*Department of Mathematics*

#### Department Faculty

The minor in applied mathematics is designed to give students the opportunity to complement their degree with a computational component. The minor offers a more concentrated applied curriculum and, more importantly, recognition for students working in areas where applications of mathematics have seen a greater presence in recent years. This includes, in particular, the natural sciences such as physics, chemistry, geology, and biology, but also computer science, economics, and business, where mathematical modeling has become very important. Adding the applied mathematics minor to such a degree will give students the more specific recognition for their course work, thereby enhancing their resume.

## Requirements for the Applied Mathematics Minor

Nineteen (19) credits are required. Seven credits come from MATH 122 and 312; nine additional upper level credits must come from MATH 300, 351, 352, 411, 421, STAT 381, 382, MATH or STAT 361 (with departmental approval), MATH or STAT 461 (with departmental approval), and MATH or STAT 491/492 (with departmental approval); the final three credits may be taken from any course in the additional upper level list above or MATH 224, STAT 280, CPSC 220, ECON 301, or any 300/400 level course in a related discipline with mathematics department approval. At most three credits of MATH or STAT 491 (directed study) may be counted toward the applied mathematics minor.

## Mathematics Course Offerings

**Mathematics course offerings will be found under the 4 letter code of MATH in the course listings.**

**110 – Finite Mathematics with Applications (3)**

Includes topics such as sets, logic, probability, statistics, and counting. Other topics are at the discretion of the instructor. Designed for the non-major.

**111 – Precalculus (3)**

Emphasis on elementary functions including rational, exponential, logarithmic and trigonometric functions. Designed for students who intend to take calculus.

**115 – Introduction to Mathematical Modeling (3)**

Mathematical topics include linear functions, linear regression, curve fitting, probability models, and difference equations. Emphasis on environmental issues such as population growth, pollution, natural disasters, epidemics, genetics, and patterns in nature.

**120 – Quantitative Reasoning for the Sciences (3)**

Designed to prepare students for success in the sciences by providing them with appropriate mathematics and quantitative reasoning skills. Course topics include measurement and estimation, growth and decay phenomena, scaling transformations, and an introduction to probability and statistics.

**121 – Calculus I (4)**

First course in calculus. Topics include limits, derivatives and their applications, antiderivatives, definite integrals, the fundamental theorems of calculus, the substitution rule for integrals, and transcendental functions

**122 – Calculus II (4)**

Prerequisite: MATH 121. Topics include techniques and applications of integration, sequences and series.

**201 – Introduction to Discrete Mathematics (3)**

Designed to prepare prospective mathematics majors for advanced study in the field by introducing them to a higher level of mathematical abstraction. Topics include sets and logic, functions and relations, methods of mathematical proof including mathematical induction, and elementary counting techniques. (Prospective mathematics majors should take this course during their freshman year.)

**204 – Mathematical Concepts and Methods I (4)**

Prerequisite: EDUC 203. Mathematical concepts and methods of teaching for the elementary school. Topics include number systems and their properties, problem solving, and topics in number theory. Course intended for students certifying to teach grades PreK-6. Significant field experience required. (3 lecture credits, 1 practicum credit).

**205 – Selected Topics in Mathematics (1-3)**

Prerequisite: Course dependent. Opportunity for additional study of lower-level topics in mathematics.

**207 – History of Mathematics (3)**

The history of mathematics begins with the early numbering systems and mathematics of the Egyptians and the Babylonians. The course then turns to the Greeks and their emphasis on logical deduction and geometry. The Arabs develop algebra in the Middle Ages, and calculus is created during the Age of Reason. The development of individual branches of mathematics then is studied (probability, number theory, non-Euclidean geometry, set theory, and topology). The course ends with the Computer Age and implications for the future.

**224A – Multivariable Calculus (4)**

Prerequisite: MATH 122. Topics include parametric equations, vectors, polar, cylindrical, and spherical coordinates, vector-valued functions, functions of several variables, partial derivatives, multiple integrals, and vector calculus.

**253 – Introduction to Cryptography (3)**

Prerequisites: MATH 201 or CPSC 284. An introduction to standard encryption schemes and the relevant mathematics, including the classical symmetric ciphers, Diffie-Hellman key exchange, and modern public key encryption systems. Also includes cryptanalysis techniques in the context of standard message attacks.

**300 – Linear Algebra (3)**

Prerequisites: MATH 122 and either MATH 201 or CPSC 284. An introduction to linear algebra. Usually includes matrix algebra, systems of equations, vector spaces, inner product spaces, linear transformations, and eigenspaces.

**312 – Differential Equations (3)**

Prerequisite: MATH 122. Ordinary differential equations which may include Laplace transformations, linear differential equations, applications, approximations, and linear systems of equations.

**321 – Number Theory (3)**

Prerequisite: MATH 201 or CPSC 284. An elementary, theoretical study of the properties of the integers.

**325 – Discrete Mathematics (3)**

Prerequisite: MATH 201 or CPSC 284. Includes topics such as discrete probability, graph theory, recurrence relations, topics from number theory, semigroups, formal languages and grammars, finite automata, Turing machines, and coding theory.

**330 – Foundations of Advanced Mathematics (3)**

Prerequisite: MATH 122 and either MATH 201 or CPSC 284. Introduction to mathematical reasoning and rigor. Includes topics such as basic logic, set theory, mathematical induction, relations, functions, sequences, cardinality, elementary number theory, and axiomatic construction of the real numbers. Emphasis placed on reading mathematics, understanding mathematical concepts, and writing proofs.

