The focus of the Department of Mathematics and Statistics is to create an environment for the appreciation and understanding of two important branches of knowledge in the liberal arts: mathematics and statistics.
Specifically, it provides students guided opportunities to develop powers of logical thought and critical analysis together with an orientation for mathematical and statistical modeling in applications. Culturally, the department aims to demonstrate the precision, beauty, and power of mathematics and statistics, their systematic organization, symbolic clarity and exact reasoning, and their capacity for yielding generalizations and predictions from data submitted to mathematical and statistical laws. Departmental courses are designed to provide an appropriate mathematical or statistical experience for students whether they are majoring in the department, taking courses to complement another major, or taking courses in the general education program.
General Department Goals
The overarching goals of the department are to help students to:
- Communicate about and with mathematics and statistics in oral and written formats;
- Understand and use mathematical and statistical theory and techniques to analyze and solve problems; and
- Translate real-world problems into mathematical situations and then apply mathematics and/or statistics to solve the problems.
As part of the university advising program, the department makes recommendations for each first-year student concerning the preparatory mathematics and statistics courses they are required/qualified to take. These recommendations are based on the ACT subscore in mathematics and/or the department placement tests. Placement tests are offered to incoming freshmen during the summer orientation sessions. They may also be taken at almost any time by arrangement with the department chair.
Students who have a high school background in calculus are encouraged to apply for credit through advanced standing. A sufficiently high score on the national advanced placement (AP) College Entrance Examination, the CLEP Calculus Test, or the Saint Mary's University Advanced Placement Calculus Test is required. Advanced placement information is available from the department chair.
There is an active student-operated Mathematics and Statistics Club, which freshmen through seniors are welcome to join. In addition, the department has its own chapter, Minnesota Zeta, of the national honorary mathematics society, Pi Mu Epsilon, to which qualified sophomores, juniors, and seniors may earn membership.
Besides the Mathematics major, the department also offers a secondary Mathematics Education major and a Mathematics endorsement for the Elementary Education major. Both are designed to deepen the student’s mathematical knowledge and prepare him or her to be a stronger mathematics teacher. See the Education Department's section of the website for more information.
The Mathematics and Statistics Department also supports and staffs the minor.
Click on courses below for descriptions
Successful completion of this course satisfies the mathematics competency requirement for graduation. This course prepares students for M108, M109, M145, and ST132. Topics include algebra concepts, including solving equations, systems of equations, and graphing; geometry concepts; and some concepts from probability and statistics. Students use graphing calculators to solve problems involving numerical, graphical, and symbolic data.
Students planning to take M148 and M149 should not take this course; they should take M102 to satisfy their mathematics competency, if necessary. Credit is not granted for both this course and M102. Prerequisite: departmental placement.
Successful completion of this course satisfies the mathematics competency requirement for graduation. This course is especially recommended for students who intend to take M148 and M149 and need a good review of algebra. Topics include: algebraic expressions, first-degree equations and inequalities, systems of equations in two variables, polynomials, rational expressions, exponents and radicals, and quadratic equations.
Credit is not granted for both this course and M100. Offered fall semester. Prerequisite: departmental placement.
This course includes concepts essential to mathematics and is required for elementary education majors. Topics include: set theory, numbers and numeration, operations, number theory, rational numbers, and problem solving. This course is open only to elementary education majors.
Offered spring semester. Prerequisite: mathematics competency.
This course includes concepts essential to mathematics and is required for elementary education majors. Topics include: informal geometry, measurement, problem solving, descriptive statistics, and elementary probability. This course is open only to elementary education majors.
Offered fall semester. Prerequisite: mathematics competency.
This course provides an introduction to noncalculus mathematical modeling methods prevalent in business. Topics include: matrix methods, systems of linear equations and inequalities, linear programming by the geometric method and by the simplex method, and the mathematics of finance.
Prerequisite: mathematics competency.
This course, followed by M149, provides a two-semester sequence that covers the material of a traditional Calculus I course along with built-in coverage of precalculus topics. Topics in M148 include: solving equations, functions, classes of functions (polynomial, rational, algebraic, exponential, logarithmic), right triangle trigonometry, angle measure, limits and continuity, derivatives, rules for derivatives. Credit is not granted for this course and M151 or courses equivalent to college algebra and college trigonometry.
Prerequisite: mathematics competency satisfied.
