# Houston Baptist University Catalog

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Mathematics (MATH) Course Descriptions

MATH 1301 Introductory Algebra Prerequisite: NoneThe quantitative tools required in a modern society, including a brief review of arithmetic, graphical representation of data, and beginning algebra. This course is offered to aid students with deficiencies in basic mathematical skills. Students who already have credit in a higher-level mathematics course will not be given credit in this course. This course may not be counted as part of the mathematics major.

MATH 1302 Intermediate Algebra PREREQS: MATH 1301, MATH SAT score of at least 400 or MATH ACT score of at least 18, or a satisfactory score on a math placement examThis course is intended for students who have had some previous exosure to algebra, either an introductory algebra course or two years of high school algebra. Topics include: linear equations and inequalities, absolute value, quadratic equations, polynomials, rational functions, algebraic fractions, exponentials and radicals, systems of linear equations, and applications. Students who already have credit for a higher-level mathematics course will not be given credit for this course. This course may not be counted as part of the mathematics major or the mathematical studies major.

MATH 1305 Math for Critical ThinkingPrerequisite: MATH 1301 or 1302 or a MATH SAT/ACT score of at least 400/18 or a satisfactory score on a departmental placement examMathematical topics needed for the critical evaluation of quantitative information and arguments, including logic and the critical appraisal of graphs and tables including the use of some simple mathematical models and an introduction to elementary probability, statistics, and finance. This course may not be counted as part of a mathematics major, or a mathematical studies major.

MATH 1313 College AlgebraPrerequisite: MATH 1302 or a MATH SAT/ACT score of at least 550/25 or a satisfactory score on a departmental placement examEvaluating and manipulating algebraic expressions, the laws of exponents, polynomials, factoring, rational expressions, radicals, the quadratic formula, solving equations and inequalities, systems of linear equations, an introduction to graphing, and applications. Students with no previous exposure to algebra should take MATH 1304 before MATH 1313. MATH 1313 may not be counted as part of a mathematics major. It may not be counted as part of a mathematical studies major except by students with a specialization in middle grades.

MATH 1323 TrigonometryPrerequisite: MATH 1313 or a satisfactory score on a departmental placement examA study of trigonometric functions, exponentials, logarithms, and applications for students needing a more comprehensive background than the accelerated coverage given in MATH 1434. This course may not be counted as part of the mathematics major.

MATH 1434 Precalculus MathematicsPrerequisites: MATH 1313 and MATH 1323 or a satisfactory score on a departmental placement examSets, relations, functions, roots of polynomial equations, trigonometry, and analytic geometry. This course may not be counted as part of the mathematics major. This course includes one semester hour credit for laboratory sessions.

MATH 1451 Calculus IPrerequisite: MATH 1434 or a satisfactory score on a placement testLimits, continuity, differentiation and integration of elementary and transcendental functions, L¿Hôpital¿s Rule. Applications, including rates of change, max/min problems, and area between curves. This course includes one semester hour credit for laboratory sessions.

MATH 1452, Calculus IIPrerequisite: MATH 1451A continuation of MATH 1451. Topics include: Techniques and applications of integration, improper integrals, parametric representations of curves, polar coordinates, L'Hopital's Rule, numerical approximation of integrals, an introduction to differential equations, and infinite series. This course includes one semester hour credit for laboratory sessions.

MATH 2181, Special Topics/Independent StudyTopics are selected on the basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit.

MATH 2201 Foundations of Higher Mathematics PREREQ: MATH 1451 or consent of the instructorThis course is a mathematically rigorous introduction to fundamental concepts required for higher-level mathematics. Topics include logic, sets, relations, functions, and algebraic structures, with an emphasis on formal mathematical proof techniques. It is required for the mathematics major.

MATH 2281 Special Topics/Independent StudyTopics are selected on the basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit.

MATH 2302 Foundations of Arithmetic and NumerationPrerequisite: MATH 1305 or higher level mathematicsA study, from an advanced perspective, of the concepts and skills involved in arithmetic and numeration. Topics include sets, rational numbers (whole numbers and place value, fractions, integers and decimals), number theory, properties and algebraic reasoning, arithmetic operations, percents, ratios, and proportions. Problem solving is emphasized. This course, designed for education majors, may not be counted as part of the mathematics major or minor or meet the Liberal Arts Core Curriculum, math proficiency requirement.

MATH 2303 Foundations of Geometry, Measurement, Probability & StatisticsPrerequisite: MATH 1305 or higher level mathematicsA study, from an advanced perspective, of the basic concepts and methods of geometry, measurement, probability and statistics. Topics include representation and analysis of data; discrete and conditional probability; measurement; and geometry as approached through similarity and congruence, through coordinates, and through transformations. Problem solving is emphasized. This course, designed for education majors, may not be counted as part of the mathematics major or minor or meet the Liberal Arts Core Curriculum, math proficiency requirement.

