Mathematics, Optimization and Operations Research Specialty, B.S.

Degree Requirements

The Bachelor of Science degree requires a minimum of 61 credits. The Bachelor of Arts degree requires a minimum of 50 credits, and a minor in mathematics requires a minimum of 31 credits. These are allocated below between core requirements, upper-division mathematics/statistics elective requirements and supplementary elective requirements.

For all mathematics majors and minors, a common core of courses is required. These core requirements are the same for candidates for the Bachelor of Arts and for mathematics minors. Candidates for the Bachelor of Science degree must complete three additional courses for their core requirements.

Core Requirements for the Bachelor of Arts Degree and for Minors

MATH 151 - Calculus and Analytic Geometry I (4.00)
MATH 152 - Calculus and Analytic Geometry II (4.00)
MATH 221 - Introduction to Linear Algebra (3.00)
MATH 225 - Introduction to Differential Equations (3.00)
MATH 251 - Multivariable Calculus (4.00)
MATH 301 - Introduction to Mathematical Analysis I (4.00)
CMSC 201 - Computer Science I for Majors (4.00)

Note:

Core requirements MATH 151 , MATH 152 , CMSC 201 are fulfilled by sufficiently high scores on AP or CLEP or IB examinations. See Appendices of this catalog for details.
The sequence MATH 140 , MATH 141 , MATH 142 is equivalent to MATH 151 , MATH 152 . Students may not receive credit for both sequences.
Students may need to take CMSC 104 prior to CMSC 201 .

Core Requirements for the Bachelor of Science Degree

In addition to the core requirements listed above, the Bachelor of Science degree requires the following:

PHYS 121 - Introductory Physics I (4.00)
PHYS 122 - Introductory Physics II (4.00)

Select one course: 3 Credits

MATH 302 - Introduction to Mathematical Analysis II (3.00)
MATH 401 - Mathematical Analysis (3.00)

Note:

The above cannot be used to fulfill mathematics elective requirements or supplementary elective requirements.

Mathematics/Statistics Elective Requirements

After completion of the core requirements, each major or minor is required to take a certain number of additional three- or four-credit mathematics or statistics courses numbered 300 or higher. MATH 380 , STAT 350 and STAT 351 , designed for other majors, are not allowed to meet the requirements below. MATH 432 may not be used as a mathematics elective, but it may be used as a supplementary elective. NOTE: MATH 432 and MATH 481 are GEP writing intensive courses.

B.S. degree

Six courses

For one of the mathematical electives, a major may bundle together three or more credits from courses carrying one or two credits. These include:

MATH 426 - Introduction to Math Software Packages: MATLAB (2.00)
MATH 427 - Mathematical Software Packages: Maple (1.00)
MATH 479 - Mathematical Problem Solving Seminar (1.00)
MATH 480 - Senior Seminar (1.00)
MATH 490 - Special Topics in Mathematics (1.00 - 4.00)
MATH 496 - Mathematics Practicum (1.00 - 4.00)
MATH 499 - Independent Study in Mathematics (1.00 - 4.00)
STAT 432 - Statistical Computer Packages and Their Applications: SAS and R (1.00)
STAT 470 - Probability for Actuarial Science (1.00)
STAT 490 - Special Topics in Statistics (1.00 - 4.00)
STAT 496 - Statistics Practicum (1.00 - 4.00)
STAT 499 - Independent Study in Statistics (1.00 - 4.00)

Note:

For the B.S. in Mathematics, at least three of the mathematics/statistics electives must be at the 400 level.

Specialty in Optimization and Operations Research

Listed below are suggested electives for each specialty mentioned previously.

MATH 381 - Linear Methods in Operations Research (3.00)
MATH 411 - Linear Algebra (3.00)
MATH 430 - Matrix Analysis (3.00)
MATH 452 - Introduction to Stochastic Processes (3.00)
MATH 475 - Combinatorics and Graph Theory (3.00)
MATH 481 - Mathematical Modeling (3.00)
MATH 482 - Nonlinear Optimization (3.00)
MATH 483 - Linear and Combinatorial Optimization (3.00)
MATH 484 - Stochastic Methods in Operations Research (3.00)
MATH 495 - Topics in the Mathematics of Operations Research (3.00)
STAT 451 - Introduction to Probability Theory (3.00)

Supplementary Requirements

Mathematics and statistics have proven indispensable in many disciplines in the physical sciences, the social sciences and even in the humanities and arts. Much of mathematics and statistics has developed with a view toward its applications in other fields. To develop an appreciation of the connection, mathematics majors are required to take three courses for the B.A. and two courses for the B.S. additional to the core from other departments reflecting these interconnections. These are listed below. From time to time, special topics courses offered by other departments may be used to satisfy supplementary requirements, subject to departmental approval. Occasionally mathematics or statistics courses are cross-listed in other departments. Taken under the other department these count as supplementary electives. Mathematics minors are not subject to these supplementary requirements.

