfer electricity from the generators to consumers have a tremendous scale and are becoming ever more complicated as more power plants are built to meet the ever increasing demand.
This year the students in the Applied Math Master’s Degree Program worked on three different projects that deal with three different aspects of power grids and energy transmission.2010-11: Numerical Optimization of Airport Traffic For this year’s group project in applied math, the students modeled the efficiency of airport taxi way operations, with the aim of improving the scheduling of departing and arriving flights at a busy airport.This problem was suggested by a former graduate from our department, Richard Jordan (Ph., 1994), who is currently working for the MIT Lincoln Laboratories.
Rich’s group in the Lincoln Lab is under contract from the FAA to update various aspects of airport operations by means of modern automation.2009-10: Microscopic Traffic Flow Modeling, and Compressive Sampling In the past year, the Applied Mathematics Masters students were divided into two groups and worked on two separate projects.The first group worked on a project about “Compressive Sampling,” which is a state-of-the-art technique to compress data during acquisition.The basic idea goes back to the 1970s, when seismologists first use the reflected waves to construct an image of the Earth’s interior structure.But the field exploded around 2004 after David Donoho, Emmanuel Candes, Justin Romberg and Terence Tao discovered that the minimum number of data needed to reconstruct an image is less than that required by the famous Nyquist-Shannon criterion.
The second group worked on a project of Microscopic Traffic Flow Modeling.Different from macroscopic models, which treat traffic flow as an effectively one-dimensional compressible fluid, microscopic traffic models are built up from the minute level of individual cars and the interactions between them.The car-following model is one such model based on the stimulus-response mechanism — the following car takes actions like acceleration or deceleration whenever there is stimulus from the leading car, like a change of relative speed or headway.Ideally, models of this kind should be able to reproduce common traffic phenomena, such as stop-and- go, platoon diffusion, or spontaneous congestion.In practical situations they could be used to predict traffic conditions on major roads and to aid traffic control procedures.
2008-09: Modeling Climate Change At first sight, there is no easy entry point for mathematical modelers into the extremely complex subject of climate dynamics.State-of-the-art climate predictions are based on elaborate numerical models that attempt to include all relevant physical processes in the entire Earth system.These numerical simulators, which grew out of weather-prediction technology, are generically called GCMs, meaning General Circulation Models, although nowadays perhaps Global Climate Models is a more appropriate term.Their governing equations incorporate the circulation of the atmosphere as well as its radiative physics and chemistry (carbon dioxide, ozone, aerosols), the circulations of the oceans and coupling through the hydrosphere (water vapor, clouds, glaciers, sea ice), and even aspects of the biosphere (forests, soils, marine biota).Models with this level of complexity take decades to develop, test, and tune, and they are very expensive to run.
Moreover, the results and predictions that they produce are often quite hard to interpret, especially if the goal is to identify a particular mechanism and its effects.2007-08: Cancerous Tumor, and Data Compression This year, students in the program worked on two projects.In the first project they looked at models of blood vessel growth towards a cancerous tumor.A critical question for a patient diagnosed with cancer is whether the disease is local or has spread to other locations.Cancer cells penetrate into lymphatic and blood vessels, circulate through the bloodstream, and then invade and grow in normal tissues elsewhere.
This mechanism of spreading is called metastasis.Its ability to spread to other tissues and organs makes cancer a life-threatening disease.Hence, there is naturally a great interest in understanding what makes metastasis possible for a malignant tumor.One of the key findings of cancer researchers studying the conditions necessary for metastasis is the fact that the growth of new blood vessels is critical in this respect.In the second group project, the applied math studied data compression.
In computer science and information theory, data compression is the process of encoding information using fewer bits than in the uncoded representation.A popular instance of compression is the ZIP file format.As with any communication, compressed data communication is useful only when the sender and receiver understand the coding scheme.Compression is useful because it reduces the amount of space required for storage of the original data.On the other hand, compressed data must be decompressed in order to be used, and the additional processing could be harmful to some applications.
For example, a compressed video may require expensive hardware for the video to be decompressed fast enough to be viewed while it is being decompressed.2006-07: The Mathematics of Climate The group worked on mathematical models of global climate.The first person in history to publish a scientific paper on the physical principles that underlie climate — namely, the overall effect of solar radiation and its interaction with the Earth’s surface and atmosphere — was the famous mathematician Joseph Fourier.In the 1820s the father of the heat equation asked himself how it is that the Earth maintains an equilibrium temperature and what that temperature should be.