This course completes the two-semester sequence that begins with M148, and together with M148 provides a two-semester sequence that covers the material of a traditional Calculus I course along with built-in coverage of precalculus topics. Topics in M149 include: trigonometric and inverse trigonometric functions, rules for derivatives, applications of derivatives, and definite and indefinite integrals. Credit is not granted for this course and M151.
This course provides an introduction to the differential and integral calculus. Topics include: the concepts of function, limit, continuity, derivative, definite and indefinite integrals, and an introduction to transcendental functions.
Credit cannot be granted for this course and M308 or M309.Prerequisites: M115 and M116, or departmental placement.
This course is a continuation of M151. Some of the topics of M151 are revisited at a higher mathematical level. Topics include: limits, differentiation, applications of the definite integral, inverse trigonometric functions, techniques of integration, improper integrals, indeterminate forms, numerical methods for integration and approximation, curves in the plane given parametrically, polar coordinates, and vectors in 2-space and 3-space.
Prerequisite: Minimum grade of C in either M149 or M151 or departmental placement.
This course continues the development of Calculus from M151 and M152. Topics include: sequences and series, conic sections, and differentiation and integration of functions of several variables.
Offered fall semester. Prerequisite: minimum grade of C in M152.
This course provides an introduction to techniques and applications of linear algebra. Topics include: systems of linear equations, matrices, determinants, Euclidean n-space, real vector spaces, basis and dimension, linear transformations, inner products, and eigenvalues and eigenvectors.
Offered spring semester. Prerequisite: minimum grade of C in M152.
This course looks at topics central to further study in mathematics. Topics include symbolic logic, especially as it applies to mathematical proof; methods of mathematical proof such as direct proof, indirect proof, proof by induction; use and meaning of mathematical quantifies and predicates; sets; relations; equivalence relations and partitions; order relations; functions and their properties; and complex numbers. A junior assessment test is administered as part of this course.
Offered fall semester. Prerequisite: M251 (may be concurrent).
This course provides an introduction to combinatorial and graph theoretical techniques in mathematics. It is also designed for students in computer science. Topics include: sets, functions, combinatorial techniques, graph theory, searching algorithms, and trees.
Prerequisites: CS106 or CS110/111, and M152.
This course provides an introduction to elementary number theory. Topics include: divisibility, prime and composite numbers, congruences, arithmetical functions, primality testing, factorization techniques, and applications to cryptography.
This course is required for the Mathematics Education major. The course is designed to be an introduction to the foundations of geometry. Topics include: Euclidean geometry, non-Euclidean geometry, projective geometry, and geometric transformations.
Offered in alternate spring semesters. Prerequisite: M152.
This calculus-based course is designed to provide mathematics majors and minors with an introduction to the mathematical underpinnings of statistics. Topics include: probability axioms, probability, Bayes’ Theorem, random variables, discrete and continuous probability distributions, and expected value.
Offered spring semester. Prerequisite: M152.
This course provides an introduction to the theory, methods, and applications of ordinary differential equations. Topics include: first order differential equations, linear differential equations with constant coefficients, and systems of differential equations.
Prerequisites: M251 and M252 (may be concurrent).
This course provides an introduction to the theory and methods of numerical analysis. Topics include: numerical methods for solving linear and nonlinear equations, polynomial approximation of functions, numerical integration and differentiation, numerical approximation to solutions of differential equations, direct and iterative methods for solving systems of equations.
Prerequisites: either CS106 or CS110/111, and M251, M252.
This course serves physics majors as well as those mathematics majors whose area of interest is analysis. Topics include: Fourier series, the complex numbers, analytic functions, and derivatives and integrals of complex functions. Other topics may include Laurent series and residues, partial differential equations and boundary value problems.
Prerequisites: M251 and M252.
This course provides an introduction to the theory of functions of one complex variable. Topics include: the complex numbers, the complex derivative, analytic functions, power series, complex integration, Cauchy’s Theorem and Cauchy’s Integral Formula, Laurent series, and residues and poles.
Special topics in mathematics may be offered depending on student interest.
A course designed to provide undergraduates students with the basic computational tools and techniques needed for their study in science and mathematics. Students learn by doing projects that solve problems in physical sciences and mathematics using symbolic and compiled languages with visualization. By use of the Sage problem-solving environment and the Python programming language, the students learn programming and numerical analysis in parallel with scientific problem solving. Also offered as CS356 and P356.
