MATH 129-Analytic Geometry and Calculus I (4 credits). The first calculus course in a three-course sequence. Intended primarily for chemistry, computer science, or mathematics majors. Topics include equations; inequalities; analytic geometry; trigonometric functions; an introduction to exponential and logarithmic functions; limits; continuity; derivatives; differentials; maxima and minima problems; graphing techniques; the defi nite integral. Prerequisite: MATH 110. Offered Fall semesters.

MATH 231-Analytic Geometry and Calculus III (4 credits). Topics include polar coordinates; parametric equations; conics; solid analytic geometry; vectors; partial differentiation; multiple integration; vector fi elds; line integrals; and Green's Theorem. Prerequisite: MATH 130 or the approval of the department chairperson. Offered Fall semesters.

MATH 361-Probability and Statistics (3 credits) Topics include events; laws of probability; discrete and continuous random variables; measures of central tendency; measures of variability; properties of expectation; independence; multivariate distributions; sampling distributions; central limit theorem; and large sample statistical inference. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years: Offered Fall 2011.

MATH 425-Abstract Algebra (3 credits). Emphasis on students formulating and testing their own conjectures. Topics include groups; cyclic groups; subgroups; direct products; cosets; normal subgroups; quotient groups; homomorphisms; rings; subrings; ideals; ring homomorphisms; fields. Approval of the Department Chairperson is required. Offered Fall semesters.

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MATH 235-Discrete Mathematics (3 credits). A survey of some of the fundamental ideas of discrete mathematics. Topics include set theory, relations on sets (especially equivalence relations, partial orders, and functions), number theory, induction and recursion, combinatorics, and graph theory. Prerequisite: MATH 127 and MATH 130 or approval of the Department Chairperson. Offered Fall semesters.

MATH 367-Real Analysis I (3 credits). The first of a two-semester sequence in real analysis. Emphasis is on theory and rigor. Topics include limits; continuity; uniform continuity; the intermediate value theorem; mean value theorems; the Heine-Borel theorem; the Bolzano-Weierstrass theorem; nested intervals; the Cauchy criterion; derivatives; differentials; and the riemann integral. Prerequisite: MATH 231 and MATH 250 or approval of the department chairperson. Offered Fall semesters.

MATH 363-Mathematical Modeling (3 credits). Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; and repeated games. Topics in curve fi tting include: curve fi tting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions; curve fitting with splines; and smoothing techniques. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years.

MATH 127-Logic and Axiomatics (3 credits). Topics include logic; inductive and deductive reasoning; direct and indirect proofs; proof by counter-example: set theory: axiom systems; consistency and independence of axiom systems; axiom system design. Prerequisite: CORE 098 Mathematical skills. Offered Fall semesters.

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MATH 130-Analytic Geometry and Calculus II (4 credits). Topics include exponential and logarithmic functions; applications of the defi nite integral; techniques of integration; improper integrals; indeterminate forms; sequences; series. Prerequisite: MATH 129 or the approval of the department chairperson. Offered Spring semesters.

MATH 250-Linear Algebra (4 credits). Topics include vector spaces; linear transformations; matrices; systems of linear equations; determinants; eigenvectors and eigenvalues. Computers are used both computationally and graphically. Prerequisite: MATH 127 and MATH 231 or permission of department chairperson. Offered Spring semesters.

MATH 362-Statistics (3 credits). Topics include functions of random variables; sampling theory; methods of estimation; properties of estimators; hypothesis testing; correlation and simple linear regression; elementary design of experiments; analysis of variance; analysis of categorical data; and nonparametric statistics. Prerequisite: MATH 361. Alternate years: Offered Spring 2012.

MATH 420-Complex Variables (3 credits). Topics include complex numbers; geometry of the complex plane; functions and mappings; the Cauchyriemann equations; harmonic functions; the line integral; the Cauchy integral formula; Laurent series; theory of residues; conformal mapping. Prerequisite: MATH 367. Alternate years: Offered Spring 2011.

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MATH 365-Numerical Analysis (3 credits). Topics include numerical integration and differentiation; direct and iterative methods for linear systems; numerical solution of linear and nonlinear algebraic equations and eigenvalue problems; numerical solutions for ODEís and PDEís if time permits. Prerequisite: MATH 231 and MATH 250 and one of CS 111, CS112, CIS 116. Alternate years: Offered Spring 2019.

MATH 129-Analytic Geometry and Calculus I (4 credits). The first calculus course in a three-course sequence. Intended primarily for chemistry, computer science, or mathematics majors. Topics include equations; inequalities; analytic geometry; trigonometric functions; an introduction to exponential and logarithmic functions; limits; continuity; derivatives; differentials; maxima and minima problems; graphing techniques; the defi nite integral. Prerequisite: MATH 110 PreCalculus. Offered Fall semesters.

