1. ANU, (BComptlSci)

The typical degree structure: core courses shown in green, application courses in orange and possible electives in yellow.

 2.  Brockport , CSL Computational Science Major

CPS 433 Scientific Visualization. Prerequisites: MTH 424 and CSC 205. This course provides concepts and techniques for visualization and its implementation. Specifically, use of visualization tools in mathematical simulation modeling such as data entry and data integrity, code debugging and code performance analysis, interpretation and display of final results will be emphasized. Hands-on experience with visualization software packages in X-Windows environment will be provided. Students may be required to develop a new visualization software designed to aid in the analysis of a chosen problem. Knowledge of programming in a high-level language is essential. 3 Cr.

3. BSc Compl Science Singapoor

2.1 BSc in Computational Science

It should be noted that some required modules from other departments have prerequisites that are not major requirements.  Students should check the appropriate departmental prerequisites for listed required modules.

For the Bsc degree in Computational Science, a candidate must
 

(a)	Pass the 9 essential CZ modules from level 1 to 3 (3 at each level).
(b)	Pass 2 CZ elective modules at level 3 or 4.
(c)	Pass 6 science modules (from either MA, PC, or CM) according to one of three options:
	i)	MA1101, MA2101, MA2210, MA2216 or ST2131, MA2221, and one elective from the following: MA3229, MA3236, MA3238, and MA3245.  (MA2221 may be replaced by MA1104 and MA2108;
	ii)	CM1121, CM1131, PC1134, PC2134, CM2132, and CM3231;
	iii)	PC1132, PC1133, PC1134, PC2134, and two electives (one from level 2 and one from level 3) from the following: PC2130, PC2131, PC3130, PC3231, and PC3233.
	The total MCs relevant to the major is 66.  Other variations are possible;  candidates are encouraged to seek advice from one of the departmental advisors.

Candidates for the CZ Honours Programme are required to
 

2.6 Advisory Service

CZ1102 Problem Solving and Computation (Essential, 4MC)
Prerequisite: AO-Level Math
Solution of scientific problems in terms of algorithmic steps using high-level languages (such as C).  Basic computer arithmetic.  Floating point numbers and numerical accuracy.  Control of computation steps with loops, conditional constructs, and multiple choices.  Handling of large data sets with arrays.  Organization of computation in small units (subprograms).  Examples: computation of mathematical functions, statistical data analysis, sorting of data set, and numerical integration.

GEM1504K/CZ1105 Overview of Scientific Computation  (Essential, GER, 4MC)
Prerequisite: None
Computing in early history (Babylonian, Kepler, Newton).  The idea of computing with machines: abacus, Babbage's computing engine, von Neumann's computer architecture, first digital computer (ENIAC), Connection Machine.  Examples of using a computer to solve scientific problems.  Arithmetic of the computer, integer and floating point number representations (accuracy and limitation).  Modeling and simulation of natural phenomena in science - planetary motion, granular flow, biomolecules, etc. This essential module for CZ students does not count towards GER requirements for CZ majors.

CZ1106 Programming Techniques in Scientific Computing (Essential, 4MC)
Prerequisite: CZ1102 or CS1101C
Handling of data files.  Efficient implementations of data structures for scientific computations, such as linked lists, sparse matrices, and spatial data structure.  Overview of scientific programming languages, scientific libraries and application software, such as C/C++, Fortran, NAG, MATLAB, and Maple.  UNIX environment and visualization tools (e.g., awk, gnuplot, xmgr).  Debugging and profiling tools.  A project may be required.
 

5.2 Level 2000 Modules

CZ2102 Algorithms (Essential, 4MC)
Prerequisite: CZ1106
Efficiency of algorithms, algorithmic complexity, algorithms for sorting and searching, algorithms with graphs, fast arithmetic algorithms, FFT.  Approximate algorithms for optimization problems.

CZ2105 Numerical Methods for Scientific Computing I (Essential, 4MC)
Prerequisite: CZ1102
Overlap: MA2213
Suggested: CZ1106 and (PC1134 or M2101)
Introduction to scientific computing. Computer arithmetic, numerical errors.  Examples of linear systems, e.g., resistor network, truss.  System of linear equations, gaussian elimination, LU factorization, SOR method.  Norms and condition numbers, accuracy of solutions.  Fitting of experimental data, least-square and interpolation.  Vibrating springs: eigenvalues.  Nonlinear equations, Newton iteration.

CZ2106 Simulation (Essential, 4MC)
Previous module code CZ2205
Prerequisite: CZ1102/CS1101
A review of probability theory.  Random number generations, Metropolis sampling.  Discrete event simulation, queuing, inventory system, output data analysis, variance reduction technique.  Application examples in finance and engineering.  Introduction to simulation software.

GEMxxxxK/CZ2307 Thinking Science on Computer (Enrichment, GER, 4MC)
Prerequisite: None
Explore simple computer models to understand how nature works. Emergence of complexity in self-organizing systems. Examples from predator-prey system, vehicular traffic flow, ant colonies, earthquakes, river network, turbulence, disease spreading, and social-economic systems.  Evolution, punctuated equilibrium, and self-organized criticality.
 

5.3 Level 3000 Modules

CZ3101 High Performance Computing (Essential, 4MC)
Prerequisite: CZ2102
Introduction to high-performance computing. Vector and parallel computers, shared vs distributed memory.  Message passing, MPI or other programming environment.  Timing and performance analysis of parallel programs. Parallel algorithms in scientific computations, such as matrix-vector multiplication, solution of linear system.  Parallel software, e.g., ScaLapack.