He first wondered why the Earth is not much hotter than it is, given that it is continually heated by the Sun.
He realized that the Earth balances the solar radiation it receives by emitting lower frequency (infrared) radiation back into space.But then his calculations suggested that the equilibrium temperature should be below freezing worldwide.The discrepancy lay in the fact that some gases in the atmosphere absorb the reflected radiation even though they are almost transparent to the solar radiation.Of course, these are the greenhouse gases, principally water vapor and carbon dioxide.Although science was much too primitive in Fourier’s time for him to make a thorough analysis, his simple picture of the key processes has stood the test of time, and today it underlies the urgent debate on global warming.
2005-06: The Google Search Engine and the Mechanics of Human Locomotion The group worked on two projects.The first project was to model the search engine Google.After people type keywords in Google, it prepares a list of websites associated with those keywords.By applying the power method in numerical analysis, the students were able to simulate the page-rank processing of a network.They wrote a program, called a webcrawler, that crawls the internet site by site to determine how sites are interconnected.
This created a network of 60,000 sites containing the Department of Mathematics and Statistics and its connected sites.
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The students then applied the page-rank algorithm to this network.The students also applied the same algorithm to other topics such as developing a ranking system of US airports that would help determine which airports are the most important according to the numbers of passengers.Once again using the power method and applying it to an actual data set obtained from the Bureau of Transportation, the students concluded that Dallas/Fort Worth International Airport is the most important airport in the US Help me with a college research paper applied mathematics high quality CSE Premium British Business.Once again using the power method and applying it to an actual data set obtained from the Bureau of Transportation, the students concluded that Dallas/Fort Worth International Airport is the most important airport in the US.
Undertaking this project involved input from many academic areas.The students first had to understand the physiology of the leg as well as the mechanics of how the leg moves and interacts with various forces during running.As they learned, the running process can be broken down into two phases.The stance phase is the period of time when the foot is still in contact with the ground, and the flight phase is the period of time when the foot and the body are in the air.Each phase is governed by a different set of equations derived from Newton's laws of motion.
The stance phase is described by three second-order differential equations while the flight phase is described by the equations for common projectile motion found in physics.The students solved the coupled differential equations for the two phases numerically in order to simulate running.2004-05: Pattern Formation, Tumor Growth and Turing Instability The spots and stripes which occur on plants and animals is modeled by the group.The model is based on Turing instability or diffusion driven instability.A coupled pair of partial differential equations are used to model the pattern formation.
These equations are studied analytically to understand when instabilities will occur.The equations are then solved with a finite difference method numerically in different domains with varying parameters producing spots, stripes and combinations of the two.A simple model of tumor growth is also proposed.The model is based on the tumor releasing a chemical(TAF) and using this chemical to recruit blood vessels to proliferate in its direction and eventually vascularize the tumor.The model involved a partial differential equation for the chemical and one for the blood vessels.
The equations were solved with a finite difference method numerically.The solutions were similar to what is observed.2003-04: Traffic Flow with Cellular Automata and Kinetic Models The group looked at different models for simulating traffic flow.The primary model was one based on cellular automata.This model uses a finite set of vehicles with a finite set of rules governing their interaction.
The results gave very realistic results.The group showed that one can predict the mean velocity of a collection of vehicles depending on the density.One and two lanes were modeled along with stop lights and ramps.The group also derived a kinetic model, one between the microscopic cellular automata and the macroscopic partial differential equation.The kinetic model produced solutions similar to the cellular automata which the differential equation is not capable of.
2002-03: Modeling of the Kidney and Lungs The regulation of sodium chloride in the kidney is modeled.Each kidney contains over one million nephrons, the basic functional unit of the kidney.Each nephron regulates the composition of sodium chloride amongst other things.The transport of sodium chloride in the loop of Henle, which is part of the nephron, is modeled with a partial differential equation.Using analysis, the partial differential equation is studied to understand when stable and unstable solutions might occur.
The equation is solved numerically using the Lax-Wendroff method.The computed solutions exhibit oscillations in the sodium concentration in time as is predicted by the analysis.The group also worked with a research pulmonologist at Bay State Medical Center looking at the amount of carbon dioxide exhaled in healthy patents and patents with asthma versus time.
The group tested different methods for removing the noise from the data(smoothing the data).
