Mathematics (B.A., Secondary Ed Certification, Minor)
The mathematics program at AU provides service courses for students in
a wide variety of fields, as well as offering both a major and a minor.
The minor in mathematics prepares students for teaching math at the middle
school level, while the major prepares students for teaching math at the
secondary level, entering business or industry, or pursuing graduate work
in mathematics, computer science or related fields. Several of our graduates
are currently pursuing graduate degrees; others are teaching in a number
of middle schools and high school; some are employed at research institutions
such as Fermi National Accelerator Lab and Lucent Technologies; still
others are working in a variety of industrial settings. ±
The mathematics program offers two tracks for interested students at the undergraduate level. The first track is designed for students interested in entering careers in business and industry or pursuing graduate training in mathematics or other disciplines. The second track is for students seeking teacher certification in mathematics at the pre-college level. Career areas for which the math major is appropriate preparation in addition to teaching include: actuarial science, computer science, operations research, and a variety of research and engineering applications. An undergraduate major in mathematics is also becoming increasingly popular as a stepping-stone to graduate study in a wide range of disciplines from business administration to oceanography. Students considering the mathematics concentration should plan to begin the calculus sequence as early as possible in their college careers. A minimum of 38 semester hours from the following lists is required for the mathematics major.
MAJOR IN MATHEMATICS — 38 semester hours
Required Core: 17 semester hours
CSC1500 Computer Science I (4)
MTH2210 Calculus I (4)
MTH2220 Calculus II (4)
MTH2230 Calculus III (4)
MTH4990 Senior Seminar in Mathematics (1)
Selected Courses: Choose at least 21 semester hours from the selected list
MTH3210 Introduction to Advanced Mathematics (3)
MTH3240 Probability and Statistics (3)
MTH3250 Linear Algebra (3)
MTH3270 Discrete Mathematics (3)
MTH3300 Differential Equations (3)
MTH3320 Modern Geometry (3)
MTH3350 History of Mathematics (3)
MTH3490 Numerical Analysis (3)
MTH4260 Number Theory (3)
MTH4450 Abstract Algebra (3)
MTH2810,3810,4810 Selected Topic in Mathematics (3)
MTH3830,4830 Directed Study (1-3)
MTH4970 Research in Mathematics (1-3)
MTH4980 Independent Study (1-3)
MAJOR IN MATHEMATICS for Secondary Certification Option
A minimum of 42 semester hours from the following lists is required for the mathematics major, secondary certification option.
Required Core: 39 semester hours
CSC1500 Computer Science I (4)
MTH2210 Calculus I (4)
MTH2220 Calculus II (4)
MTH2230 Calculus III (4)
MTH3240 Probability and Statistics (3)
MTH3250 Linear Algebra (3)
MTH3270 Discrete Mathematics (3)
MTH3320 Modern Geometry (3)
MTH3820 Methods for Teaching Secondary Mathematics (4)
MTH4260 Number Theory (3)
MTH4450 Abstract Algebra (3)
MTH4990 Senior Seminar in Mathematics (1)
Select one course (3 semester hours) from the following list:
MTH3210 Introduction to Advanced Mathematics (3)
MTH3300 Differential Equations (3)
MTH3350 History of Mathematics (3)
MTH3490 Numerical Analysis (3)
MTH2810,3810,4810 Selected Topic in Mathematics (3)
MTH3830,4830 Directed Study (1-3)
MTH4970 Research in Mathematics (1-3)
MTH4980 Independent Study (1-3)
MINOR IN MATHEMATICS - 18 semester hours
Required Courses:
MTH2210 Calculus I (4)
MTH2220 Calculus II (4)
MTH2230 Calculus III (4)
Selected Courses:
Students must choose at least 6 semester hours offered in the Mathematics program at the 300-level or above, excluding MTH2810/3810/4810, MTH3820, MTH 3830/4830, MTH4970, MTH4980 and MTH4990.
MATHEMATICS COURSE DESCRIPTIONS
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.
No prerequisites.
MTH1100 College Algebra 3 semester hours
The fundamentals of algebra for students of all majors. Prepares the student mathematically for such courses as MTH1120, MTH1310, MTH2320, CSC1500, ECN2010, ECN2020, and CHM1310. Real numbers, polynomials, linear equations and inequalities, functions, rational expressions, exponents, quadratic equations, and systems of linear equations.
Prerequisite: Placement in MTH1100 is based on demonstrated student outcomes of AU mathematics competency examination, or MTH0990 with a grade of “C” or better.
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.
MTH1120 Finite Mathematics 3 semester hours
Students will be introduced to the tools of finite mathematics: review of basic functions, linear equations, matrices, financial mathematics, linear programming. It enables the business or social science student to read mathematics and use it as a tool.
Prerequisite: MTH1100 or placement in MTH1120 based on demonstrated student outcomes of AU mathematics competency examination.
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.
Prerequisite: 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. Topics include probability, statistics and statistical graphs, fundamentals of geometry, geometric constructions, motion geometry, the Pythagorean theorem, and measurement.
Prerequisite: 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 for elementary education majors.
MTH1310 Precalculus 4 semester hours
Prepares the student for calculus. Topics include the algebraic, exponential, logarithmic, and trigonometric functions and their graphs.
Prerequisite: MTH1100 with a grade of “C” or better or its equivalent as demonstrated on the 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.
Prerequisite: MTH1310 or placement in MTH2120 is 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.
Prerequisite: MTH1310 with a grade of “C” or better 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.
Prerequisite: MTH2210.
MTH2230 Calculus III 4 semester hours
A continuation of MTH2220. Topics include vectors, vector functions and their derivatives, partial derivatives, multiple integrals, vector analysis, and infinite series.
Prerequisite: MTH2220.
MTH2320 General Statistics 3 semester hours
This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: measures of central tendency, variability, probability, standard scores, confidence intervals, hypothesis testing, correlation, and regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.
Prerequisite: MTH1100 or MTH1110.
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.
Prerequisite: MTH1310.
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.
Prerequisite: MTH2220 or consent of department.
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.
Prerequisite: MTH2230.
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.
Prerequisite: MTH2220.
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.
Prerequisite: MTH2220.
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.
Prerequisite: MTH2230.
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: MTH2230 or consent of department.
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.
Prerequisite: 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.
MTH3820 Secondary Methods in Mathematics 4 semester hours
This course presents techniques that are effective in teaching in the content areas. The course includes lesson planning, classroom arrangement, curriculum design, alternative teaching strategies, and evaluation. In addition to the classroom hours there is a simultaneous practicum. This is usually the last course the student takes prior to student teaching. (Fall)
Prerequisites: Acceptance into the College of Education including passing the Basic Skills Test, maintaining a GPA of 3.00, passing a background check, and EDU2200 and EDU2260. Placement applications for the practicum are due to the College of Education placement coordinator the January before the academic year of the practicum or for transfer students upon acceptance into the College of Education.
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.
Prerequisite: MTH3210 or consent of department.
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 MTH3250 or consent of department.
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.
Please Note: The information listed on this page is current according to the 2006-2008 Undergraduate Catalog, unless otherwise noted.
±This information is additional information specific to the Web site, not provided in the Undergraduate Catalog.
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