CZ3105 Numerical Methods for Scientific Computing II (Essential, 4MC)
Prerequisite: CZ2105
Overlap: MA3227
Suggested:  (PC2134 or MA2221)
Area and volume of geometric shapes: numerical integration, gaussian quadrature.  Differential equations in science (pendulum, population model, chemical reaction rates, electrical circuits, Newton equation).  Initial value problem,  boundary value problem.  Solution methods - Finite difference, Euler, Runge-Kutta, etc.  System of ODEs.

CZ3106 Symbolic Computing (Essential, 4MC)
Prerequisite: CZ2102
Symbolic vs numerical computation.  Introduction to Mathematica or Maple.  Symbolic programming environment.  Data representation. Polynomial algorithms.  Newton iteration and Chinese remainder theorem in symbolic computing.

CZ3234 Evolutionary Computation and Optimization (Elective, 3MC)
Prerequisite: CZ3105
Introduction to optimisation and evolutionary computing.  Genetic algorithms to solve optimisation problems, e.g., traveling salesman problem.  Simulated anneal and other heuristics.  Introduction to neural network such as multilayer perceptron, Hopfield network.  Supervised learning.  Industry applications.

CZ3242 Computational Techniques for Quantum Systems (Elective, 3MC)
Prerequisites: PC2130 or CM3231
Numerical schemes for time-independent and time-dependent Schroedinger equations: variational methods, Hartree-Fock method, quantum Monte Carlo methods, R-matrix method, wave-packet method.  Gaussian software.

CZ3272 Monte Carlo and Molecular Dynamics (Elective, 3MC)
Prerequisites: CZ3105 and PC2230 or CM3231(can be corequisite)
Introduction to Markov chain Monte Carlo, Monte Carlo numerical integration, Metropolis algorithm, cluster algorithms. Simulation of phase transitions in physical systems (Ising model). Integrators in molecular dynamics, structure of liquid and solid  by molecular dynamics, computation of physical quantities (total energy, pressure, equation of state, etc).  Simulation of biomolecules.  Simulation software.

CZ3273 Signal Processing (Elective, 3MC)
Prerequisite: CZ2105
Fourier series, discrete Fourier transform, FFT algorithms, convolution.  Band-limited signals and sampling theorem, filter design, parametric signal modeling.
 

5.4 Level 4000 Modules

CZ4105 Numerical Methods for Partial Differential Equations (Essential, 4MC)
Prerequisite: CZ3105
Physical and mathematical principles leading to partial differential equations, such as locality, conservation laws, and variational principles.  Classification of PDE. Review of matrix techniques used in numerical solutions of PDE's. Numerical methods for PDE, e.g., finite difference and spectral method, including their consistency and stability.

CZ4106 Scientific Modeling and Visualization (Essential, 4MC)
Prerequisite: CZ4105
Models to represent reality through equations, relationship between model and empirical data, level of approximations in models, validation of models.  Modeling techniques, dimension analysis.  Modeling case studies: e.g., vibration of structures, biological pattern formation, wave propagation, traffic modeling, financial modeling.  Visualization of volume data, software for visualization.

CZ4242 Molecular Systems (Elective, 4MC)
Prerequisite: CZ3242
Computational approaches in molecular systems.   Topics to be addressed include electronic structure of molecular systems, Hartree-Fock approximation, electron correlation, density functional calculations, Gaussian software.  Molecular structure and spectroscopy.  Chemical reaction dynamics, wave-packet method.

CZ4273 Image Processing (Elective, 4MC)
Prerequisite: CZ3273
Imaging processes and image models.  Image transformations, enhancement, restoration, and segmentation.  Image analysis and computer vision.  Data compression techniques.

CZ4275 Condensed-Matter Systems (Elective, 4MC)
Prerequisite: CZ3272
Selected topics in condensed matter physics and materials science and the related computational techniques, e.g., density functional theory. Structural and electronic properties of solid.  Polymer and complex fluid simulation.
 

5.5 Level 5000 Modules

CZ5201 Advanced Computational Methods (Elective, 4MC)
Prerequisite: Departmental approval
Advanced ODE and PDE methods, symplectic integration, finite-element method, grid generation techniques, artificial boundaries, multi-grid method. Lattice Boltzmann equations, particle methods.

CZ5202 High Performance Computing Techniques (Elective, 4MC)
Prerequisite: Departmental approval
Computation and visualization tools and libraries  (e.g., MATLAB, Mathematica, MPI, AVS, Lapack, NAG).  Programming techniques for large-scale computations, vector and parallel computation algorithms.  Symbolic computations for science and engineering problems.  Application examples.

CZ5206 Advanced Simulation Methods (Elective, 4MC)
Prerequisite: Departmental approval
Monte Carlo and molecular dynamics simulation techniques.  Application examples: structure phase transitions, surfaces, protein simulation.  Application of quantum simulation techniques to materials.  Application examples, electronic and structural properties.  Introduction to simulation software, e.g., Celrius 2, insight II, MONPAC.

CZ5211 Topics in Computational Science (Elective, 4MC)
Prerequisite: Departmental approval
Current topics in computational science to be determined by the Department.  Examples are computational techniques such as collocation/Galerkin/wavelets methods, ab initio method, atomistic simulation of fracture and wear, granular dynamics, chemical reaction dynamics, quantum Monte Carlo, spatial and temporal chaos, wavelets,  protein structure and folding, computer aided drug design.