The group proposed several good methods that the pulmonologist could use in his work.2001-02: Artificial Neural Networks 1999-00: Modeling and visualizing human movement via mechanics and optimal control Image(s) from this project: 1998-99: Quasi-geostrophic turbulence modelling using pseudospectral methods The objective of this project is to develop a mathematical model for forcasting atmospheric pressure patterns.The common assumption is made that the atmosphere can be modelled as an incompressible fluid.The laws governing atmospheric pressure changes are then described using a Navier-Stokes equation in a rotating coordinant frame.Solutions to this nonlinear partial differential equation are obtained numerically, by means of pseudospectral method.
Image(s) from this project: 1997-98: Macroscopic modelling of traffic flow Traffic flow is modelled through a hydrodynamic analogy, and the resulting nonlinear hyperbolic partial differential equation is solved numerically.In addition, on-ramps, off-ramps, and bottlenecks are modelled, and these complexities also are implemented in the computer simulation program.Then, in order to model a two lane highway, the concept of lane changing is examined.A model of lane changing from the literature is discussed, and it is argued that this formulation is incorrect.Moreover, a modified lane changing model is presented, and its validity is supported by the results of several simulations, again performed through the numerical solution of the governing differential equation.
Finally, in order to illustrate the interrelationship between the effects of ramps and bottlenecks and the process of lane changing, results are presented for simulations which model ramps and bottlenecks along a two lane highway.Image(s) from this project: 1996-97: Monte-Carlo simulation of turbulent atmospheric diffusion The physical and mathematical diffusion of particles through a turbulent velocity field was calculated via two methods, a Random Eddy Model and Fourier Spectrum Model.Spatial correlation experiments were performed to ensure appropriate behavior for the moving particles, as well as parameter choices.Simulations of particle emanation from a smoke stack were also performed.
Image(s) from this project: 1995-96: Acoustic radiation and propagation The sound field of a planar generator of general shape and/or mode was calculated by using a surface integral representation of the solution to the governing Helmholtz equation.Comparisons were made with some classical formulas available either in simple, symmetric cases, or in asymptotic regimes.Interesting interference patterns in the sound intensity nearby the radiator were detailed over a range of frequencies and generator characteristics.The directivity of these sound generators was also studied.Image(s) from this project: 1994-95: Models of convective turbulent diffusion The steady-state concentration field of a pollutant introduced into a flowing, turbulent atmosphere was analyzed.
A finite-difference method (alternating direction implicit) was implemented to solve the variable-coefficient diffusion equation in three dimensions, under a parabolic approximation in which the downstream variable is time-like.The plume formed by a source was computed and displayed graphically for various sheared wind-flow conditions.Image(s) from this project: 1993-94: Optics analysis The design of a lens system was tackled using a direct numerical approach based on ray-tracing for the geometrical optics.Optical properties (focussing, magnification) of various instruments (simple telescopes, microscopes) were examied by computing the three-dimensional pencils of rays, without the classical paraxial approximation.Then the aberrations (spherical, coma, astigmatism, .
) were quantified numerically, and an optimization code was used to vary the lens system parameters so as to minimize a given aberration.Image(s) from this project: 1992-93: Spectral computations in fluid dynamics The behavior of a two-dimensional viscous fluid was simulated by a direct numerical computation using a pseudospectral method.First, some simpler one-dimensional codes were written for the Burgers and Korteweg-DeVries equations, and some wave interaction phenomena governed by these equations were studied.Then, the full code for a Navier-Stokes flow in two dimensions was implemented, and various vortex interactions were displayed.Those wishing to be considered for Fall admission should submit all application materials to the Graduate Admissions Office during the preceding Spring.
Applications are reviewed beginning on February 1, with precedence given to those before that date.Later applications are considered provided that openings are available.Applicants are encouraged to visit in person, if possible, to meet the faculty and students in the program.All applicants are expected to have a strong undergraduate preparation in mathematics, including advanced calculus, linear algebra, and differential equations.Some exposure to computer science and/or scientific computing is also desirable, as is some knowledge of another area of science or engineering.
A Bachelor's Degree in Mathematics, however, is not necessary.Students with undergraduate majors in Physics or Engineering, for instance, and with sufficient mathematical background, are encourage to apply.The program is able to offer a tuition waiver and a stipend to a limited number of students upon admission.This financial support takes the form of a teaching assistantship in the department.The duties of the students in the Master's Degree Program are usually restricted to grading or consulting for an undergraduate course, although instructing in an elementary course is also possible.
