### Courses Offered

Valparaiso University’s mathematics and statistics department offers a large variety of courses, from general courses taken by students in many programs to applied mathematics courses useful as electives in some programs and courses for mathematics majors. Click on one of the tabs below to see courses of each type.

**MATH 110: Quantitative Problem Solving** (4 Cr.)

A course to assist students in developing fundamental mathematical concepts and processes. Emphasis is placed on problem solving, reasoning, communication, and mathematical connections. Students recommended for this course should take it prior to enrolling in courses with quantitative content. This course may not be used to fulfill the General-Education Requirement in the College of Arts and Sciences nor be counted toward a major or minor in mathematics. This course may not be taken by a student with credit for any other mathematics course. S/U grade only.

**MATH 114: Precalculus ** (4 Cr.)

A course for students who plan to take a calculus sequence. Topics may include sets and numbers, relations and functions, trigonometric functions, and exponential and logarithmic functions. This course may not be used to fulfill the General-Education Requirement in the College of Arts and Sciences nor be counted toward a major or minor in mathematics. Prerequisite: MATH 110 or placement higher than MATH 110 on the math placement examination.

**MATH 120: Mathematical Ideas ** (3 Cr.)

A one-semester course intended primarily for students majoring in the humanities. The relationship between mathematics and modern society is studied. Emphasis is placed on the development of mathematical concepts. The course may be used to fulfill the Quantitative Analysis component of the General-Education Requirements. Some sections of this course may be used to fulfill the Writing-Intensive General-Education Requirement. Usually offered every spring semester. Prerequisite: MATH 110 or placement higher than MATH 110 on the math placement examination.

**MATH 122: Applied Calculus ** (4 Cr.)

A course for students with a good foundation in mathematics who are interested in mathematical models for management or the life or social sciences. Topics include limits, continuity, derivatives and their applications, integrals and their applications, and selected topics in multivariate calculus. The course may be used to fulfill the Quantitative Analysis component of the General-Education Requirements. ** Currently listed only for transfer credit equivalence. ** Students with credit for MATH 131 may not receive credit for this course.

**MATH 124: Finite Mathematics** (4 Cr.)

A course for students with a good foundation in mathematics who are interested in mathematical models for management or the life or social sciences. Topics include matrix algebra, linear programming, probability, counting methods, Markov chains, and game theory. The course may be used to fulfill the Quantitative Analysis component of the General-Education Requirements. Prerequisite: MATH 110 or placement higher than MATH 110 on the math placement examination.

**MATH 131: Calculus I** (4 Cr.)

The first course in the calculus sequence. Topics include limits, continuity, differentiation, application of the derivative, the Intermediate Value Theorem, definite integrals, and the Fundamental Theorem of Calculus, with transcendental functions throughout. The course may be used to fulfill the Quantitative Analysis component of the General-Education Requirements. This course is not open to students with credit for MATH 122. Prerequisite: Grade of C- or higher in MATH 114 or placement of MATH 131 on the math placement examination.

**MATH 132: Calculus II** (4 Cr.)

A continuation of MATH 131. Topics include techniques of integration, applications of the definite integral, improper integrals, an introduction to differential equations, convergence of sequences and series, Taylor series, parametric equations, and polar coordinates. Prerequisite: Grade of C- or higher in MATH 131.

**MATH 253: Calculus III** (4 Cr.)

A continuation of MATH 132. Topics include conic sections, vector algebra, space curves, calculus of functions of several variables, multiple integration, and calculus of vector fields. Prerequisite: Grade of C- or higher in MATH 132.

**MATH 220: Discrete Mathematics ** (3 Cr.)

(Also offered as ECE 357.) An introduction to mathematical reasoning, algorithm analysis, and the concepts that provide a mathematical foundation for computer science. Topics include a review of sets, relations, functions and matrices, logic, proof techniques including mathematical induction, counting techniques, difference equations, applications, and elementary analysis of iterative and recursive algorithms. Usually offered every spring semester. Prerequisite: MATH 131 (may be taken concurrently).

**MATH 260: Linear Systems and Matrices** (1 Cr.)

Students will study properties of, and solutions to, linear equations and systems of linear equations. Related topics include matrices, properties of matrices, matrix algebra, determinants, eigenvalues, real vectors in two and three dimensions, vector algebra (including dot and cross products), linear combinations, and linear independence. This class is not open to students with credit for MATH 264. Prerequisite: MATH 114.

#### Of Particular Interest to Education Students

**MATH 211: Laboratory in Elementary Mathematics I ** (1 Cr.)

This course is designed to provide an opportunity for prospective elementary teachers to learn mathematical concepts in an active, materials-oriented context and to acquaint them with materials appropriate for use at the elementary school level. Topics correspond to those in MATH 213. Enrollment is restricted to students majoring in elementary education. S/U grade only. Usually offered every fall semester. Prerequisite: concurrent registration in MATH 213.