CZ5235 Wavelets and Applications (Elective, 4MC)
Prerequisite: Departmental Approval
Othogonal and biothogonal systems.  Wavelets and frames.  Multiscale decomposition and reconstruction algorithms.  Fourier transform, Z-transform, wavelet transform, Wigner transform.  Wavelet applications to signal and image processing, data and image compression, pattern recognition, application to partial differential equations.

CZ5274 Fluid Dynamics (Elective, 4MC)
Prerequisite: Departmental Approval or CZ4105(co-requisite for undergraduates)
Introduction to theoretical and computational fluid dynamics, assuming no prior knowledge.  Kinematics of fluid flow, stresses and conservation laws, the governing equations and vorticity transport. Topics include hydrostatics, incompressible and irrotational flows, vorticity, and an introduction to boundary layers and hydrodynamic stability.  There will be extensive computational work on sample applications (e.g. nozzle flows, Orr-Sommerfeld equations, vortex simulation methods, etc.)
 
 
 

5. Pittsburgh, Scientific Computing

Course Requirements

The following proposed curriculum for the B.S. degree in Scientific Computing was developed by an Ad Hoc Committee composed of the following faculty members:

-- Department of Mathematics: W. Layton, T. A. Porsching, W. C. Rheinboldt, -- Department of Computer Science: R. Melhem, K. Pruhs, M. L. Soffa.

The basic major in Scientific Computing consists of at least 52 credits of courses in mathematics and computer science and, in addition, requires a minor of at least 12 credits of courses in a related area of the physical or biological sciences, economics, or an approved area of engineering. Students in the program must fulfill the following minimal requirements, earning a grade of C or higher in each course. Students contemplating graduate study should discuss with their advisor at as early a date as possible the additional courses they should take to prepare for graduate study in their desired area.

1. Basic Courses of the Program (6 cr. total)

1.1 MATH 0400 Discrete Mathematical Structures (3 cr) or

CS 0441 Discrete Structures for Computer Science (3 cr) - When enrollments warrant it, a new version of the course will be developed specifi- cally for scientific computing majors.

1.2 MATH 1110 Industrial Mathematics (3 cr) or

CS 1542 Introduction to Simulation (3 cr) - When enrollments warrant it, a new version of the course entitled "Computational Modelling and Simulation (3 cr)" will be developed specifically for scientific computing majors.

5 2. Basic Mathematics (15 cr. total)

2.1 MATH 0220, MATH 0230, MATH 0240 Analytic Geometry and Calculus, Parts 1, 2,

3 : (4 cr. each)

2.2 One of the following courses:

MATH 0250 Matrix Theory and Differential Equations (4 cr) MATH 0280 Introduction to Matrices and linear algebra (3 cr) MATH 1180 Linear Algebra I (3 cr) MATH 1185 Honors Linear Algebra (3 cr)

3. Basic Computer Science (13 cr. total)

3.1 CS 0401 Introduction to Computer Science (4 cr) 3.2 CS 0445 Introduction to Information Structures (3 cr) 3.3 CS 0447 Computer Organization and Assembly Language Programming (3 cr) 3.4 CS 1501 Data Structures and Algorithms (3 cr)

4. Advanced Undergraduate Computational Mathematics (9 cr. total)

4.1 MATH 1070 Numerical Mathematics: Analysis (3 cr.) 4.2 MATH 1080 Numerical Linear Algebra (3 cr.) 4.3 One of the following courses:

MATH 1100 Linear Programming (3 cr) MATH 1270 Ordinary Differential Equations (3 cr) MATH 1470 Partial Differential Equations and Applications (3 cr) - When the program develops, it will be necessary to add further undergraduate computational mathematics courses to this list. In particular, it appears to be essential to develop a course on "Methods of Computational Geometry" and to modify and rename MATH 1100 to "Introduction to Computational Optimization". Computational geometry has been taught before in the form of graduate special topics courses.

5. Advanced Undergraduate Computer Science (9 cr. total)

5.1 CS 1566 Introduction to Computer Graphics (3 cr) 5.2 CS 1645 High Performance Computing (3 cr) 5.3 One of the following courses:

CS 1510 Design and Analysis of Algorithms (3 cr) CS 1520 Programming Languages (3 cr) CS 1530 Software Engineering (3 cr) CS 1555 Data Base Management Systems (3 cr) CS 1557 Computer Organization (3 cr) - When the program develops, it may be necessary to add further undergraduate computer science courses to this list.

6 6. Applications Area Requirement (12 cr total)

6.1 An application area to be approved by the Program Committee consisting of a coherent

sequence of courses in the physical or biological sciences, economics, or an area of engineering.

7 (4) Course Descriptions New Course: Existing Mathematics Courses: MATH 0220: Analytical Geometry and Calculus 1 (4 cr) This is the first course in the basic calculus sequence and is intended for all mathematics, engineering, science, and statistics students. Math 0220 covers the derivative and integral of functions of a single variable. A lab component in which students apply numeric, algebraic, and graphing technologies to calculus problems is an integral part of the course. A scientific calculator is required, preferably a graphing calculator. Prerequisites: Math 0031 and 0032. Recitations: One classroom recitation and one computer lab. Class size: Lectures 50-75, recitations 25-30. Honors section 25-50. Frequency: This course is offered every term.

MATH 0230: Analytical Geometry and Calculus 2 (4 cr) This is the second course in the basic calculus sequence and is intended for all mathematics, engineering, science, and statistics students. Math 0230 covers symbolic and numerical integration techniques and applications, modeling, differential equations, and Taylor series. A lab component in which students apply numeric, algebraic, and graphing technologies to calculus problems is an integral part of the course. A scientific calculator is required, preferably a graphing calculator. Prerequisites: A grade of C or better in Math 0220. Recitations: One classroom recitation and one computer lab. Class Size: Lectures 50, recitations 25. Honors sections 25. Frequency: This course is offered every term.