For additional information, contact the Program Director Qian-Yong Chen.
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Possible interdisciplinary courses COMPSCI 513: Logic in Computer Science Rigorous introduction to mathematical logic from an algorithmic perspective.Topics include: Propositional logic: Horn clause satisfiability and SAT solvers; First Order Logic: soundness and completeness of resolution, compactness theorem.We will use the Coq theorem prover and Datalog Best websites to purchase a research paper applied mathematics American 24 hours Master's Writing from scratch.We will use the Coq theorem prover and Datalog.
Prerequisites: COMPSCI 250 and COMPSCI 311.
COMPSCI 575: Combinatorics and Graph Theory This course is a basic introduction to combinatorics and graph theory for advanced undergraduates in computer science, mathematics, engineering and science The Master's Degree Program in Applied Mathematics is specially designed to prepare graduates for a successful career in today's industrial/business world. Accordingly, the I also enjoyed enormously the course I took outside the department in fluid dynamics, which set the foundation of my current research work. .COMPSCI 575: Combinatorics and Graph Theory This course is a basic introduction to combinatorics and graph theory for advanced undergraduates in computer science, mathematics, engineering and science.Topics covered include: elements of graph theory; Euler and Hamiltonian circuits; graph coloring; matching; basic counting methods; generating functions; recurrences; inclusion-exclusion; and Polya's theory of counting The Master's Degree Program in Applied Mathematics is specially designed to prepare graduates for a successful career in today's industrial/business world. Accordingly, the I also enjoyed enormously the course I took outside the department in fluid dynamics, which set the foundation of my current research work. .Topics covered include: elements of graph theory; Euler and Hamiltonian circuits; graph coloring; matching; basic counting methods; generating functions; recurrences; inclusion-exclusion; and Polya's theory of counting.Undergraduate Prerequisites: mathematical maturity; calculus; linear algebra; strong performance in some discrete mathematics class, such as COMPSCI 250 or MATH 455.
Modern Algebra - MATH 411 - is helpful but not required.
COMPSCI 585: Introduction to Natural Language Processing Natural Language Processing (NLP) is the engineering art and science of how to teach computers to understand human language.NLP is a type of artificial intelligence technology, and it's now ubiquitous -- NLP lets us talk to our phones, use the web to answer questions, map out discussions in books and social media, and even translate between human languages.Since language is rich, subtle, ambiguous, and very difficult for computers to understand, these systems can sometimes seem like magic -- but these are engineering problems we can tackle with data, math, machine learning, and insights from linguistics.This course will introduce NLP methods and applications including probabilistic language models, machine translation, and parsing algorithms for syntax and the deeper meaning of text.
During the course, students will (1) learn and derive mathematical models and algorithms for NLP; (2) become familiar with basic facts about human language that motivate them, and help practitioners know what problems are possible to solve; and (3) complete a series of hands-on projects to implement, experiment with, and improve NLP models, gaining practical skills for natural language systems engineering.Undergraduate Prerequisites: COMPSCI 220 (or COMPSCI 230) and COMPSCI 240.An alternate prerequisite of LINGUIST 492B is acceptable for Linguistics majors.COMPSCI 589: Machine Learning This course will introduce core machine learning models and algorithms for classification, regression, clustering, and dimensionality reduction.
On the theory side, the course will focus on understanding models and the relationships between them.On the applied side, the course will focus on effectively using machine learning methods to solve real-world problems with an emphasis on model selection, regularization, design of experiments, and presentation and interpretation of results.The course will also explore the use of machine learning methods across different computing contexts.Students will complete programming assignments and exams.Python is the required programming language for the course.
Prerequisites: COMPSCI 383 and MATH 235.COMPSCI 590D: Algorithms for Data Science Big Data brings us to interesting times and promises to revolutionize our society from business to government, from healthcare to academia.As we walk through this digitized age of exploded data, there is an increasing demand to develop unified toolkits for data processing and analysis.In this course our main goal is to rigorously study the mathematical foundation of big data processing, develop algorithms and learn how to analyze them.
Specific Topics to be covered include: 1) Clustering 2) Estimating Statistical Properties of Data 3) Near Neighbor Search 4) Algorithms over Massive Graphs and Social Networks 5) Learning Algorithms 6) Randomized Algorithms.This course counts as a CS Elective toward the CS major (BS/BA).Undergraduate Prerequisites: COMPSCI 240 and COMPSCI 311.COMPSCI 590IV + 690IV: Intelligent Visual Computing The course will teach students algorithms that intelligently process, analyze and generate visual data.
