**MATH 100 PRE-CALCULUS** Basic set theory. Functions and their graphs. Linear and quadratic equations and systems. Trigonometry. Cartesian Coordinates. Congruence transformations in the plane. Preparation for Calculus (3 credits).

**MATH 102 MATHEMATICAL MODELING (C)**

Communication through graphs. Linear, exponential and logarithmic modeling of real data. Regression analysis, critical evaluation of appropriateness of a model, quality-of-fit analysis. Unit conversions (3 credits).

**MATH 119 – STATISTICS (C)**

Communicating with Graphs. Data Analysis and Sample statistics. Sampling methods. Probability. Combinatorics. Normal Distribution, other probability distributions. Hypothesis testing. Optionally, Monte Carlo Simulation (3 credits).

Pre-requisite: Mathematical Modeling

**MATH 120 – COMPUTATIONAL MATHEMATICS (C)**

Processing of deterministic and stochastic data structures by spreadsheets. Development of graphic user interfaces for robust processing of a developed hypothesis. Processing of experimental data structures by databases. Emulation of experimental data by mathematical models and generators of random numbers.

Pre-requisite: Mathematical Modeling (3 credits).

**MATH 131 - CALCULUS I (C)**

Real functions of a single real variable: limits, continuity, derivatives, integrals, Fundamental Theorem of Calculus. Prerequisite: Pre-Calculus or approval of Department chairperson (4 credits).

**MATH 132 - CALCULUS II (C)**

Techniques of Integration. Transcendental functions. Optimization. Convexity and Concavity. Improper integrals. Sequences and series, convergence criteria. Taylor series. Applications in physics (4 credits).

Pre-requisite: Calculus I.

**MATH 217 – DISCRETE MATHEMATICS**

Introduction to a variety of discrete Math topics such as Combinatorics, Graph Theory, Linear Programming, Game Theory, Voting Theory, Theory of Fair Divisions, Fractals. Emphasis on recursion and algorithms with and without computers. Pre-requisite: Calculus I (3 credits).

**MATH 212 – BIOMEDICAL STATISTICS (C)**

Rigorous introduction to statistics with applications in biological and health sciences using available public domain biomedical data sets. Exploratory data analysis, elements of probability, parametric and nonparametric statistical methods, contingency table analysis and linear regression. Hypothesis testing. Survival analysis. Pre-requisite: Mathematical Modeling (4 credits).

**MATH 222 – MATHEMATICS FOR ELEMENTARY EDUCATION**

Theory and application of arithmetic, algebra, geometry, and probability at the primary school level. This course is exclusively for students pursuing a certification in elementary school education; it is a co-requisite of EDUC 322 (3 credits).

**MATH 231 - CALCULUS III**

Vectors, vector operations, dot product, cross product. Multivariate functions and vector valued functions, continuity, partial derivatives. Gradient, tangent plane, total derivative. Classification of quadratic surfaces. Multiple integrals (3 credits).

Pre-requisite: Calculus II.

**MATH 241 – LINEAR ALGEBRA I**

The first part of a two semester sequence. Linear equations and matrices, matrix algebra, vector spaces, subspaces, linear independence, bases, dimension, linear transformations, - Diagonalization of matrices. Gauss-Jordan elimination, L-U factorization. Applications of Linear Algebra in the sciences and business (3 credits).

Pre-requisite: Calculus II

**MATH 242 –LINEAR ALGEBRA II - Elective**

The second part of a two semester sequence. A continuation of topics in Linear Algebra, with emphasis on inner product spaces, orthogonality, -Eigenvalues and -Eigenvectors, canonical forms, quadratic forms. Numerical Methods, least squares analysis, principal component analysis, single value decomposition.

Pre-requisites: Calculus III and Linear Algebra I (3 credits).

**MATH 255 – ORDINARY DIFFERENTIAL EQUATIONS - Elective**

Ordinary differential equations of first and second order: exact solutions and numerical methods, use of mathematical software. Systems of differential equations. Laplace transforms, if time permits. Applications in physics, chemistry, biology (3 credits).

