# MTH - Mathematics

## MTH 105 Mathematics for Elementary Teachers I

Rational numbers and subsystems. Probability and statistics. Real numbers and geometry. Algebraic structures. Emphasis on problem solving. (Does not fulfill the core requirement.)

## MTH 106 Mathematics for Elementary Teachers II

Rational numbers and subsystems. Probability and statistics. Real numbers and geometry. Algebraic structures. Emphasis on problem solving. (Does not fulfill the core requirement.)

### Prerequisites

MTH 105## MTH 111 Precalculus I

Review of basic algebra, functions, graphing, logarithm, and exponential functions, systems of linear equations. (Does not fulfill the core requirement.)

## MTH 112 Precalculus II

Review of exponential and logarithmic functions, their graphs, trigonometric and inverse trigonometric functions. Analytic geometry, sequences, and series.(Does not fulfill the core requirement.)

## MTH 115 Teaching Mathematics with Technology

Two mathematical areas provide the content of the course: (1) Geometry and (2) Algebra and Modeling. Mathematical content and pedagogy are fully integrated using contemporary classroom technologies. (Does not fulfill the core requirement.)

## MTH 121 Calculus for Business and Social Science

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

## MTH 141 Finite Mathematics

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

## MTH 160 Quantitative Reasoning

## 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.

## MTH 201 Calculus I

The study of the differential and integral calculus with emphasis on applications in the natural and physical sciences.

### Prerequisites

MTH 112 with a grade of C- or better or a passing score on the math placement test.## MTH 202 Calculus II

Techniques of integration, numerical integration, applications of integration, sequences and series, including Taylor series.

### Prerequisites

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

### Prerequisites

MTH 202 with a grade of C- or higher or permission of instructor.## MTH 303 Computational Methods in Physical Sciences

### Prerequisites

PHY 204 or PHY 201, MTH 202### Cross Listed Courses

CHM 303, PHY 303## MTH 311 Discrete Structures

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

### Prerequisites

MTH 201 with a grade of C- or better or MTH 202 as a prerequisite or concurrent.## MTH 321 Ordinary Differential Equation

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

### 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.

### Prerequisites

MTH 321## 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.

### Prerequisites

MTH 321## MTH 341 Introduction to Linear Algebra

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

### Prerequisites

MTH 202## 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.

### Prerequisites

MTH 311## MTH 351 Numerical Methods in Computing I

Numerical techniques for computer-aided solution of non-linear equations, systems of equations, interpolation, numerical integration and differentiation, and solution of ordinary differential equations. Fee: $25.

### Prerequisites

CS 203, MTH 321 or MTH 341## 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.

### Prerequisites

MTH 202## 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.

### Prerequisites

MTH 201## MTH 387 Service Learning in Mathematics

This seminar supports students working in local schools as part of the Outreach Excel Program. Students discuss questioning and group work strategies, classroom management, current school mathematics curriculum, and interaction techniques with middle and high school students. This is a Pass/No Pass course and may be repeated for credit. Does not count towards math major.

## 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.

### Prerequisites

MTH 311## MTH 402 Real Analysis II

Topics may include sequences and series of functions, uniform convergence, Fourier series, the Riemann-Stieltjes integral, and functions in several variables.

### Prerequisites

MTH 401## MTH 404 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.

### Prerequisites

MTH 301, MTH 311## 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.

### Prerequisites

MTH 301, MTH 341## 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.

### Prerequisites

MTH 311## MTH 441 Modern Algebra I

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.

### Prerequisites

MTH 311, MTH 341## MTH 442 Modern Algebra II

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.

### Prerequisites

MTH 441## MTH 461 Probability and Statistics I

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

### Prerequisites

MTH 202, MTH 311## MTH 462 Probability and Statistics II

Topics from simple linear and multiple regression, analysis of variance and design of experiments, methods for categorical data, distribution-free methods.

### Prerequisites

MTH 461## MTH 491 Seminar in Mathematics

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

## 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.

### Prerequisites

Senior standing; 3.0 G.P.A. in the thesis area or good standing in the honors program.## MTH 501 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.

### Prerequisites

MTH 311## MTH 502 Real Analysis II

Topics may include sequences and series of functions, uniform convergence, Fourier series, the Riemann-Stieltjes integral, and functions in several variables.

### Prerequisites

MTH 501## MTH 504 Introduction to 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.

### Prerequisites

MTH 401## MTH 535 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.

### Prerequisites

MTH 311## MTH 541 Modern Algebra I

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.

### Prerequisites

MTH 311, MTH 341## MTH 542 Modern Algebra II

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.

### Prerequisites

MTH 541## MTH 561 Probability and Statistics I

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

### Prerequisites

MTH 301, MTH 341## MTH 562 Probability and Statistics II

Topics from simple linear and multiple regression, analysis of variance and design of experiments, methods for categorical data, distribution-free methods.