HANDBOOK
FOR THE
APPLIED DISCRETE
MATHEMATICS OPTION
Department of Mathematics
Virginia Polytechnic Institute & State University
Revised June 2015
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THE APPLIED DISCRETE MATHEMATICS OPTION
The Applied Discrete Mathematics (ADM) 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 Computational Mathematics Option. As computer power and
applications have evolved, the importance of combinatorics and discrete
mathematics has grown tremendously.
Techniques that employ
combinatorics and discrete mathematics are being used in almost every
area where mathematical computations are found. In response to this
area’s increased importance and utility, the Department has developed the
ADM Option, in which the student is given exposure to fundamental ideas
and techniques in discrete mathematics and combinatorics.
Since
computers are central in these applications we also require the students in
this option to develop a strong foundation in Computer Science.
The ADM Option is designed to allow students either to enter the job
market after their undergraduate years or to continue their studies at a
graduate-degree level. Those students who wish to begin work after their
undergraduate degree will have training in combinatorial techniques,
including graph theory (used in electrical circuits, optimization problems
among many other areas), number theory (basic to coding theory and
algorithm development), counting techniques (employed in almost every
area where mathematics is applied), and general algebraic theories
(providing the student with a strong abstract mathematical foundation). A
student completing the ADM Option will be employable in many different
capacities. For example, our students would be prepared to work for the
National Security Agency (which employs many mathematicians and is
interested in applications of coding theory), software development
companies, engineering companies that need software development, and
research laboratories such as Bell Laboratories and IBM Laboratories.
Students who complete the ADM Option will have both the mathematical
sophistication to handle abstractions and a firm grounding in applicable
techniques. These skills will be enhanced by a strong background in the
use of computers that will include programming proficiency.
For those students who wish to continue their education, the ADM Option
requires the student to complete the basic mathematics courses that are
required for admission to most graduate programs in mathematics. By
adding three additional credits in Computer Science, students can obtain a
minor in that area, and possibly continue on to graduate school in
Computer Science.
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For additional information on the ADM Option, you should contact Ezra
Brown (540-231-6950). 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.
SAMPLE PROGRAM OF STUDY
There is considerable flexibility in designing a program of study. The example given below is not likely to fit every situation and is
provided for information as you develop your own plan with your advisor.
Bachelor of Science (B.S.) in MATH (BS MATH) - ADM Option, Path 2 (new calculus sequence)
Freshman
1st Semester
ENGL 1105 Freshman English (Area 1)
MATH 1225 Calculus of a Single Variable
MATH 2984 SS: Discovering Mathematics I
CS
1114 Intro to Software Design
Area 2 - Ideas, Cultural Traditions and
Values
3
4
1
3
3
2nd Semester
ENGL 1106 Freshman English (Area 1)
MATH 1226 Calculus of a Single Variable
MATH 2984 SS: Discovering Mathematics II
CS
2114 Software Design and Data Structures
Area 2 - Ideas, Cultural Traditions and
Values
Area 3 - Society and Human Behavior
14
3
4
1
3
3
3
17
Sophomore
1st Semester
2nd Semester
1
MATH 2114 Introduction to Linear Algebra
MATH 2204 Intro Multivariable Calculus
CS
2505 Introduction to Computer Organization
Area 3 - Society and Human Behavior
Area 4 – Scientific Reasoning and
Discovery
3
3
3
3
3
MATH 2214 Intro Diff Equation
MATH 3034 Introduction to Proofs
STAT 4714 Probability and Statistics for EE's
Area 6 - Creative and Aesthetic
Area 4 – Scientific Reasoning and
Discovery
15
3
3
3
3
3
15
Junior
1st Semester
MATH 3124 Modern Algebra
MATH 3214 Calculus of Several Variables
MATH 3134 Applied Combinatorics
CS
3114 Data Structures and Algorithms
Area 7 - Critical Issues
3
3
3
3
3
15
2nd Semester
MATH 3144 Linear Algebra I
MATH 3224 Advanced Calculus
CS
4104 Data and Algorithm Analysis
Free Elective
Free Elective
3
3
3
3
3
15
Senior
1st Semester
MATH 4xxx 4000-level Math Course2
MATH 4xxx 4000-level Math Course2
Free Elective
Free Elective
Free Elective
1
2nd Semester
3
3
3
3
3
15
MATH 4134 Number Theory (S)
3
2
MATH 4xxx 4000-level Math Course
Free Elective
Free Elective
Free Elective
If you do not have Math 1114 credit prior to fall 2014, take Math 2114 instead. Check prerequisites to determine the appropriate semester to take Math 2114.
At least one of MATH 4144 (S), 4124 (F), 4175 (F), 4176 (S) or 5114 (S) must be taken to satisfy 4000-level course requirements.
(F) = offered fall semesters only
(S) = offered spring semesters only
2
3
3
3
3
15