Pre-requisite: Calculus III.

**MATH 261 –SYMBOLIC COMPUTING - Elective**

Concepts and practical use of a Computer Algebra System such as Maple: Data types and control structures. Two- and three dimensional plotting. Symbolic computing of solutions to selected problems in algebra and analysis. Contrasting exact and numerical solutions (3 credits).

**MATH 262 –NUMERICAL COMPUTING - Elective**

Programming constructs and data structures for a programming language suitable for compute intensive applications, such as C++. Development, implementation, and debugging of algorithms for selected computational problems on workstations and clusters (3 credits).

Pre-requisite: Computing or permission of the Department chairperson.

**MATH 263 –COMPUTING I**

Intro to basic computer programming: control structures, data types, data structures, formatting, input/output control, debugging, documenting applied to simple algorithms. Implementing algorithms in various software systems such as Basic, Visual Basic, Maple, Matlab, Mathematica (3 credits).

**MATH 311 – PROBABILITY DISTRIBUTIONS & STATISTICAL INFERENCE**

Random variables. Discrete and Continuous Probability Distributions (Binomial, Poisson, Normal, T). Statistical moments, point estimation, interval estimation. Hypothesis Testing. Optionally, Analysis of Variance and Covariance, Simulation, Introduction to Experimental Design. Prerequisite: Calculus I (3 credits).

**MATH 321 –INTRODUCTION TO HIGHER GEOMETRY**

Euclidean, Non-Euclidean, Axiomatic Geometry, Formal Proofs. Optionally, analytic geometry of conic sections. Projective Geometry (3 credits).

Pre-requisite: Calculus III.

**MATH 331 – REAL ANALYSIS**

Calculus of a single real variable, with emphasis on proofs. Axiomatic foundation of real number system. Rigorous development of Riemann integration. Optionally, Introduction to theory of measure, Fourier analysis (3 credits).

Pre-requisites: Calculus III and Linear Algebra I.

**MATH 341 –ABSTRACT ALGEBRA I**

The first part of a two semester sequence. An introduction to algebraic structures with an emphasis on groups, normal subgroups, cosets, Lagrange’s Theorem, and the fundamental homomorphism theorems (3 credits).

Pre-requisites: Linear Algebra I.

**MATH 342 – ABSTRACT ALGEBRA II - Elective**

The second part of a two semester sequence. Further study of algebraic structures, such as rings, integral domains, fields. The homomorphism theorem and its applications (3 credits).

Pre-requisites: Abstract Algebra I.

**MATH 431 – VECTOR CALCULUS - Elective**

Calculus for vector functions. Line and surface integrals. Theorems of Gauss, Green, and Stokes. Applications in electrostatics, electrodynamics, fluid dynamics (3 credits).

Pre-requisite: Calculus III.

**MATH 453 –COMPLEX FUNCTIONS - Elective**

Complex plane and elementary complex functions. Analytic functions, Cauchy-Riemann equations, and Cauchy integral theorem. Taylor series, Laurent series, singularities, zeroes, and calculus of residues. Conformal mapping and its applications (3 credits).

Pre-requisite: Real Analysis.

**MATH 455 – LINEAR PARTIAL DIFFERENTIAL EQUATIONS - Elective**

Classification of second-order linear partial differential equations. Method of separation of variables, methods of Fourier series and Taylor series. Method of Laplace transforms if time permits. General solutions, initial problems, boundary problems, and initial-boundary value problems. Prerequisite: Ordinary Differential equations (3 credits).

**MATH 465 – TOPICS IN MATHEMATICS - Elective**

A special topic will be offered when demand warrants. Registration requires permission by department chairperson (3 credits).

**MATH 469 –INDEPENDENT STUDY - Elective**

Independent study and/or research under faculty guidance. Registration requires approval of chair person (3 credits).