# MATHEMATICS (MATH)

College of Arts and Sciences, Department of Mathematics

O’Shaughnessy Science Hall (OSS) 201, (651) 962-5520

Van Fleet (chair), Anderson, Axtell (Actuarial Science Director), DeCelles, Dokken, Glover, Hoft, Knudson, Kroschel, Li, Loe(associate chair), Lopukhova, Peterson (MaRC Director) Rawdon, Rezac, Shakiban, Shemyakin, Shvartsman, Stolarksa, Tang, Yang, Zhang

Mathematics Department Web Site

The Department of Mathematics offers major tracks that can satisfy a variety of student interests and careers. Majors in mathematics can prepare themselves for graduate study in mathematics or related areas, for the teaching of mathematics at the secondary school level, for professional school in law or health science, or for the application of mathematics and statistics in science, business, industry and government.

Students majoring in mathematics are encouraged to use elective courses to broaden their background in mathematics or in a related area of special interest. Coursework in biology, chemistry, economics, engineering, finance, geology, physics, psychology and computer and information sciences combines well with a major in mathematics.

Students graduating with a major in mathematics will be able to demonstrate an understanding of the fundamental notions of mathematics, including rigorous proof. They will be able to model and solve real-world problems arising in business and industry. They will be able to effectively communicate, both orally and in writing, mathematical concepts to their peers and to an audience of non-majors. They will be able to learn and apply mathematics on their own through independent study, research and participation in non-class-related lectures.

In all of the department’s major tracks, a student must successfully complete at least 16 credits in mathematics courses numbered 300 and above at the University of St. Thomas.

A minor in mathematics is available to support majors in many other departments. A strong mathematical background is of great benefit to students majoring in engineering, actuarial science and the physical sciences.

In addition to the mathematics tracks described below, the department offers a major in actuarial science (see Actuarial Science) and has programs to prepare students for teacher licensure (see Education). An interdisciplinary major in statistics is offered jointly with the Department of Computer and Information Sciences (see Statistics, Computer and Information Science).

Students should see the chair of the Department of Mathematics for advice in selecting courses for a particular purpose. The department offers a number of courses for non-majors to fulfill the mathematics portion of the core curriculum.

###### Center for Applied Mathematics

Within the Department of Mathematics, the Center for Applied Mathematics (CAM) provides opportunities for students to work on significant mathematical problems of current interest to business, industry, and government. The CAM summer student research program funds a number of student projects each year.

## Major in Mathematics

###### Complete the following:

- MATH 113 Calculus I (4 credits) (or 108 and 109)
- MATH 114 Calculus II (4 credits)
- MATH 200 Multi-Variable Calculus (4 credits)
- MATH 210 Introduction to Differential Equations and Systems (4 credits)
- MATH 240 Linear Algebra (4 credits)
- MATH 301 Abstract Algebra I (4 credits)
- MATH 317 Real Analysis (4 credits)

#### Allied requirement

- CISC 130 Introduction to Programming and Problem Solving in the Sciences (4 credits)

or

*Note:* CISC 130 is recommended for this major

#### Plus one of the mathematics tracks below:

**Pure Mathematics Track**

###### Eight credits from the following:

- MATH 302 Abstract Algebra II (4 credits)
- MATH 419 Complex Variables (4 credits)
- MATH 420 Topology (4 credits)

###### Plus:

- Eight credits of courses MATH 300 or higher not already taken

#### Applied Mathematics Track

- MATH 315 Applied Mathematics and Modeling I (4 credits)
- MATH 316 Applied Mathematics and Modeling II (4 credits)

###### Plus eight credits from the following:

- MATH 300 Advanced Differential Equations (4 credits)
- MATH 302 Abstract Algebra II (4 credits)
- MATH 303 Statistics for the Applied Sciences (4 credits)
- MATH 313 Probability (4 credits)
- STAT 314 Mathematical Statistics (4 credits)
- MATH 385 Mathematical Methods of Numerical Analysis (4 credits)
- MATH 400 Dynamical Systems and Chaos (4 credits)
- MATH 419 Complex Variables (4 credits)
- MATH 420 Topology (4 credits)

