HANDBOOK FOR THE APPLIED AND COMPUTATIONAL MATHEMATICS OPTION Department of Mathematics Virginia Polytechnic Institute & State University Revised June 2013 2 THE APPLIED AND COMPUTATIONAL MATHEMATICS OPTION The Applied and Computational Mathematics (ACM) Option is one of the four options or paths toward a B.S. in Mathematics offered at Virginia Tech, the others being (1) the Traditional Option, (2) Mathematics Education Option, and (3) the Applied and Discrete Mathematics Option. The ACM program is designed to train students for successful entry into jobs in laboratories and industrial organizations, as well as to prepare students for graduate study in applied mathematics, mathematics, and the sciences. The ACM option has four components, each of which plays a crucial role in the career of a working applied mathematician. Area of Applications. One of the main components of the ACM program is the requirement that all students taking the option acquire a substantial knowledge in some area of applications. Each student will be required to make (with the help of his or her advisor) an individual program of study. The program will contain 12 credits in a single technical discipline (i.e. usually from a single department). Scientific Computing. Since computational hardware has become faster, cheaper and more common, all applied mathematicians (especially those who work in laboratories and taking the ACM option will be trained in the skills necessary to analyze, employ, and evaluate large-scale algorithms for solving applied problems. This is accomplished through courses in programming, scientific computing and numerical analysis. Technical Tools of Applied Mathematics. Applied mathematics employs a broad spectrum of techniques, methods and tools in attacking real-world problems. Students in the ACM program will develop skills in discrete mathematics, ordinary differential equations, partial differential equations, numerical analysis, and scientific computation. Mathematical Rigor. Students in the ACM option will receive a firm background in rigorous mathematics through such courses as Calculus of Several Variables, Advanced Calculus, Linear Analysis, Applied Discrete Mathematics, and Numerical Analysis. Courses such as Partial Differential Equations and Scientific Computing will provide links between mathematical rigor and applied problems. For additional information on the ACM Option, you should contact Serkan Gugercin (231-6549). For information concerning aspects that uniformly affect all four Mathematics undergraduate degree options, you should examine the “Handbook for Mathematics Majors” available in the Mathematics Office, 460 McBryde Hall. These topics include scholarships, advising, University and College of Science Curriculum for Liberal Education requirements, course content explanations, the Honors Program, dual majors, minors, the Cooperative Education Program, undergraduate activities, mathematics competitions, job placement, and preparation for graduate school. 3 Requirements in Mathematics Credits 1205 - 1206 1114, 1224 3, 3 2, 2 2214, 2224 3034 3144 3214 3224 4425 - 4426 4445 – 4446 4414 Calculus Elementary Linear Algebra and Vector Geometry Elementary Differential Equations and Multivariable Calculus Proofs Linear Algebra Calculus of Several Variables Advanced Calculus Fourier Series and Partial Differential Equations Introduction to Numerical Analysis Scientific Computing Math Electives1 3, 3 3 3 3 3 3, 3 3, 3 3 6 Requirements in Applied Areas CS 1044, CS 1054, CS 1114, or Math 3054 Intro Prog in C/Intro Prog in Java Intro Software Design Prog & Math Problem Solving 3 Application Area Program2 12 College of Science Requirements3 Area 1: Writing and Discourse Area 2: Ideas, Cultural Traditions and Values Area 3: Society and Human Behavior Area 4: Natural Sciences Area 6: Creativity and Aesthetic Experience Area 7: Critical Issues in a Global Context 6 6 6 6 3 3 Free electives4 : Hours needed to achieve 120 credit graduation requirement. This will be approximately 26 hours. _______ Total Credits 120 1 The six hours of math electives must be chosen from Mathematics courses numbered between 4024 and 4454 with the following exceptions: (a) MATH 3124 can be used to satisfy three of the six hours requirements. (b) No more than 3 hours from MATH 4044. 4334. 4344 can be used to satisfy the six hour requirement. 2 See attached description of applications area program of study. 3 See current Curriculum for Liberal Education Handbook or Catalog. 4 A maximum of 60 hours in Mathematics is allowed to be counted toward the 120 credit total. 