MATH 0240: Analytical Geometry and Calculus 3 (4 cr) This is the third course in the basic calculus sequence and is intended for all mathematics, engineering, science and statistics students. Math 0240 covers the calculus functions of two and three variables and vector calculus, including the theorems of Green and Gauss. A lab component in which students apply numeric, algebraic, and graphing technologies to calculus problems is an integral part of the course. A scientific calculator is required, preferably a graphing calculator. Prerequisites: A C or better in Math 0230. Recitations: One classroom recitation and one computer lab. Class size: Lectures 50, recitations 25-30. Honors section 25. Frequency: This course is offered every term.

MATH 0250: Matrix Theory and Differential Equations (3 cr) This course is designed primarily for engineering students. The main subject of the course is ordinary differential equations. Topics include first order differential equations, higher order linear differential equations and systems of first order linear and nonlinear differential equations. Matrix methods will be introduced and used to solve systems of linear equations. The computer package Matlab will be used to assist in computations.

8 Prerequisites: Math 0230 Recitations: two Class size: Lecture 75, recitation 25 This course is offered Fall, Spring, 12 WK and 6WK2 terms.

MATH 0280: Introduction to Matrices and Linear Algebra (3 cr) The topics which this course cover include: vectors, matrices, determinants, linear transformations, eigenvalues and selected applications. This course is suitable for CS majors, Economics and other Social Science majors. No credit will be given for this course if the student already has credit for Math 1180 or Math 0250. Prerequisites: Math 0120 or 0220 Recitations: none Class Size: 37. Frequency: This course is offered every term.

MATH 0400: Discrete Math Structures (3 cr) This course will focus on discrete mathematics and its applications. Topics of discussion may include sets and functions, counting, finite probability and statistics, matrices and logic. Applications from various disciplines will be discussed throughout. Students will see new and interesting facets of the world of mathematics within a course aimed at students of disciplines other than mathematics. Prerequisites: Students are expected to have algebra skills equivalent to the material taught in Math 0031 or Math 7010-7020 or mastery of high school algebra. Recitations: none. Class Size: 30. Frequency: This course is offered each Fall, Spring and Summer 12WK.

MATH 1070: Numerical Mathematical Analysis (3 cr) This course is an introduction to numerical analysis at the advanced undergraduate level and includes interpolation, numerical differentiation and integration, solution of non linear equations, numerical solution of systems of ordinary differential equations, and additional topics as time permits. Emphasis is on understanding the algorithms rather than on detailed coding, although some programming will be required. Prerequisites: OLD: Math 0420 and one of CS 0002, 0007, 0132. NEW: Math 0240 plus programming experience in FORTRAN , C or PASCAL Recitations: none. Class Size: 25-35. Frequency: This course is offered every Fall.

MATH 1080: Numerical Mathematics: Linear Algebra (3 cr) This course is an introduction to numerical linear algebra which addresses numerical methods for solving linear algebraic systems, matrix eigenproblems, and applications to partial differential equations. Although the course will stress a computational viewpoint, analysis of the convergence and stability of the algorithms will be investigated. Prerequisites: OLD: Computer Science 0002 or 0007, or a computing language acceptable to the instructor. and Math 0250, 0280 or 1180 and Math 0420. NEW: MATH 0240

9 and MATH 0250, 0280, 1180 or 1185, plus programming experience in FORTRAN, C or PASCAL Recitations: none. Class Size: 25. Frequency: This course is offered during the Spring term.

MATH 1100: Linear Programming (3 cr) Topics covered will include general linear programming problems, the simplex method, duality, revised simplex method and the transportation problem. Emphasis will be on actual computational techniques. Prerequisites: OLD: Math 1180 or 1185 and one of CS 0002, 0007, 0132, 0401. NEW: MATH 0250 or 0280 or 1180 or 1185 plus programming experience in FORTRAN, C or PASCAL Recitations: none Class Size: 15. Frequency: This course is offered once every two years.

MATH 1110: Industrial Math (WRIT) (3 cr) This is a "W" course that is designed for science majors interested in how mathematics is used in industry. It is concerned with numerical solution problems of types which can arise in an industrial environment. Topics covered include physical interpretation of a mathematical model, use of library software, through five stages of the "evolution and dispatch" of an industrial problem; problem recognition, problem formulation, specification of a solution, computation of results, and explanation of the problem and its solution. Prerequisites: OLD: MATH 1180, and one of CS 0002, 0007, 0132, 0401. NEW: MATH 0250 or 0280 or 1180 or 1185 plus programming experience in FORTRAN, C or PASCAL Recitations: none. Class Size: 20. Frequency: This course is offered every Spring Term.

Math 1180: Linear Algebra I (3 cr) This course stresses the theoretical and rigorous development of linear algebra. Major topics include the theory of vector spaces, linear transformations, matrices, eigenvalues and vectors, bases and canonical forms. Other topics may be covered as time permits. Prerequisites:Math 0413 Recitations: none Class Size: 24. Frequency: This course is offered every term.

