Houston Christian University Catalog
Mathematics ( MATH ) Course Descriptions

MATH 1034 Precalculus Mathematics Laboratory
Prerequisite(s): MATH 1313 or a satisfactory score on a departmental placement exam
Corequisite(s): MATH 1434This is the laboratory portion of MATH 1434, Precalculus Mathematics.

MATH 1051 Calculus I Laboratory
Prerequisite(s): MATH 1434 or a satisfactory score on a departmental placement exam
Corequisite(s): MATH 1451This is the laboratory portion of MATH 1451, Calculus I.

MATH 1052 Calculus II Laboratory
Prerequisite(s): MATH 1451
Corequisite(s): MATH 1452This is the laboratory portion of MATH 1452, Calculus II.

MATH 1301 Introductory Algebra
Prerequisite(s): NoneAn indepth review of arithmetic and algebraic skills including fractions, signed arithmetic, order of operations, signed and fractional exponents, solving linear equations and inequalities. This course is offered to aid students with deficiencies in basic mathematical skills. Students who already have credit in a higherlevel mathematics course will not be given credit in this course. This course may not be counted as part of the mathematics major or mathematical studies major.

MATH 1302 Intermediate Algebra
Prerequisite(s): None.A review of arithmetic and algebraic skills needed for success in collegelevel mathematics. Students take assessments and will study and practice topics needed to strengthen their math skills as identified by their personal assessment. Topics may include fractions, signed arithmetic, order of operations, signed and fractional exponents, solving linear equations and inequalities, absolute value, quadratic equations, polynomials, rational functions, algebraic fractions, exponentials and radicals. This course is offered to aid students needing to strengthen their basic mathematical skills. Students who already have credit for a higherlevel 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 Thinking
Prerequisite(s): MATH 1301 or MATH 1302 or a MATH SAT/ACT score of at least 530/22 or a satisfactory score on a HBU required math placement examMathematical topics needed for the critical evaluation of quantitative information and arguments, including set theory, counting, logic, and the critical appraisal of graphs and tables, including the use of some simple mathematical models, and an introduction to probability and statistics. Additional topics may be selected from finance, graph theory, number theory, geometry and matrix theory. This course may not be counted as part of a mathematics major or a mathematical studies major.

MATH 1313 College Algebra
Prerequisite(s): MATH 1302 or a satisfactory score on a HBU required math 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 1302 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 Trigonometry
Prerequisite(s): MATH 1313 or a satisfactory score on a HBU required math 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 Mathematics
Prerequisite(s): MATH 1313 or a satisfactory score on a HBU required math placement exam
Corequisite(s): MATH 1034Sets, 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 I
Prerequisite(s): MATH 1434 or a satisfactory score on a HBU required math placement test
Corequisite(s): MATH 1051Limits, 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 II
Prerequisite(s): MATH 1451
Corequisite(s): MATH 1052A continuation of MATH 1451. Topics include: Techniques and applications of integration, improper integrals, parametric representations of curves, polar coordinates, L’Hôpital’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 2023 Linear Algebra Laboratory
Prerequisite(s): MATH 1451
Corequisite(s): MATH 2323This is the laboratory portion of MATH 2323, Linear Algebra.

MATH 2051 Calculus III Laboratory
Prerequisite(s): MATH 1452
Corequisite(s): MATH 2451This is the laboratory portion of MATH 2451, Calculus III.

MATH 2181 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included.

MATH 2201 Foundations of Higher Mathematics
Prerequisite(s): MATH 1451This course is a mathematically rigorous introduction to fundamental concepts required for higherlevel 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 Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included.

MATH 2302 Foundations of Arithmetic and Numeration
Prerequisite(s): 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 & Statistics
Prerequisite(s): 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 2323 Linear Algebra
Prerequisite: MATH 1451Introduction to linearity in mathematics. Topics include: matrices, determinants, abstract vector spaces, linear dependence, bases, eigenvalues and eigenvectors, and linear transformations.

MATH 2381 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included.

MATH 2423 Linear Algebra
Prerequisite(s): MATH 1451
Corequisite(s): MATH 2023Introduction 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(s): MATH 1452
Corequisite(s): MATH 2051A continuation of MATH 1452. Topics include: threedimensional 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 Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included.