The course will start by covering the most commonly used image and shape descriptors.It will proceed with statistical models for representing 2D images, textures, 3D shapes and scenes.The course will then provide an in-depth background on topics of shape and image analysis and co-analysis.Finally, the course will cover topics on automating the design and synthesis of 3D shapes with machine learning algorithms and advanced human-computer interfaces.
Students will read, present and critique state-of-the-art research papers on the above topics.This course counts as a CS Elective toward the CS major (BA/BS).COMPSCI 590N: Introduction to Numerical Computing with Python This course is an introduction to computer programming for numerical computing.The course is based on the computer programming language Python and is suitable for students with no programming or numerical computing background who are interested in taking courses in machine learning, natural language processing, or data science.
This course counts as a CS Elective toward the CS major (BA/BS).Undergraduate Prerequisite: COMPSCI 220 or 230.No prior knowledge of data visualization or exploration is assumed.This course counts as a CS Elective toward the CS major (BA/BS).
CICS 597C Introduction to Computer Security This course provides an introduction to the principles and practice of computer and network security with a focus on both fundamentals and practical information.The key topics of this course are applied cryptography; protecting users, data, and services; network security, and common threats and defense strategies.Students will complete several practical lab assignments involving security tools (e., OpenSSL, Wireshark, Malware detection).
The course includes homework assignments, quizzes, and exams.Prerequisites are CICS 290S or equivalent experience with instructor permission.COMPSCI 611: Advanced Algorithms Principles underlying the design and analysis of efficient algorithms.Topics to be covered include: divide-and-conquer algorithms, graph algorithms, matroids and greedy algorithms, randomized algorithms, NP-completeness, approximation algorithms, linear programming.
Prerequisites: The mathematical maturity expected of incoming Computer Science graduate students, knowledge of algorithms at the level of COMPSCI 311.COMPSCI 617: Computational Geometry Geometric algorithms lie at the heart of many applications, ranging from computer graphics in games and virtual reality engines to motion planning in robotics or even protein modeling in biology.This graduate course is an introduction to the main techniques from Computational Geometry, such as convex hulls, triangulations, Voronoi diagrams, visibility, art gallery problems, and motion planning.The class will cover theoretical as well as practical aspects of the field.
The goal of the class it to enable students to exploit a broad range of algorithmic tools from computational geometry to solve problems in a variety of application areas.Prerequisite: Mathematical maturity; CMPSCI 611 or CMPSCI 601.COMPSCI 660 Advanced Information Assurance This course provides an in-depth examination of the fundamental principles of information assurance.While the companion course for undergraduates is focused on practical issues, the syllabus of this course is influenced strictly by the latest research.We will cover a range of topics, including authentication, integrity, confidentiality of distributed systems, network security, malware, privacy, intrusion detection, intellectual property protection, and more.Prerequisites: COMPSCI 460 or 466, or equivalent.COMPSCI 682: Neural Networks: A Modern Introduction This course will focus on modern, practical methods for deep learning.The course will begin with a description of simple classifiers such as perceptrons and logistic regression classifiers, and move on to standard neural networks, convolutional neural networks, and some elements of recurrent neural networks, such as long short-term memory networks (LSTMs).The emphasis will be on understanding the basics and on practical application more than on theory.Most applications will be in computer vision, but we will make an effort to cover some natural language processing (NLP) applications as well, contingent upon TA support.The current plan is to use Python and associated packages such as Numpy and TensorFlow.
Prerequisites include Linear Algebra, Probability and Statistics, and Multivariate Calculus.Some assignments will be in Python and some in C++.COMPSCI 687: Reinforcement Learning This course will provide an introduction to, and comprehensive overview of, reinforcement learning.In general, reinforcement learning algorithms repeatedly answer the question "What should be done next?", and they can learn via trial and error to answer these questions even when there is no supervisor telling the algorithm what the correct answer would have been.
