|Undergraduate Catalog 2004-2006: Courses|
NOTE: All entering students without accepted transfer work at the level of college algebra (or the equivalent in contemporary mathematics) or above must complete the Mathematics Competency Examination. Successful completion of the Mathematics Competency Examination meets the Aurora University general education mathematics requirement. Additional coursework in mathematics may be required as prerequisites to courses in specific majors.
MTH0990 Preparatory Math (3 semester hours)
Introduction to natural numbers, fractions, negative numbers, and the irrationals including addition, subtraction, multiplication, and division. Introduction to exponents and radicals, variables and linear equations. Placement in MTH0990 is based on demonstrated student outcomes of AU mathematics competency examination. Credit earned in MTH0990 is in addition to the 120 semester hours required for graduation.
MTH1100 College Algebra (3 semester hours)
The fundamentals of algebra for students of all majors. Prepares the student mathematically for such courses as MTH1800, MTH1310, CSC1500, SBS2320, ECN2010, ECN2020, and CHM1310. Real numbers, polynomials, linear equations and inequalities, functions, rational expressions, exponents, quadratic equations, and systems of linear equations.
Prerequisites: Placement in MTH1100 is based on demonstrated student outcomes of AU mathematics competency examination, or MTH0990.
MTH1110 Contemporary Mathematics (3 semester hours)
Several topics are studied in depth: logic/set theory, mathematics of personal finance, counting techniques and probability, and statistics. The use of calculators and computer is required. May be used to meet AU math requirement in lieu of MTH1100.
Prerequisite: Placement in MTH1110 is based on demonstrated student outcomes of AU mathematics competency examination, or MTH0990.
MTH1210 Mathematics for Elementary Teachers I (3 semester hours )
The first of a two-course sequence for those majoring in elementary education. Topics include problem solving, set operations, numeration systems, whole number operations, estimation, integer operations, number theory concepts, rational numbers and their forms, radicals and rational exponents, and irrational numbers.
Prerequisites: Placement in MTH1210 is based on demonstrated student outcomes of AU mathematics competency examination, or MTH0990.
MTH1220 Mathematics for Elementary Teachers II (3 semester hours)
A continuation of MTH1210. Topic include probability, statistics and statistical graphs, fundamentals of geometry, geometric constructions, motion geometry, the Pythagorean theorem, and measurement.
Prerequisites: Placement in MTH1220 is based on demonstrated student outcomes of AU mathematics competency examination, or MTH1210.
Note: Successful completion of MTH1210 and MTH1220 satisfies the mathematics competency requirement for graduation.
MTH1310 Precalculus (4 semester hours)
Prepares the student for calculus. Topics include the algebraic, exponential, logarithmic, and trigonometric functions and their graphs.
Prerequisites: MTH1100 or its equivalent as demonstrated on the AU mathematics competency examination.
MTH1800 Quantitative Business Methods (4 semester hours)
This course has two major components: first, the student will be introduced to the tools of finite mathematics: linear equations, linear programming, matrices, and financial mathematics. Second, the course will acquaint the student with the principles of descriptive and inferential statistics. Topics in this segment will include: measures of central tendency, variability, probability, confidence intervals, hypothesis testing, correlation, and regression analysis.
Prerequisites: MTH1100 or placement in MTH1800 is based on demonstrated student outcomes of AU mathematics competency examination.
MTH2120 Calculus for Management and Sciences (3 semester hours)
A short calculus course designed for the management and social/life science student. Includes elementary functions and their graphs, limits and continuity, the derivative and applications to extreme value problems, the integral and its applications, and methods of integration.
Prerequisites: MTH1310 or placement in MTH2120 based on demonstrated student outcomes of AU mathematics competency examination.
MTH2210 Calculus I (4 semester hours)
The first of three courses covering the fundamentals of calculus and its applications. Topics include limits, continuity, derivatives, implicit differentiation, applications of differentiation, indefinite integral, the definite integral, numerical integration, logarithmic and exponential functions, and inverse functions.
Prerequisites: MTH1310 or its equivalent as demonstrated on the AU mathematics competency examination.
MTH2220 Calculus II (4 semester hours)
A continuation of MTH2210. Topics include application of integration, area, volume of revolution, arc length, techniques of integration, L'Hopital's rule, improper integrals, sequences, infinite series, power series, conics, parametric equations, polar, cylindrical, and spherical coordinates.
