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.
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Be sure to go to http://www.stat.vt.edu/students/courses.html to check course duplications.
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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)
.