# Courses

Course offerings reflect the 2021-2022 Elmhurst University Catalog. **One unit of credit equals four semester hours.**

This course provides an overview of common mathematical concepts and the use of the computer in applying these in practical problem solving. The basic operation of the computer is studied, as are computer logic and programming, and methods of computation that employ software tools such as spreadsheets. Other mathematical topics include estimation, statistics, algebra and geometry. Students seeking to fulfill the mathematics component of secondary-school licensure requirements are encouraged to take this course.

Concepts of algebra including polynomials and rational expressions, exponents and roots. A brief study of systems of equations, linear programming, exponential and logarithmic functions, and mathematics of finance. Students wishing to review basic math skills in advance of this course may do so through the Learning Center. *A placement test is required.*

Review of elementary algebra, equations, relations, functions and transformations, inequalities and quadratic functions, systems of linear equations and inequalities, polynomial equations and their graphs.

*Prerequisites: Two years of high school algebra and one year of high school geometry with a grade of C or better is recommended. A placement test is required.*

Applications of mathematics to the social sciences and business with a functions approach, applications of elementary functions, differential and integral calculus of the elementary functions, and applications of calculus. The course also contains topics selected from linear programming, mathematics of finance and mathematical modeling. Some sections require use of a graphics calculator.

*Prerequisite: Students should have an algebra background at least equivalent to MTH 111 with a grade of C or better. A placement test is required.*

Relations, functions and transformations, exponential and logarithmic functions, the circular functions, trigonometric functions of angles, identities, inverse functions, triangles and applications, vectors and applications, and complex numbers. *A placement test is required. *

*Prerequisite: MTH 121 or equivalent.*

Rate of change of a function, limits, continuity, derivatives of algebraic and trigonometric functions, applications of the derivative, and introduction to integration and applications.

*Prerequisite: MTH 132 or equivalent.*

Transcendental functions, methods of integration, parametric equations, polar coordinates and infinite series.

*Prerequisite: MTH 151 with a grade of C or better.*

Vectors in three-space, quadric surfaces, partial derivatives with applications and multiple integrals with applications, introduction to vector analysis.

*Prerequisite: MTH 152 with a grade of C or better.*

Logic and proof, elementary number theory, mathematical induction and recursion, set theory, functions, relations, and combinatorics.

*Prerequisite: MTH 151.*

Mathematical properties and applications of tree structures and graph theory are studied along with related algorithms. Fundamental concepts of discrete probability, including the binomial, negative binomial, Poisson and normal distributions and Bayes’ theorem, are presented and used in the context of introductory analysis of algorithms. Computational linear algebra techniques and matrix operations are expressed algorithmically. Computations and algorithms for all topics in this course are implemented with an interpreted translator system, such as Python, Matlab, Octave or ML.

*Prerequisite: MTH 301 and familiarity with a programming language.*

An introduction to the modeling process including creative and empirical model construction, model analysis and research using the model. This is accomplished using a problem-solving approach on a number of models of common static and dynamic problems.

*Prerequisite: MTH 152. Alternate years.*

Set theory; numeration systems, operations, properties and computing algorithms for whole numbers, fractions, decimals and integers, ratio and proportion. Problem solving is used throughout the course.

*Pre- or corequisite: EDU 104 or consent of the instructor. Restricted to early childhood, elementary education or special education majors or middle school mathematics education minors.*

**.50 credit**

Geometric shapes and relationships, measurement and patterns, probability and statistics and algebraic skills. Problem solving is used throughout the course. Restricted to early childhood, elementary education or special education majors.

*Prerequisite: MTH 325.*

**.50 credit**

Designed to prepare students in elementary education to meet the required statistics standards. Students will learn to construct and analyze data sets, understand probability distributions, perform hypotheses tests on a single population, and understand linear regression equations. May not be taken for credit if credit for PSY 355, MTH 345 or 346, or an equivalent course at another college has already been given. Does not count toward a major or minor in mathematics.

*Pre- or corequisite: EDU 104 or consent of the instructor. Restricted to early childhood, elementary education or special education majors. Spring Term.*

Euclidean and non-Euclidean geometry and the nature of proof using the axiomatic method. Designed to provide an important learning experience both for the mathematics major who needs to acquire mathematical maturity required for more advanced mathematics courses, and for prospective teachers of geometry.

*Prerequisite: MTH 152 or MTH 301 or consent of instructor. Fall Term.*

First order differential equations, linear differential equations, Laplace transforms, power series methods and solution of systems of differential equations.

*Prerequisite: MTH 251. Spring Term.*

Fourier Series and convergence of Fourier Series, selected topics in boundary value problems including the heat and wave equations, Laplace’s equation, and Bessel functions.

