Mathematics

NOTE: All entering students without accepted transfer work at the level of intermediate algebra or above must complete the math placement exam to determine the level of their first math course at Aurora University.

MTH099 Preparatory Math (3 semester hours)
Introduction to natural numbers, fractions, negative numbers, the irrationals including addition, subtraction, multiplication, and division. Introduction to exponents and radicals. Introduction to variables and linear equations. Credit earned in MTH099 is in addition to the 120 semester hours required forgraduation.
No prerequisites

MTH101 Algebra (2 semester hours)
The fundamentals of algebra for students of all majors. Prepares the student mathematically for such courses as MTH112, MTH210, CSC110, SBS232, ECN201, ECN202, and CHM131. Real numbers, polynomials, linear equations and inequalities, systems of linear equations. The MTH101/MTH102 sequence duplicates the material in MTH110; students who have received a passing grade in MTH110 cannot also earn credit in the MTH101/MTH102 sequence.
Prerequisites: At least one year of high school algebra or equivalent as demonstrated on the AU mathematics placement exam, or MTH099.

MTH102 Algebra (2 semester hours)
Continuation of MTH101. The MTH101/MTH102 sequence duplicates the material in MTH110; students who have received a passing grade in MTH110 cannot also earn credit in the MTH101/MTH102 sequence.

MTH110 Algebra (3 semester hours)
The fundamentals of algebra for students of all majors. Prepares the student mathematically for such courses as MTH112, MTH210, CSC110, SBS232, ECN201, ECN202, and CHM131. Real numbers, polynomials, linear equations and inequalities, systems of linear equations. This course is also offered as a sequence of two courses, MTH101 and 102; students who have received a passing grade in MTH101 or MTH102 cannot also earn credit in MTH110.
Prerequisites: At least one year of high school algebra or equivalent as demonstrated on the AU mathematics placement exam, or MTH099.

MTH111 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 MTH110 or MTH101/102.
Prerequisite: At least one year of high school algebra or equivalent as demonstrated on the AU mathematics placement exam, or MTH099.

MTH112 Mathematics for Decision Making (3 semester hours)
Sets, probability, linear equations matrices, and linear programming. Enables the business or social science student to read mathematics and use it as a tool.
Prerequisites: MTH110 or its equivalent as demonstrated on the AU mathematics placement exam.

MTH121 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, sets and relations, numeration systems, whole numbers, integers, number theory concepts, linear equations and inequalities, radicals and rational exponents, rational and irrational numbers.
Prerequisites: At least one year of high school algebra or equivalent as demonstrated on the AU mathematics placement exam.

MTH122 Mathematics for Elementary Teachers II (3 semester hours)
Continuation of MTH121. Topics include: problem solving, probability and statistics, informal geometry, motion geometry, geometric constructions, Pythagorean theorem, fundamentals of coordinate geometry, quadratic equations, systems of linear equations, measurement and an introduction to computers.
Prerequisite: MTH121.
NOTE: Successful completion of MTH121 and 122 satisfies the algebra requirement for graduation.

MTH201 Precalculus (2 semester hours)
Prepares the student for calculus. Topics include the algebraic, exponential, logarithmic, and trigonometric functions and their graphs. The MTH201/MTH202 sequence duplicates the material in MTH210; students who have received a passing grade in MTH210 cannot also earn credit in the MTH201/MTH202 sequence.
Prerequisites: MTH110, or both MTH101 and MTH102, or equivalent as demonstrated on the AU mathematics placement exam.

MTH202 Precalculus (2 semester hours)
Continuation of MTH201. The MTH201/MTH202 sequence duplicates the material in MTH210; students who have received a passing grade in MTH210 cannot also earn credit in the MTH201/MTH202 sequence.
Prerequisite: MTH201.

MTH210 Precalculus (4 semester hours)
Prepares the student for calculus. Topics include the algebraic, exponential, logarithmic, and trigonometric functions and their graphs. This course is also offered as a sequence of two courses, MTH201 and MTH202; students who have received a passing grade in MTH201 or MTH202 cannot also earn credit in MTH210.
Prerequisites: MTH110, or both MTH101 and MTH102, or equivalent as demonstrated on the AU mathematics placement exam.

MTH212 Calculus for Decision Making (3 semester hours)
A short calculus course designed for the social 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: A pre-calculus course such as MTH112 or MTH210 or its equivalent as demonstrated on the AU mathematics placement exam.

MTH221 Calculus I (3 semester hours)
The first of four courses covering the fundamentals of calculus and its applications to the physical sciences. Designed primarily for students concentrating in mathematics and the natural sciences. Topics include limits, continuity, derivatives and their applications, and the indefinite integral.
Prerequisites: MTH210 or its equivalent as demonstrated on the AU mathematics placement exam.

MTH222 Calculus II (3 semester hours)
A continuation of MTH221. Topics include the definite integral and its applications, transcendental and hyperbolic functions, and methods of integration.
Prerequisite: MTH221.

MTH223 Calculus III (3 semester hours)
A continuation of MTH222. Topics include infinite series, plane curves, polar coordinates, vectors, and parametric equations.
Prerequisite: MTH222.

MTH320 Calculus of Several Variables (3 semester hours)
A continuation of MTH223. Topics include vector functions and their derivatives, partial derivatives, multiple integrals, vector analysis, and infinite series.
Prerequisite: MTH223.

MTH321 Intermediate Analysis (3 semester hours)
An introduction to real analysis that emphasizes the structure of mathematical proofs. Topics include logic, sets, the real numbers, sequences, continuity, and infinite series.
Prerequisite: MTH320.

MTH324 Probability and Statistics (3 semester hours)
The theory of probability and statistics in both the discrete and the continuous cases. Topics include the binomial, geometric, Poisson, uniform, exponential, and normal random variables, the Central Limit Theorem, and an introduction to statistical inference.
Prerequisite: MTH320.

MTH325 Linear Algebra (3 semester hours)
Topics include real vector spaces, bases, dimension, linear transformations, matrices, and inner products.
Prerequisites: MTH223 or MTH212.

MTH326 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.
Prerequisite: Consent of instructor.

MTH327 Discrete Mathematics (3 semester hours)
Logic, Boolean algebra, groups and homomorphisms, machine design, theory of automata, Turing machines, computability, and formal language theory.
Prerequisite: MTH223.

MTH330 Differential Equations (3 semester hours)
Topics include equations of order one, elementary applications, linear equations with constant coefficients, nonhomogeneous equations, variation of parameters, and Laplace transformations.
Prerequisite: MTH320.

MTH332 Modern Geometry (3 semester hours)
A study of absolute, finite, and non-Euclidean geometries from an axiomatic viewpoint.
Prerequisite: MTH223.

MTH335 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: MTH222 or MTH212.

MTH345 Abstract Algebra (3 semester hours)
Utilizes the axiomatic method to study and develop abstract algebraic systems such as groups, rings, integral domains and fields. Sets, mappings, and relations are studied in the context of these systems.
Prerequisites: MTH223 required and MTH321 recommended.

MTH349 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, and numerical methods in linear algebra.
Prerequisites: MTH223, CSC150, and CSC160.

MTH499 Senior Seminar in Mathematics (1 semester hour)
This course will aid students in integrating their experience in the math program at AU and to prepare for entry into the job market or graduate school. Sessions will include interviewing skills, portfolio organization and analysis.
Prerequisites: Senior standing, consent of department.