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Applications of reinforcement learning span across medicine (How much insulin should be injected next? What drug should be given next?), marketing (What ad should be shown next?), robotics (How much power should be given to the motor?), game playing (What move should be made next?), environmental applications (Which countermeasure for an invasive species should be deployed next?), and dialogue systems (What type of sentence should be spoken next?), among many others.), hierarchical reinforcement learning, representations for reinforcement learning (including deep learning), and connections to animal learning.Special topics may include ensuring the safety of reinforcement learning algorithms, theoretical reinforcement learning, and multi-agent reinforcement learning MSc Mathematical Modelling UCL.Special topics may include ensuring the safety of reinforcement learning algorithms, theoretical reinforcement learning, and multi-agent reinforcement learning.
This course will emphasize hands-on experience, and assignments will require the implementation and application of many of the algorithms discussed in class.
PREREQUISITES: COMPSCI 589, or COMPSCI 689, or COMPSCI 683, with a grade of C or better.Familiarity with an object oriented programming language is required (assignments will use C++, but familiarity with C++ specifically will not be assumed) The objectives of this report are to attempt to define the core areas and scope of CSE, to provide ideas, advice and information regarding curriculum and graduate Research in CSE involves the development of state of the art computer science, mathematical and computational tools directed at the effective solution of .Familiarity with an object oriented programming language is required (assignments will use C++, but familiarity with C++ specifically will not be assumed).COMPSCI 688: Probabilistic Graphical Models Probabilistic graphical models are an intuitive visual language for describing the structure of joint probability distributions using graphs.They enable the compact representation and manipulation of exponentially large probability distributions, which allows them to efficiently manage the uncertainty and partial observability that commonly occur in real-world problems.
As a result, graphical models have become invaluable tools in a wide range of areas from computer vision and sensor networks to natural language processing and computational biology.The aim of this course is to develop the knowledge and skills necessary to effectively design, implement and apply these models to solve real problems.The course will cover (a) Bayesian and Markov networks and their dynamic and relational extensions; (b) exact and approximate inference methods; (c) estimation of both the parameters and structure of graphical models.Although the course is listed as a seminar, it will be taught as a regular lecture course with programming assignments and exams.
Students entering the class should have good programming skills and knowledge of algorithms.
Undergraduate-level knowledge of probability and statistics is recommended.COMPSCI 689: Machine Learning Machine learning is the computational study of artificial systems that can adapt to novel situations, discover patterns from data, and improve performance with practice.This course will cover the popular frameworks for learning, including supervised learning, reinforcement learning, and unsupervised learning.The course will provide a state-of-the-art overview of the field, emphasizing the core statistical foundations.
Detailed course topics: overview of different learning frameworks such as supervised learning, reinforcement learning, and unsupervised learning; mathematical foundations of statistical estimation; maximum likelihood and maximum a posteriori (MAP) estimation; missing data and expectation maximization (EM); graphical models including mixture models, hidden-Markov models; logistic regression and generalized linear models; maximum entropy and undirected graphical models; nonparametric models including nearest neighbor methods and kernel-based methods; dimensionality reduction methods (PCA and LDA); computational learning theory and VC-dimension; reinforcement learning; state-of-the-art applications including bioinformatics, information retrieval, robotics, sensor networks and vision.Prerequisites: undergraduate level probability and statistics, linear algebra, calculus, AI; computer programming in some high level language.COMPSCI 690LG: Advanced Logic in Computer Science Rigorous introduction to mathematical logic from an algorithmic perspective.Topics include: Propositional logic: Horn clause satisfiability and SAT solvers; First Order Logic: soundness and completeness of resolution, compactness theorem, automatic theorem proving, model checking.
We will learn about and use the Coq theorem prover, Datalog, a Model Checker, and SAT and SMT solvers.Prerequisites: Students taking this course should have undergraduate preparation in discrete math and algorithms.Requirements will include readings, class participation, weekly problem sets, a midterm and a final project.COMPSCI 690M: Machine Learning Theory When, how, and why do machine learning algorithms work? This course answers these questions by studying the theoretical aspects of machine learning, with a focus on statistically and computationally efficient learning.
Broad topics will include: PAC-learning, uniform convergence, and model selection; supervised learning algorithms including SVM, boosting, kernel methods; online learning algorithms and analysis; unsupervised learning with guarantees.Special topics may include: Bandits, active learning, semi-supervised learning and others.COMPSCI 690V: Visual Analytics In this course, students will work on solving complex problems in data science using exploratory data visualization and analysis in combination.Students will learn to deal with the Five V s: Volume, Variety, Velocity, Veracity, and Variability, that is with large data, complex heterogeneous data, streaming data, uncertainty in data, and variations in data flow, density and complexity.
