The study of mathematics has occupied humans from ancient times to the present. It is an intellectual process requiring creativity, analysis, logic, decision-making, synthesis of ideas, and communication. Mathematics exists in and for itself but also provides the technical basis for problem-solving in a wide variety of fields. The Saint Mary’s graduate equipped with a strong mathematical background will be in the enviable position of being able to utilize her expertise in areas where rigorous thought and precision of results are necessary.
The courses in mathematics are offered for those studying the subject as part of a liberal education; for majors as a preparation for graduate studies, careers in business, or industry; and for those who intend to teach mathematics. In addition to the Major in Mathematics, we offer four tracks for those with special interests. The Statistics and Actuarial Mathematics Major is a sequence of courses giving the student experience in statistics with an emphasis on risk modeling and is recognized by the Society of Actuaries as a pre-actuarial program. The Computing and Applied Mathematics Major enables those students with a strong interest in computer science to pursue an integrated program of mathematics and computer science. Similarly, the Physics and Applied Mathematics Major enables those students with interests in physics and mathematics to pursue both. The Mathematics Major with Teacher Concentration enables the student to obtain secondary school certification in the State of Indiana.
Courses in computer science are designed to educate students of the liberal arts in computer literacy; to provide computer programming instruction for students of mathematics, science, business and social science; and to establish a solid foundation in computer software theory and practice for students of all disciplines. The courses are taught by the Mathematics Department. The College offers a major in Computing and Applied Mathematics that combines mathematics and computer science (see Mathematics), a concentration in Management Information Systems within the Business Administration major (see Business Administration and Economics), and a minor outlined below.
Saint Mary’s has a long history of providing quality international programs as an essential part of our educational mission—forming women leaders who will make a difference in the world. As this world becomes increasingly interdependent, the College offers an expanding range of semester, year, semester break, and summer study and service programs in a wide variety of countries, and encourages students to take advantage of them. Learn more about the various Study Abroad opportunities.
The Department encourages students to prepare for teaching on all levels. Through the Teacher Concentration, courses are provided which enable mathematics majors to fulfill Indiana secondary teaching certification requirements. Students interested in secondary teaching are counseled within the Department to add professional education courses to their mathematics major program. Elementary education students may take courses leading to a mathematics minor or a double major in mathematics and elementary education.
Any of the majors in mathematics and computer science can be combined with the Masters of Science in Data Science so that a student can complete the requirements for her undergraduate degree and the M.S. in Data Science in five years. Interested students should consult the director of the Data Science Program to develop a five-year plan. For the M.S. in Data Science program and course descriptions, see the M.S. in Data Science in the Graduate Studies section of the Bulletin.
334 Madeleva Hall
S. Cox, C. Dwyer, C. Hoover, K. Kuter, E. Misiolek, C. Periton, M. Porter, R. Rohatgi, R. Solava, J. Snow, B. Vajiac, C. Wedrychowicz
S. Cox, E. Misiolek, R. Solava, C. Wedrychowicz
Intensive study of the problem-solving process. Algebraic, patterning, modeling, and geometric strategies are explored. Includes a review of basic algebra skills and concepts necessary for problem solving. Consent of the Department is required. This does not fulfill the Mathematical Arts requirement of the Sophia Program.
Mathematical modeling through the use of graph theory. Topics include graphs, directed graphs, trees, matchings and network flows. Designed primarily for first year college students. Prerequisite: MATH 100 or recommendation of Math Placement Advisor.
This course studies polynomial, rational, exponential, logarithmic, and trigonometric functions from the symbolic, numeric, and graphical perspectives. The emphasis on these concepts will provide solid preparation for a college-level calculus course. This does not fulfill the Mathematical Arts requirement of the Sophia Program. Prerequisite: MATH 102 or recommendation of Math Placement Advisor.
Set theory, counting techniques, probability, random variables, expected value, variance, standard deviation, and linear programming. Prerequisite: MATH 103 or recommendation of Math Placement Advisor.
Introduction to differential and integral calculus designed primarily for liberal arts students and those in the professional programs. Limits are treated intuitively. Emphasis on applications.
Introduction to differential and integral calculus designed primarily for liberal arts students and those in the professional programs. Limits are treated intuitively. Emphasis on applications. Prerequisite: MATH 105.
This course develops and applies mathematical concepts and tools to quantitatively explore sustainability issues. Topics such as industrial agriculture, energy sustainability, population growth, and ecological footprints will be explored from environmental, social, and economic perspectives wherever possible. Mathematical concepts developed in the course are motivated through the study of these topics and allow students to survey several mathematical areas. Particular concepts covered include properties of real numbers, algebraic simplification of expressions, solving equations and inequalities, rates of change, interpretation of numerical information, functions and inverses, modeling, differentiation/integration, qualitative analysis of differential equation models, calculating probabilities, statistical techniques on real data, and graph paths and connectivity.
