MTH - Mathematics

MTH 105 Mathematics for Elementary Teachers I

This course is intended for future elementary teachers and explores mathematical knowledge, communication, and student thinking. Content includes number theory, number systems, operations with numbers, integers, and algebra. There will be an underlying theme of mathematical communication, problem solving, and justification.  (Does not fulfill the core requirement.)

3

MTH 106 Mathematics for Elementary Teachers II

The second half of the sequence of mathematics courses for future elementary teachers includes data analysis and visualization, statistics, measures of center, fraction representations, fraction operations and geometry, with underlying themes of problem solving, math modeling, justification, and mathematics as a representational tool for social justice.  (Does not fulfill the core requirement.)

3

Prerequisites

MTH 105 with a grade of C- or higher

MTH 112 Precalculus II

The ideas necessary for the study of calculus, including modeling and representing exponential, logarithmic, rational, and trigonometric functional relationships.  Precalculus seeks develop a productive mathematical disposition, including persistence in problem-solving, evaluating the reasoning of others, and formulating mathematical justifications. Targeted toward students continuing to MTH 201. (Does not fulfill the core requirement.)

4

MTH 121 Calculus for Business and Social Science

Introduction to differential and integral calculus with emphasis on applications to business and economics.

3

MTH 141 Finite Mathematics

Matrices, systems of linear equations, linear programming. Sets and counting, probability.

3

MTH 160 Quantitative Reasoning

Students will be able to understand, process, and interpret statistical information arising in everyday life using real world examples and case studies from a variety of disciplines. Critical thinking and quantitative decision-making skills will be taught. This course focuses on being a consumer of statistics, interpreting research studies, and learning how statistics are used in the real world.
3

MTH 161 Elementary Statistics

Elementary statistical calculations and statistical thinking. Examples will be chosen from various disciplines. Topics include sampling, normal distribution, central limit theorem, hypothesis testing, and simple regressions.

3

MTH 201 Calculus I

The ideas of continuity, limits, differentiation, and integration are explored at both a theoretical level and in applied contexts by studying the relationships between changing quantities. Students will further develop problem-solving skills and improve mathematical communication. Sections labelled BI are designated for Biology majors and focus on applications in the life sciences.

4

Prerequisites

MTH 112 with a grade of C- or better or a passing score on the math placement test.

MTH 202 Calculus II

This course deepens the understanding of the foundational topics in calculus, including techniques of integration, applications of integration, and infinite sequences and series, including Taylor series with an emphasis on problem-solving strategies and the development of mathematical communication.

4

Prerequisites

MTH 201 with a grade of C- or higher or permission of instructor.

MTH 290 Directed Study

Credit arranged.

Variable

MTH 301 Vector Calculus

The study of functions in several variables: vectors, matrices, partial derivatives, gradients, optimization, and integration. Differentiation and integration of vector-valued functions, line integrals, surface integrals, curl, divergence, Green's Theorem, and Stokes' Theorem.

4

Prerequisites

MTH 202 with a grade of C- or higher or permission of instructor.

MTH 303 Computational Methods in Physical Sciences

Computational techniques for solving physics and chemistry problems as well as for simulating, analyzing, and graphically visualizing physical systems and processes. Offered fall of odd years.
3

Prerequisites

PHY 204 or PHY 201, MTH 202 with a grade of C- or higher

Cross Listed Courses

CHM 303, PHY 303

MTH 304 Complex Variables

Complex numbers and functions of a complex variable; limits, differentiability; Cauchy's theorem; power series, Laurent series, residue theorem with applications, maximum modulus theorem, Liouville's theorem; conformal mapping and applications.
3

Prerequisites

MTH 301 with a grade of C- or higher

MTH 311 Discrete Structures

Topics may include: set theory, logic, methods of proof, combinatorics, recurrence relations, graphs, and Boolean algebra.

3

Prerequisites

MTH 202 with a grade of C- or better.

MTH 321 Ordinary Differential Equations

Introduction to elementary ordinary differential equations with applications to physical processes with emphasis on first and second order equations, systems of linear equations, and Laplace transforms.

3

Prerequisites

MTH 202 with a grade of C- or higher or permission of instructor.

MTH 322 Partial Differential Equations

Fourier series. Inner product spaces. Solutions to heat, wave, and Laplace's equations. Green's functions.

3

Prerequisites

MTH 301 with a grade of C- or higher

MTH 323 Nonlinear Dynamics

This course introduces the basic concepts and techniques in the study of dynamical systems, including nonlinear ordinary differential equations, difference equations, and systems of equations. Using a wide variety of applications from the physical sciences, we will cover analytical methods such as linear stability, bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, and fractals.

