Aurora University

Mathematics (MTH)

MTH-1010  Foundations of Algebra  (4 semester hours)  

This course includes a review of natural numbers, fractions, negative numbers, and the irrationals. Concepts of algebra including polynomials and rational expressions, exponents and roots, variables and linear equations will be covered. Note: does not satisfy General Education Mathematical Competency. Placement in MTH1010 is based on SAT or ACT mathematics sub-score.

MTH-1030  Quantitative Reasoning  (4 semester hours)  

This course is designed to fulfill the general education core requirement in quantitative and formal reasoning for students whose majors do not require specific skills in mathematics. Topics in logic/set theory, algebraic thinking, probability, and statistics will enable students to develop the ability to use data and observations to make informed decisions by interpreting and analyzing information. The effective use of evidence, methods, and models in real world applications will be highlighted.

MTH-1100  College Algebra  (4 semester hours)  

This course addresses the fundamentals of algebra for students of all majors. It prepares the student mathematically for such courses as MTH-1310, MTH-2320, CSC-1700, ECN-2030 and CHM-1310. Topics include equations and systems of linear equations, inequalities, graphs, and functions, including polynomial, rational, inverse, exponential, and logarithmic functions.

MTH-1210  Mathematics for Elementary Teachers I  (4 semester hours)  

This course is the first of a three-course sequence (MTH-1210, MTH-1220, NSM-2500) 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.

MTH-1220  Mathematics for Elementary Teachers II  (4 semester hours)  

This course is a continuation of MTH-1210. 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(s): MTH-1210.
MTH-1310  Precalculus  (4 semester hours)  

This course is a preparation for calculus beyond college algebra. Topics include a brief review of functions and graphs, trigonometric functions, analytic trigonometry, vector arithmetic, and analytic geometry in two and three dimensions.

Prerequisite(s): Placement in MTH-1310 is based on SAT or ACT mathematics sub-score or MTH-1100 with a grade of "C" or better or its equivalent as demonstrated on the AU Mathematics Competency Examination.
MTH-1810-9  Selected Topics in Mathematics  (Variable semester hours)  

This course will address a specific area of study in Mathematics not already covered by other course offerings. Prerequisites vary by topic.

MTH-2210  Calculus I  (4 semester hours)  

This is 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(s): Placement in MTH-2210 is based on SAT or ACT mathematics sub-score or MTH-1310 with a grade of "C" or better or its equivalent as demonstrated on the AU Mathematics Competency Examination.
MTH-2220  Calculus II  (4 semester hours)  

This course is a continuation of MTH-2210. 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(s): MTH-2210.
MTH-2230  Calculus III  (4 semester hours)  

This course is a continuation of MTH-2220. This is a multivariable calculus course. Topics include vectors, vector functions and their derivatives, partial derivatives, multiple integrals, vector analysis, and infinite series.

Prerequisite(s): MTH-2220.
MTH-2320  General Statistics  (4 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 exercise science, pre-nursing and business.

Prerequisite(s): Placement in MTH-2320 is based on SAT or ACT mathematics sub-score or MTH-1100 or MTH-1310 or MTH-2210 or the equivalent as demonstrated on the AU Mathematics Competency Examination.
MTH-2700  Statistics for Research  (4 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(s): MTH-1310 or MTH-2210.
MTH-2810-9  Selected Topics in Mathematics  (Variable semester hours)  

This course will address a specific area of study in Mathematics not already covered by other course offerings. Prerequisites vary by topic.

MTH-3100  Theory of Interest  (4 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.

Co/prerequisite(s): MTH-2220.
MTH-3200  Actuarial Mathematics I  (4 semester hours)  

This course prepares students to take SOA/CAS actuarial Exam P/1. Students will apply the concepts learned in MTH-3260 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(s): MTH-3260.
MTH-3240  Probability and Statistics I  (4 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(s): MTH-2210.
MTH-3250  Linear Algebra  (4 semester hours)  

Topics in this course 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(s): MTH-2220.
MTH-3260  Probability and Statistics II  (4 semester hours)  

This course serves as a continuation of MTH-3240, 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.

Prerequisite(s): MTH-2230; MTH-3240.
MTH-3270  Discrete Mathematics  (4 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(s): MTH-2210.
MTH-3280  Biostatistics  (4 semester hours)  

This course provides an introduction to statistical concepts and techniques commonly encountered in the biological sciences. Lecture topics include study design, probability, comparing sample means and proportions, survival analysis, and sample size/power calculations. Computer software is used to describe and analyze data.

Prerequisite(s): MTH-3240.
MTH-3300  Differential Equations  (4 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(s): MTH-2230.
MTH-3320  Modern Geometry  (4 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(s): MTH-3270.
MTH-3460  Introduction to Crypotography  (4 semester hours)  

This is an introductory course in cryptography, the design and analysis of various encryption schemes. Mathematical concepts in probability theory and basic number theory, including proofs will be considered. Both private-key and public-key encryption models will be investigated.

Prerequisite(s): CSC-2660; MTH-2220.
MTH-3490  Numerical Analysis  (4 semester hours)  

This course addresses 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.

Prerequisite(s): MTH-2230; CSC-1700.
MTH-3505  Data Science I - Analysis and Modeling  (4 semester hours)  

This is a course in predictive analytics, including theoretical background, tools, and techniques used to obtain insight into the properties of datasets. Regression analysis will be discussed in detail, including analysis of real data. Topics may include data exploration, principle component analysis, model selection, cross validation and goodness of fit, resampling, and classification. Students will learn to, visualize, explore, and interpret datasets as well as to apply and evaluate models using statistical software.