#### Statistics Track

- MATH 313 Probability (4 credits)
- STAT 314 Mathematical Statistics (4 credits)
- STAT 333 Applied Statistical Methods: Regression, Time Series, Forecasting (4 credits)
- MATH 385 Mathematical Methods of Numerical Analysis (4 credits)

###### Plus:

- STAT 320 Statistics II (4 credits)

#### Math Education Track

- MATH 325 Geometry (4 credits)
- MATH 450 Advanced Mathematics: Exploration and Exposition (4 credits)

###### Plus:

- MATH 313 Probability (4 credits) and STAT 314 Mathematical Statistics (4 credits)

*or*

- MATH 303 Statistics for the Applied Sciences and any MATH 300+ not already included

## Minor in Mathematics

#### Complete the following:

- MATH 113 Calculus I (4 credits) (or 108-109)
- MATH 114 Calculus II (4 credits)

###### Plus at least four credits from the following:

- MATH 200 Multi-Variable Calculus (4 credits)
- MATH 210 Introduction to Differential Equations and Systems (4 credits)

###### Plus:

- A minimum of twelve additional credits in courses numbered above 200 (or approved by the department chair)

A student minoring in mathematics must successfully complete a minimum of 8 credits in mathematics numbered 200 and above at St. Thomas.

## Teacher Licensure

Elementary Education with a Co-major in Science, Technology, Engineering and Mathematics (STEM) for Elementary Education

Major in Mathematics with a Co-major in Secondary Education (5-12)

*See Education*

#### Placement

Entry-level mathematics courses require students to have an appropriate Math Placement level. The student’s ACT Math score or performance on the Math Placement Exam determines this placement level. Students that do not have the placement level required for their desired course can now take MATH 005 and/or MATH 006. These are 0-credit courses, offered every Fall, J-term and Spring semester. MATH 005 has no placement requirement, and successful completion would allow a student to take MATH 006, MATH 100 or MATH 101. MATH 006 requires a Math Placement Level of 101 or of MATH 005, and successful completion allows a student to take MATH 103 or MATH 108. Both MATH 005 and MATH 006 have affordable registration fees instead of regularly priced tuition, as they are 0-credit classes.

In some cases, students have earned AP credit for Math 113 Calculus I but elect not to transfer this credit to St. Thomas. In such a case, students should understand that if AP credit is declined, an ACT (or equivalent SAT) score of 28 or above or a St. Thomas math placement score of 76 or above is required in order to take Math 113 at St. Thomas.

Course Number | Title | Credits | |
---|---|---|---|

MATH 005 | Basic Math Skills | 0 | |

Description of course Basic Math Skills : | The objective of this course is to provide background knowledge necessary for students to place into MATH 006, MATH 100, or MATH 101. This course serves as a prerequisite for MATH 006, MATH 100, or MATH 101. Topics covered include the real numbers, operations with real numbers, first degree equations and inequalities, Cartesian coordinate system and lines, linear functions, and problem solving. This course does not satisfy the core requirement in Natural Science and Mathematical and Quantitative Reasoning. This non-credit course is typically offered during J-Term and the first half of the Fall and Spring semesters. | ||

MATH 006 | Basic Math Skills II | 0 | |

Description of course Basic Math Skills II : | The objective of this course is to provide background knowledge necessary for students to place into MATH 108. This course serves as a prerequisite for MATH 108. Topics covered include polynomials, rational expressions, exponents, and radicals, quadratic equations, problem solving. This course does not satisfy the core requirement in Natural Science and Mathematical and Quantitative Reasoning. Prerequisite: Successful completion of MATH 005 or a mathematics placement score of 101 or above. This non-credit course is typically offered during J-Term and the second half of Fall and Spring semesters. | ||