Math 1185: Honors Linear Algebra (3 cr) This UHC course provides an introduction to both computational and theoretical aspects of linear algebra, and is suitable for those wanting both theory and applications. Linear algebra is a combination of algebra and geometry. The geometry is relatively simple, as it only deals with lines, planes, and high-dimensional analogues. The algebra is also simple in concept, as it mostly involves adding columns and rows of numbers or multiplying a whole column or row of numbers by the same constant. In this course the geometry will be

10 stressed by many examplses in two and three dimensions, while the algebraic computations for more complicated examples will be done by computer. Use will be made of the computer algebra program Mathlab, which will be introduced from scratch in this course. Majors in mathematics or any of the sciences, engineering, economics, or buisiness will find this a valuable tool in their discipline. Among the specific applications which may be covered are computer graphics, game theory, and Leontief models in economics. Prerequisites: Instructor's Approval Recitations: none Class size: 10. Frequency: This course is offered in the Fall term.

MATH 1270: Ordinary Differential Equations (3 cr) This course covers methods of solving ordinary differential equations which are frequently encountered in applications. General methods will be taught for single n th order equations, and systems of first order linear equations. An introduction will be given to the qualitative theory of first order nonlinear systems. This will include phase plane methods and stability analysis. Computer experimentation may be used to illustrate the behavior of solutions of various equations. Prerequisites: One of Math 0420, 0450, and one of Math 1180,1185. (Math 0250 or 0280 may, with the consent of the instructor be substituted for Math 1180). Recitations: none Class Size: 30 Frequency: This course is offered every Fall and Spring Term and Summer 6WK2.

MATH 1470: Partial Differential Equations (3 cr) This is the first term of a two term sequence in elementary PDE's. The objectives of the course are to provide students with the techniques necessary for the formulation and solution of problems involving PDE's and to prepare students for further study in PDE's. The three main types of second order linear PDE's parabolic, elliptic, and hyperbolic are studied. In addition, the tools necessary for the solution of PDE's such as Fourier series and Laplace transforms, are introduced. Prerequisites: Math 0250 or 1270 Recitations: none Class Size: 35 Frequency: This course is offered in the Fall term.

Existing Computer Science Courses: CS 0401: Introduction to Computer Science (4 cr) The purpose of this course is to introduce the student to some fundamental topics in computer science and to improve programming skills through an introduction to the programming language C++. This is a first course for students intending to major in computer science. Prerequisites: Previous programming experience, including arrays, records, and functions with parameters. These topics are typically taught in a high school level Pascal course. Requirements and grading: Grading will be based on programming assignments, laboratory reports, and exams.

11 Recitations: A lab associated with the selected class section is required. Class size: 60 Frequency: This course is offered every term.

CS 0441: Discrete Structures for Computer Science (3 cr) The purpose of this course is to understand and use (abstract) discrete structures that are backbones of computer science. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, and probability, with an emphasis on applications in computer science. Prerequisites: None. Requirements and grading: Grading will be based on homework and exams. Recitation: A recitation associated with the selected class section is required. Class size: 40 Frequency: This course is offered every term.

CS 0445: Introduction to Information Structures (3 cr) This course emphasizes the study of the basic data structures of computer science (stacks, queues, trees, lists, graphs) and their implementations using the C++ language. Included in this study are programming techniques which use recursion and pointer variables. Students in this course are also introduced to various searching and sorting methods and also expected to develop an intuitive understanding of the complexity of these algorithms. Prerequisites:CS 0401 Requirements and grading: Between 5 and 7 programming assignments, 2 or 3 exams, and a cumulative final exam. Recitation: A recitation associated with the selected class section is required. Class size: 40 Frequency: This course is offered every term.

CS 0447: Computer Organization and Assembly Language Programming (3 cr) The purpose of this course is to study the components of computing systems common to most computer architectures. In particular, this class is meant to introduce data representation, types of processors (e.g., RISC V. CISC), memory types and hierarchy, assembly language, linking and loading, and an introduction to device drivers. Prerequisites: CS 0441 (Note that CS 0445 may be taken concurrently) Requirements and grading: Grading will be based on homeworks (4), programming projects (4), and exams (2). Recitation: A recitation associated with the selected class section is required. Class size: 48 Frequency: This course is offered every term

CS 1501: Data Structures And Algorithms (3 cr) All problem solving methods of computer science involve the manipulation of data. Some of the tools, called data structures, used in storing and manipulating data are studied in this course. Among these data structures are lists and trees. Problem solving methods investigated include divide and conquer techniques, greedy methods, and dynamic programming. Various sorting and searching methods will also be studied. Finally, students

12 in this course will be introduced to methods of analyzing the efficiency of an algorithm. Prerequisites: CS 0441, CS 0445, CS 0447, and Math 0220 Requirements and grading: Between 4 and 6 programming assignments, pencil and paper assignments, 1 or 2 progress exams, and a cumulative final exam. Recitation: A recitation associated with the selected class section is required. Class size: 60 Frequency: This course is offered every term.

CS 1520: Programming Languages (3 cr) Several programming languages selected from: Ada, Smalltalk, PROLOG, Scheme, and ICON will be studied from a programming (rather than an implementation) point of view. The study of these diverse programming languages will exemplify differing approaches to concepts such as scope of declaration, storage allocation, data structure variety, binding times, and control structures. Prerequisites: CS 0445 Requirements and grading: Exams and programming assignments. Recitation: A recitation associated with the selected class section is required. Class size: 48 Frequency: This course is offered every term

CS 1530: Software Engineering (3 cr) The purpose of this course is to provide a general survey of software engineering. Some of the topics covered include project planning and management, design techniques, verification and validation, and software maintenance. Particular emphasis is on a group project in which a group of 4-5 students implement a system from its specification. Prerequisites: CS 0445 Requirements and grading: Written assignments, a group project, one or two progress exams and a final exam. Recitation: No recitation sections. Class size: 48 Frequency: This course is offered in the Spring term.

