Course Descriptions - Mathematics

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 Mathematics
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 higher.


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. They will review the basic functions, their graphs, transformations, and applications. Financial mathematics, including interest, present value, future value, and amortization calculations are taught. Systems of linear equations, linear inequalities and linear programming are also covered. This course 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 three-course sequence (MTH1210, MTH1220, NSM2500) for those majoring in elementary education. Topics include problem solving, sets and set operations, numeration systems, whole number operations, estimation, integer operations, number theory concepts, rational numbers and proportional reasoning. 
No prerequisites.


MTH1220 Mathematics for Elementary Teachers II
3 semester hours
A continuation of MTH1210. Topics include decimals, percents, operations with decimals, probability, statistics and statistical analysis, fundamentals of geometry, congruence and similarity, geometric constructions, motion geometry, the Pythagorean Theorem, measurement, area and volume.
Prerequisite: MTH1210.


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 higher 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 higher 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’Hôpital’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. This is a multivariable calculus course. 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: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student’s t distributions, standard scores, confidence intervals, hypothesis testing, correlation and linear 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.


MTH3100 Theory of Interest
3 semester hours
This course gives a comprehensive overview of the theory of interest and its appli­cation to a wide variety of financial instruments. Topics include rates of interest, present and future value, effective and nominal rates, annuities, loans, bonds, rate of return, stocks, fixed income investment, cashflow duration and immunization.
Prerequisite: MTH2220.


MTH3200 Actuarial Mathematics I
3 semester hours
This course prepares students to take SOA/CAS actuarial Exam P/1.  Students will apply the concepts learned in MTH3260 to solve advanced problems in probability.  Topics include: discrete and continuous random variables, functions of random variables, special probability distribution functions, multivariate distributions, covariance and moment generating functions. Test-taking strategies unique to Exam P/1 will also be discussed.
Prerequisite: MTH3260. 


MTH3220 Actuarial Mathematics II
3 semester hours
This course prepares students to take SOA/CAS actuarial Exam FM/2. Students will apply the concepts learned in MTH3100 to solve advanced problems in interest theory. Students will learn the fundamentals of derivatives markets including: general derivatives, options, hedging and investment strategies, forwards, futures and swaps. Test-taking strategies unique to Exam FM/2 will also be discussed.
Prerequisite: MTH3100.


MTH3240 Probability and Statistics I
3 semester hours
This course provides students with the fundamentals of statistical methods, probability and data analysis. It includes descriptive measures for data characterization (statistics), graphical representations and organization of data, random variables, expectation, distribution functions, central limit theorem, and an introduction to statistical inference. The theories of probability and statistics and their relational value to applied real-world problem solving are studied.
Prerequisite: MTH2220. 


MTH3250 Linear Algebra
3 semester hours
Topics include systems of linear equations, matrices, determinants, vector spaces, subspaces, bases, dimension, eigenvalues and eigenvectors, inner products, linear transformations and matrices of linear transformations. Mathematical proofs of theorems and properties are also introduced in the course.
Prerequisite: MTH2220.


MTH3260 Probability and Statistics II
3 semester hours
This course serves as a continuation of MTH3240, Probability and Statistics I. Topics include: continuous random variables, continuous distributions, bivariate and multivariate distributions, covariance, correlation, moment-generating func­tions, and the Central Limit Theorem. 
Prerequisites: MTH2230, MTH3240.


MTH3270 Discrete Mathematics
3 semester hours
This course will provide students with the fundamentals of mathematical proof. Different proof techniques, such as direct proof and induction, will be introduced. Logic, graph theory, set theory, Boolean algebra, theory of automata, computability, Turing machines, and formal language theory will also be presented.
Prerequisite: MTH2210.


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
This course will provide students with the fundamentals of mathematical proof. It will entail a study of Euclidean and non-Euclidean geometries from an axiomatic viewpoint, convexity, and constructions.
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, CSC1700, CSC2650.


MTH3500 Applied Statistical Methods
3 semester hours 
Regression analysis and time series will be discussed in detail, including analysis of real data. The topics to be discussed are: least squares estimates of parameters, single linear regression, multiple regression, hypothesis testing and confidence intervals in linear regression models, testing of models, appropriateness of models, linear time series models, moving averages, autoregressive or ARIMA models, estimation, forecasting with time series models, forecast errors, and confidence intervals. 
Prerequisite: MTH2320.


MTH3590 Business Analytics
3 semester hours
Students will learn how statistical and quantitative data analysis, modeling and optimization are used to drive business performance.  The use of descriptive, predictive and prescriptive analytics will be explored in the context of real data.  Topics to be discussed include statistical analysis and inference, regression analysis, forecasting and optimization.
Prerequisite:  MTH2320.


MTH3600 Models for Financial Economics
3 semester hours
This course is designed to teach the fundamental concepts that are tested on the SOA Exam MFE and CAS Exam 3F. Topics to be covered are put-call parity, exploiting arbitrage, binomial pricing models, Black-Scholes pricing formula, options Greeks, lognormal distributions, Ito’s lemma, variance reduction, and delta-hedging. 
Prerequisite: MTH3420.


MTH3700 Models for Life Contingencies
3 semester hours
This course is designed to teach the fundamental concepts that are tested on the SOA Exam MLC and CAS Exam 3L. Topics to be covered are survival models, Markov chain models, life insurances and annuities, premiums, liabilities, recursive calculation of expected values and variances, and Poisson processes. 
Prerequisites: MTH3260, MTH3100.


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. 
Prerequisites: Acceptance into the School of Education including passing the Basic Skills Test/TAP; maintaining a content GPA of 3.00; passing an FBI national fingerprint screening that encompasses passing a criminal background/sex offender check; passing a TB test and EDU2200, EDU2260, EDU3720. Placement applications for the practicum are due to the School of Education placement coordinator the January before the academic year of the practicum or for transfer students upon acceptance into the School 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.
Prerequisites: MTH2220 and MTH3270 or MTH3320 or consent of department.


MTH4300 Introduction to Real Analysis
3 semester hours
This course introduces students to the theory of the calculus of functions of one variable. Introduction to advanced proof techniques is an emphasis of this course. Topics in this course could include, but are not limited to functions, limits, continuity, differentiability and integrability for functions of one variable.
Prerequisites: MTH2230, MTH3270. 


MTH4450 Abstract Algebra
3 semester hours
This course is an introduction to abstract algebra. Topics include groups, subgroups, factor groups, polynomial rings, general rings, and fields. Emphasis is placed on both the writing of clear and logically correct proofs as well as demonstration of computational proficiency.
Prerequisites: MTH2220 and MTH3270 or MTH3320 or consent of department.

 
MTH4940 Internship in Actuary Science
The goal of the internship is to provide an opportunity for students to apply knowledge learned in the classroom and grow professionally.  It gives new graduates an edge in the current competitive job market and a formal experience within their chosen industry.  As a result, internships are a key component in the transformative power of learning, aiding students’ transition from the role of student to that of a professional.


MTH4950 Senior Seminar in Actuarial Science
1 semester hour
The goal of this seminar is to aid the students in integrating and applying their experience in the actuarial science program at AU and to prepare for successful entry into the job market. The seminar includes interviewing skills, discussion of the current job market, production of a professional resume and portfolio, dis­cussion of professional development opportunities, and discussion of contem­porary topics in actuarial science.
Prerequisites: Senior standing actuarial science major; 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. In some 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 mathematics education. 
Prerequisites: Senior standing; consent of department.