Problem solving and strategies; properties of whole numbers, integers, rational numbers, and real numbers; algorithms and computation; elementary number theory. The course follows the recommendations of the Mathematical Association of America and the National Council of Teachers of Mathematics for the training of elementary teachers. Prerequisite: One Mathematical Arts Sophia Program course.
Algebraic and transcendental functions; limits; continuity; derivatives; maxima and minima; concavity; related rates; Taylor polynomials; Mean Value Theorem; anti-differentiation; Riemann sums; the Fundamental Theorem of Calculus; techniques of integration; sequences and series. The course is based on graphical, numerical, and symbolic points of view. Graphing calculators are used throughout the course. Prerequisite: At least four years of high school mathematics.
Algebraic and transcendental functions; limits; continuity; derivatives; maxima and minima; concavity; related rates; Taylor polynomials; Mean Value Theorem; anti-differentiation; Riemann sums; the Fundamental Theorem of Calculus; techniques of integration; sequences and series. The course is based on graphical, numerical, and symbolic points of view. Graphing calculators are used throughout the course. Prerequisite: At least four years of high school mathematics. Prerequisite: MATH 131.
This course is designed for students who have completed a full year of calculus in high school and have mastered the mechanics of differentiation and integration. The basic concepts of a two-semester college calculus sequence, including limits, derivatives, integrals, sequences and series, will be explored in depth. The emphasis of the course is on understanding the theory of calculus and constructing mathematical models. Prerequisite: A minimum score of 3 on the AP Calculus exam or permission of instructor.
This course in applied math and politics will focus on the mathematics behind voting in both two-party and multi-party systems, comparing systems in the US with those in France and Ireland. Students will explore both implemented and theoretical social choice functions and analyze each, subject to standard criteria. They will develop an understanding for how formal rules and procedures have an impact on policy outcomes and informal institutions such as political parties.
Basic number theoretic concepts are studied, with an emphasis on writing proofs. Divisibility; primes; Euclid’s algorithm and its consequences; linear diophantine equations; residue classes; linear congruences; arithmetic functions. Applications of number theory to computer science (cryptography, complexity of computations). Prerequisite: MATH 118 or MATH 131.
Set theory, logic, relations, functions, and an introduction to abstract mathematical structures, with an emphasis on reading and writing mathematical proofs. Prerequisite: one calculus course or permission of instructor.
Three-dimensional space: parametric equations, lines, planes, vectors, dot product, cross product. Polar coordinates. Vector-valued functions. Functions of several variables: partial derivatives, linear approximation, gradient, directional derivatives, maxima, minima, chain rule. Multiple ntegrals. Vector Calculus (including Green’s Theorem and Stokes’ Theorem). Prerequisite: MATH 132 or MATH 133.
Sampling studies, design of experiments, hypothesis testing, analysis of variance, regression and correlation, regression modeling, time series. Introduction to operations research: queuing, systems analysis, quality assurance, acceptance sampling. Emphasis on applications to business and economic decision making. Prerequisite: MATH 114 with a grade of “C” or higher (also listed as BUAD 341).
An introduction to Operations Research—quantitative models used in management decision-making. The course will focus on the models as tools with computer software used extensively for problem solving and assignments. Case studies are used. Prerequisite: One year of Calculus or MATH 114 (also listed as BUAD 427).
Mathematical theory of interest, annuities, amortization schedules, yield rates, and sinking funds. Prerequisite: Two semesters of calculus or equivalent or permission of the instructor.
This course has three major components: an overview of the history of mathematics, the lives and contributions of selected women mathematicians throughout history, and the experiences of women in the contemporary mathematical community. In our general exploration of history, we focus on the development of mathematical ideas and the contributions made by various cultures and individuals. Among the historical figures studied in depth are Hypatia, Maria Agnesi, Sophie Germain, Sofia Kovaleskaia, Emmy Noether, Julia Robinson. The course will examine the ways in which the views of the modern mathematical community and the broader society discourage or encourage the participation of women and other under-represented groups in mathematics. Prerequisite: One semester of college-level calculus or equivalent.
Review of basic properties of the real number system. Foundations of Euclidean geometry with additional study of transformational geometry. Elementary probability and statistics. This course meets for two hours of class instruction and has a two-hour laboratory component. Recommendations of MAA and NCTM are continued. Prerequisite: Two MATH courses including MATH 118 with a grade of C or higher in MATH 118.
Linear systems; linear independence; matrix algebra; determinants; vector spaces including subspaces, dimension, rank, change of bases; linear transformations; eigenvalues and eigenvectors; inner product; orthogonality; and Gram-Schmidt. An introduction to differential equations, including first order linear, separable, and exact; second order with constant coefficients and variation of parameters, reduction of order, and undetermined coefficients. Applications included. Prerequisites: MATH 231.
A study of methods for solving higher order linear ordinary differential equations, linear first order systems, and boundary value problems for the heat and wave equations. Analysis of nonlinear systems of first order ordinary differential equations using approximation by linear systems, numerical solutions and phase portraits. The course will use mathematical software to solve differential equations and systems of differential equations symbolically, numerically and graphically. Prerequisite: MATH 326.