*Note:*None of the mathematics electives nor the supplementary electives are elective except for choices within categories; all are required by the certificate program in mathematics education.

Courses for Supplementary Requirements

BIOL 463 - Theoretical and Quantitative Biology (4.00)
CHEM 401 - Chemical and Statistical Thermodynamics (3.00)
CHEM 415 - Statistical Mechanics and Theory of Rate Processes (3.00)
CMPE 320 - Probability, Statistics, and Random Processes (3.00)
CMPE 323 - Signal and Systems Theory (3.00)
CMSC 203 - Discrete Structures (3.00)
*(Must be taken before MATH 301 to be accepted as a supplementary elective)
CMSC 341 - Data Structures (3.00)
CMSC 441 - Design and Analysis of Algorithms. (3.00)
CMSC 442 - Information and Coding Theory (3.00)
CMSC 443 - Cryptology (3.00)
CMSC 451 - Automata Theory and Formal Languages (3.00)
CMSC 452 - Logic for Computer Science (3.00)
CMSC 453 - Applied Combinatorics and Graph Theory (3.00)
ECON 309 - Survey of Economic and Finance For Scientists and Engineers (3.00)
ECON 311 - Intermediate Microeconomic Analysis (3.00)
ECON 374 - Financial Management (3.00)
ECON 417 - The Economics of Strategic Interaction (3.00)
ECON 421 - Introduction to Econometrics (3.00)
EDUC 420 - Teaching Mathematics in the Elementary School (3.00)
EDUC 426 - Mathematics in the Secondary School (3.00)
ENCH 300 - Chemical Process Thermodynamics (3.00)
ENME 217 - Engineering Thermodynamics (3.00)
ENME 315 - Intermediate Thermodynamics
ENME 320 - Fluid Mechanics (3.00)
ENME 410 - Operations Research I (3.00)
MATH 432 - History of Mathematics (3.00)
PHIL 248 - Introduction to Scientific Reasoning (3.00)
PHIL 346 - Deductive Logic (3.00)
PHIL 372 - Philosophy of Science (3.00)
PHYS 121 - Introductory Physics I (4.00)
PHYS 122 - Introductory Physics II (4.00)
PHYS 224 - Vibrations and Waves (3.00)
PHYS 303 - Thermal and Statistical Physics (3.00)
PHYS 321 - Intermediate Mechanics (3.00)
PHYS 407 - Electromagnetic Theory (3.00)
PHYS 424 - Introduction to Quantum Mechanics (3.00)
PHYS 440 - Computational Physics (3.00)

General Education Requirements for Mathematics Majors

Mathematics majors who are considering courses to satisfy General Education Requirements will satisfy the biological/physical science requirements if they take PHYS 121 and PHYS 122 and a lab course. For the social science (SS) General Education Requirement, good choices would be ECON 101 and ECON 102 , which are prerequisite to supplementary requirement courses ECON 311 , ECON 374 , ECON 417 and ECON 421 . These are recommended in particular for those pursuing the specialty in actuarial science or, to a lesser extent, specialties in statistics science or optimization and operations research. PHIL 146 and PHIL 248 are recommended as choices for AH General Education Requirement courses. The latter is also a supplementary requirement for the major. Note that those pursuing the Bachelor of Science degree need only take one culture course. Both MATH 432 and MATH 481 satisfy the GEP writing intensive requirements. Students may also wish to consider ENGL 393 .

Note: Before registering in any mathematics course up to MATH 151 or MATH 155 , students must have completed a placement test administered by the Learning Resources Center if they have not completed the prerequisite college-level course with a “C” or better. This is normally done prior to the first semester at UMBC.

Passage of AP Calculus exams with a suitable score is considered the equivalent of MATH 150 , MATH 151 or MATH 152 . The AP Statistics exam with a score of 4 or 5 is equal to STAT 121 .

Otherwise students must complete MATH 106 with a “C” or better. Even higher algebra skills are recommended for MATH 150 or MATH 155 .

The specific courses listed as prerequisites indicate the level of maturity necessary for the course. A student who does not have a formal prerequisite for a particular course must request the consent of the instructor to take that course. Prerequisites for all mathematics courses must be satisfied with a grade of “C” or better.

All courses for major or minor requirements must be passed with a grade of “C” or better.