Course Descriptions

DEVELOPMENTAL COURSES
MATH091 and MATH092 are provided for students not achieving a score of at least P2 on the Mathematics Placement Examination (MPE). Students complete the sequence MATH091/092 by passing a set of proficiency tests in arithmetic and algebra, at which time a P2 score is awarded. When this occurs, the student has completed the Math Skill part of the General Education requirement, and is considered ready to take MATH 145, 166, 168, or STAT285. Depending on the diligence and previous preparation of the student, this may occur at any time in the MATH091/092 sequence.

MATH091 (3)
Arithmetic and Algebra Review I
Individualized review of arithmetic and algebra skills. Provides computer-generated drill problems, instant scoring and explanation, with conceptual instruction as required. Students completing the sequence requirements while enrolled in MATH091 are not required to take MATH092. Fall, Spring

MATH092 (3)
Arithmetic and Algebra Review II
Continuation of MATH091. Students not completing the sequence requirements but fulfilling attendance, participation, and progress requirements may receive an R grade requiring re-registration the next semester. Prerequisite: Math 091. Fall, Spring

UNDERGRADUATE COURSES
MATH141 (4)
Calculus I
MATH141, 142 is a standard introduction to single-variable calculus. MATH141 includes limits, continuity, derivatives, applications, and integration up through substitution.  Formal definitions of limit, derivative, and Riemann integral. Proofs of standard theorems, including the Fundamental Theorem of Calculus. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE=P5 or MATH167 or MATH168 with grade no lower than C. Fall, Spring

MATH142 (4)
Calculus II
Continuation of MATH141. Riemann sums, Riemann integral, Fundamental Theorem of Calculus, techniques of integration, improper integrals, applications, sequences, series, and tests of convergence. Prerequisite: MATH141. Fall, Spring

MATH145 (3)
Reasoning with Functions
Logic, sets; functions given by tables, formulas, graphs; inverse functions; linear, quadratic, exponential and trigonometric functions; rates of change and applications to science and business. Additional topics may be selected by the instructor. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE > P2. Fall, Spring

MATH165 (3)
College Algebra
AU/HSI course. A study of linear equations and inequalities; algebraic, logarithmic, and exponential functions; polynomials and complex numbers. Includes applications in business and science. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE > P2.

MATH166 (3)
Precalculus Algebra
Equations and inequalities; systems of linear equations; algebraic, polynomial, rational, exponential, and logarithmic functions; inverse functions, complex numbers, applications, and selected topics. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE > P2. Fall, Spring

MATH167 (2)
Precalculus Trigonometry
Trigonometric functions and their inverses, identities, trigonometric equations; laws of sines and cosines, vectors, applications, and selected topics. Fulfills the General Education Mathematics reasoning requirement.
Prerequisite: MPE > P3 or MATH166 or MATH145. Fall

MATH168 (4)
Precalculus
Covers most of the content of MATH166 and MATH167. Equations and inequalities; systems of linear equations; algebraic, polynomial, rational, exponential, and logarithmic functions; inverse functions, complex numbers, trigonometric functions and their inverses, identities, trigonometric equations, laws of sines and cosines, vectors, applications, and selected topics. Fulfills the General Education Mathematics reasoning requirement.
Prerequisite: MPE > P2. Fall, Spring

MATH168 (4)
Precalculus
AU/GU course—see content above. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE > P2.

MATH182 Alt (3)
Calculus with Applications
Introduction to single-variable calculus, including limits, differentiation, optimization, and integration with applications to problems in business and the social sciences. Some topics from multivariable calculus, including partial derivatives and extrema of functions of two variables. Fulfills the General Education Mathematics reasoning requirement. Prerequisite: MPE > P4 or MATH166, 167 or 168 preferred; MATH145 is acceptable. Spring

MATH215 (3)
Introduction to Linear Algebra
Vectors, Euclidean n-space, matrices, systems of linear equations, determinants, eigenvalues, eigenvectors, vector spaces, and linear transformations with emphasis on applications and computation. Prerequi­site: MATH182 or 141. Fall