3

Prerequisites

MTH 321

MTH 332 Graph Theory

This course surveys many of the ideas, methods and applications of graph theory. Topics may include: connectivity, matchings, graph algorithms, network flows, graph colorings, planarity, circuits, cycles, and tournaments.
3

Prerequisites

MTH 311 with a grade of C- or higher

MTH 341 Introduction to Linear Algebra

Systems of linear equations and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

3

Prerequisites

MTH 202 with a grade of C- or higher

MTH 342 Applied Linear Algebra

This course covers systems of linear equations and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

3

Prerequisites

MTH 202 with a grade of C- or higher

MTH 345 Number Theory

An introduction to the study of the integers and related objects. Topics are taken from among the following: divisibility, primes and the Euclidean algorithm, the Euler phi function, special primes and perfect numbers, congruences mod n, quadratic residues, continued fractions, quadratic forms, Diophantine equations.

3

Prerequisites

MTH 311 with a grade of C- or higher

MTH 356 Mathematical Methods for Science and Engineering

Ordinary differential equations, complex variables and matrices are developed and illustrated through applications in physics with emphasis on examples from the fields of vibrations and waves.

3

Prerequisites

MTH 202

Cross Listed Courses

PHY 356

MTH 361 Applied Statistics I

An introduction to statistical methods utilized across disciplines. Topics include experimental design, randomization and sampling distributions, tests of statistical significance, normal model, confidence intervals, t-procedures, two-sample comparisons, one-way analysis of variance, simple linear regression, and bootstrapping. The course makes substantial use of programming in a statistical software package.

3

Prerequisites

MTH 201 with a grade of C- or higher

MTH 381 Math Modeling

Survey of applied mathematics with an emphasis on modeling problems from science and engineering. Process of formulating the model, solving/simulating, and analyzing/interpreting results. Applications may include: continuous- and discrete-time population models, models of physical and biological phenomena, and statistical models.
3

Prerequisites

MTH 321 with a grade of C- or higher

MTH 390 Directed Study

Credit arranged.

Variable

MTH 392 Seminar

Credit arranged.

Variable

MTH 393 Research in Mathematics

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Variable

MTH 397 Internship

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.
Variable

MTH 401 Real Analysis I

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

3

Prerequisites

MTH 311 with a grade of C- or higher

MTH 402 Real Analysis II

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

3

Prerequisites

MTH 401 with a grade of C- or higher

MTH 431 Modern Geometry

A foundations course in elementary geometry discussing the following: incidence geometries; finite, metric, and synthetic geometries; Euclidean, hyperbolic, and elliptical geometries; and some axiomatic theory.

3

Prerequisites

MTH 311 with a grade of C- or higher

MTH 435 Topology

An introduction to fundamental concepts in point-set topology. Topics are taken from the following: open and closed sets, continuity, connectedness, compactness, separability, metric spaces.

3

Prerequisites

MTH 311 with a grade of C- or higher.

MTH 441 Group Theory

The study of algebraic structures that are like the integers, polynomials, and the rational numbers. The integers and their properties. Groups: examples, properties, and counting theorems. Rings: examples and properties. Fields: roots of polynomials and field extensions.

3

Prerequisites

MTH 311, MTH 341 with a grade of C- or higher.

MTH 442 Rings and Fields

Unique factorization in special rings. Field theory and the use of groups to understand field extensions: finite fields, Galois theory. Classical construction problems, solution of n-th degree polynomials.

3

Prerequisites

MTH 441, MTH 311 or MTH 341 with a grade of C- or higher

MTH 443 Cryptography

Cryptography is the science of encoding and decoding information for the purpose of secure communication. With an emphasis on utilization of both modern and classical cryptosystems, this course introduces students to the mathematical underpinnings of cryptography.
3

Prerequisites

MTH 311 with a grade of C- or higher; MTH 341 strongly recommended

MTH 451 Numerical Methods in Computing I

Numerical techniques for computer-aided solution and analysis of systems using MATLAB. Emphasis on applications from engineering and the physical sciences. Topics covered may include non-linear equations, systems of equations, interpolation, integration and differentiation, and ordinary and partial differential equations.
3

Prerequisites

MTH 321 or MTH 341

Corequisites

MTH 321 or MTH 341

Cross Listed Courses

EGR 551

MTH 461 Probability and Statistics I

Probability, discrete and continuous random variables, expectation, important probability distributions, introduction to sampling, estimation, and hypothesis testing.

3

Prerequisites

MTH 202 and MTH 311 with a grade of C- or higher.

MTH 490 Directed Study

Credit arranged.

Variable

MTH 491 One Time Course Offering

Carries a title reflecting the subject or subjects studied and/or the nature of the class structure. May be repeated for credit.

Variable

MTH 493 Research in Mathematics

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Variable

MTH 497 Internship

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.
Variable

MTH 497I Industrial Mathematics Internship

Math 497 is a course for students with strong mathematical preparation.  Students will work in teams on a project from an industrial or governmental firm.  Student success will depend on realistic industry evaluations such as teamwork, communication, individual initiative, and final products.
3

Prerequisites

Instructor permission

MTH 499 Senior Thesis

Research, study, or original work under the direction of a faculty mentor, leading to a scholarly thesis document with a public presentation of results. Requires approval of thesis director, department chair, dean, and the director of the honors program, when appropriate.

3

Prerequisites

Senior standing; 3.0 G.P.A. in the thesis area or good standing in the honors program.