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**MA-116** Discrete Structures

Introduces mathematical structures and concepts such as functions, relations, logic, induction, counting, and graph theory. Their application to Computer Science is emphasized.

FallYearly4 CreditsN, Q**Pre-requisite high school algebra.**

--OR--

**CS-116 ** Discrete Structures

Discrete Structures (Fall; Yearly; 4.00 Credits; N, Q) Introduces mathematical structures and concepts such as functions, relations, logic, induction, counting, and graph theory. Their application to Computer Science is emphasized.

VariableYearly4 CreditsQ,N**Pre-requisite: high school algebra. **

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**MA-130** Calculus I

An introduction to calculus including differentiation and integration of elementary functions of a single variable, limits, tangents, rates of change, maxima and minima, area, volume, and other applications. Integrates the use of computer algebra systems, and graphical, algebraic and numerical thinking.

Fall & SpringYearly4 CreditsN, QM

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**MA-160** Linear Algebra

An introduction to systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, and applications.

Fall & SpringVariable3 CreditsN, QM**Prerequisites: MA130.**

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**MA-210** Foundations of Mathematics

An introduction to the logical and set-theoretic basis of modern mathematics. Topics covered include propositional and predicate logic; induction; naive and axiomatic set theory, binary relations, mappings, infinite sets and cardinality; finite sets and combinatorics; and an introduction to the theory of computability. Students will learn to read and to express mathematical ideas in the set-theoretic idiom.

FallYearly3 CreditsCW**Prerequisites: MA160 or MA116 or PL208 or MA208 or permission of the instructor.**

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**MA-220** Introduction to Probability & Statistics

An introduction to the basic ideas and techniques of probability theory and to selected topics in statistics, such as sampling theory, confidence intervals, and linear regression.

Fall & SpringVariable4 CreditsN, QS, CTGES**Prerequisite: MA130**

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**MA-230** Calculus II

Expands the treatment of two-space using polar and parametric equations. Emphasizes multivariable calculus, including vectors in three dimensions, curves and surfaces in space, functions of several variables, partial differentiation, multiple integration, and applications.

Fall & SpringYearly4 CreditsN, QM**Prerequisite: MA130**

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**MA-235** Calculus III

A continuation of the calculus sequence. Topics include methods of integration by Simpson's Rule, applications, Taylor and Fourier series; introduction to ordinary differential equations; integration in polar, cylindrical, and spherical coordinates; differential and integral vector calculus.

FallYearly4 CreditsN, QM**Prerequisites: MA230.**

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**CS-110 ** Computer Science I

An introductory study of computer science software development concepts. Python is used to introduce a disciplined approach to problem solving methods, algorithm development, software design, coding, debugging, testing, and documentation in the object oriented paradigm. This is the first course in the study of computer science.

VariableYearly3 CreditsN,CTGES,CTGIS**Recommended programming experience or IT110 or IT100, IT111 or IM110 or MA103 but
not necessary. **

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**MA-480** Mathematics Seminar I

A discussion-based study of current mathematical literature and modeling problems. Students will both apply their previous mathematical knowledge and explore new topics. In addition, students may use this course as preparation for an individual research project to be completed in MA485. A junior taking this course may repeat it as a senior as MA481.

FallYearly1 CreditN**Prerequisites: junior or senior standing, MA160, MA210 and MA235 or permission of
the instructor.**

**Total credit hours = 30**

Students should complete the POE by including at least 18 upper-level credits (300- or 400-level) from the lists below, at least 12 of which must be mathematics (MA) credits. Students must take at least one upper-level MA course (of at least 3 credits) with a prerequisite of MA 210, and at least one upper-level MA course (of at least 3 credits) without a prerequisite of MA 210.

##### Applied Mathematics:

**MA-303** Mathematical Modeling

How to use mathematics to model " real-world " problems. Modeling topics range from population dynamics to economics to the nuclear arms race. Mathematical tools range from calculus to curve fitting to computer simulation. How to make a little bit of mathematics go a long way.

FallYearly3 CreditsN, QM, CW**Note: MA160 is recommended. Prerequisite: MA130 and experience with programming and
Minitab.**

**MA-321** Multivariate Statistics

A class in multivariate statistical techniques including non-parametric methods, multiple regression, logistic regression, multiple testing, principle analysis.

SpringVariable3 CreditsN, QS**Prerequisites: An introductory statistics course ( MA220 or BI305 or PY214 or EB211)
and linear algebra (MA 160) or Calculus 1 (MA 130).**

**MA-322** Probability

Topics in probability including discrete and continuous random variables, expectations, mean, variance, moment generating functions, multivariate distributions, correlation, and independence, all leading to an efficient study of the binomial, Poisson, gamma, chi-square, and normal distributions.

