# MATH - Mathematics

## MATH 130 Numbers and Operations for Teachers

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## MATH 131 Geometry and Probability for Teachers (MT)

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## MATH 140 Quantitative Reasoning (MT)

For students with one or two years of high school algebra. This course is at the level of college algebra, but is not focused on algebra. It stresses application of mathematics in careers of non-scientists and in the everyday lives of educated citizens, covering basic mathematics, logic, and problem solving in the context of real-world applications.

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## MATH 150 Pre-Calculus (MT)

Algebra review, functions and graphs, logarithmic and exponential functions, analytic geometry, trigonometric functions, trigonometric identities and equations, mathematical induction, complex numbers. Students completing this course are prepared to enter calculus.

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## MATH 151 Calculus I (MT)

Limits and continuity for functions of one real variable. Derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions. Applications of the derivative. Introduction to related numerical methods.

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## MATH 152 Calculus II

Techniques of integration, numerical integration, and applications of integrals. Infinite series including Taylor series. Introduction to differential equations. Calculus in polar coordinates.

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## MATH 153 Calculus III

The calculus of vector-valued functions, functions of several variables, and vector fields. Includes vector operations, equations of curves and surfaces in space, partial derivatives, multiple integrals, line integrals, surface integrals, and applications.

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## MATH 200 Foundations of Mathematics

Bridges the gap between computational, algorithmic mathematics courses and more abstract, theoretical courses. Emphasizes the structure of modern mathematics: axioms, postulates, definitions, examples conjectures, counterexamples, theorems, and proofs. Builds skill in reading and writing proofs. Includes careful treatment of sets, functions, relations, cardinality, and construction of the integers, and the rational, real, and complex number systems.

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MATH 152## MATH 220 Linear Algebra

Vector spaces, linear independence, basis and dimension, linear mappings, matrices, linear equations, determinants, Eigen values, and quadratic forms.

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MATH 152## MATH 310 Differential Equations

Methods of solving first and second order differential equations, applications, systems of equations, series solutions, existence theorems, numerical methods, and partial differential equations.

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MATH 152## MATH 315 Probability and Statistics

Probability as a mathematical system, random variables and their distributions, limit theorems, statistical inference, estimation, decision theory and testing hypotheses.

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MATH 152## MATH 320 Discrete Structures

Topics to be selected from counting techniques, mathematical logic, set theory, data structures, graph theory, trees, directed graphs, algebraic structures, Boolean algebra, lattices, and optimization of discrete processes.

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## MATH 330 History of Mathematics (W)

The history of mathematics from ancient to modern times. The mathematicians, their times, their problems, and their tools. Major emphasis on the development of geometry, algebra, and calculus.

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MATH 200## MATH 335 Modern Geometry

A review of Euclidean geometry, an examination of deficiencies in Euclidean geometry, and an introduction to non-Euclidean geometrics. Axiomatic structure and methods of proof are emphasized.

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MATH 200## MATH 340 Abstract Algebra

A survey of the classical algebraic structures taking an axiomatic approach. Deals with the theory of groups and rings and associated structures, including subgroups, factor groups, direct sums of groups or rings, quotient rings, polynomical rings, ideals, and fields.

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## MATH 345 Topology

An introduction to topological structures from point-set, differential, algebraic, and combinatorial points of view. Topics include continuity, connectedness, compactness, separation, dimension, homeomorphism, homology, homotopy, and classification of surfaces.

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## MATH 350 Real Analysis

This course develops the logical foundations underlying the calculus of real-valued functions of a single real variable. Topics include limits, continuity, uniform continuity, derivatives and integrals, sequences and series of numbers and functions, convergence, and uniform convergence.

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## MATH 355 Complex Analysis

A study of the concepts of calculus for functions with domain and range in the complex numbers. The concepts are limits, continuity, derivatives, integrals, sequences, and series. Topics include Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formulas, Taylor and Laurent series, and special functions.

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## MATH 490 Senior Seminar

This course reviews and correlates the courses in the mathematics major. Each student is responsible for preparing the review of one area. Students also read papers from contemporary mathematics journals and present them to the class. The course uses the ETS mathematics major exam.