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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 (CORE)
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 107 – COMPUTATIONAL MATH WITH SPREADSHEETS (CORE)
General computer concepts and important applications of numerical evaluation of formulas and statistical, logical, mathematical, financial, date-time, and database functions in the environment of separate and related spreadsheets (3 credits).
Co-requisite of Pre-requisite: Mathematical Modeling.
MATH 119 – STATISTICS (CORE)
Communicating with Graphs. Data Analysis and Sample statistics. Sampling methods. Probability. Combinatorics. Normal Distribution. Hypothesis testing. Optionally, Monte Carlo Simulation (3 credits).
Pre-requisite: Mathematical Modeling
MATH 120 – COMPUTATIONAL MATHEMATICS (CORE)
Numerical, graphical, critical, logical, and statistical analysis of experimental data from databases by mapping of mathematical structures. Development of graphic user interfaces for mathematical modeling and statistical processing of a developed hypothesis. Presentation of computed results (3 credits).
Pre-requisite: Mathematical Modeling.
MATH 121 – BIOMEDICAL STATISTICS (CORE)
Rigorous introduction to statistics with applications in biological and health sciences using available public domain biomedical data sets. Exploratory data analysis, elements of probability, one- and two sample tests, nonparametric methods, contingency table analysis and linear regression (4 credits).
Pre-requisite: Mathematical Modeling.
MATH 131 - CALCULUS I
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
Techniques of Integration. Transcendental functions. Optimization. Convexity and Concavity. Improper integrals. Sequences and series, convergence criteria. Taylor series. Applications in physics (4 credits).
Prerequisite: Calculus I.
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).
Prerequisite: Calculus II.
MATH 241 – LINEAR ALGEBRA I
The first part of a two semester sequence. Linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, inner product, linear transformations, Eigenvalues and -Eigenvectors, orthogonal matrices, diagonalization (3 credits).
Prerequisite: Calculus II
MATH 242 –LINEAR ALGEBRA II
The second part of a two semester sequence. A continuation of topics in Linear Algebra, with emphasis on orthogonality, inner product spaces, -Eigenvalues and -Eigenvectors, canonical forms, quadratic forms. Numerical Methods (3 credits).
Prerequisites: Calculus III and Linear Algebra I
MATH 255 – ORDINARY DIFFERENTIAL EQUATIONS
Ordinary differential equations of first and second order: exact solutions and numerical methods, use of mathematical software. Systems of differential equations. Laplace transforms. Applications in physics, chemistry, biology (3 credits).
Prerequisite: Calculus III.
MATH 261 –SYMBOLIC COMPUTING
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
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).
Prerequisite: Symbolic Computing or permission of the Department chairperson.
MATH 321 –INTRODUCTION TO HIGHER GEOMETRY
Euclidean, Non-Euclidean, Axiomatic Geometry. Optionally, analytic geometry of conic sections. Projective Geometry (3 credits).
Prerequisite: 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).
Prerequisites: 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).
Prerequisites: Linear Algebra I.
MATH 342 – ABSTRACT ALGEBRA II
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).
Prerequisites: Abstract Algebra I.
MATH 431 – VECTOR CALCULUS
Calculus for vector functions. Line and surface integrals. Theorems of Gauss, Green, and Stokes. Applications in electrostatics, electrodynamics, fluid dynamics (3 credits).
Prerequisite: 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).
Prerequisite: Real Analysis.
MATH 455 – PARTIAL DIFFERENTIAL EQUATIONS (ELECTIVE)
Classification of second-order linear partial differential equations. The method of separation of variables, the method of Fourier series, and the method of integral transforms. General solutions, initial problems, boundary problems, and initial-boundary value problems (3 credits).
Prerequisite: Ordinary Differential equations.
MATH 465 – TOPICS IN MATHEMATICS (ELECTIVE)
A special topic will be offered when demand warrants. Participation requires permission by department chairperson (3 credits).
MATH 469 –INDEPENDENT STUDY (ELECTIVE)
Independent study and/or research under faculty guidance. Requires approval of chair person (3 credits).