MATH 2381, Special Topics/Independent StudyTopics are selected on the basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit.

MATH 2423, Linear AlgebraPrerequisite: MATH 1451Introduction to linearity in mathematics. Topics include: matrices, determinants, abstract vector spaces, linear dependence, bases, eigenvalues and eigenvectors, and linear transformations. This course includes one semester hour credit for laboratory sessions.

MATH 2451, Calculus III Prerequisite: MATH 1452A continuation of MATH 1452. Topics include: three-dimensional coordinate systems, quadric surfaces, cylindrical and spherical coordinates, vector calculus in three dimensions, partial derivatives, the total differential, multiple integrals, line integrals, surface integrals, vector fields, Green's Theorem, Stokes' Theorem, the Divergence Theorem, and applications. This course includes one semester hour credit for laboratory sessions.

MATH 2481 Special Topics/Independent StudyTopics are selected on the basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit.

Math 3181, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

Math 3281, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 3302 Foundations of GeometryPrerequisite: MATH 1451 (or 2434) or consent of instructorA study of classical Euclidean geometry using both analytic and synthetic techniques, with an emphasis on the formal development of geometry. Topics include axiomatic systems, congruence and similarity, transformations, area and volume, Euclidean construction, finite geometries, and a brief introduction to non-Euclidean geometry. This course is required for the mathematical studies major but may not be counted as part of a mathematics major.

MATH 3311, Introduction to Discrete Mathematics and CombinatoricsPrerequisites: MATH 1451; MATH 2201 is highly recommended.This course introduces students to elements of combinatorics, number theory, and discrete structures. Topics covered include permutations, combinations, prime factorizations, the Euclidean Algorithm, relations, the pigeonhole principles, inclusion and exclusion, and finite state machines. It exposes students to areas of mathematics of current practical interest and involves the use of proof and algorithmic thinking.

MATH 3331, Nonlinear Dynamics and ChaosPrerequisite: MATH 3333An introduction to dynamical systems. This course develops the theory for normal forms, structural stability of solutions, robust behavior, transversality, and local bifurcations.

MATH 3333 Ordinary Differential EquationsPREREQS: MATH 1452 and MATH 2423 A first course. Topics include: existence and uniqueness of solutions, initial and boundary value problems, solutions of first order equations, solutions of higher order linear equations with constant coefficients, infinite series solutions, numerical solutions, solutions of linear systems, solutions using Laplace transforms, and applications.

MATH 3334, Partial differential EquationsPrerequisites: MATH 3333An introduction to the basic properties of partial differential equations, including ideas and techniques that have proven useful in analyzing and solving them. Topics include vibrations of soilds, fluid flow, molecular structure, photon and electron interactions, and radiation of electromagnetic waves, with emphasis on the role of partial differential equations in modern mathematics, especially in geometry and analysis.

MATH 3353 Introduction to Abstract AlgebraPrerequisite: MATH 1452, 2201 and 2423An introduction to algebraic structures. Topics include sets, operations, relations, groups, subgroups, equivalence classes, Lagrange¿s Theorem, homomorphisms, rings, and ideals.

MATH 3364, Mathematical ComputingPREREQ: MATH 1451 or consent of instructorAn introductory course in computer programming with applications to mathematics. The programming language used will vary; possible choices include but are not restricted to Java, C++, C#, Maple, and MATLAB. Topics include: design of algorithms, structured programming, data types, control structures, functions and procedures, and mathematical problem solving. This course may be repeated for credit provided a different computer programming language is used.

MATH 3371, Introduction to Complex Variables(Previously offered as MATH 4333)Prerequisite: MATH 2451An introduction to complex analysis and the study of complex-valued functions of a single complex variable. Topics include the complex number system, the Cauchy-Riemann conditions, analytic functions including linear, exponential, logarithmic and trigonometric transformations, differentiation and integration of complex-valued functions, line integrals, and Taylor and Laurent Series expansions.

Math 3381, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 3383 Mathematical Methods for Science and EngineeringPrerequisites: Credit for or concurrent enrollment in MATH 3333 and 3414Advanced techniques in applied mathematics for students of science and engineering, with topics chosen from partial differential equations, Laplace transforms, Fourier series, complex analysis, and vector analysis. (Offered also as PHYS 3383.)