Computer arithmetic and algorithm convergence. Solutions of equations. Optimization. Numerical linear algebra. Numerical solutions to ordinary differential equations. Numerical differentiation and integration. Error analysis. Prerequisite or corequisite: MATH 326.
Construction of the reals; Sequences; Real valued functions of a single real variable: continuity, uniform continuity, sequences and series of functions, uniform convergence, differentiation, integration. Prerequisite: MATH 341.
A calculus-based approach to probability theory. Topics include probability spaces, classical theory, random variables, discrete and continuous distributions, multivariant distributions, transformations of random variables, random sampling, the law of large numbers, the central limit theorem and moment generating functions. Prerequisite: MATH 231 or equivalent.
Topics include sampling distributions, estimation, theory of estimators, test of hypotheses, analysis of variance, regression and correlation analysis, time series, experimental design, modeling and decision criteria. The use of statistical analysis in decision problems is stressed. Prerequisite: MATH 345 or equivalent.
Basic algebraic systems: groups, rings, and fields. Homomorphisms and factor groups, rings. Polynomial rings and field extensions. Applications, including symmetry groups and algebraic coding theory. Prerequisite: MATH 353.
Historical and formal development of Euclidean and non-Euclidean geometries; role of axiom systems; congruence, parallelism, measurement. Prerequisite: MATH 225.
Stochastic models of contingent payment, survival, frequency, severity and ruin. Compound distribution models. Emphasis on application to actuarial models. Prerequisite: MATH 345.
In this course, students study the modeling process with application from difference equations, probability, dynamical systems, optimization, and simulation. Students will design, develop, implement, evaluate, and present mathematical models using real data for observable phenomena. Models and issues related to environmental and sustainability studies are emphasized. Prerequisites: MATH 326 and MATH 345.
Topics in Mathematics not covered in the regular department offerings. May be repeated with a different topic.
Student presentation of selected topics. Prerequisite: Permission of the department chair.
Provides properly qualified students with an opportunity for independent study and careful consideration from an advanced standpoint of selected topics in undergraduate mathematics. Prerequisite: Permission of the department chair. May be repeated.
Professional work experience in mathematics or statistics with a business or organization. May be repeated.
This course introduces the student to an integrated spreadsheet application. Topics covered include: cell formulas and built-in functions, formatting, charting, templates, “what-if” analysis, pivot tables, macros and integration of spreadsheet data into a word processor. Graded S/U.
This course includes a brief history of computing, uses of computers in networking and programming, and ethical issues in computing. Students learn to use a database application as they create and manipulate tables, forms, queries, reports, macros and other database objects.
This course explores program development and design with objects; the designs are implemented in a commonly used, current programming language. The emphasis is on designing, writing, and correcting programs. Topics include the internal organization of the computer, procedures and functions, elementary data structures, and techniques of problem solving. No previous experience with computers is required. The course is focused around a weekly two-hour laboratory and provides in-depth programming experience.
A weekly two-hour laboratory and provides in-depth programming experience.
This course is designed to deepen a student’s understanding of how a computer works by studying the C programming language and how it interfaces with assembly language. A weekly laboratory provides experience in controlling the behavior of the computer in ways not possible in higher level languages. Topics include computer organization, assemblers, loaders, link editors, and memory management. Prerequisite: CPSC 207 or equivalent.
This introduction to data communications examines the fundamentals of network architecture including layers, protocols, client/server model, file transfers, and other low-level communications issues. Students will experience hands-on internet related programming including web page development using HTML, and CSS. Prerequisites: CPSC 207 or permission of instructor.
Theory of computer simulation, including applications of discrete models of industrial and management systems. Topics include probability distributions, random number generation, queuing, design, and analysis of simulation experiments. Includes significant use of simulation software. Prerequisites: CPSC 207 and either MATH 114 or MATH 345.
This course introduces the concepts and techniques of structuring data for complex problems, and provides experience in accessing and processing this data. An object-oriented paradigm is used throughout the course. The course is designed especially for students who will choose a career in information technology. Prerequisite: CPSC 207.
This course includes a study of systems, particularly those which lend themselves to computer representation, a study of systems analysis and design, and the completion of a major systems project done in a team environment. The project will involve the analysis of an actual system problem, the writing of a system proposal to solve the problem, the presentation of the proposal to the users of the system, and the design and construction of a prototype to implement the proposal. Prerequisite: CPSC 328 or permission of instructor.
CPSC 417 lab
Fundamental concepts of database development, in particular data modeling, database design, and database implementation, as well as managing, retrieving, and updating data within a relational database system. Hands-on experience includes use of the Structured Query Language (SQL) to define, construct, and query a database. Students complete a semester-long project done in a team environment. Prerequisite: CPSC 207 or permission of instructor.
Provides properly qualified students with an opportunity for independent study and careful consideration from an advanced standpoint of selected topics in computer science. Departmental approval required. May be repeated.
Professional work experience in computer science with a business or organization. Graded S/U. May be repeated.