MATH220 Alt (3)
Geometry and Numbers
Euclidean geometry and number systems for elementary and middle school teachers. Topics include proofs, algorithms, and historical development. Prerequisite: MATH145. Fall

MATH240 (4)
Calculus III
Standard introduction to multivariable calculus. Vectors and vector functions, curves and surfaces, partial derivatives, multiple integrals, line and surface integrals. Stokes', Green's, and divergence theorems. Prerequisite: MATH142. Fall

MATH286 (3)
Differential Equations
Ordinary differential equations as dynamical systems. Linear and nonlinear first order equations and systems, higher order linear equations, modeling, standard analytic and qualitative methods of solution, equilibria and stability, phase plane analysis. Computer graphing tools will be used. Prerequisite: MATH142. Spring

MATH295 (1-3)
Independent Study
Independent study of selected topics in mathemat­ics under the supervision of a mathematics professor. Ordinarily a minimum of three hours of study per week is expected for each credit. The instructor may require written reports or oral presentations. Repeatable. Prerequisite: Consent of the instructor.

MATH315 Alt (3)
Linear Algebra
Vector spaces, eigenspaces, linear transformations, orthogonality, inner product spaces, quadratic forms, and selected topics. Prerequisites: MATH215, 355. Spring

MATH355 (3)
Discrete Mathematics

Selected topics in discrete mathematics, including logic, set theory, relations, functions, properties of integers, modular arithmetic, and RSA encryption. Mathematical reasoning and the writing of proofs will be emphasized. Prerequisites: MATH141 or 182. Spring

MATH389 (0.5)
Mathematics Colloquium
Participation in at least 10 mathematics colloquia or approved colloquia of other departments. Grade is based on attendance and notes taken at the colloquia, and a project. Repeatable to 2 credits. S/U. Fall, Spring

MATH405 Alt (3)
Applied Mathematics
Solutions of first and second order partial differential equations, and applications. Prerequisites: MATH240, 286. Fall

MATH408 Alt (3)
Complex Analysis
Elementary complex analysis, contour integrals, complex series. Prerequisites: MATH240 and 355. Spring

MATH426 Alt (3)
Mathematical Modeling in Biology
Theory and application of linear and nonlinear mathematical models of biological processes. Topics selected from discrete- and continuous-time deterministic and stochastic modeling, analytic solution techniques, linearization, bifurcations, chaos, computer simulation, model parameterization, and model validation. Prerequisite: MATH141. Fall

MATH431, 432 Alt (3, 3)
Advanced Calculus
Theorems on continuity, differentiation, integration, and convergence; additional selected topics such as topology, differentiable manifolds, and real analysis. Prerequisite: MATH240 and 355. Fall/Spring Sequence

MATH441, 442 Alt (3, 3)
Abstract Algebra
Study of groups, rings, fields, modules, vector spaces, and algebras. Prerequisite: MATH240 and 355.

MATH475 Alt (3)
Geometry
Axiomatic development and history of Euclidean and non-Euclidean geometries, constructions, geometric transformations, and selected topics from finite, fractal, affine, and projective geometries. Relation of these topics to secondary teaching. Prerequisite: MATH355. Fall

MATH487 Alt (1-3)
Special Topics in___________
Consult the instructor with regards to the topic to be covered. Prerequisite: Consent of instructor. Repeatable in different areas.

MATH495 (1-3)
Independent Study
Independent study of selected topics in mathematics to enable advanced students to pursue topics not offered in other scheduled courses. The student will study under the supervision of a mathematics professor whose prior approval is required. Ordinarily a minimum of three hours of study per week is expected for each credit. Grades are assigned on the basis of an instructor-selected procedure such as oral or written exams or reports.