MATH 231-Analytic Geometry and Calculus III (4 credits). Topics include polar coordinates; parametric equations; conics; solid analytic geometry; vectors; partial differentiation; multiple integration; vector fields; line integrals; and Green's Theorem. Prerequisite: MATH 130 or the approval of the department chairperson. Offered Fall semesters.

MATH 425-Abstract Algebra (3 credits). Emphasis on students formulating and testing their own conjectures. Topics include groups; cyclic groups; subgroups; direct products; cosets; normal subgroups; quotient groups; homomorphisms; rings; subrings; ideals; ring homomorphisms; fields. Approval of the Department Chairperson is required. Offered Fall semesters.

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MATH 235-Discrete Mathematics (3 credits). A survey of some of the fundamental ideas of discrete mathematics. Topics include set theory, relations on sets (especially equivalence relations, partial orders, and functions), number theory, induction and recursion, combinatorics, and graph theory. Prerequisite: MATH 127 and MATH 130 or approval of the Department Chairperson. Offered Fall semesters.

MATH 367-Real Analysis I (3 credits). The first of a two-semester sequence in real analysis. Emphasis is on theory and rigor. Topics include limits; continuity; uniform continuity; the intermediate value theorem; mean value theorems; the Heine-Borel theorem; the Bolzano-Weierstrass theorem; nested intervals; the Cauchy criterion; derivatives; differentials; and the riemann integral. Prerequisite: MATH 231 and MATH 250 or approval of the department chairperson. Offered Fall semesters.

MATH 363-Mathematical Modeling (3 credits). Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; and repeated games. Topics in curve fi tting include: curve fi tting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions; curve fitting with splines; and smoothing techniques. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years.

MATH 127-Logic and Axiomatics (3 credits). Topics include logic; inductive and deductive reasoning; direct and indirect proofs; proof by counter-example: set theory: axiom systems; consistency and independence of axiom systems; axiom system design. Prerequisite: CORE 098 Mathematical skills. Offered Fall semesters.

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MATH 130-Analytic Geometry and Calculus II (4 credits). Topics include exponential and logarithmic functions; applications of the defi nite integral; techniques of integration; improper integrals; indeterminate forms; sequences; series. Prerequisite: MATH 129 or the approval of the department chairperson. Offered Spring semesters.

MATH 250-Linear Algebra (4 credits). Topics include vector spaces; linear transformations; matrices; systems of linear equations; determinants; eigenvectors and eigenvalues. Computers are used both computationally and graphically. Prerequisite: MATH 127 and MATH 231 or permission of department chairperson. Offered Spring semesters.

MATH 362-Statistics (3 credits). Topics include functions of random variables; sampling theory; methods of estimation; properties of estimators; hypothesis testing; correlation and simple linear regression; elementary design of experiments; analysis of variance; analysis of categorical data; and nonparametric statistics. Prerequisite: MATH 361. Alternate years: Offered Spring 2012.

MATH 301-Financial Mathematics (3 credits). The topics covered in this course will be: time value of money, annuities with payments that are not contingent, loans, bonds, general cash fl ows and portfolios, Immunization, general derivatives, options, hedging and Investment strategies, forwards, futures, and swaps. The course will be designed to prepare students to pass actuarial exam #2. Prerequisite: MATH 130. Alternate years: Offered Spring 2011.

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MATH 490-Junior Seminar (1 credit). Students rework and refi ne the small axiom system that they designed in MATH 127 (Logic and Axiomatics). The axiom system is then presented to the students and faculty of the Mathematics department during the presentation phase of the seminar. Students are also strongly encouraged to present their systems at local Mathematical Association of America meetings and in other such forums. Prerequisite: MATH 127. Offered Spring semesters.

MATH 365-Numerical Analysis (3 credits). Topics include numerical integration and differentiation; direct and iterative methods for linear systems; numerical solution of linear and nonlinear algebraic equations and eigenvalue problems; numerical solutions for ODE's and PDEís if time permits. Prerequisite: MATH 231 and MATH 250 and one of CS 115 and CIS 116. Alternate years: Offered Spring 2011.

MATH 418-Topology (3 credits). Elementary defi nitions, examples, counterexamples, and theorems of point set topology. Emphasis on students presenting proofs in class. Topics include topologies and topological spaces; functions; mappings; homeomorphisms; connected spaces; compact spaces; separation axioms; metric spaces; quotient spaces; product spaces. Prerequisite: MATH 367. 4 hours per week. Alternate years: Offered Spring 2012.