**MATH 212: Laboratory in Elementary Mathematics II ** (1 Cr.)

A continuation of MATH 211. Topics correspond to those in MATH 214. S/U grade only. Prerequisite: concurrent registration in MATH 214.

**MATH 213: Mathematics for Elementary Teachers I ** (4 Cr.)

This course is restricted to students majoring in elementary education. Topics include elementary logic, sets, problem solving, numeration systems, the whole number system, the rational number system, and elementary number theory. Usually offered every fall semester. Prerequisite: MATH 110 or placement higher than MATH 110 on the math placement examination.

**MATH 214: Mathematics for Elementary Teachers II ** (4 Cr.)

A continuation of MATH 213. Topics include two-and three-dimensional geometry, measurement, functions, graphing, probability, and statistics. Usually offered every spring semester. Prerequisite: MATH 213.

**MATH 270: Ordinary Differential Equations ** (3 Cr.)

Study of linear differential equations of a single variable, and their solutions (graphical, exact, and numerical), applications of ordinary differential equations, Laplace transforms, introduction to systems of linear differential equations, and use of eigenvalues and eigenvectors in solving such systems. Prerequisites: Grade of C- or better in MATH 132 and either MATH 260 or MATH 264. (The latter may be taken concurrently.)

**MATH 320/520: Dynamical Systems ** (3 Cr.)

Theory and applications of mathematical models of dynamical systems (discrete and continuous). Topics include linear and non-linear equations, linear and non-linear systems of equations, bifurcation, chaos, and fractals. Usually offered in the fall semester of odd-numbered years. Prerequisite: MATH 132.

**MATH 321/521: Mathematical Models of Infectious Disease ** (3 Cr.)

(Also offered as BIO 321.) An application of mathematical methods, such as differential equations and elementary matrix algebra, to the study of infectious diseases and the analysis of outbreaks and control methods (such as vaccinations). Usually offered online during the summer. Prerequisite: MATH 131 and one of the following: STAT 140, STAT 240, IDS 205, CE 202, ECE 365, or PSY 201.

**MATH 322/522: Optimization ** (3 Cr.)

Theory of, and computer algorithms for, the solution of mathematical programming problems and applications. Topics include the simplex method, cutting planes, branch and bound methods, and numerical methods for unconstrained optimization, game theory, and dynamic programming. Usually offered in the spring semester of even numbered years. Previous computer programming or spreadsheet experience is recommended but not required. Prerequisites: MATH 260 or MATH 264.

**MATH 323/523: Game Theory ** (3 Cr.)

An introduction to the fundamentals of game theory, including dominance, Nash equilibria, and evolutionary stable solutions. Students will explore various models of strategic games and apply them to economics, biology, and other disciplines. Usually offered in the summer. Prerequisites: MATH 131 and one of the following: STAT 140, STAT 240, IDS 205, CE 202, ECE 365, or PSY 201.

**MATH 330/530: Partial Differential Equations ** (3 Cr.)

Theory of, and solution techniques for, partial differential equations of first and second order, including the heat equation and wave equation in rectangular, cylindrical, and spherical coordinates. Tools include Fourier series, Bessel functions, Legendre polynomials, and transform techniques. Usually offered in the spring semester of odd-numbered years. Prerequisites: MATH 253 and MATH 270.

**MATH 334/534: Complex Variables ** (3 Cr.)

A study of mathematics in the complex plane, including analytic functions, derivatives, power and Laurent series, integrals, residues, and conformal mapping, with applications to partial differential equations. Usually offered in the fall semester of even-numbered years. Prerequisite: MATH 253.

**MATH 370/570: Numerical Analysis ** (3 Cr.)

Analysis and implementation of numerical techniques such as polynomial interpolations, root finding, matrix solutions to systems of equations, numerical solutions to differential equations (the finite different method), and numerical integration, with an emphasis on theory and error analysis. Usually offered in the spring semester of even-numbered years. Previous computer programming or spreadsheet experience is recommended but not required. Prerequisite: MATH 260 or MATH 264.

**MATH 371/571: Experimental Mathematics ** (3 Cr.)

A study of the role of computation and experimentation in mathematical proof. Students will learn to write code in a mathematical programming language (e.g. Maple) and then apply programming skills to a variety of mathematical problems. Topics include enumeration, continued fractions, high-precision computing, and numerical integration, among others. Students will also study famous proofs that integrate computation in nontrivial ways and the current state of automated theorem proving/automated proof-checking software. Usually offered in the spring semester of odd-numbered years. Prerequisites: MATH 266 or consent of the instructor.