CS 1538: Introduction To Simulation (3 cr) This course introduces students to the concepts, definitions, and techniques applicable to the simulation of systems. Both continuous and discrete modeling are covered, with emphasis on the latter. The objective of this course is to familiarize the student with several modern discrete simulation languages, and their use in modeling. GPSS/H is an interactive, transaction-oriented tool whereas SIMSCRIPT is an event-oriented language. Programming is done in the ULTRIX environment. Topics include: systems characterization, classification, and modeling; pertinence of probability and statistics theory for stochastic processes and model measurement; discrete systems simulation viewpoints; software modeling techniques in SIMSCRIPT and GPSS. Prerequisites: CS 0447 and one statistics course. Requirements and grading: Two simulation programming projects and two examinations. Recitation: No recitation sections. Class size: 35

13 Frequency: This course is not offered on a regular basis. CS 1566: Introduction to Computer Graphics (3 cr) The basic concepts, tools and techniques of computer graphics are described, and the fundamental transformations of scaling, translation, rotation, windowing and clipping are presented. Particular emphasis will be placed on new developments in microcomputer graphics. Students will be expected to develop a graphics application in C in conjunction with a specially developed graphics library. Prerequisites:CS 0445, CS 0447 and Math 0280 Requirements and grading: About five programming assignments (using locally available graphics system(s)), possibly some written homework assignments, and examinations. Recitation: None. Class size: 40 Frequency: This course is usually offered twice a year.

CS 1645: Introducti

Research project
A minimum of a one semester research project with a member of the program faculty.

Sample course schedule for a computer science major.

Sample course schedule for a physics major.

1.  Carlton Comp Chem

Sample Program: Honours in Computational Chemistry (4-year program)

Computer Science:

Introduction to Programming, C, C++
Problem Solving in Systems Programming
Numeric and Non-Numeric Programming
Design, Construction of Computer Programs
Development of Complex Software Systems
Construction of Large Software systems
Database Management
Numerical Analysis: Software Reliability
Advanced Specialization

Chemistry/Computational Chemistry:

Introductory Chemistry
Biophysical Chemistry
Physical Chemistry
Organic Chemistry
Organic Chemistry/Computational Lab
Quantum Chemistry
Methods of Computational Chemistry
Computational Chemistry Lab
Advanced Organic Chemistry
Inorganic Chemistry: Structure, Energetics
Inorganic Chemistry: Electronic Structure
Pharmaceutical Drug Design
Advanced specialization
Final Year Research Project

Biochemistry, Biology, Physics, Mathematics

Cell Biology
General Biochemistry
Advanced Specialization (Biochemistry)
Introductory Physics
Calculus I
Algebra
Calculus II

1. Buffalo, Comp Physics

Required Courses for the B.S. in Computational Physics

Acceptance Criteria: GPA of 2.5 in CSE 115 & 116, MTH 141 & 142, PHY 107 & 108/158.

Total Required Credit Hours in Computer Science, Mathematics, and Physics: 85-88

A. REQUIRED COURSES for the B.S. in Computational Physics

• CSE 115-116 Introduction to Computer Science for Majors I-II (4-4)
• CSE/MTH 191-192 Introduction to Discrete Mathematics I-II (4-4)
• CSE 250 Algorithms and Data Structures (4)
• CSE 305 Introduction to Programming Languages (4)
• CSE 351 Software Design, Development, and Testing (4)
• CSE/MTH 437-438 Introduction to Numerical Analysis I-II (4-4) or PHY 410-411 Computational Physics I-II (3-3)
• MTH 141-142-241 College Calculus I-II-III (4-4-4)
• MTH 306 Introduction to Differential Equations (4)
• MTH 309 Introductory Linear Algebra (4)
• PHY 107-108 General Physics I-II (4-3) or PHY 117-118 Honors Physics I-II (4-4)
• PHY 158 General Physics II Lab (1)
• PHY 207 General Physics III (3) or PHY 217 Honors Physics III (3)
• PHY 207 General Physics III Lab (1)
• PHY 208 General Physics IV (3)
• PHY 208 General Physics IV Lab (1)
• PHY 301 Intermediate Mechanics I (3)
• PHY 401 Modern Physics I (3)
• PHY 403 Electricity and Magnetism I (3)
• PHY 405 Thermal and Statistical Physics I (3)
• PHY 407 or 408 Advanced Physics Lab (3-3)

B. GENERAL EDUCATION REQUIREMENTS AND ELECTIVES: 32-35 Credit-Hours

TOTAL CREDIT-HOUR REQUIREMENTS: 120

RECOMMENDED SEQUENCE FOR THE B.S. IN COMPUTATIONAL PHYSICS

Year            Fall Semester                Spring Semester

Freshman        CSE 115                      CSE 116
                MTH 141                      MTH 142
                General Education            PHY 107 or PHY 117
                General Education            General Education

Sophomore       CSE/MTH 191                  CSE/MTH 192
                MTH 241                      CSE 250
                MTH 306                      PHY 207/207LAB
                PHY 108/158 or PHY 118/158   PHY 208

Junior          CSE 305                      CSE 351
                PHY 208 LAB                  MTH 309
                PHY 301                      General Education
                PHY 401                      General Education

Senior          PHY 403                      PHY 408
                PHY 405                      CSE/MTH 438 or PHY 411
                CSE/MTH 437 or PHY 410       General Education
                General Education            General Education

Course Descriptions

2. ISU, Comp Physics

 This is a four year professional physics program with a strong emphasis on computation. It is designed for students seeking graduate study in computational physics and related fields, or industrial employment. Majors complete a well-balanced curriculum concentrating on theoretical, experimental, and computational physics. The program is supported by excellent facilities, including scientific workstation labs and well-equipped experimental laboratories.