SpringEven Years3 CreditsN, QM**Prerequisites: MA220 and MA230; MA235 is recommended.**

**MA-325** Statistical Consulting

The participating students will receive training during the semester in consulting on statistical problems and to assist in collaborative efforts with faculty and/or staff on client-partnered projects that are pre-determined. The semester-long project provides the student with both real work experience in the field of statistics and a project-based learning experience in partnership with the client. May be taken multiple times for credit.

VariableYearly3 CreditsN, QS, CW, SW-LE** **

**MA-335** Differential Equations

Theory and application of ordinary differential equations. Emphasis on modern qualitative techniques, with numerical and analytical approaches used when appropriate. Contains a brief introduction to partial differential equations.

SpringYearly4 CreditsN, QM**Prerequisites: MA130 and MA230 and MA235 or MA233.**

**MA-340** Numerical Analysis

Theory and application of numerical approximation techniques. Topics included are numerical error, root-finding, interpolation and polynomial approximation, numerical differentiation and integration, and differential equations.

SpringEven Years3 CreditsN, QM**Prerequisites: MA160, MA130 and CS110 or permission. (Also listed as CS340.)**

**MA-399** Special Topics

An introduction to one of the branches of mathematics not currently included in the regular course offerings, such as number theory, history of mathematics, chaos and fractals, topology, graph theory, mathematical logic.

VariableVariable1-4 Credits **Prerequisites: Vary depending on course offering. Note: abbreviated ST: Students may
take each ST: course for credit.**

##### Theoretical Mathematics

**MA-316** Combinatorics

Advanced counting: what they didn't teach you on Sesame Street. An introduction to graphs, trees, and enumeration techniques with applications to computer science and biology.

FallEven Years3 CreditsQM, N**Prerequisites: MA116 or MA210 or MA220 or permission of the instructor.**

**MA-322** Probability

Topics in probability including discrete and continuous random variables, expectations, mean, variance, moment generating functions, multivariate distributions, correlation, and independence, all leading to an efficient study of the binomial, Poisson, gamma, chi-square, and normal distributions.

SpringEven Years3 CreditsN, QM**Prerequisites: MA220 and MA230; MA235 is recommended.**

**MA-335** Differential Equations

Theory and application of ordinary differential equations. Emphasis on modern qualitative techniques, with numerical and analytical approaches used when appropriate. Contains a brief introduction to partial differential equations.

SpringYearly4 CreditsN, QM**Prerequisites: MA130 and MA230 and MA235 or MA233.**

**MA-350** Topics in Geometry

Examines the history and development of geometry with an axiomatic development of Euclidean geometry leading to an investigation of hyperbolic and elliptical non-Euclidean geometries. The roles of these discoveries in the history of mathematics are emphasized.

SpringOdd Years3 CreditsN**Prerequisites: MA210 or PL208 or MA208.**

**MA-355** Nature of Mathematics

An introduction to the history and philosophy of mathematics. Briefly traces the historical development of mathematics from its Oriental and Greek origins to modern times. Surveys the different philosophies of mathematics and provides some insight into the current crisis in the foundations of mathematics.

SpringOdd Years1 Credit **Corequisite: MA350. Prerequisite: MA210 or PL208 or MA208.**

**MA-360** Abstract Algebra

Investigates the algebraic properties of the real numbers and their generalizations. Emphasis on group theory, with introductions to integral domains, rings, fields and vector spaces.

SpringEven Years3 Credits **Prerequisites: MA160 and MA210.**

**MA-365** Number Theory

An investigation of topics in Elementary Number Theory including divisibility, primes, congruence, congruence equations, quadratic residues and quadratic reciprocity, arithmetic and multiplicative functions, Diophantine equations, and other topics selected according to interest.

FallOdd Years3 CreditsN**Prerequisites: MA210 or permission of the instructor.**

**MA-370** Real Analysis

Focuses on functions of a real variable, sequences, limits, continuity, differentiation and the derivation of standard theorems of the differential calculus.

SpringOdd Years3 CreditsN**Prerequisites: MA210 and MA230 and MA235.**

**MA-375** Complex Analysis

Algebra and geometry of the complex numbers, analytic functions, complex integration, Taylor and Laurent series, residue theory, physical applications, and other topics as time allows.

FallEven Years3 CreditsN**Prerequisites: MA235**

**MA-399** Special Topics

An introduction to one of the branches of mathematics not currently included in the regular course offerings, such as number theory, history of mathematics, chaos and fractals, topology, graph theory, mathematical logic.