Prerequisites: CS106, M251,M252, and ST232.
This course is required for the mathematics education major, providing an introduction to techniques and applications of operations research. Topics include: linear programming, game theory, queuing theory, Markovian decision processes, and decision theory.
Offered in alternate spring semesters. Prerequisites: M252 and M332.
This course provides an introduction to algebraic structures. Topics include: groups, subgroups, quotient groups, group homomorphisms, rings, ideals, and fields.
Offered in alternate spring semesters. Prerequisites: M251, M252, and M301.
This course is designed to strengthen the mathematical background of students in elementary education. It is required for the endorsement in mathematics for elementary education. The course consists of a selection of mathematical topics of wide interest and applicability. Topics include: graph models, linear programming, scheduling and packing problems, allocation problems, and social decision problems. This course may not be used as an upper-division elective for the mathematics major or minor or the mathematics education major.
Offered in alternate spring semesters. Prerequisites: M109 and elementary education major.
This course provides a rigorous treatment of topics in calculus. Topics include: sequences, functions, limits, continuity, derivatives, and integration.
Offered in alternate spring semesters. Prerequisites: M251, M252, and M301.
This course is required for all Scientific Computing minors. Its purpose is to provide students the opportunity to develop a research project or participate in an ongoing research project under direction of a faculty advisor. The project must combine scientific computing tools and techniques with a substantive scientific or engineering problem. It is also intended to give students experience in experimental design, recordkeeping, and scientific writing. Also offered as CS456 and P456.
Prerequisites: consent of both the faculty advisor and the minor supervisor, and CS/M/P356.
This course consists of student presentations from mathematics, mathematical modeling, mathematics education, or statistics. Each student chooses a topic in consultation with the instructor, do appropriate background reading, and prepare an oral presentation and written paper on the topic. A senior assessment test is administered as part of this course.
Offered spring semester. Prerequisite: senior mathematics major.
This opportunity provides the student with experience in mathematical research or applications. The internship must be approved by the department and, depending on the nature of the internship, may be counted towards the major. Students generally are expected to give a presentation following the internship.
This course is designed to develop student facility in the use of statistical methods and the understanding of statistical concepts. The course takes a practical approach based on statistical examples taken from everyday life. Topics include: descriptive and inferential statistics, an intuitive introduction to probability, estimation, hypothesis testing, chi-square tests, regression and correlation. Appropriate technology is used to perform the calculations for many applications, and correspondingly an emphasis is placed on interpreting the results of statistical procedures.
Credit is not granted for this course and any of the following: BU215, B392 or ST232. Prerequisite: mathematics competency.
This course is designed to provide the basic ideas and techniques of statistics. Topics include: descriptive and inferential statistics, an intuitive introduction to probability, estimation, hypothesis testing, chi-square tests, regression and correlation. This course makes significant use of appropriate technology. Topics in this course is treated at a higher mathematical level than they are treated in ST132.
Credit is not granted for this course and any of the following: BU215, B392 or ST132. Offered fall semester. Prerequisite: departmental placement or minimum C grade in M148.
M115 College Algebra
Selected topics in statistics may be offered depending on student interest.
This course provides students with an introduction to linear and non-linear models in statistics. Topics include: linear regression, multiple regression, one-, two-, and higher-way analysis of variance, and popular experimental designs. Real-world problems are analyzed using appropriate technology.
Prerequisites: M251, M332, and ST232.
This course provides an introduction to the principles of the design of experiments from a statistical perspective. Topics include: Analysis of variance, covariance, randomization, completely randomized, randomized block, Latin-square, factorial, response surface methods and other designs.
Prerequisites: M152 and ST232.
This course provides a mathematical treatment of probability and statistics. Topics include: several descriptions of the concept of probability, univariate and bivariate probability distributions, joint and marginal probability distributions, covariance, hypothesis testing, estimation, data analysis, and sampling distributions.
Prerequisites: M332 (may be concurrent) and ST232.
This opportunity provides the student with experience and training in statistical techniques. The internship must be approved by the department and, depending on the nature of the internship, may be counted towards the major. Students usually are expected to give a presentation following the experience.
Kevin Dennis, Ph.D.
Chair, Mathematics & Statistics Department
Saint Mary's University of Minnesota
700 Terrace Heights #59
Winona, MN 55987-1399
(800) 635-5987, Ext. 6650