MTH2230 Calculus III (4 semester hours)
A continuation of MTH2220. Topics include, and vectors, vector functions and their derivatives, partial derivatives, multiple integrals, vector analysis, and infinite series.
MTH2700 Statistics for Research (3 semester hours)
This course is designed to provide the science student with the requisite background in descriptive and inferential statistics to design and analyze results of research in his/her field. Special emphasis is placed on experimental design, derivations of statistics, and will use applications from the sciences. Topics will include measures of central tendency, measures of variability, probability, the normal distribution, confidence intervals, hypothesis testing, correlation, linear regression, analysis of variance, and multiway factorial design. Students will use a statistical calculator, and be given an introduction to computer software packages applicable to statistical analysis.
MTH3210 Introduction to Advanced Mathematics (3 semester hours )
The fundamentals of advanced mathematics and an introduction to mathematical proofs. Topics include: logic, quantifier notation, set operations, functions, relations, the
integers, and study of rational, real, and complex numbers as fields.
MTH3240 Probability and Statistics (3 semester hours)
The theory of probability and statistics in both the discrete and continuous cases. Topics include the binomial, geometric, Poisson, uniform, exponential, and normal distributions. Also included is the Central Limit Theorem and an introduction to statistical inference.
MTH3250 Linear Algebra (3 semester hours)
Topics include systems of linear equations, matrices, determinants, vector spaces, subspaces, bases, dimension, eigenvalues and eigenvectors, inner products, and linear transformations.
MTH3270 Discrete Mathematics (3 semester hours)
Logic, Boolean algebra, groups and homomorphisms, graph theory, machine design, theory of automata, Turing machines, computability, and formal language theory.
MTH3300 Differential Equations (3 semester hours)
Topics include mathematical modeling, graphical solutions, techniques for solving first order differential equations, Euler's method, homogeneous constant coefficient linear equations, nonhomogeneous linear equations and their solutions, and Laplace transformations.
MTH3320 Modern Geometry (3 semester hours)
A study of finite and non-Euclidean geometries from an axiomatic viewpoint, convexity, constructions, and modern Euclidean geometry.
Prerequisite: MTH3210 or consent of instructor.
MTH3350 History of Mathematics (3 semester hours)
The development of mathematics from the early Babylonian, Greek, and Arabic mathematics to the modern mathematics of the last 300 years; the development of numeration, geometry, algebra, and the calculus. Highly recommended for students in secondary education.
Prerequisites: MTH2220 or MTH2120.
MTH3490 Numerical Analysis (3 semester hours)
The use of the computer in solving mathematical problems: roots of algebraic equations, nonlinear equations, numerical integration, differential equations, curve fitting, error analysis, iterative processes, non-linear equations, and numerical methods in linear algebra.
Prerequisites: MTH2230, CSC1500, and CSC1600.
MTH4260 Number Theory (3 semester hours)
Theory of mathematical induction, divisibility theory, prime numbers and their distribution, theory of congruences and modular arithmetic, Fermat's theorem, and number theoretic functions and their applications.
Prerequisites: MTH3210 or consent of instructor.
MTH4450 Abstract Algebra (3 semester hours)
Topics include equivalence relations, groups, subgroups, cyclic groups, permutation groups, isomorphisms, cosets, external direct products, normal subgroups, factor groups, group homomorphisms, rings, and integral domains.
Prerequisite: MTH3210 or consent of instructor.
MTH4990 Senior Seminar in Mathematics (1 semester hour)
The goal of this course is to aid the students in integrating their experience in the math program at AU and to prepare for entry into the job market or graduate school. Some sessions will be held regarding interviewing skills and the current job market. In other sessions, students will meet with their individual advisors during the term to analyze the contents of the portfolio they have been preparing during their tenure at AU, to organize its contents, and to finalize its format as a tool in the job search or admission to graduate school. Students will write an essay summarizing their experience in the mathematics program and indicating their special interests in the field for inclusion in the portfolio. Students will also compile a bibliography of internet sites relevant to their special interests in the field of mathematics and/or math education.
Prerequisites: Senior standing, consent of department.
31 December 2003
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