MATH 129-Analytic Geometry and Calculus I (4 credits). The first calculus course in a three-course sequence. Intended primarily for chemistry, computer science, or mathematics majors. Topics include equations; inequalities; analytic geometry; trigonometric functions; an introduction to exponential and logarithmic functions; limits; continuity; derivatives; differentials; maxima and minima problems; graphing techniques; the defi nite integral. Prerequisite: MATH 110. Offered Fall semesters.

MATH 231-Analytic Geometry and Calculus III (4 credits). Topics include polar coordinates; parametric equations; conics; solid analytic geometry; vectors; partial differentiation; multiple integration; vector fields; line integrals; and Green's Theorem. Prerequisite: MATH 130 or the approval of the department chairperson. Offered Fall semesters.

MATH 361-Probability and Statistics (3 credits) Topics include events; laws of probability; discrete and continuous random variables; measures of central tendency; measures of variability; properties of expectation; independence; multivariate distributions; sampling distributions; central limit theorem; and large sample statistical inference. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years: Offered Fall 2011.

MATH 363-Mathematical Modeling (3 credits). Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; and repeated games. Topics in curve fi tting include: curve fi tting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions;curve fitting with splines; and smoothing techniques. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years.

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MATH 220-Secondary Mathematics Methods (3 credits). This course deals with educational perspectives, which pertain to the teaching of Mathematics at the secondary level (grades 7 through 12). Topics of discussion include recommendations by the National Council of Teachers of Mathematics (NCTM) regarding instructional methods, state standards for Mathematics curricula, assessment techniques, curricular issues, and the appropriate use of technology in the classroom. Students will be expected to complete a fi eld-based experience. Does not satisfy CORE 120, requirements for Mathematics major or minor, or Pennsylvania Department of Education Mathematics requirements for secondary education majors outside of Mathematics. Alternate years:

MATH 367-Real Analysis I (3 credits). The first of a two-semester sequence in real analysis. Emphasis is on theory and rigor. Topics include limits; continuity; uniform continuity; the intermediate value theorem; mean value theorems; the Heine-Borel theorem; the Bolzano-Weierstrass theorem; nested intervals; the Cauchy criterion; derivatives; differentials; and the riemann integral. Prerequisite: MATH 231 and MATH 250 or approval of the department chairperson. Offered Fall semesters.

MATH 425-Abstract Algebra (3 credits). Emphasis on students formulating and testing their own conjectures. Topics include groups; cyclic groups; subgroups; direct products; cosets; normal subgroups; quotient groups; homomorphisms; rings; subrings; ideals; ring homomorphisms; fields. Approval of the Department Chairperson is required. Offered Fall semesters.

MATH 127-Logic and Axiomatics (3 credits). Topics include logic; inductive and deductive reasoning; direct and indirect proofs; proof by counter-example: set theory: axiom systems; consistency and independence of axiom systems; axiom system design. Prerequisite: CORE 098 Mathematical skills. Offered Fall semesters.

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MATH 235-Discrete Mathematics (3 credits). A survey of some of the fundamental ideas of discrete mathematics. Topics include set theory, relations on sets (especially equivalence relations, partial orders, and functions), number theory, induction and recursion, combinatorics, and graph theory. Prerequisite: MATH 127 and MATH 130 or approval of the Department Chairperson. Offered Fall semesters.

MATH 130-Analytic Geometry and Calculus II (4 credits). Topics include exponential and logarithmic functions; applications of the defi nite integral; techniques of integration; improper integrals; indeterminate forms; sequences; series. Prerequisite: MATH 129 or the approval of the department chairperson. Offered Spring semesters.

MATH 250-Linear Algebra (4 credits). Topics include vector spaces; linear transformations; matrices; systems of linear equations; determinants; eigenvectors and eigenvalues. Computers are used both computationally and graphically. Prerequisite: MATH 127 and MATH 231 or permission of department chairperson. Offered Spring semesters.

MATH 236-Geometry (3 credits). This course considers geometry from several perspectives: the classical, axiomatic approach, analytic methods linking geometry to algebra, and the modern theory of geometric transformations. Topics include Euclidean and non-Euclidean geometries, constructions, similarity, trigonometry, transformations, and symmetries. The history of geometry and key historical fi gures in its development are emphasized, as are connections between geometry and other branches of mathematics. Prerequisite: Math 127 or approval of the department chairperson. Alternate years: Offered Spring 2012.

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MATH 362-Statistics (3 credits). Topics include functions of random variables; sampling theory; methods of estimation; properties of estimators; hypothesis testing; correlation and simple linear regression; elementary design of experiments; analysis of variance; analysis of categorical data; and nonparametric statistics. Prerequisite: MATH 361. Alternate years: Offered Spring 2012.