# MTH - Mathematics Course Descriptions

## MTH 120 Survey of Mathematics

Is an introduction to various topics in mathematics designed to teach critical thinking and to impart a general knowledge and appreciation of mathematics. Topics will be selected from logic, geometry, linear and exponential growth, personal finance, discrete mathematics, probability, statistics, and social choice theory.

## MTH 121 Mathematics for Early and Middle Grade Teachers I

includes such topics as an introduction to problem solving, set theory, functions, logic, numeration systems, and other number bases, and an overview of the real number system with its subsystems and related properties. Historical development and mathematical connections are stressed. The course is only for majors pursuing early and middle childhood, intervention specialist, and adolescent to young adult licensure, other than mathematics.

## MTH 122 Mathematics for Early and Middle Grade Teachers II

Provides application of real and complex numbers, algebraic thinking, Cartesian coordinate system, computing interest, probability and multistage experiments, statistics, and geometry, utilizing graphic calculators, and stressing the historical. This course is only for majors pursuing early and middle childhood or intervention specialist licensure.

## MTH 123 MATH/AYA Mathematics

Explores an overview of linear regressions, recursive powers, matrices, definite integrals, statistics, trigonometry and transformations using the TI Smartview CE. Explores constructions for geometry, conjectures, triangular centers, graphs and functions, transformational symmetry, iterations, sine wave tracers, ovals, and logarithmic curves using the Geometer's Sketchpad. Utilizes Fathom Statistical Software for data surveys, correlation coefficients, scatter plots, and sums of squares.

## MTH 155 Finite Mathematics

Is an introduction to mathematical topics and applications required by many college-level major programs. The material covered includes equations, inequalities, systems of linear equations and matrices, linear programming, mathematics of finance and probability.

### Prerequisites

1 year of high school algebra## MTH 156 Applied Calculus

Is intended to follow MTH 155. Topics include precalculus review, functions, limits differentiation and application of the derivative, and integration and applications of the integral.

### Prerequisites

2 years of high school algebra## MTH 160 Precalculus

Presents selected topics from algebra and elementary functions as preparation for studying calculus.

### Prerequisites

2 years of high school mathematics including algebra and plane geometry## MTH 161 Analytic Geometry and Calculus I

Studies inequalities, relations, functions, graphs, straight lines, limits and continuity, differentiation, and the definite integral. Students will complete computer symbolic algebra (e.g. Maple) experiments. Historical and career information is included.

### Prerequisites

Three years of high school mathematics including two years of algebra or MTH 160## MTH 162 Analytic Geometry and Calculus II

Studies conics, trigonometric and exponential functions, parametric equation and arc length, polar coordinates, infinite series, and methods of integration and applications. Students will complete symbolic algebra (e.g. Maple) experiments.

### Prerequisites

MTH 161## MTH 171 Matrix Theory I

Focuses on elementary matrix algebra, which has become an integral part of the mathematical background necessary for such diverse fields as electrical engineering, education, chemistry and sociology, as well as for statistics, computer science, and pure mathematics. Application is made to the solution of linear systems.

### Corequisites

MTH 161## MTH 172 Matrix Theory II

Continues with the applications of matrix algebra to the solution of linear systems and to linear transformations on abstract vector spaces. A special emphasis is placed on applications to computer science.

### Prerequisites

MTH 171### Corequisites

MTH 162## MTH 179 History of Mathematics

Provides an introduction and philosophical development of mathematics related to number and number concepts, algebra, Euclidean and non-Euclidean geometries, calculus, discrete mathematics, statistics and probability, and measurement and measurement systems, including contributions from diverse cultures.

## MTH 204 Research Statistics

is based on the principle that a scientific study requires the measurement and description of phenomena in an objective, systematic manner. This course introduces the student to the fundamental statistical techniques used in the behavioral sciences and other areas of research. These methods include sampling techniques , measures of central tendency, variability, probability, and inferential testing(e.g., t-tests, correlation, confidence intervals).

### Notes

for Mathematics majors, this course does not count as one of their needed upper-level electives.

### Prerequisites

Two years of high school mathematics including high school algebra, or MTH 155### Cross Listed Courses

PSY 204## MTH 210 Euclidean and Non-Euclidean Geometry

Begins with a close study of portions of Euclid's Elements, including complete coverage of the first book. The historical impact of his axiomatic approach and its ultimate refinement in Hilbert's axioms will be explored. This course will cover some of the history of the attempts to prove the Parallel Postulate, leading up to the discovery of non-Euclidian geometries in the 19th century. The two main models of non-Euclidean geometries (elliptic and hyperbolic) will be described and some of their properties investigated. Finally, the history of geometry since the discovery of non-Euclidean geometries (e.g. Kline's Erlanger Program) will be briefly covered.