STATISTICS
STAT285 (3)
Elementary Statistics
A study of basic descriptive and inferential statistics, including elementary probability and probability distributions, statistical inference involving binomial, normal, and t-distributions, and hypothesis testing. Prerequisite: MPE > P2. Fall, Spring

STAT285 (4)
Elementary Statistics
AU/GU course — see content above. Prerequisite: MPE > P2.

STAT340 (3)
Probability Theory with Statistical Applications
Probability theory and statistics for students having preparation in calculus. Topics include probability models, combinatoric problems, random variables, discrete and continuous distributions, expectation, moment generating functions, central limit theorem. Prerequisite: MATH141 or 182. Spring

HONORS
MATH271-50 (1)
Honors in Mathematics
The study of mathematical problems where the solution depends more on insight and creativity than on routine computation. Repeatable to 2 credits. Prerequisite: MATH142 and consent of instructor.

GRADUATE COURSES
MATH530 (2-3)
Topics in Teaching Mathematics
A. Algebra
B. Geometry
C. Analysis
D. Applications
Consult with department chair regarding availability in any given year. Repeatable to 6 credits.

MATH540 Alt (2-3)
Topics in Mathematics
Consult with the instructor in regard to the topic to be covered. Prerequisite: Consent of the instructor. Repeatable to 6 credits.

MATHEMATICS EDUCATION COURSES
MAED505 through MAED625 are available only to participants in the Alternative Certification Experimental Program (Math Endorsement Program) for Middle School Educators, which is jointly administered by the Andrews University School of Education and the Berrien County Intermediate School District. Applications to this Program are initially screened by the School of Education and the Department of Mathematics, and then go through the regular Andrews admissions process. These courses will be taught in rotation, during the regular school year and during the summer, according to a schedule set by the Administrative Committee for the Program.

MAED505 (2)
Understanding Numbers and Operations for Middle Grades Educators
This course is designed to strengthen middle school teachers' rational number knowledge and number sense. This includes the in-depth study of rational numbers and operations on rational numbers, the structure of the rational and real number systems, algorithms for computation, estimation strategies, and working with very large and very small numbers. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED510 (3)
Exploring Algebra and Functions for Middle Grades Educators
This course extends the middle school teachers' understanding of algebra as a symbolic language. This course moves beyond symbol manipulation to include modeling of physical situations. Students will explore algebraic, linear, and non-linear functions within the context of the course. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED515 (3)
Data Analysis for Middle Grades Educators
This course presents an integrated approach to data analysis, statistics, and probability for middle grades math teachers. Instruction focuses on specific real-world data sets and statistical investigations. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED521 (2)
Informal Geometry and Measurement for Middle Grades Educators
This course is the first of two which lead prospective mathematics teachers through a series of explorations to develop competence in geometric reasoning, including conjecture, proving, and disproving. Prospective teachers develop a deeper understanding of the role of proof in geometry. The pedagogy of this course models that of effective middle school mathematics teachers.

MAED522 (2)
Formal Geometry for Middle Grades Educators
This course is the second of two which lead prospective mathematics teachers through a series of explorations to develop competence in geometric reasoning, including conjecturing, proving, and disproving. Prospective teachers refine their understanding of the role of proof in geometry. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED600 (2)
Discrete Mathematics and Number Theory for Middle Grades Educators
Students investigate concepts of number theory, discrete mathematics, and logic as they apply to middle grades mathematical education. Each topic includes a study of graphic representation of concepts and applications in technology. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED610 (4)
Mathematical Modeling for Middle Grades Educators
Investigation of concepts and practices of mathematical modeling with an emphasis on application to middle grades education. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED625 (2)
Mathematical Investigations for Middle Grades Classrooms
Participants investigate topics in mathematics, including probability, programming, fractals, and chaos theory. Emphasis is placed on participant understanding of these topics and their appropriate use as investigations with middle grades students. The pedagogy of the course models that of effective middle school mathematics teachers.

MAED 630 (1-4)
Seminar:________________
Seminar in specific topics relevant to mathematics education. Each seminar examines one topic in detail. Repeatable with different topics. May be graded S/U.