MATH 3001 Introductory Statistics for the Life Sciences Laboratory
Prerequisite(s): MATH 1434 or MATH 1451 or a satisfactory score on a departmental placement examination
Corequisite(s): MATH 3401This is the laboratory portion of MATH 3304, Introductory Statistics for the Life Sciences.

MATH 3004 Probability and Statistics with Computer Applications Laboratory
Prerequisite(s): MATH 1451
Corequisite(s): MATH 3404This is the laboratory portion of MATH 3404, Probability and Statistics with Computer Applications.

MATH 3181 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included.

MATH 3281 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. A laboratory may or may not be included.

MATH 3302 Foundations of Geometry
Prerequisite(s): MATH 1451A 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 nonEuclidean geometry. This course is required for the mathematical studies major but may not be counted as part of a mathematics major.

MATH 3304 Introductory Statistics for the Life Sciences
Prerequisite(s): MATH 1434 or MATH 1451 or a satisfactory score on a Calculus I qualifying HBU required math placement examinationAn 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, analysis of variance, and an introduction to 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 3304 and MATH 3404.

MATH 3311 Introduction to Discrete Mathematics and Combinatorics
Prerequisite(s): MATH 1451.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 Chaos
Prerequisite(s): 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 Equations
Prerequisite(s): MATH 1452A first course. Topics include: existence and uniqueness of solutions, solutions of linear equations, solutions of higher order linear equations with constant coefficients, infinite series solutions, numerical solutions, solutions of linear systems, an introduction to nonlinear differential equations, and application.

MATH 3334 Partial differential Equations
Prerequisite(s): 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 solids, 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 Algebra
Prerequisite(s): MATH 1452 and MATH 2323An introduction to algebraic structures. Topics include: sets, operations, relations, groups, subgroups, equivalence classes, Lagrange’s Theorem, homomorphisms, rings, and ideals.

MATH 3364 Mathematical Computing
Prerequisite(s): 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
Prerequisite(s): MATH 2451An introduction to complex analysis and the study of complexvalued functions of a single complex variable. Topics include: the complex number system; the CauchyRiemann conditions; analytic functions including linear, exponential, logarithmic and trigonometric transformations; differentiation and integration of complexvalued functions; line integrals; and Taylor and Laurent Series expansions.

MATH 3381 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included.

MATH 3383 Mathematical Methods for Science and Engineering
Prerequisite(s): Credit for or concurrent enrollment in MATH 3333 and MATH 2451Advanced 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 3404 Probability and Statistics with Computer Applications
Prerequisite(s): 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. Students may not receive credit for both MATH 3304 and MATH 3404.

Math 3481 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included.

MATH 4181 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included.

MATH 4201 Mathematical Topics for Teachers
Prerequisite(s): 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 Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included.

MATH 4301 Real Variables I
Prerequisite(s): MATH 2451A 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(s): 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 4303 Introduction to Numerical Analysis
Prerequisite(s): MATH 2451 and MATH 3364An 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 equations 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 4310 Advanced Discrete Mathematics and Combinatorics
Prerequisite(s): 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 I
Prerequisite(s): 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 II
Prerequiste(s): 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 Bifurcations
Prerequiste(s): MATH 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 Biology
Prerequisite(s): MATH 3333Introduction to modeling in biology and genetics. Some of the models covered include populations models; hostparasite 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 Algebra
Prerequisite(s): MATH 3353A continuation of MATH 3353. The focus of this course is on rings, domains, fields, polynomials, Galois theory, Boolean algebra, and modules. Other topics may be covered if time permits.

MATH 4372 Advanced Complex Variables
Prerequisite(s): MATH 3371Further study of differentiable complexvalued functions of a single complex variable. Topics include: residue theory and contour integrals, ztransforms, conformal mapping, harmonic functions and their applications, Fourier Series, and Laplace transforms.

MATH 4380 Differential Geometry
Prerequisite(s): MATH 2451An introduction to diffeomorphisms and smooth manifolds. Topics covered include: tangent spaces, orientation of manifolds, vector fields, homotopy, and the index of a map.

MATH 4381 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included.

MATH 4481 Special Topics/Independent Study
Prerequisite(s): NoneTopics are selected on basis of student need and academic qualifications of staff. If regular lectures are not given, a minimum of 30 hours of work for each hour credit must be included. Laboratory may or may not be included.