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Course Descriptions
MATH 101 — Theory of Arithmetic (3)
Procedures of arithmetic computation will be developed using inductive and deductive reasoning. Topics include numeration systems, whole numbers, integers, rational numbers, and number theory. Word problems will be stressed. Prerequisite: COre 098 Mathematical skills. Offered Fall semesters.
MATH 102 — Algebra and Geometry (3)
Topics include real numbers and their properties, equations and inequalities, elementary functions and their graphs, polygons, circles, three-dimensional shapes, congruent and similar triangles, the Pythagorean Theorem, perimeter, area, and volume. Word problems will be stressed. Prerequisites: COre 098 Mathematical skills and MATH 101 Theory of Arithmetic. Offered Spring semesters.
MATH 123 — Finite Mathematics (3)
Topics include lines and linear functions; a geometric approach to linear programming; mathematics of finance; sets and counting; elementary probability; probability distributions and statistics. Business applications emphasized. excel utilized. Prerequisite: CORE
098 Mathematical skills.
MATH 124 — Probability and Statistics for Education Majors (3)
Topics include: measures of central tendency and dispersion, percentiles, the normal distribution, graphical representation of data, probability, and simulations. Course includes use of technology. education applications are emphasized. Prerequisite: CORE 098
Mathematical skills. Closed to Mathematics majors as well as students who have taken or who are currently taking MATH 126, MATH 128, PSYC 335, or SOCS 261.
MATH 125 — Calculus (4)
Topics include: equations and inequalities; polynomial, rational, exponential, logarithmic, and trigonometric functions; limits, continuity; derivatives; graphs; maxima and minima problems; growth and decay problems; antiderivatives; the definite integral; basic integration techniques; area between curves. Biological applications emphasized. Prerequisite: COre 098 Mathematical skills. Closed to non-freshmen Mathematics majors.
MATH 126 — Introduction to Statistics (3)
Basic methods of data analysis. emphasis on the use of logical reasoning and careful and precise communication in analyzing and presenting statistical data. Topics include displaying data graphically; measures of central tendency; measures of variability; general laws of probability; normal, t, and chisquare distributions; sampling distributions; confidence intervals; hypothesis testing; two way tables; use of statistical software. Prerequisite: CORE
098 Mathematical skills. Closed to students who have taken or who are currently taking
MATH 128. Offered Spring semesters.
MATH 127 — Logic and Axiomatics (3)
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.
MATH 128 — Introduction to Statistics, Data Analysis, and
Applications to Life Science (4)
Basic methods of data analysis. emphasis on the use of logical reasoning and careful and precise communication in analyzing and presenting statistical data. Topics include displaying data graphically; measures of central tendency; measures of variability; general laws of probability; normal, t, chi-square, and F distributions; sampling distributions; confidence intervals; hypothesis testing; analysis of variance; two-way tables; use of statistical software. Biological applications are emphasized. Three 50-minute lectures and one 75-minute lab per week. Prerequisite: COre 098 Mathematical skills. Closed to students who have taken or who are currently taking MATH 126. Offered Fall semesters.
MATH 129 — Analytic Geometry and Calculus I (4)
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 definite integral. Prerequisite: COre 098 Mathematical skills. Offered Fall semesters.
MATH 130 — Analytic Geometry and Calculus II (4)
Topics include exponential and logarithmic functions; applications of the definite integral; techniques of integration; improper integrals; indeterminate forms; sequences; series. Prerequisite: MATH 129 or the approval of the department chairperson. Offered Spring semesters.
MATH 220 — Secondary Mathematics Methods (3)
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 field-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 231 — Analytic Geometry and Calculus III (4)
Topics include polar coordinates; parametric equations; conics; solid analytic geometry; vectors; partial differentiation; multiple integration; vector fields; line integrals; Green’s Theorem. Prerequisite: MATH 130 or the approval of the department chairperson. Offered Fall semesters.
MATH 235 — Discrete Mathematics (3)
Topics include: Mathematical induction, recursion, graph theory, combinatorics, discrete probability, and matrix operations. Prerequisite: MATH 127 and MATH 130. Offered Fall semesters.
MATH 236 — Geometry (3)
An introduction to both euclidean and non-euclidean geometry. Topics include construction; synthetic and coordinate proof; triangles and polygons; circles and spheres; similarity; area and volume. Geometer’s sketchpad and historical figures in the history of geometry are emphasized. Prerequisite: Math 127 or approval of the department chairperson. Alternate years: Offered Spring 2010.
MATH 237 — Mathematics for the Physical Sciences I (3)
Topics include calculus beyond MATH 125, an introduction to linear algebra, including: systems of linear equations, matrices, and determinants; differential equations; and use of multivariable functions. The emphasis is on the applications to physical systems. Prerequisite: MATH 125 or the approval of the department chairperson. Offered Fall semesters.
MATH 238 — Mathematics for the Physical Sciences II (3)
Topics include calculus beyond MATH 125, linear transformations, eigenvalues and eigenvectors, systems of differential equations, the Laplace transform, and the Fourier transform. The emphasis is on the applications to physical systems. Prerequisite: MATH
237. Offered Spring semesters.
MATH 250 — Linear Algebra (4)
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 361 — Probability and Statistics (3)
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; large sample statistical inference. Prerequisite: MATH 231 or approval of the department chairperson. Offered Fall semesters
MATH 362 — Statistics (3)
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; non- parametric statistics. Prerequisite: MATH 361. Offered Spring semesters.
MATH 363 — Mathematical Modeling (3)
Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; repeated games. Topics in curve fitting include: curve fitting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions; curve fitting with splines; smoothing techniques. Prerequisite: MATH 231 or approval of the department chairperson. Alternate years.
MATH 365 — Numerical Analysis (3)
Topics include numerical integration and differentiation; direct and iterative methods for linear systems; numerical solution of linear and nonlinear algebraic equations and Eigen value problems; numerical solutions for ODe’s and PDe’s if time permits. Prerequisite: MATH 231 and MATH 250 and one of CS 115 and CIS 116. Alternate years.
MATH 367 — Real Analysis I (3)
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; the riemann integral. Prerequisite: MATH 231 and MATH 250 or approval of the department chairperson. Offered Fall semesters.
MATH 416 — Real Analysis II (3)
Topics include infinite series; uniform convergence of infinite series and sequences; power series; Maclaurin series; Taylor series; generalized Fourier series; the sturm-Liouville theorem; the eigenfunction technique for solving partial differential equations. Prerequisite: MATH 367.
MATH 418 — Topology (3)
elementary definitions, 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. Offered alternate years: Offered Spring 2010.
MATH 420 — Complex Variables (3)
Topics include complex numbers; geometry of the complex plane; functions and map- pings; the Cauchy-riemann equations; harmonic functions; the line integral; the Cauchy integral formula; Laurent series; theory of residues; conformal mapping. Prerequisite: MATH 367. Offered alternate years.
MATH 425 — Abstract Algebra (3)
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 490 — Junior Seminar (1)
students rework and refine 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 491 — Topics in Mathematics (3)
A special studies course. Past topics have included number theory; transfinite theory; probability theory; partial differential equations; problems in applied Mathematics. Lebesque integration and measure theory; calculus on manifolds; linear programming; advanced linear algebra; Mathematical modeling. Approval of the department chairperson is required.
MATH 497 — Independent Study in Mathematics (3)
Advanced work in areas of Mathematics under the supervision of a Department Mentor.
Open to Junior and Senior MATH majors. Approval of the department chairperson is required
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