MATH 3401, Introductory Statistics for the Life SciencesPrerequisite: MATH 1434 or MATH 1451 or a satisfactory score on a departmental placement examination.An introduction to elementary probability and statistics with applications to the life sciences. Topics include frequency distributions, measures of central tendency and spread, probability concepts, discrete and continuous distributions, point and interval estimation, hypothesis testing, and an introduction to analysis of variance, linear correlation and regression. This course includes one semester hour credit for laboratory sessions. May not be counted as part of a math major or a math studies major. Students may not receive credit for both MATH 3401 and MATH 3404.

MATH 3404 Probability and Statistics with Computer ApplicationsPrerequisite: MATH 1451A mathematical development of the basic concepts of probability and statistics, emphasizing the theory of discrete and continuous random variables, with applications in science and engineering. Topics include descriptive statistics, probability theory, random variables, expected value, probability density functions, probability distributions, correlation and regression, and an introduction to statistical inference. This course includes one semester hour credit for laboratory sessions.

Math 3481, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 4181, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 4201, Mathematical Topics for TeachersPrerequisites: 15 hours of mathematics and junior or senior standingA review of mathematical topics of special interest to students obtaining teacher certification in mathematics, including material from algebra, geometry, probability, statistics, linear algebra, discrete math, and others. This course includes instruction on technology used in teaching mathematics, both graphing calculators and computer software. Required for the mathematical studies major, but may not be counted as part of a mathematics major.

MATH 4281, Special Topics/Independent StudyTopics are selected on basis of student needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 4301 Real Variables I Prerequisites MATH 2451 and MATH 2201A rigorous introduction to mathematical analysis. Topics covered include the real and complex number systems, basic topology, numerical sequences and series, continuity of functions, and differentiation.

MATH 4302 Real Variables II Prerequisite: MATH 4301A continuation of MATH 4301. Further study of mathematical analysis. Topics covered include Riemann integration, sequences and series of functions, functions of several variables, and integration of differential forms.

MATH 4310 Advanced Discrete Mathematics and CombinatoricsPrerequisite: MATH 3311Further study of enumerative techniques and discrete structures including generating functions, recurrence relations, graph theory, spanning trees, optimization, and Boolean Algebras.

MATH 4311 Topology IPREREQ: MATH 3353 or MATH 4301An introduction to topology and its applications. Topics include a review of basic abstract algebra; the definition of a topological space, interior, closure, and boundary of sets; subspace, product, and quotient topologies; continuity and homeomorphisms; metrics and metric spaces; connectedness; and compactness.

MATH 4312 Topology IIPrerequiste: MATH 4311A continuation of MATH 4311. Topics include dynamical systems and chaos, homotopy and degree theory, fixed point theorems, embeddings, knots, graphs, and manifolds.

MATH 4332 Dynamics and BifurcationsPrerequistes: MATH 2201 and 2451Introduction to the theory of equilibrium solutions of nonlinear equations. Presentation of the theory of bifurcations includes the analysis of the nonlinear ordinary and algebraic equations that arise from the methods of reduction by projections.

MATH 4341 Mathematical BiologyPrerequisites: MATH 3333Introduction to modeling in biology and genetics. Some of the models covered include populations models, host-parasite models, and gene spread models as described by difference equations, differential equations, and partial differential equations. The emphasis of this course will be to familiarize students with the selection of models and predictions based on the models chosen.

MATH 4353 Advanced Abstract AlgebraPrerequisite: MATH 3353A continuation of MATH 3353. The focus of this course is on rings, domains, fields, polynomials, Galois theory, Boolean algebra, and modules. Other topiocs may be covered if time permits.

MATH 4372 Advanced Complex VariablesPrerequisite: MATH 3371Further study of differentiable complex-valued functions of a single complex variable. Topics include residue theory and contour integrals, z-transforms, conformal mapping, harmonic functions and their applications, Fourier Series, and Laplace transforms.

MATH 4380 Differential GeometryPrerequisites: MATH 2451 and 2201An introduction to differomorphisms and smooth manifolds. Topics covered include tangent spaces, orientation of manifolds, vector fields, homotopy, and the index of a map.

MATH 4381 Special TopicsTopics are selected on basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.

MATH 4401 Introduction to Numerical AnalysisPrerequisites: MATH 2451 and either MATH 3364 or consent of the instructor.An introduction to modern approximation techniques. This course shows how, why, and when numerical techniques can be expected to work and fail. It demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. Topics covered include approximating solutions to equation in one variable, interpolation and approximation of polynomials, numerical differentiation and integration, applications to differential equations, and solutions of both linear and nonlinear systems of equations.

MATH 4481 Special Topics/Independent StudyTopics are selected on basis of students needs and the academic qualifications of the staff. A minimum of 30 hours of study is required for each semester hour of credit. Up to one semester hour credit for laboratory sessions may be included.