Mathematics & Computer Science Dept.

MATHEMATICS COURSES

Math 132 General College Mathematics I credit 3 hrs.

A review of arithmetic concepts and operations; consumer mathematics including discount, simple andcompound interest; algebraic concepts including simple equations and their solutions; literal equationsand problems in applying formulae; concepts of measurement; geometry: angles and lines, perimeter,area and volume of geometric figures including the Pythagorean theorem, similar and congruent triangles, and unit circle; and problem solving skills emphasizing applications to daily life.

Math 134 General College Mathematics II credit 3 hrs.

A study of the real number system and its applications; introduction to sets, functions, and logic;selected topics from probability and statistics; coordinate geometry; graphs; and building skills in analytical reasoning. Prerequisite: Math 132.

Math 136 Discrete Mathematics credit 3 hrs.

The course covers logic, prepositional logic, predicate logic, proof techniques, mathematical induction, recursion analysis algorithms, recurrence relations, sets and combinations, principle of inclusionand exclusion, permutation and combinations, generating functions, graphs and trees, binary relationsand Warshall's algorithm, decision trees, and Hamiltonian circuits, minimal spanning tree. This course is recommended for students with advanced placement.

Math 138 College Algebra credit 3 hrs.

The course covers rational expressions, roots and radicals, quadratic equations, relations and functions, graph of polynomial and rational functions, zeros and factors of polynomial functions, matricesand determinants, systems of equations and inequalities. An honors section is offered as Math 138 (H).

Math 140 Precalculus credit 4 hrs.

The course covers exponential and logarithmic functions, linear programming, trigonometry, laws ofsine and cosine, trigonometric forms of complex numbers, sequences and counting principles. An honors section is offered as Math 140 (H). Prerequisite: Math 138.

Math 143 Calculus I credit 4 hrs.

Differential Calculus: limit, continuity, differentiation, Mean Value Theorem, techniques of differentiation, implicit differentiation and applications of derivatives including extrema of functions, concavity,curve sketching, and Newton's method. Integral Calculus: antiderivatives, indefinite integral, changeof variables, definite integration, Fundamental Theorems of integral calculus, numerical integration. Conic Sections: The parabola, ellipse, and hyperbola. An honor section is offered as Math 143 (H). Prerequisite: Math 140.

Math 144 Calculus II credit 4 hrs.

Integration techniques; improper integrals, application of integrals; sequences, convergence ofsequences; infinite series; tests of convergence, including comparison, ratio and root, alternatingseries; power series; Maclaurin and Taylor series. Prerequisite: Math 143.

Math 230 Linear Algebra credit 3 hrs.

The course covers matrices and systems of linear equations: Gaussian elimination, Echelon form,matrix operations, matrix inverse, solution sets of systems of linear equations, real-world applications;vector spaces and linear transformations: vector space, the image space, orthogonal basis, Gram-Schmidt Theorem; determinants and eigenvalue problems; properties of determinants, Cramer rule,characteristic polynomial, Eigenspaces, diagonalization; Eigenvalues and applications: quadraticforms, Householder transformations, QR factorization and least square. Prerequisite: Math 140.

Math 234 Abstract Algebra I credit 3 hrs.

Sets, mappings, composite mappings, binary operations, relations, integers, Mathematical induction,divisibility, prime factorization and greatest common divisors, congruence of integers, congruenceclass, introduction to groups to include definition of a group, examples of familiar and non-familiargroups, subgroups, cyclic groups and homomorphisms, introduction to rings to include definition of aring and integer domains, examples of familiar and non-familiar rings. Prerequisites: Math 136 andMath 143.

Math 235 Abstract Algebra II

Course covers isomorphisms of groups, finite permutation groups, Cayley's theorem, normal subgroups, quotient groups, finite Abelian groups, the field of quotients of an integer domain, ideals andquotient rings, ring homomorphisms, the field of real numbers, polynomials over a ring, divisibilityand greatest common divisor. Prerequisite: Math 234.

Math 236 Probability and Statistics credit 3 hrs.

Populations; samples; data; frequency distributions; graphic representations of frequency distributions; measures of central tendency: mean, mode, median; variability: range, variance, standard deviation, Z-scores; finite probability; conditional probability and Bayes's Theorem; descriptive treatmentof binomial, Poisson, normal and chi-square distributions; correlation and regression; confidence limits; using curve fitting to predict from data; and testing hypothesis. Research project requirement.Prerequisite: Math 143.

Math 237 Differential Equations I credit 3 hrs.

Ordinary differential equations of first order, higher order linear equations, D-operator techniques, andLaplace transform and series method and applications to the physical sciences and engineering.Prerequisite: Math 144.

Math 238 Differential Equations II credit 3 hrs.