MATH 100 | Mathematical Sampler | 4 | |

Description of course Mathematical Sampler : | This survey of basic mathematical concepts includes both modern and historical perspectives. Emphasis is on the development and appreciation of mathematical ideas and their relationship to other disciplines. Topics include, among others: mathematical problem-solving, set theory, graph theory, an introduction to randomness, counting and probability, statistics and data exploration, measurement and symmetry, and recursion. Prerequisite: Successful completion of Math 005 or placement of MATH 101 or above. | ||

MATH 101 | Finite Mathematics | 4 | |

Description of course Finite Mathematics : | Elementary set theory, linear equations and matrices, linear programming, finite probability, applications primarily in business and the social sciences. Offered Fall, J-Term, Spring and Summer. Prerequisite: Placement of MATH 101 or above, or successful completion of MATH 005. | ||

MATH 103 | College Algebra | 2 | |

Description of course College Algebra : | The purpose of this course is to provide knowledge of pre-calculus topics necessary for MATH 111. This course serves as a prerequisite for MATH 111 and can also serve as a prerequisite for MATH 104. This two-credit course does not satisfy a student's core curriculum requirement in mathematics. Topics covered include solving equations, inequalities, and systems of equations; graphing functions; inverse functions, polynomials; complex numbers; rational functions; exponential functions; properties of logarithms and logarithmic functions; applications. Offered as a directed study in Fall and Spring. Note: Students who receive credit for this course may not receive credit for MATH 105, MATH 108, or MATH 109. Prerequisite: Math placement at 108 or above, or successful completion of MATH 006 | ||

MATH 104 | Trigonometry | 2 | |

Description of course Trigonometry : | The purpose of this course is to provide knowledge of trigonometric topics necessary for MATH 113. This course serves as a prerequisite for MATH 113. This 2-credit course does not satisfy a student's core curriculum requirement in mathematics. Topics covered include radian/degree measure; trigonometric and inverse trigonometric functions; graphs of trig functions; applications of trigonometry; analytic trigonometry; trigonometric formulae. Offered as a directed study in Fall and Spring. Prerequisite: Math placement at 111 or above, or a C‐ or above in MATH 103. NOTE: Students who receive credit for this course may not receive credit for MATH 105, MATH 108, or MATH 109. | ||

MATH 105 | Precalculus | 4 | |

Description of course Precalculus : | The real numbers; basic algebra; analytical treatment of the elementary functions emphasizing the exponential, logarithmic and trigonometric functions and their graphs. (This course is intended as preparation for 113 and does not fulfill a general graduation requirement.) Prerequisite: Palcement at MATH 105 or above. NOTE: Students who receive credit for MATH 105 may not receive credit for MATH 108 or 109. | ||

MATH 108 | Calculus with Review I | 4 | |

Description of course Calculus with Review I : | The first course of a two-course sequence designed to integrate introductory calculus material with the algebraic and trigonometric topics necessary to support that study. Review topics include: number systems, basic algebra, functions, the Cartesian coordinate system and graphing. Calculus topics include limits, continuity, derivatives for algebraic functions, applications of derivatives and more graphing. This course is intended only for students planning to take MATH 109 and does not satisfy the mathematics requirement in the core curriculum. Offered Fall, Spring and Summer. Prerequisite: Placement at MATH 108 or above, or successful completion of MATH 006. NOTE: Students who receive credit for MATH 108 may not receive credit for MATH 105, 111, or 113. | ||

MATH 109 | Calculus with Review II | 4 | |

Description of course Calculus with Review II : | The second course of a two-course sequence designed to integrate introductory calculus material with the algebraic and trigonometric topics necessary to support that study. Review topics include: exponential and logarithmic functions, trigonometric functions and their inverses and associated graphs. Calculus topics include: derivatives of the transcendental functions, applications of those derivatives and an introduction to integration. Offered Fall, Spring and Summer. Prerequisite: a grade of C- or better in MATH 108 NOTE: Students who receive credit for MATH 109 may not receive credit for MATH 105, 111, or 113. | ||