### Prerequisites

One year of high school geometry or MTH 134## MTH 220 Discrete Mathematics

Surveys proof techniques, recursion, induction, modeling, and algorithmic thinking. Other topics covered include set theory, discrete number systems, combinatorics, graph theory, Boolean algebra, and a variety of applications. There is an emphasis on oral and written communication of mathematical ideas, cooperative learning, and the proofs of mathematical conjectures.

### Prerequisites

MTH 161## MTH 261 Analytic Geometry and Calculus III

Considers solid analytic geometry, vectors, partial differentiation, and multiple integration. Students will use graphing calculators and will complete computer symbolic algebra (e.g. MAPLE) experiments.

### Prerequisites

MTH 162## MTH 265 Differential Equations

Presents ordinary differential equations and their applications with an emphasis on techniques of solution including numerical methods.

### Prerequisites

MTH 261## MTH 270 Chaos and Fractals

Examines the mathematics behind two fascinating and inter-related topics, fractals and chaos. Chaos and fractals are components of dynamics, a subject that studies how systems change over time. Through computer experimentation and simulations, students will experience how new mathematics is developed. Topics covered include fractals: feedback and the iterator; classical fractals and self-similarity; length, area, and dimension; fractals with a random component; recursive structures including L-systems; attractors; deterministic chaos; fixed points, stable and unstable; and the period-doubling route to chaos.

## MTH 305 Introduction to Abstract Algebra

Develops the structural concepts that characterize abstract algebra. Topics in this course will be selected from the following: elementary number theory, groups, rings, integral domain, fields, and vector spaces. There is an emphasis on the oral and written communication of mathematical ideas. Students will frequently work in groups on special projects.

## MTH 311 Linear Programming

Covers both the theory and applications of linear programming, one of the leading methods for large-scale optimization. The simplex method will be studied in detail. Applications include product mix, diet, transportation, and network flow problems. Integer programming will be touched on briefly. Computer tools such as spreadsheet solvers will be introduced and used.

### Prerequisites

MTH 220## MTH 330 Number Theory and Cryptography

Covers the fundamental algorithms used in both private key and public key cryptography. Algorithms covered will include DES, AES, Diffie-Hellman, and RSA. Traditional encryption methods such as Vigenere ciphers and their cryptanalysis will be briefly described. The number theory needed to understand primality testing and RSA encryption will be developed in detail. Several programming projects aimed at implementing some of the material will be given throughout the semester.

### Cross Listed Courses

CSC 330## MTH 333 Intermediate Linear Algebra

Is a course in finite dimensional vector spaces and linear transformations, including inner product spaces, determinants, eigenvalues, and eigenvectors.

## MTH 335 Junior Seminar

Is designed to teach mathematical science majors the skills necessary to learn mathematics on their own and communicate their knowledge to others in oral and written form. All students will attend presentations made by senior mathematics students. Students will be required to write a short, independently-researched paper and present it to the other students in the junior seminar.

## MTH 391 Advanced Calculus for Applications

Covers the topics of vector field theory, Fourier series, and partial differential equations.

### Prerequisites

MTH 265## MTH 400 Internship

is a work experience opportunity with the purpose of expanding education by applying accumulated knowledge in mathematical science. The availability of internships is limited to upper-level students, normally seniors with a 2.5 quality point average. Students are approved individually by the academic department. A contract can be obtained from the Career Services Office in Starvaggi Hall. Internships count as general electives.

### Prerequisites

Mathematical science junior or senior standing and permission of the department chair. Internships must be pre-approved.## MTH 401 Mathematical Statistics I

Introduces a statistical basis for decision making to the student of applied science in this modern tool of analysis. This will be accomplished by studies in probability theory for both discrete and continuous sample spaces and in an introduction to statistical inference.

## MTH 402 Mathematical Statistics II

Is a continuation of MTH 401, covering additional concepts and techniques of statistics with an emphasis on problem-solving approaches.

### Prerequisites

MTH 401## MTH 408 Introduction to Functions of a Complex Variable

Liberates the mathematician from the restrictions imposed by the domain of real numbers when the broader field of complex numbers is made available. Beginning with a study of complex numbers, this course introduces the algebra and the calculus of elementary functions.

### Prerequisites

MTH 261## MTH 420 Introduction to Real Analysis

Gives a theoretical presentation of the real numbers, sequences, and their limits, including lim sup and lim inf; continuity; sequences of functions and pointwise and uniform convergence; and the (point set) topology of the reals.

## MTH 430 Numerical Analysis

Provides students with an intuitive and working understanding of numerical methods of problem solving, an appreciation of the concept of error and the need to control it, and the ability to implement numerical methods using a computer. Topics include: approximation of functions, interpolation, error analysis, numerical integration and differentiation, numerical linear algebra, and numerical solutions to differential equations.

## MTH 434 Senior Thesis

Requires all mathematical science students to write a thesis on an approved mathematical topic. Students must consult closely with a departmental faculty member at each stage in the development of their theses. The thesis will be presented to students in the Junior Seminar.