### MATHEMATICS CORE

*Take one of the following courses:*

**
**

**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.

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

**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.

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

*Take the following courses:*

**
**

**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.

4 CreditsN, QM

**
**

**MA-160** Linear Algebra

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

3 CreditsN, QM**Prerequisites: MA130.**

**
**

**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.

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

**
**

**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.

4 CreditsN, QM**Prerequisite: MA130**

**
**

**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.

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

**
**

**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.

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

**
**

**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.

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

*Take one of the following courses:*

**MA-205** Elementary Statistics

Introduction to traditional statistical concepts including descriptive statistics, binomial and normal probability models, confidence intervals, tests of hypotheses, linear correlation and regression, two-way contingency tables, and one-way analysis of variance.

4 CreditsN, QS, WK-SP**Prerequisite: FYC-101 or EN-110 or EN-109**

**
**

**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.

4 CreditsN, QS, CTGES**Prerequisite: MA130**

### ADDITIONAL COURSES

##### PROOF BASED MATHEMATICS:

*Take one of the following courses:*

**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.

3 CreditsN**Prerequisites: 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.

3 Credits **Prerequisites: MA160 and MA210.**

**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.

3 CreditsN**Prerequisites: MA210 and MA230 and MA235.**

##### APPLIED MATHEMATICS:

*Take one of the following courses:*

**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.

3 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.

3 CreditsN, QS**Prerequisites: MA-130 or MA 160; an introductory statistics course from the following
list: BI-305, EB-211, ESS-230, ESS-309, MA-205, MA-220, PY-366, or SW-215**

**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.

3 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.

3 CreditsN, QS, CW, SW-LE**Prerequisite: Take one course from this list: BI-305, EB-211, ESS-230, ESS-309, MA-205,
MA-220, PY-361, PY-366, SW-215. Also take FYC-101 or EN-110 or EN-109.**

**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.

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

**MA-341** Scientific Computing

This course begins with an introduction to fundamental concepts in Scientific Computing and concludes with domain-specific projects in areas like Bioinformatics, Data Science, Physical Systems, and Numerical Analysis. The common content will include command-line interfaces (Linux), programming languages (Jupyter/Python), numerical and graphical libraries (NumPy and Matplotlib), version-control (Git/Github), and relational databases (SQL).

3 CreditsN**Pre-Req: CS-110**

**CS-341** Scientific Computing

This course begins with an introduction to fundamental concepts in Scientific Computing and concludes with domain-specific projects in areas like Bioinformatics, Data Science, Physical Systems, and Numerical Analysis. The common content will include command-line interfaces (Linux), programming languages (Jupyter/Python), numerical and graphical libraries (NumPy and Matplotlib), version-control (Git/Github), and relational databases (SQL).

3 CreditsN**Pre-Req: CS-110**

### UPPER-LEVEL COURSES

*Take six credits from the following Mathematics courses:*

*
*

**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.

3 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.

3 CreditsN, QS**Prerequisites: MA-130 or MA 160; an introductory statistics course from the following
list: BI-305, EB-211, ESS-230, ESS-309, MA-205, MA-220, PY-366, or SW-215**

**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.

3 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.

3 CreditsN, QS, CW, SW-LE**Prerequisite: Take one course from this list: BI-305, EB-211, ESS-230, ESS-309, MA-205,
MA-220, PY-361, PY-366, SW-215. Also take FYC-101 or EN-110 or EN-109.**

**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.

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

**MA-341** Scientific Computing

This course begins with an introduction to fundamental concepts in Scientific Computing and concludes with domain-specific projects in areas like Bioinformatics, Data Science, Physical Systems, and Numerical Analysis. The common content will include command-line interfaces (Linux), programming languages (Jupyter/Python), numerical and graphical libraries (NumPy and Matplotlib), version-control (Git/Github), and relational databases (SQL).

3 CreditsN**Pre-Req: CS-110**

**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.

3 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.

1 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.

3 Credits **Prerequisites: MA160 and MA210.**

**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.

3 CreditsN**Prerequisites: MA210 and MA230 and 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.

1-4 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.

3-5 CreditsN**Prerequisites: MA480.**

### COURSES FROM OTHER DEPARTMENTS

*Take an additional six credits from the Mathematics, Computer Science, Data Science,
ABE or Physics departments:*

**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.

3 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.

3 CreditsN, QS**Prerequisites: MA-130 or MA 160; an introductory statistics course from the following
list: BI-305, EB-211, ESS-230, ESS-309, MA-205, MA-220, PY-366, or SW-215**

**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.

3 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.

3 CreditsN, QS, CW, SW-LE**Prerequisite: Take one course from this list: BI-305, EB-211, ESS-230, ESS-309, MA-205,
MA-220, PY-361, PY-366, SW-215. Also take FYC-101 or EN-110 or EN-109.**

**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.

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

**MA-341** Scientific Computing

3 CreditsN**Pre-Req: CS-110**

**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.

3 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.

1 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.

3 Credits **Prerequisites: MA160 and MA210.**

**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.

3 CreditsN**Prerequisites: MA210 and MA230 and 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.

1-4 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.

3-5 CreditsN**Prerequisites: MA480.**

**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.

3 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.

4 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.

3 CreditsN**Prerequisite: CS-240.**

**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.

4 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.

3 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.

1-4 Credits **Prerequisites: Variable depending upon the course. Note: Students may take each ST
course for credit. **

**DS-352 ** Machine Learning

This course considers the use of machine learning (ML) and data mining (DM) algorithms for the data scientist to discover information embedded in datasets from the simple tables through complex and big data sets. Topics include ML and DM techniques such as classification, clustering, predictive and statistical modeling using tools such as R, Matlab, Weka and others. Simple visualization and data exploration will be covered in support of the DM. Software techniques implemented the emerging storage and hardware structures are introduced for handling big data.

3 CreditsN**Prerequisite: CS-110, DS-110, and an approved statistics course from this list: MA-205,
MA-220, BI-305, PY-214, PY-260, PY-366, or EB- 211. **

**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.

3 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.

3 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.

3 CreditsS**Prerequisite: EB-100**

**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.

3 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.

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

**PC-301 ** 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. (Previously titled Theoretical Modern Physics)

3 CreditsN**Prerequisite: MA-230 or PC-203. Pre- or co-requisite: MA-235.**

**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.

3 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.

3 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.

3 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.

3 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 PC-301 and/or CH-305, 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 thebehavior 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 mathematicalbackground.

4 CreditsN**Prerequisites: MA-235 and either PC-301 or CH-305**

**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.

4 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.

4 CreditsN**Prerequisite: PC-203.**

**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.

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

### CAPSTONE

*Take one of the following courses:*

**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.

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

**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.

3-5 CreditsN**Prerequisites: MA480.**

#### 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.

#### POE Credit Total = 48

Students must complete at least 18 credits at the 300/400-level at least 12 credits of which must be from courses with an MA prefix (excluding MA 480 Mathematics Seminar). Any course exception must be approved by the advisor and/or department chair.