**351, 352 – Numerical Analysis I. II (3, 3)**

Prerequisite: MATH 300 or 312. Mathematics 351 introduces the theory and applications of the basic computational techniques of numerical approximation. Topics include an introduction to computer programming and algorithms, root finding, interpolation, polynomial approximation, numerical differentiation and integration, and numerical linear algebra. MATH 352 expands on the basic approximation techniques to include scientific computing. Topics include methods of simulation, initial value problems and boundary value problems for ordinary/partial differential equations, and applications in science and engineering. Only in sequence.

**361 – Topics in Mathematics (3)**

Prerequisite: Course dependent. Opportunity for additional study of mathematical topics.

**372 – Modern Geometry (3)**

Prerequisite: MATH 300. Axiomatic development of various geometries including modern Euclidean and non-Euclidean geometry, finite geometries, hyperbolic geometry, and elliptic geometry. Topics could also include convexity, transformational geometry, projective geometry, and constructability.

**411- Chaotic Dynamical Systems (3)**

Prerequisite: MATH 122. Chaotic dynamical systems including iteration, graphical analysis, periodic points, bifurcations, the transition to chaos, fractals, Julia sets and the Mandelbrot set.

**412 – Complex Variables (3)**

Prerequisite: MATH 300. Analytic functions, Cauchy-Riemann conditions, integration, power series, calculus of residues, conformal mappings and applications.

**421 – Applied Partial Differential Equations (3)**

Prerequisites: MATH 224 and 312. This course introductions three main types of partial differential equations (PDEs): parabolic, elliptic and hyperbolic as well as mathematical and computational tools for solving PDEs. It balances mathematical rigor, computational techniques, and real-world applications. Topics include heat equation, method of separation of variables, Laplace’s equation, Fourier series, wave equation, finite difference/element methods, and high-dimensional PDEs.

**431, 432 – Abstract Algebra (3, 3)**

Prerequisite: MATH 300 and 330. Mathematical systems including groups, rings, fields, and vector spaces. Only in sequence.

**441 – Topology (3)**

Prerequisite: MATH 300 and 330. Includes topics from point-set topology such as continuity, connectedness, compactness, and product and quotient constructions.

**461 – Topics in Mathematics (3)**

Prerequisite: Course dependent. Topics such as partial differential equations, optimization, Fourier series, ring theory, cryptology, algebraic number theory, coding theory, and modeling. May be taken up to three times for credit.

**471, 472 – Real Analysis (3, 3)**

Prerequisites: MATH 300 and 330. A rigorous, real analysis approach to the theory of calculus. Only in sequence.

**481 – Theory of Interest (3)**

Prerequisite: MATH 122. This course introduces the mathematical concepts underlying the theory of interest. Topics include measurement of interest (including accumulated and present value factors), annuities, yield rates, amortization schedules and sinking funds, bonds and related securities, derivative instruments, and hedging and investment strategies.

**491, 492 – Directed Study (1-3, 1-3)**

Prerequisite: Departmental permission. Individual study beyond the scope of normal course offerings, done under the direction of a faculty member. May lead to graduation with Honors in Mathematics.

**499 – Internship (credits variable)**

Supervised off-campus experience, developed in consultation with the department. Does not count in the major program or minors.

## Statistics Course Offerings

#### Statistics course offerings will be found under the 4 letter code of STAT in the course listings.

*180 – Introduction to Statistics (3)*

First course in statistical methods. Includes descriptive and inferential techniques and probability, with examples from diverse fields. Topics vary with instructor and may also include sampling methods, regression analysis, and computer applications.

*205 –Selected Topics in Statistics (1-3)*

Prerequisite: Course dependent. Opportunity for additional study of lower-level topics in statistics.

*280 – Statistical Methods (3)*

Prerequisite: STAT 180 or equivalent. Second course in statistical methods. Include one-way and higher ANOVA, multiple regression, categorical data analysis, and nonparametric methods with examples from diverse fields. Topics vary with instructor and may also include time series and survival analysis.

*320 – Applied Regression Analysis (3)*

Prerequisite: STAT 280. Topics include simple linear regression, multiple linear regression, categorical predictors, model building principles, residual analysis, multicollinearity and other regression problems, robust regression, nonlinear regression, logistic regression, time series and generalized linear models.

*361 –Topics in Statistics (3)*

Prerequisite: Course dependent.** **Opportunity for additional study of statistical topics.

*381, 382 – Probability and Statistical Inference (3, 3)*

Prerequisite: MATH 122. An introduction to probability theory and calculus-based statistics including probability distributions of discrete and continuous random variables, functions of random variables, methods of estimation, and statistical inference. Only in sequence.

*420 – Applied Multivariate Statistics (3)*

Prerequisite: STAT 280. Topics include visualization techniques, principal component analysis, factor analysis, multidimensional scaling, canonical correlation analysis, correspondence analysis, cluster analysis and structural equation models.

*461 –Topics in Statistics (3)*

Prerequisite: Course dependent. Topics such as time series analysis, computational statistics, design of experiments, probability theory, stochastic processes, and queuing theory. May be taken up to three times for credit.

*491, 492 – Directed Study (1-3, 1-3)*

Prerequisite: Departmental permission. Individual study beyond the scope of normal course offerings, done under the direction of a faculty member. May lead to graduation with Honors in Mathematics.

*499 – Internship (credits variable)*

Supervised off-campus experience, developed in consultation with the department. Does not count in the major program or minors.