Prerequisite(s): MTH-3240.
MTH-3510  Data Science II - Advanced Modeling and Statistical Programming  (4 semester hours)  

This course will expand on the content in Data Science I: Analysis and Modeling. Students will implement advanced modeling strategies using extensive statistical programming. Topics may include advanced model selection, decision trees, neural networks, K means, K neighbors and hierarchical clustering.

Prerequisite(s): MTH-3505; CSC-1700.
MTH-3590/BUS-3590  Business Data Analytics  (4 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(s): MTH-2320 or MTH-3240.
MTH-3720  Mathematics for the Secondary Classroom  (4 semester hours)  

An overview of mathematics content commonly taught in grades 9-12. This fast-paced course will review content in algebra, linear algebra, tigonometry, number theory, calculus, geometry, discrete mathematics, and probability. Students will further develop mathematical thinking and reasoning, connect ideas within and between mathematical concepts, develop problem solving skills, and reflective practice. This course is suggested for students the semester before they take MTH-3820.

Corequisite(s): EDU-3620; EDU-3720.
MTH-3810-9  Selected Topics in Mathematics  (Variable semester hours)  

This course will address a specific area of study in Mathematics not already covered by other course offerings. Prerequisites vary by topic.

MTH-3820/CSC-3820  Secondary Methods in Mathematics and Computer Science  (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. 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.

Prerequisite(s): Passing an FBI national fingerprint screening that encompasses passing a criminal background/sex offender check; passing a TB test; EDU-2100; EDU-2260; EDU-3620; EDU-3720.
MTH-3830  Directed Study in Mathematics  (0.5-17 semester hours)  

This is a course in which a student or students study on campus under the close supervision of an Aurora University faculty member. This is not "field experience," does not cover material in the regular curriculum, and is not as research and/ or independently oriented in its instructional methodology as an independent study. Descriptions of directed studies are contained in the petition by which the learning experience was approved. Students should file the Directed Study Petition prior to registration. This petition must be signed/approved by the Instructor, Department chair, and Academic Dean. Regular tuition is charged, and additional fees may apply.

MTH-4260  Number Theory  (4 semester hours)  

This course addresses the 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(s): MTH-3270.
MTH-4300  Introduction to Real Analysis  (4 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.

Prerequisite(s): MTH-3270.
MTH-4450  Abstract Algebra  (4 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.

Prerequisite(s): MTH-3270.
MTH-4810-9  Selected Topics in Mathematics  (Variable semester hours)  

This course will address a specific area of study in Mathematics not already covered by other course offerings. Prerequisites vary by topic.

MTH-4830  Directed Study in Mathematics  (0.5-17 semester hours)  

This is a course in which a student or students study on campus under the close supervision of an Aurora University faculty member. This is not "field experience," does not cover material in the regular curriculum, and is not as research and/ or independently oriented in its instructional methodology as an independent study. Descriptions of directed studies are contained in the petition by which the learning experience was approved. Students should file the Directed Study Petition prior to registration. This petition must be signed/approved by the Instructor, Department chair, and Academic Dean. Regular tuition is charged, and additional fees may apply.

MTH-4940  Internship in Actuary Science  (4 semester hours)  

An advanced academic internship experience for credit requires the student to be at least a junior in standing, although individual programs may require senior standing. The academic internship experience requires a faculty sponsor, educational criteria, and a current executed affiliation agreement and Schedule A on file. Internships can be designated as either credit/no credit or letter grade, depending on the school or program. Regular tuition is charged, and additional fees may apply.

Prerequisite(s): Instructor Permission.
MTH-4970  Research in Mathematics  (1-4 semester hours)  

This course is designed to provide students with the opportunity to do mathematical research that has the potential to be published in a peer-reviewed scientific journal and/or presented at a scientific meeting. Students will accomplish these goals by performing a supervised research project and attending weekly seminars with their supervising instructor on how to conduct scientific research. Permission of the Instructor or Department Chair required.

MTH-4980  Independent Study in Mathematics  (0.5-17 semester hours)  

Descriptions of independent studies are contained in the petition by which the learning experience was approved. Prior to registration, students must file the Independent Study Petition. This petition requires the signature/approval of the Instructor, Department Chair, and Academic Dean. Regular tuition is charged. In most cases, Independent Study should be within the field of the student's major and should be something that cannot be pursued through established courses. These are pursued on campus under the direct supervision of an Aurora University faculty member. Regular tuition is charged, and additional fees may apply.

MTH-4990  Senior Capstone in the Mathematical Sciences I  (2 semester hours)  

This course is the culmination of the mathematics and actuarial science major's academic experience. Students engage in independent research on a chosen topic or question under the direction of a faculty member. Guest lectures by various faculty members will expose students to content suitable for independent research. The course will also prepare students for entry into the job market or graduate school. Permission of the instructor/department.

Prerequisite(s): Senior standing, permission of the Instructor/Department Chair.
MTH-4991  Senior Capstone in the Mathematical Sciences II  (2 semester hours)  

This course is a continuation of MTH-4990. During the semester, students will finish their research and present their conclusion to other students and faculty in a public venue. Students will write a paper summarizing their work.

Prerequisite(s): MTH-4990.