**STAT 140: General Statistics ** (3 Cr.)

A noncalculus-based introduction to the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: planning a study, exploring data, anticipating patterns, and statistical inference. This course may be used to fulfill the Quantitative Analysis component of the General-Education Requirements. Prerequisite: MATH 110 or placement higher than MATH 110 on the math placement examination.

**STAT 240: Statistical Analysis ** (3 Cr.)

An introduction to probability and statistics for students who have completed a semester of calculus. Topics include probability, empirical and theoretical frequency distributions, sampling, correlation and regression, testing hypotheses, and estimation of parameters, with an emphasis on illustrations and applications of these techniques. This course is not open to students with credit for STAT 140, IDS 205, ECE 365, CE 202, or PSY 201. Prerequisites: MATH 122 or Math 131.

**STAT 340/540: Statistics for Decision Making ** (3 Cr.)

(Also offered as IDS 340.) A study of statistical concepts and methods to facilitate decision-making. Content includes analysis of variance, simple and multiple regression, correlation, time-series analysis, and nonparametric methods. This course is not open to students who have completed IDS 340. Prerequisite: one of the following: IDS 205, STAT 140, STAT 240, PSY 201, CE 202, or completion of (or concurrent enrollment in) ECE 365.

**STAT 343/543: Time Series Analysis ** (3 Cr.)

This course studies statistical modeling and forecasting of time series, which are observations made sequentially through time. Applications of time series discussed are selected from finance, economics, health sciences, meteorology, and many other fields. Students will participate in periodic computer lab sessions with the software SAS. Usually offered every spring semester. Prerequisite: one of the following: STAT 340, ECON 325, or ECE 365.

**STAT 344/544: Stochastic Processes ** (3 Cr.)

A survey of probabilistic models used in decision theory. Topics include stochastic processes, queuing theory, forecasting, Bayesian decision theory, reliability, and simulation. Usually offered every third semester. Prerequisite: one of the following: STAT 240, IDS 205, CE 202, or ECE 365.

**STAT 441/541: Probability ** (4 Cr.)

A course in probability with some topics applicable to statistics. Topics include probability spaces, random variables, classical discrete and continuous probability distributions, multivariate probability distributions (with an introduction to multivariable calculus), and joint and conditional distributions. Usually offered every third semester. Prerequisite: MATH 132.

**STAT 442/542: Mathematical Statistics ** (3 Cr.)

A continuation of STAT 441. Topics include the central limit theorem, covariance, moments, estimation, tests of hypotheses, and sampling theory. Usually offered every third semester. Prerequisite: STAT 441.

**STAT 493/593: Seminar in Applied Statistics (Currently: Introduction to SAS) ** (3 Cr.)

An intensive study of selected topics, methods, techniques, and problems in applied statistics. Only offered when there is sufficient demand. Prerequisite: STAT 340, IDS 340, or ECON 270.

**MATH 264: Linear Algebra ** (3 Cr.)

A study of linear algebra and an introduction to mathematical reasoning. Topics include systems of linear equations, matrices, determinants, vectors in n-space, abstract vector spaces, and linear transformations. Usually offered every fall semester. Prerequisite: MATH 132 or MATH 220.

**MATH 266: Transitions in Mathematics ** (3 Cr.)

In this class, students prepare to become professional mathematicians. Major course components are 1) a study of common proof techniques using linear algebra and number theory as foundations, and 2) an introduction to current professional practices such as the use of mathematical typesetting software, the use of computational software, finding and reading mathematical literature, and a survey of current issues in mathematics. Usually offered every spring semester. Prerequisite: MATH 264 or MATH 132 and consent of the department chair. Recommended to be taken concurrently with MATH 299.

**MATH 290: Topics in Mathematics (Currently: History of Women in Mathematics; Cryptography** (1-3 Cr.)

Topics may include problem-solving techniques, computer applications, or topics from finite mathematics. Only offered when there is sufficient demand. Prerequisite: consent of the instructor.

**MATH 312: History of Mathematics ** (3 Cr.)

Students will study the development of mathematics, usually through a survey of mathematics from earliest times to the present. Special topics may be chosen according to the interest of the class. Usually offered in the fall semester of even-numbered years.

**MATH 314: Elements of Geometry ** (3 Cr.)

Logic, axiom systems, and models; consistency, independence, and completeness; consideration of the foundations of Euclidean and non-Euclidean geometries; topics from projective and transformational geometries. Usually offered in the fall semester of odd-numbered years. Prerequisite: MATH 264 or MATH 266.