VariableVariable1-4 Credits **Prerequisites: Vary depending on course offering. Note: abbreviated ST: Students may
take each ST: course for credit.**

**MA-485** Mathematics Research

Allows students to pursue a program of directed original research in pure or applied mathematics. Required of candidates for distinction in mathematics POE.

Fall & SpringYearly3-5 CreditsN**Prerequisites: MA480.**

##### Courses from Other Departments

**CS-220 ** Computer Organization

An introduction to digital computer systems including a treatment of logic and digital circuits, data representation, device characteristics and register transfer notation covered in a manner that stresses application of basic problem solving techniques to both hardware and software design. Students gain experience programming in an assembly language to reinforce these systems and design concepts.

FallYearly4 CreditsN**Prerequisites: CS110.**

*Not an upper level class**

**CS-240 ** Computer Science II

A continued study of computer science foundations as begun In Computer Science I. An object-oriented language such as JAVA is used to develop and implement large programs involving various data structures and data abstraction as exemplified by packages and modules. Search, sorting, advanced data structures, programming methodology and analysis are emphasized.

SpringYearly4 CreditsN**Prerequisites: CS110 and MA116 or MA210. **

Not an upper level class*

**
CS-255C
** C++ Programming

The students will prepare a portfolio of computer programs written in the language. The programs are reviewed, critiqued, and then the student has an opportunity to revise them as needed for final inclusion in the portfolio.

SpringYearly2 CreditsN**Prerequisites: CS110 and Sophomore standing and permission. **

Not an upper level class*

**CS-300 ** Software Engineering

An introduction to the issues of software design. Topics include software engineering, software project management and development of projects in a modern design environment. The focus of the course is on the process used to develop quality software. The students work in teams to develop, implement and fully document a computer project to apply these concepts.

SpringYearly3 CreditsN**Prerequisite: CS240. **

**CS-315 ** Algorithms and Analysis

The study and analysis of algorithms, their complexity and supporting data structures. Topics include searching, sorting, mathematical algorithms, tree and graph algorithms, the classes of P and NP, NP-complete and intractable problems, and parallel algorithms.

Either SemesterOdd Years4 CreditsCW,N**Prerequisites: CS240 and MA116. **

**CS-330 ** Computer Graphics

An introduction to both the hardware and software utilized in computer graphics. The emphasis is on a top-down, programming approach, using a standard application programmer's interface. Students will create three-dimensional and interactive applications, in addition to studying several of the classic, low-level, rendering algorithms.

SpringEven Years3 CreditsN**Prerequisites: CS240. Corequisite: CS255C. **

**CS-362 ** Languages and Translation

A systematic approach to the study and analysis of computer programming languages. The procedural, functional, object- oriented and logical language paradigms are examined through the use ofrepresentative languages. Syntax and semantics issues are emphasized through the study of translation techniques in formal labs and group projects.

Either SemesterOdd Years4 CreditsN**Prerequisites: CS220 and CS240. Must have Junior or Senior standing. **

**CS-370 ** Database Management Systems

Focuses on concepts and structures necessary to design and implement a database management system. Various modern data models, data security and integrity, and concurrency are discussed. An SQL database system is designed and implemented as a group project.

FallYearly3 CreditsN,CTGIS**Prerequisites: CS110. **

**CS-399 ** Special Topics

An introduction to one of the branches of computer science not currently included in the regular course offerings, such as Theory of Computation, Artificial Intelligence, Parallel processing, computer architecture, etc.

VariableVariable1-4 Credits **Prerequisites: Variable depending upon the course. Note: Students may take each ST
course for credit. **

**EB-222 ** Principles of Macroeconomics

Macroeconomic conditions affect individuals and businesses in numerous ways: employment opportunities, the purchasing power of wages and salaries, the cost of borrowing money, sales, profits, and competitiveness against foreign businesses. This course develops the theories relevant to understanding the business cycle, inflation, unemployment, deflation, exchange rates and balance of payments problems. It also examines the options and tradeoffs governments face as they seek to provide a stable macroeconomic environment through monetary and fiscal policies. Case studies of the macroeconomic performance and policies of diverse countries provide a comparative orientation.

Fall & SpringYearly3 CreditsS**Prerequisites: Sophomore, Junior, or Senior standing **

Not an upper level class*

**EB-223 ** Principles of Microeconomics

The optimizing behavior of households and firms serves as the focal point in this study of market-based resource allocation. Supply and demand analysis, spending and saving decisions of households, production and employment decisions of firms, alternative market structures, and environmental economics are among the topics covered.