Required Courses:                                          

  PHYSICS

• 107 Frontiers in Physics
• 110 Physics for Scientists and Engineers I
• 111 Physics for Scientists and Engineers II
• 112 Physics for Scientists and Engineers III
• 217 Methods of Theoretical Physics
• 220 Mechanics I
• 240 Electricity and Magnetism I
• 270 Experimental Physics
• 284 Quantum Mechanics I
• 288 Methods of Computational Science
• 325 Thermal Physics
• 388 Advanced Computational Physics
• 390 Computational Research in Physics
• At least one from:
•   320 Mechanics II
•   340 Electricity and Magnetism II
•   384 Quantum Mechanics II

 
  APPLIED COMPUTER SCIENCE

• 254 Hardware and Software Concepts

Elective Courses:
  Three additional hours to be chosen from 300-level Physics courses. Recommended Electives

• 380.02 Molecular Dynamics
• 380.03 Nonlinear Science

 
Prerequisite Courses:

• ACS 165 Programming for Scientists
• MAT 145 Calculus I
• MAT 146 Calculus II
• MAT 147 Calculus III
• MAT 175 Linear Algebra
• MAT 340 Differential Equations I

2. OSU- Complt Physics

Bachelor of Science, Arts in Computational Physics

Oregon State University, College of Science, Department of Physics

Total Credits: 180 (quarter system)

To qualify for the Bachelor of Arts degree in Computational Physics, the student must take 18 of the 21 listed upper-division Physics courses (excluding MTH 341), four courses from the group: CS 391, CS 395, PH 423, PH 431, PH 461, plus 9 credits of approved electives in the College of Liberal Arts. In addition, the student must complete or demonstrate proficiency in the second year of a foreign language.

Core Courses, Physics

PH 211+221, 212+222, 213+223, General Physics  + Recitation (4+1, 4+1, 4+1);
PH/MTH/CS  265, Scientific Computing I (3);
PH 314, Introductory Modern Physics (4);
PH 365, ** (NEW) Scientific Computing II (3); **
PH 401, Thesis (4);
PH 407, Computational Physics Seminar (2);
PH 417, ** (NEW) ** Advanced Computational Physics Laboratory 3; **
PH 421, Oscillations (2);
PH 422, Static Vector Fields (2);
PH 423, Energy and Entropy (2);
PH 424, Waves in One Dimension(2);
PH 425, Quantum Measurement (2);
PH 426, Central Forces (2);
PH 427, Periodic Systems (2);
PH 431, Electromagnetism (3);
PH 435, Classical Mechanics (2); or 451, Quantum Mechanics (2);
PH 461, Mathematical Methods of Physics (3);
PH 465, 466, Computational Physics Simulations I & II (3,3);

    Core Courses, Mathematics

MTH 251, Differential Calculus (4);
MTH 252, Integral Calculus (4);
MTH 254, 255, Vector Calculus I, II (4,4);
MTH 235, Discrete Mathematics (3), or 231, Elements of Discrete Mathematics (4);
MTH 253, Infinite Series and Sequences (4);
MTH 256, Applied Differential Equations (4);
MTH 341, Linear Algebra (3);
MTH 361, Introductory Probability (3);

    Core Courses, Computer Science

CS 407, Seminar (1);
CS 161, 162, Introductory Computer Science, (4, 4);
CS 261, Data Structures, (4);
CS 391, Social & Ethical Issues in Computer Science (3);
CS 395, Interactive Multi Media (4);

    Elective Courses & Substitutions

                Substitution of other courses  may be made after written approval from the program director.

PH 451, Quantum Mechanics may be substituted  for PH 435, Classical Mechanics.

MTH 231, Elements of Discrete Mathematics may be substituted for MTH 235,
Discrete Mathematics.

MTH 452, Numerical Solution of Ordinary Diffrntl Equations or MTH 453,
Numerical Solution of Partial Diffrntl Equations, may be substituted for
CS 395.

CS 311, Operating Systems or CS 361, Fundamentals of Software
Engineering may be substituted for CS 395 or for CS 391.

PH 428, Rigid Bodies or Ph 441, Physical Optics may be substituted for
PH 423 or PH 427.

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1. Rice, Computl Math

Degree Requirements for B.A. in Computational and Applied Mathematics

Students majoring in computational and applied mathematics are required to complete the 51 semester hours spelled out in the following program of study.

Introductory Courses: Typically completed during the first two years

MATH 101 and 102 Single Variable Calculus I and II
(or honors equivalent)
MATH 211 Ordinary Differential Equations and Linear Algebra
MATH 212 Multivariable Calculus
COMP 110 Computation in Science and Engineering
CAAM 210 or 211 Introduction to Engineering Computation

Intermediate Courses: Typically completed by the end of the third year

CAAM 321 Introduction to Real Analysis
CAAM 322 Introduction to Real Analysis II
CAAM 335 Matrix Analysis
CAAM 336 Differential Equations in Science and Engineering
(or STAT 310 Probability and Statistics or STAT 331 Applied Probability)

Advanced Courses: Two full-year sequences chosen from the following 5 areas

Numerical Analysis
CAAM 451 Numerical Linear Algebra
CAAM 453 Numerical Analysis and Ordinary Differential Equations
Operations Research
CAAM 471 Linear Programming
CAAM 475 Integer and Combinatorial Optimization
Optimization
CAAM 454 Optimization Problems in Computational Engineering and Science
CAAM 460 Optimization Theory
Differential Equations
CAAM 436 Partial Differential Equations I
CAAM 437 Partial Differential Equations II
Scientific Computation
CAAM 420 Computational Science I
CAAM 421 Computational Science II
Electives
At least 3 courses, at or above the 300 level, selected upon consultation with the CAAM undergraduate adviser. The department strongly recommends that majors include ENGL 308 Engineering Communications among their electives.
 