* Prerequisite: MTH 341. Alternate years.*

Statistical methods applied to economic and social data. Descriptive statistics, probability distributions, hypothesis testing, confidence intervals, correlation and regression. Students wishing to review basic math skills in advance of this course may do so through the Learning Center. *May not be taken for credit if credit has already been given for PSY 355, MTH 346 or an equivalent course at another college. Does not count toward a major or minor in mathematics.*

Designed for mathematics and science students with an emphasis on the analysis of scientific data. Probability, probability distributions and their applications, estimation and confidence intervals, goodness of fit, hypothesis testing, experimental design, regression and correlation, analysis of variance, and nonparametric tests.* May not be taken for credit if credit for MTH 345, PSY 355 or an equivalent course at another college has already been given. *

*Prerequisite: MTH 151 or equivalent. Spring Term.*

Statistical analysis using multiple regression, time series, and advanced forecasting techniques in business and economics applications.

*Prerequisite: MTH 345 or 346 or PSY 355 with a C or higher. Alternate years. Cross-listed with ECO 418.*

A rigorous calculus-based treatment of the mathematics of finance: time value of money, simple and compound interest, accumulation function, annuities, bonds, yield rates, amortization schedules and sinking funds, depreciation, yield curves, duration, convexity and immunization, and definition of derivative securities. This course is intended to prepare students for the Society of Actuaries examination on financial mathematics.

*Prerequisite: MTH 152. Fall Term, even-numbered years.*

The structure of algebraic systems including groups, rings, integral domains and fields.

*Prerequisite: MTH 301 or consent of instructor. Linear algebra recommended. Spring Term.*

The algebra of matrices with applications to vectors and vector spaces, linear transformations, theory of determinants and abstract Euclidean spaces.

*Prerequisites: MTH 251 and MTH 301 or consent of instructor. Fall Term.*

The real number system, functions, sequences and limits, continuity and differentiability, integration, and properties of differentiable functions.

*Prerequisites: MTH 251 and MTH 301. Fall Term.*

**.50 credit**

A course in reading, researching and writing mathematics. This course should be taken in the junior or senior year in preparation for writing the senior paper.

Combinatorics, introduction to probability from a set-theoretic point of view, functions of random variables, expected value, generating functions, jointly distributed random variables and the Central Limit Theorem.

*Prerequisites: MTH 251 and MTH 301 or consent of instructor. Fall Term, odd-numbered years.*

Mathematical theory of statistical inference. Methods of estimation, maximum likelihood estimation, properties of estimators, confidence intervals, hypothesis testing, significance and power, contingency tables, goodness-of-fit.

*Prerequisite: MTH 421. Spring Term, even-numbered years.*

An introduction to the complex number system, the theory of analytic functions of a complex variable, Taylor and Laurent expansions, contour integration, and applications to problems in physics and engineering.

*Prerequisites: MTH 251 and MTH 301 or consent of instructor. Alternate years.*

An introduction to current methods and strategies for teaching secondary school mathematics in grades 6–12. Teacher candidates will focus on the teaching of mathematics for conceptual understanding, mathematical reasoning and problem solving; fundamentals of planning, instruction and assessment in middle level and secondary mathematics classes; use of national, state and local standards for instruction and assessment; and understanding of how to transform theory into practice to ensure that all middle level and secondary students learn mathematics.

*Prerequisites: SEC 310, MTH 301 or consent of the instructor. Fall Term.*

Fundamental concepts of intuitive set theory and the real number system, structure of R and Rn, metric spaces and general topological spaces.

*Prerequisite: MTH 381 or consent of instructor. Spring Term, alternate years.*

**.50 credit**

This course is required of every student majoring in mathematics and aims to demonstrate the research, writing and analytical skills of the graduating senior. To be written in the first or second term of the senior year, this research paper will provide evidence of what the student has learned as a mathematics major in terms of knowledge, skills and insight. The topic of the paper will be selected by the student in consultation with a faculty advisor.

*Prerequisite: MTH 400 with a grade of C or better.*

**1.00 or 1.50 credits**

This course provides opportunities for junior or senior mathematics majors to apply their mathematical knowledge in a supervised business or industrial setting. Ten to 20 hours of work experience per week is required for one credit; 15 to 30 hours per week for credit of 1.50. A term project focusing on learning outcomes of the experience is required.* Repeatable for credit. Approval of the department chair is required.*

**.50 or 1.00 credit**

*Repeatable for credit.*

**.50 credit**

This course gives Honors Program students the opportunity to design and implement a significant research project in the field of mathematics, culminating in an appropriate public dissemination of research methods and findings. This research must build upon previous coursework taken within the major or minor, facilitating faculty supervision and guidance. *Repeatable for credit. Permission of the faculty supervisor and the director of the Honors Program required prior to registration.*

Varying from term to term, the course covers subjects such as manifolds, mathematical statistics, number theory, a second course in abstract algebra, a second course in advanced calculus, or chaos theory. *Repeatable for credit.*