Fall & SpringYearly3 CreditsS**Prerequisite: Sophomore, Junior, or Senior standing. **

Not an upper level class*

**EB-320 ** Intermediate Microeconomics

Microeconomics analyzes the behavior of individual economic units such as consumers and firms. Intermediate microeconomics builds on the topics covered in principles of microeconomics and principles of macroeconomics. While those courses were more intuitive, this course explores microeconomics with a deeper degree of rigor using mathematical models to predict economic behavior.

FallVariable3 CreditsS**Prerequisites include EB223 and EB222. **

**EB-321 ** Intermediate Macroeconomics

Intermediate Macroeconomics builds upon the concepts developed in principles of microeconomics and principles of macroeconomics. Macroeconomics in general tries to understand the aggregate behavior of economies rather than that of individual economic actors, and in this course we will study and use models that help explain what has happened in the past and predict what will occur.

FallVariable3 CreditsS**Prerequisites: EB222 and EB223. **

**EB-341 ** Product and Operations Management

Examines the necessary things business firms must do to efficiently convert inputs to outputs. The course is about equally divided between qualitative operations management theory and quantitative tools that have been developed to solve typically occurring problems in production/ operations.

Either SemesterYearly3 CreditsS**Prerequisites: EB201. **

**EB-463** Financial Markets & Institutions

The role of credit and capital and the function of dollar and Euro bonds in today's internationalized financial markets are investigated empirically and assessed analytically in this course. Numerous economic theories relevant to understanding the behavior of various asset markets are developed, including portfolio and asset models of exchange rate determination and currency speculation. The costs and benefits of alternative government policies such as financial regulation and capital and foreign exchange controls are weighed.

SpringVariable3 CreditsS,I**Prerequisite: EB222. **

**EB-465 ** Financial Theory and Analysis

Financial Theory & Analysis will be a finance elective aimed at juniors and seniors. EB465's purpose is to develop an understanding of traditional modern portfolio theory, recent challenges to this orthodoxy, empirical knowledge of asset performance and how to apply this knowledge to specific contexts, i.e. creating an appropriate portfolio.

SpringVariable3 CreditsS**Prerequisites: EB211 and EB362. MA220 may be used as a replacement for EB211 only. **

**PC-202** Intro Physics I

A calculus-based introduction to the basic principles of mechanics (including periodic motion and dynamics), heat and thermodynamics, and special relativity.

FallYearly3 CreditsN, QM**Corequisite: PC-202L and Corequisite or Prerequisite: MA130.**

--AND

**PC-202L** Intro Physics Lab I

This lab is a calculus-based introductory laboratory experience that is designed to accompany PC202. Individual experiments will correlate with the course, including kinematics, Newton's Laws, energy, and momentum. Note: A special fee is assessed.

Fall & SpringYearly1 CreditN**Corequisite: PC202.**

Not an upper level class*

**PC-203** Intro Physics II

A calculus-based introduction to basic principles of electricity, magnetism, electromagnetic waves and optics. Additional topics may include atoms and molecules, nuclear physics, relativity and solid state physics. Corequisite: PC-207 or PC-203L.

SpringYearly3 CreditsN, QM**Prerequisites or Corequisite: Take MA-230 and either PC-202 or PC-204.**

--AND--

**PC-203L** Intro Physics Lab II

An algebra-based introductory laboratory experience designed to accompany PC203. The individual experiments will involve topics in circuits, light and optics, and nuclear physics. Note: A special fee is assessed.

SpringYearly1 CreditN**Prerequisite: PC202. Corequisite: PC203.**

Not an upper level class*

**PC-301 ** Theoretical Modern Physics

The origins and progress of Physics in the 20th century, including relativity and quantum theory with applications in atomic and molecular physics, nuclear physics, elementary particles and possibly some solid state physics.

FallYearly3 CreditsN**Prerequisites: MA230 or PC203. Corequisite: MA235.**

**PC-320** Engineering Mechanics I: Statics

A problem-solving approach to applied mechanics involving equilibrium of co-planar and non-planar force systems, analysis of frames and trusses, friction, centroids and moments of inertia.

FallVariable3 CreditsN**Prerequisite: PC202 or PC204.**

**PC-321** Engineering Mechanics II: Dynamics

A problem-solving approach to applied mechanics involving the kinematics and kinetics of particles and rigid bodies. Techniques involving Newton's laws, work-energy and impulse momentum are presented and used extensively.