4 Applications Area Program of Study One of the main components of the ACM program is the requirement that all students taking the option acquire a substantial knowledge in some area of applications. Thus, students will be required to take 12 hours of courses in a single applications area. Each student will be required to make (with the help of his or her advisor) an individual program of study proposing the twelve credits. This plan will be submitted for approval to the ACM advisor. The program will contain 12 credits in a single technical discipline (i.e. usually from a single department). A sample of programs appears below. Note: In the lists of courses below, we have not explicitly noted prerequisites that are included in the requirements of the ACM option or that are included within the individual list; a program of study can always be selected from each list using only required courses, noted prerequisites, and courses from the list. In addition, not all courses appearing on the course catalog will be available every term. You are advised to check the relevant Timetable of Classes to determine the availability of particular classes. Aerospace Engineering ESM ESM ESM AOE AOE AOE AOE AOE ME 2104 2204 2304 3014 3024 3034 3104 3114 3134 Statics Mechanics of Deformable Bodies Dynamics Aero/Hydrodynamics Thin-Walled Structures Vehicle Vibration and Control Aircraft Performance Compressible Aerodynamics Fundamentals of Thermodynamics Biology BIOL BIOL BIOL BIOL BIOL 2304 2504 3124 3404 4004 Plant Biology General Zoology Cell Physiology Introductory Animal Physiology Freshwater Ecology 5 Economics2 ECON 2005-2006 ECON 3104 ECON 3204 ECON 4124 ECON 4304 ECON 4424 ECON 4924 Principals of Economics Microeconomic Theory Macroeconomic Theory Growth and Development Econometric Methods Theory of Games and Economic Behavior Managerial Economics Electrical and Computer Engineering3 ECE ECE ECE ECE ECE ECE ECE ECE 2004 2204 2504 2574 3054 3105 – 3106 3204 4134 Electric Circuit Analysis Electronics Intro to Computer Engineering Intro to Data Structures and Algorithms Electrical Theory Electromagnetic Fields Analog Electronics Fiber Optics & Applications Finance ACIS 2004 or 2115 ECON 2005-2006 FIN 3104 FIN 4144 Survey of Accounting Principles of Accounting Principles of Economics Introduction to Finance International Financial Management (Note: FIN 3104 is prerequisite to all advanced courses in finance.) 2 STAT 3005 is a pre-requisite for ECON 4304 ENGE 1016 is a prerequisite for ECE 2004. ECE 2274 is a corequisite for ECE 2204. PHYS 2306 is a prerequisite for ECE 3054 3 6 Business Information Technology ACIS BIT BIT BIT BIT BIT 1504 2405-2406 3424 3434 3444 4434 Intro. To Business Information Systems Quantitative Methods Intro to Business Analytics Modeling Advanced Modeling for Business Analytics Advanced Business Computing and Applications Computer Simulation in Business Operations Research4 STAT ISE ISE ISE ISE ISE 4705-4706 2404 3414 3424 3614 4404 Probability & Statistics for Engineers Deterministic Operations Research Probabilistic Operations Research Discrete Event Computer Simulation Intro to Human Factors Engineering Statistical Quality Control Physics PHYS PHYS PHYS PHYS PHYS 2305-2306 3355-3356 3405-3406 4614 4714 Foundations of Physics I Intermediate Mechanics Intermediate Electricity & Magnetism Optics Intro. To Biophysics Statistics5 STAT STAT STAT STAT STAT STAT STAT STAT STAT STAT 4 3005-3006 3104 4004 4105-4106 4204 4214 4514 4524 4604 4705-4706 Statistical Methods Probability and Distributions Methods of Statistical Computing Theoretical Statistics Experimental Designs Methods of Regression Analysis Contingency Table Analysis Sample Survey Methods Statistical Methods for Engineers Probability and Statistics for Engineers STAT 4105 is a prerequisite for ISE 3614 and can be a prerequisite for STAT 4706. ENGE 2314 is a prerequisite for ISE 3414. 5 Be sure to go to http://www.stat.vt.edu/students/courses.html to check course duplications. 7 SAMPLE PROGRAM OF STUDY MATHEMATICS/APPLIED AND COMPUTATIONAL OPTION There is considerable flexibility in designing a program of study and the one given below is not likely to entirely fit your situation. It is provided for your information only, and you should certainly not feel constrained to follow it. Fall Semester Spring Semester Freshman Year: English 1105 Math 1205 Math 1114 Area 2 Selection Area 3 Selection Total hours (3) (3) (2) (3) (3) (14) English 1106 Math 1206 Math 1224 Area 2 Selection Area 6 Selection (3) (3) (2) (3) (3) (14) (3) (3) (3) (3) (3) (15) Math 2224 Math 3034 Area 4 Selection Application Area Free Elective (3) (3) (3) (3) (3) (18) Sophomore Year: Math 2214 Area 3 Selection Area 4 Selection Area 7 Selection Free Elective Total hours Junior Year: Math 3214 (3) Math 4425 (3) Applications Area (3) CS 1044/1054/1114 (3) Math 3224 (3) Math 4426 (3) Applications Area (3) Free electives (6) MATH 3054 Free Elective Total hours (3) (15) (15) Senior Year: Math 4445 (3) Math 4414 (3) Math Elective (3) Applications Area (3) Free Elective (3) Total hours (15) Total requirement: 120 Hours Math 4446 Math 3144 Math Elective Applications Area Free electives (3) (3) (3) (3) (3) (15) .