King's College - Mathematics

Course Descriptions

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 semester.

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.  xcel 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 defi nite 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 in analyzing statistical data. Students are taught how to precisely communicate statistical results. Topics include displaying data graphically; measures of central tendency; measures of variability; general laws of probability; normal, t, and chi-square distributions; sampling distributions; confi dence intervals; hypothesis testing; two way tables; and use of statistical software. Prerequisite: CORE 098 — Mathematical skills. Closed to students who have taken or who are currently taking MATH 124 or 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 in analyzing statistical data. Students are taught how to precisely communicate statistical results. 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; confi dence intervals; hypothesis testing; analysis of variance; two-way tables; use of statistical software. Biological applications are emphasized. Three 50-minute lectures and one 50-minute lab per week. Prerequisite: CORE 098 — Mathematical skills. Closed to students who have taken or who are currently taking MATH 124 or MATH 126. Offered fall semesters.

MATH 129 — Analytic Geometry and Calculus I (4)

The fi rst 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: CORE 098 — Mathematical skills. Offered fall semesters.

MATH 130 — Analytic Geometry and Calculus II (4)

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 231 — Analytic Geometry and Calculus III (4)

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 235 — Discrete Mathematics (3)

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 236 — Geometry (3)

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 2014.

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 semester.

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 301 — Financial Mathematics (3)

Topics include time value of money, annuities with payments that are not contingent, loans, bonds, general cash fl ows and portfolios, and immunization. The course will be designed to prepare students for the "Theory of Interest" portion of actuarial exam #2. Prerequisite: MATH 130. Alternate years: Offered Spring 2013.

MATH 361 — Probability (3)

Topics include set functions, counting methods, events, independence, conditional probability, Bayes rule, univariate probability distributions; including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, and normal; multivariate probability distributions; including the bivariate normal; joint probability functions, joint probability density functions, conditional and marginal probability distributions; transformations, and order statistics. Prerequisite: MATH 231 or approval of the Department Chairperson. Offered fall semesters.

MATH 362 — Statistics (3)

Topics include sampling distributions, Central Limit Theorem, point estimators, confi dence intervals, properties of point estimators, methods of fi nding estimators, hypothesis testing, least squares linear regression, ANOVA, and analysis of categorical data. Prerequisite: MATH 361. Offered spring semesters.

MATH 363 — Mathematical Modeling (3)

Topics include difference equations, systems of difference equations, dynamical systems, geometric similarity, model fi tting, simulation modeling, discrete probabilistic modeling, optimization, modeling using graph theory, dimensional analysis, and modeling with a differential equation. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years: Offered Fall 2012.

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 eigenvalue problems; and 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: Offered Spring 2013.

MATH 367 — Real Analysis I (3)

The fi rst 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 418 — Topology (3)

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; and product spaces. Prerequisite: MATH 367. 4 hours per week. Alternate years: Offered Spring 2014.

MATH 420 — Complex Variables (3)

Topics include complex numbers; geometry of the complex plane; functions and mappings; the Cauchy Riemann equations; harmonic functions; the line integral; the Cauchy integral formula; Laurent series; theory of residues; conformal mapping. Prerequisite: MATH 367. Alternate years: Offered Spring 2013.

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; and ring homomorphisms; fi elds. Approval of the Department Chairperson is required. Offered fall semesters.

MATH 490 — Junior Seminar (1)

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 491 — Topics in Mathematics (3)

A special studies course. Past topics have included number theory; transfi nite theory; probability theory; partial differential equations; and problems in applied Mathematics. Lebesque integration and measure theory; calculus on manifolds; linear programming; advanced linear algebra; and 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 Mathematics majors. Approval of the Department Chairperson is required.

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