Course covers theoretical aspects of the solutions of differential equations, proof of the existenceand uniqueness of such solutions, power series methods, linear systems of differential equationsincluding the eigenvalue method for homogeneous systems, introduction to nonlinear systems.Partial differential equations and boundary value problems. Prerequisite: Math 237.

Math 331 Modern Geometry credit 3 hrs.

Euclid geometry: the origin of geometry, axiomatic method; Euclid's first four postulates; Incidencegeometry: models, isomorphism of models, projective and affine plane; the discovery of non-Euclidean geometry: Hilberts axioms, Neutral geometry, Hyperbolic geometry; geometric transformations: applications of geometric problems, motions and similarities, automorphisms of the Cartesian Models in thePoincare Model. Prerequisite: Math 136 and Math 144.

Math 333 Vector Calculus credit 3 hrs.

Polar coordinates: integral, area, and length in the polar coordinate system; Vectors: vector-valued functions; Vector differential calculus (partial differentiation); Vector integral calculus: line integrals, Green's Theorem and Stoke's Theorem; Functions of several variables, Fubini's Theorem for multiple integrals; Fourier Series and orthogonal functions. Prerequisite: Math 144.

Math 334 Complex Variables credit 3 hrs.

The course covers the complex plane, functions of a complex variable, Cauchy-Riemann equations,complex integration, theorems of Morera and Liouville, power series, singular points, residues,Laurent expansion, contour integration, and elementary conformal mappings. Prerequisite: Math 144.

Math 335 Number Theory credit 3 hrs.

The course covers the Chinese remainder theorem, Euler Q-function, the group of units of Z, roots ofunity in a field, integral elements of a ring, integrally closed ring, conjugate elements, conjugate fields,integers in quadratic fields, and Dedekind rings. Prerequisite: Math 234.

Math 430 Teaching of Secondary School Mathematics credit 3 hrs.

A study of the selection and organization of content and effective teaching procedures for secondary school mathematics. A senior paper is required. Twenty (20) hours of practicum are required. Prerequisite: Math 134 or Math 138.

Math 435 Statistical Methods credit 3 hrs.

This course is designed to give the students the fundamental ideas of statistical analysis that is notnecessarily in a mathematically rigorous fashion. The logic of statistical procedure will be developedwithout resorting to mathematical derivations or proofs. It is hoped that they will motivate students inpursuing further studies in statistics. The course will cover random variables and their distributions; samples and sampling distributions, sampling and nonsampling errors; estimation, determination ofthe sample size, use of statistical software packages; hypothesis testing, relationship between hypothesis testing and confidence interval estimation; hypothesis concerning the population variance andstandard deviation; hypothesis testing two populations; analysis of variance, simple regression andcorrelation, multiple correlation and regression; nonparametric statistics; statistical decision making.Prerequisite: Math 236.

Math 436 Applied Probability credit 3 hrs.

This course is designed as an intermediate course in applied probability for students in mathematics,computer science, physics -engineering, management, and biological and physical science. It is alsorecommended for students in Teaching of Mathematics. The course covers basic probability; discreterandom variables; joint distributions and independent random variables; expected values; covarianceand correlation; special discrete random variables; (binomial, geometric, negative binomial, hypergeometric), multinomial, and Poisson, moments and moment generating functions; Markov Chains;Markov property, simple queuing systems, steady-state probabilities, continuous random variables,probability density functions; joint probability distributions; special continuous random variables;(exponential, normal, gamma, and Weibull); and counting and queuing processes, (Bernoulli,Poisson). Prerequisite: Math 144, Math 230 and CSc 135 or CSc 136.

Math 437 Mathematical Analysis I credit 3 hrs.

Techniques of proof, sets, functions, structure of real numbers, the completeness axiom, density ofrational numbers in real numbers, epsilon-delta argument, sequences to include convergence, limittheorems, monotone sequences and subsequences, continuity of functions, continuity andsequences, differentiation to include definitions and Mean Value Theorem. Prerequisite: Math 144.

Math 438 Mathematical Analysis II credit 3 hrs.

Course covers sequences (revisited), Bolzano-Weierstrass Theorems, Cauchy sequences, limits atinfinity; continuity of functions to be revisited including limits of functions, uniform continuity, and discontinuities, integrals and its properties, the Fundamental Theorem of Calculus, convergence anddivergence of infinite series, absolute and conditional convergence, sequences and series of functions, power series. Prerequisite: Math 437.

MC 431 Numerical Analysis I credit 3 hrs.

Course covers interpolation; approximations; numerical differentiation and integration. Prerequisites: Math 136, Math 144 and CSc 138.

MC 432 Numerical Analysis II credit 3 hrs.

Course covers numerical techniques in linear algebra. Numerical solution of transcendental equations, systems of linear equations, Milne's method, Runge-Kutta method, modeling of continuousdiscrete systems, approximation to computer based functions, and Pade's approximation.Prerequisite: Math 431.

Source: Benedict College Catalogue, 2007-2009.