Students will be able to select the appropriate tools and visualizations in support of problem solving in different application areas.The course is a practical continuation of COMPSCI 590V - Data Visualization and Exploration and focuses on complex problems and applications, however 590V is not a prerequisiteandboth 590V and 690V may be taken independently of each other.The data sets and problems will be selected mainly from the IEEE VAST Challenges, but also from the KDD CUP, Amazon, Netflix, GroupLens, MovieLens, Wiki releases, Biology competitions and others.We will solve crime, cyber security, health, social, communication, marketing and similar large-scale problems.Data sources will be quite broad and include text, social media, audio, image, video, sensor, and communication collections representing very real problems.
Hands-on projects will be based on Python or R, and various visualization libraries, both open source and commercial.COMPSCI 691E: Interactive Machine Learning Interactive machine learning involves an algorithm or an agent making decisions about data collection, contrasting starkly with traditional learning paradigms.Interactive data collection often enables learning with significantly less data, and it is critical in a number of applications including personalized recommendation, medical diagnosis, and dialogue systems.This seminar will focus on the design and analysis of interactive learning algorithms for settings including active learning, bandits, reinforcement learning, and adaptive sensing.
We will cover foundational and contemporary papers, with an emphasis on algorithmic design principles as well as understanding and proving performance guarantees.Students enrolled in the 3 credit version of the course will present one paper in detail to the class as well as prepare notes for one additional lecture.Students enrolled in the 1 credit version of the course will prepare notes for one lecture.Mechanical and industrial engineering MIE 586 - Quantitative Decision Making Survey in operations research.
Introduction to models and procedures for quantitative analyses of decision problems.Topics include linear programming and extensions, integer programming.Required for IE graduate students who lack operations research exposure.MIE 605 - Finite Element Analysis The underlying mathematical theory behind the finite element method and its application to the solution of problems from solid mechanics.Includes a term project involving the application of the finite element method to a realistic and sufficiently complex engineering problem selected by the student and approved by the instructor; requires the use of a commercial finite element code.
MIE 644 - Applied Data Analysis The basics of data acquisition and analysis, pattern classification, system identification, neural network modeling, and fuzzy systems.Essential to students whose thesis projects involve experimentation and data analysis.MIE 684 - Stochastic Processes In Industrial Engineering Introduction to the theory of stochastic processes with emphasis on Markov chains, Poisson processes, markovian queues and networks, and computational techniques in Jackson networks.Applications include stochastic models of production systems, reliability and maintenance, and inventory control.MIE 707 - Viscous Fluids Exact solutions to Navier-Stokes flow and laminar boundary layer flow.
Introduction to transition and turbulent boundary layers, and turbulence modeling.Boundary layer stability analysis using pertubation methods.Civil and environmental enginerring CEE 511 - Traffic Engineering Fundamental principles of traffic flow and intersection traffic operations including traffic data collection methods, traffic control devices, traffic signal design, and analysis techniques.Emphasizes quantitative and computerized techniques for designing and optimizing intersection signalization.
Several traffic engineering software packages used.
CEE 548 - Finite Element Method Application of numerical methods to solution of problems of structural mechanics.Finite difference techniques and other methods for solution of problems in the vibration, stability, and equilibrium of structural elements.CEE 605 - Finite Element Analysis Introduction to finite element method in engineering science.Derivation of element equations by physical, variational, and residual methods.Associated computer coding techniques and numerical methods.
Management Sch-Mgmt 640 - Financial Analysis and Decisions Basic concepts, principles, and practices involved in financing businesses and in maintaining efficient operation of the firm.Framework for analyzing savings-investment and other financial decisions.Both theory and techniques applicable to financial problem solving.Sch-Mgmt 641 - Financial Management Internal financial problems of firms: capital budgeting, cost of capital, dividend policy, rate of return, and financial aspects of growth.
Sch-Mgmt 745 Financial Models Analytical approach to financial management.Emphasis on theoretical topics of financial decision making.Through use of mathematical, statistical, and computer simulation methods, various financial decision making models are made.Sch-Mgmt 747 - Theory of Financial Markets In-depth study of portfolio analysis and stochastic processes in security markets.
Emphasis on quantitative solution techniques and testing procedures.Sch-Mgmt 871 - Micro Theory Of Finance Optimum financial policies and decisions of nonfinancial firms.Theory of competition and optimum asset management of financial firms.