SpringVariable3 CreditsN**Prerequisite: PC320.**

**PC-340 ** Mathematical Methods in Physics

An introduction to the mathematics used in advanced physical science courses. The emphasis is on early exposure to mathematical techniques and their applications rather than on rigorous derivation. Topics include series analysis, complex variables, theory, matrix mechanics, ordinary and partial differential equations, vector and tensor analysis, and Fourier series.

VariableYearly3 CreditsN**Prerequisites: PC203 and MA230.**

**PC-350 ** Thermodynamics

An intermediate level course treating the concept of temperature and its measurement, the concepts of heat and work, the laws of thermodynamics, applications of these concepts to physical systems, the elements of statistical mechanics and as many topics of current concern as time allows.

SpringYearly3 CreditsN**Prerequisites: MA235 and PC301.**

**PC-402 ** Quantum Mechanics

This course continues the discussion of the Schrodinger Equation, the particle-in-a-box, the harmonic oscillator, angular momentum, the hydrogen atom, and electron spin started in PC300 and/or CH305, but at a level that is mathematically much more detailed and proceeds from the postulates of quantum mechanics in a logical manner. With this beginning, the course then focuses on more complex problems such as the behavior of multi-electron atoms and molecules. Issues of the meaning of measurement such as embodied in the EPR paradox, the Bell Inequality, and the interpretation of associated experiments are also discussed. The course is heavily problem oriented requiring a strong mathematical background.

FallOdd Years4 CreditsN**Additional mathematics background such as PC340 and/or MA335 is suggested in addition
to the formal prerequisites of MA235 and PC300 or CH305.**

**PC-410 ** Mechanics

A study of classical mechanics including Newtonian, Lagrangian and Hamiltonian approaches. Emphasis is placed on developing the student's ability to analyze physical problems involving particles, systems of particles and rigid bodies. Insight is provided into a variety of techniques for solving such problems.

FallOdd Years4 CreditsN**Prerequisites: PC203 and PC340.**

**PC-491 ** Electricity & Magnetism

A study of electromagnetic phenomena, including electrostatics, electric fields in matter, magnetostatics, magnetic fields in matter, introductory electrodynamics including Maxwell's equations, and electromagnetic waves, potentials, and fields.

FallEven Years4 CreditsN**Corequisite: PC340. Prerequisite: PC203.**

**PC-430 ** Optics

The wave theory of light as applied to interference, diffraction, polarization, and image formation. Major emphasis on Fourier techniques. Study of geometrical optics, quantum optics, and radiometry as time permits.

SpringVariable3 CreditsN**Prerequisites: PC300 or PC301.**

* Not upper-level courses. These are listed because they are prerequisites for upper-level courses that are listed.

**Total Credits = 48**

##### Rationale

A program in mathematics can lay the foundation for a wide variety of careers, ranging from the very specific (actuarial science) to the very general (law). Training in mathematics develops problem solving and logical reasoning skills and a perspective to analyze, organize, and synthesize. These basic analytical tools can then be enhanced by adding appropriate technical skills.

The "core" of the Mathematics POE provides an introduction to the different conceptual and technical components of an undergraduate education in mathematics (i.e., discrete mathematics, calculus, probability and statistics, and computer programming). In addition, appropriate mathematical software is integrated throughout the program to facilitate the analysis of real world problems and the multirepresentational (i.e., graphical, numerical, and algebraic) approach to problem solving. One can then specialize in the direction of classical applied mathematics by pursuing physics and furthering the study of mathematical systems applicable to this field. Or one can move in the direction of theoretical mathematics by beginning the study of the theory behind algebra, geometry, calculus, probability and statistics, or even computer science. Beyond these more traditional options, one can also select a wide range of applications such as statistics, actuarial science, operations research, economics, computer science, or data science. The requisite skills that are relevant courses for these options vary considerably and should be chosen in close consultation with an appropriate advisor.

##### Normal Progression

Fall | Spring | |
---|---|---|

Freshman | Calculus I Discrete Structures |
Calculus II Introduction to Probability & Statistics OR Linear Algebra |

Sophomore | Calculus III Foundations of Mathematics |
Introduction to Probability & Statistics OR Linear Algebra Computer Science I |

Junior | Upper level Upper level |
Upper level Upper level |

Senior | Mathematics Seminar I Upper level |
Upper level (Research) |

##### Late Progression

Fall | Spring | |
---|---|---|

Freshman | ||

Sophomore | Calculus I Discrete Structures Computer Science I |
Calculus II Introduction to Probability & Statistics Linear Algebra |

Junior | Calculus III Foundations of Mathematics |
Upper level Upper level |

Senior | Mathematics Seminar Upper level Upper level |
Upper level Upper level |