2. Stanford Mathematical & Computational Science

MCS Core

The requirement for the bachelor's degree, beyond the University's basic requirements, is an approved course program of 72 to 77 units, distributed as follows:

Mathematics (29 - 31 units)

• Math. 41 and 42. Single Variable Calculus (5 units each)
  or, Math. 19, 20, 21 (3 units each)
• Math. 51. Linear Equations & Differential Calculus(5 units)
• Math. 52. Integral Calculus of Several Variables (5 units)
• Math. 109. Applied Modern Algebra (3 units) Writing in the Major course
  or Math. 110. Applied No. & Field Theory (3 units) Writing in the Major course
  or Math. 120. Modern Algebra (3 units) Writing in the Major course
  
• Math. 113. Linear Algebra and Matrix Theory (3 units)
  or Math. 104. Matrix Theory and Its Applications (3 units)
• Math 53. Ordinary Differential Equations with Linear Algebra(5 units)
  or Math. 130. Ordinary Differential Equations (3 units)

Computer Science (16 - 18 units)

• CS 106X. Programming Methodology and Abstractions (Accelerated) (5 units)
  or CS 106A and CS 106B (5 units each)
• CS 103X. Discrete Mathematics and Structures (Accelerated) (4 units)
• or CS 103A and CS 103B (3 units each)
• Two of the following:
  • CS 107. Programming Paradigms (5 units)
  • CS 137. Introduction to Scientific Computing (4 units)
  • CS 154. Introduction to Automata and Complexity Theory (4 units)
    
  • CS 161. Design and Analysis of Algorithms(3 units)
    
  • CS 260. Concrete Mathematics (3 units)

anagement Science and Engineering (8 - 9 units)

• ENGR 62. Introduction to Optimization (4 units)
  
• MS&E 121. Introduction to Stochastic Modeling (4 units)

  or three of the following:
  

• MS&E 211. Linear and Nonlinear Optimization (4 units)
• MS&E 212. Network and Integer Programming (3 units)
• MS&E 221. Stochastic Modeling(3 units)
• MS&E 251. Stochastic Decision Analysis(3 units)

  Statistics (11 units)

  • Stat. 116. Theory of Probability (5 units)
  • Stat. 200. Introduction to Statistical Inference (3 units)
  • Stat. 191. Intro. Regression Analysis and Applied Stat.(3 units)
    or, Stat. 203. Analysis of Variance (3 units)

   

  Electives (9 units)

  Three courses in mathematical and computational science, 100-level or above, at least 3 units each.

  At least one must be chosen from the following list:

  • MCS 100. The Mathematics of Sports.(3 units) limited to freshmen
  • Math. 106. Introduction to Theory of Functions of a Complex Variable (3 units)
  • Math 108. Introduction to Combinatorics and Its Applications (3 units)
  • Math 115. Fundamental Concepts of Analysis (3 units)
  • Math 116. Complex Analysis (3 units)
  • Math. 131. Partial Differential Equations I (3 units)
    
  • Math. 132. Partial Differential Equations II (3 units)
  • Math 135. Nonlinear Dynamics and Chaos (3 units)
  • Math 160A First-Order Logic (Enroll in Phil 160A) (4 units)
  • MS&E 211. Linear and Nonlinear Optimization (4 units)
  • MS&E 212. Network & Integer Programming (3 units)
  • MS&E 224. Stochastic Models in Operations Research (3 units)
  • MS&E 251. Stochastic Decision Models (3 units)
  • Stat. 202. Data Analysis II (3 units)
  • Stat. 217. Introduction to Stochastic Processes (3 units)
    
  • EE 261. The Fourier Transform and Its Applications (3 units)
  • Econ 102C. Advanced Topics in Econometrics (5 units)
  • Econ 160. Game Theory & Economic Applications (5 units)
  • Econ 181. Optimization & Economic Analysis (5 units)
    

    
    

  • For Computer Science, suggested electives include courses not taken under the above Computer Science list and the following:
  • CS 108. Object Oriented Systems Design (4 units)
  • CS 110. Introduction to Computer Systems and Assembly Language Programming (4 units)
  • CS 112. Computer Organization & Design(3 units)
  • CS 140. Operating Systems (4 units)
  • CS 143. Compilers (4 units)
  • CS 157. Logic and Automated Reasoning (4 units)
  • CS 161. Design and Analysis of Algorithms (4 units)
  • CS 194. Software Project (3 units)
  • CS 211. Logic Design (3 units)
  • CS 212. Computer Architecture and Organization (3 units)
  • CS 221. Artificial Intelligence: Principles and Techniques (3 units)
  • CS 223A. Introduction to Robotics(3 units)
  • CS 223B. Introduction to Computer Vision(3 units)
  • CS 225A. Experimental Robotics (3 units)
  • CS 228. Knowledge Representation and Reasoning under Uncertainty (3 units)
  • CS 229. Statistical Learning(3 units)
  • CS 237A. Numerical Linear Algebra (3 units)
  • CS 243. Advanced Compiling Techniques (4 units)