**MATH 421: Combinatorics I ** (3 Cr.)

Theory of combinatorics, including elementary counting techniques, the inclusion-exclusion principle, Ramsey theory, and an introduction to graph theory. Additional topics are introduced according to the interests of the students. Usually offered every third semester. Prerequisite: MATH 266.

**MATH 422: Combinatorics II ** (3 Cr.)

A continuation of MATH 421. Topics include generating functions and recurrence relations, Polya’s theorem, matchings and coverings, and other topics based on the interests of the students. Usually offered every third semester. Prerequisite: MATH 421 or consent of the instructor.

**MATH 451: Analysis I ** (3 Cr.)

Properties of real numbers, theory of continuity, differentiation and integration of real valued functions of a real variable, sequences, series, and uniform convergence. Usually offered every third semester. Prerequisites: MATH 132 and MATH 266.

**MATH 452: Analysis II ** (3 Cr.)

Theory of continuity and differentiation of real and vector-valued multi-variable functions; multiple integration and the Jacobian; implicit and inverse function theorems; topology of real n-space. Usually offered every third semester. Prerequisites: MATH 253 and MATH 451.

**MATH 461: Abstract Algebra I ** (3 Cr.)

A course in the theory of mathematical structures, i.e. groups, rings, and fields, along with substructures, quotient structures, and homomorphisms. Usually offered every third semester. Prerequisite: MATH 266.

**MATH 462: Abstract Algebra II ** (3 Cr.)

A continuation of MATH 461. Topics may include a more detailed study of rings, polynomial rings, field extensions, field automorphisms, an introduction to Galois theory, further work in group theory, and an introduction to additional structures. Usually offered every third semester. Prerequisite: MATH 461.

**MATH 490: Advanced Topics in Mathematics (Currently: Topology) ** (1-3 Cr.)

An advanced course for mathematics majors, topics will vary according to faculty and student interest. Only offered when there is sufficient demand. Prerequisites will depend on the content.

**MATH 492: Research in Mathematics ** (1-3 Cr.)

Students undertake a research problem in mathematics under the direction of a faculty member. Written and oral reports are required. S/U grade only. Prerequisite: consent of the instructor or chair of the department.

**MATH 495: Independent Study in Mathematics ** (1-3 Cr.)

Students study advanced topics in mathematics under the supervision of a faculty member. Written work is required. Prerequisite: consent of the chair of the department.

#### The Mathematics Colloquium Sequence

**MATH 199: Mathematics Colloquium I ** (0 Cr.)

Students attend and act as moderators for sessions of MATH 499 and begin participating in co-curricular mathematical activities culminating in MATH 399. S/U grade only.

**MATH 299: Mathematics Colloquium II ** (0 Cr.)

Students are required to attend sessions of MATH 499, evaluate student presentations, and continue participating in co-curricular mathematical activities culminating in MATH 399. S/U grade. Prerequisite: MATH 199. Recommended to be taken concurrently with MATH 266.

**MATH 399: Mathematics Colloquium III ** (1 Cr.)

Students are required to attend sessions of MATH 499 and participate in activities related to mathematics that take place outside of the classroom. Examples include attending a mathematics conference, participating in service learning opportunities, or taking the national Putnam exam. Potential activities are assigned points, and students must attain a certain minimum number of points before the completion of this course to receive credit. Prerequisite: MATH 299 and at least junior standing.

**MATH 499: Mathematics Colloquium IV ** (1 Cr.)

Students explore, write about, and give presentations about a topic or topics chosen according to the interests of faculty and students. Guest speakers may be arranged in accordance with the topic or topics. Students design, implement, and run a regularly scheduled departmental colloquium, to which all faculty and students are invited. Prerequisites: MATH 266 and MATH 399.

**ACRS 325: Actuarial Modeling ** (3 Cr.)

A study of actuarial models in the context of insurance. Topics include mathematics of finance (including interest theory and annuities), mortality tables, basic life contingencies, and actuarial professional issues. Normally offered in alternate years. Prerequisite: STAT 441 (may be taken concurrently).

**ACRS 386: Internship in Actuarial Science ** (3 Cr.)

Opportunities for students to have direct, supervised experience in public agencies or private industry, such as insurance companies or consulting firms. S/U grade. Prerequisites: actuarial science major and approval of the chair of the actuarial science program.

**ACRS 495: Independent Study in Actuarial Science ** (1 Cr.)

Students study advanced topics in actuarial science under the supervision of a faculty member. Written work is required. Prerequisite: consent of the chair of the actuarial science program.

- ACRS 495 P: Preparation for the 1st (Probability) exam of the Society of Actuaries
- ACRS 495 FM: Preparation for the 2nd (Financial Mathematics) exam of the Society of Actuaries