MATH 111 | Calculus/Business & Soc Sci | 4 | |

Description of course Calculus/Business & Soc Sci : | An introductory course in calculus with motivation and examples drawn from business and the social sciences whenever possible. Does not include the calculus of trigonometric functions. Offered Fall and Spring. Prerequisite: a grade of C- or above in MATH 103 or MATH 105 or placement at MATH 111 or above. Four years of high school mathematics, including college algebra, are also recommended as background for this course. Students who are considering taking MATH 114 should take MATH 113 instead of MATH 111. NOTE: Students who receive credit for MATH 111 may not receive credit for MATH 108, 109, or 113. | ||

MATH 112 | Calc of Trig Functions | 2 | |

Description of course Calc of Trig Functions : | This course is designed for students who have taken MATH 111 but need to have credit for MATH 113; it covers the material in MATH 113 that is not covered in MATH 111. This course serves as a prerequisite for MATH 114. This 2-credit course does not satisfy a student's core curriculum requirement in mathematics. Topics covered include trigonometric functions, inverse trig functions, trigonometric identities, solving trigonometric equations, limits of trigonometric functions, derivatives of trigonometric functions, and integrals of trigonometric functions, and applications. Successfully completing this course is equivalent to successfully completing MATH 113. Offered Fall and Spring as a directed study. Prerequisite: A C‐ or above in MATH 111. | ||

MATH 113 | Calculus I | 4 | |

Description of course Calculus I : | An introductory course in calculus: limits; derivatives and integrals of algebraic, exponential, logarithmic and trigonometric functions of one real variable; applications of the derivative in engineering and the natural sciences. Offered Fall, Spring and Summer. Prerequisite: a grade of C- or above in MATH 104 or 105 or placement at MATH 113 or above. Four years of high school mathematics, including college algebra and trigonometry, also are recommended as background for this course. NOTE: Students who receive credit for MATH 113 may not receive credit for MATH 108, 109, or 111. | ||

MATH 114 | Calculus II | 4 | |

Description of course Calculus II : | Techniques of integration; applications of integration; infinite series; parametric/polar equations. Offered Fall, Spring and Summer. Prerequisite: a grade of C- or above in MATH 112 or in MATH 113 or MATH 109 | ||

MATH 121 | Structures of Elem Math I | 4 | |

Description of course Structures of Elem Math I : | An examination of the mathematical underpinnings of the K-8 school curriculum with an emphasis on the conceptual understanding of mathematics. Topics include foundations of integer and rational arithmetic, notions of place-value and base, number sense and estimation, ratio and proportion, and mathematical problem-solving. This course is recommended as the first course in a three-course sequence in mathematics for prospective elementary teachers. Offered Fall and Spring. Prerequisites: MATH placement at or above 100 or a C‐ or above in MATH 005, and concurrent registration in any EDUC course (Click here for MaRC Placement Exam Information) | ||

MATH 122 | Structures of Elem. Math II | 4 | |

Description of course Structures of Elem. Math II : | An examination of the mathematical underpinnings of the K-8 school curriculum with an emphasis on the conceptual understanding of mathematics. Concepts of shape and space will be covered, which will include geometry, measurement, area, volume, surface area, symmetry, the geometry of motion and change, and problem solving. This course is recommended as the second in a three-course sequence in mathematics for prospective elementary teachers. Offered Fall and Spring. Prerequisite: A C‐ or above in MATH 121 or permission of instructor | ||

MATH 128 | Intro to Discrete Math | 4 | |

Description of course Intro to Discrete Math : | A survey of basic discrete mathematical concepts. Topics include: Boolean algebra, logic, analysis of algorithms, mathematical induction and matrices. Focus on applications to computer science. Offered Fall and Spring.Prerequisite: A C‐ or better in either Math 109, Math 111, or Math 113 and a C‐ or better in either CISC 130 or CISC 131, or instructor permission | ||

MATH 200 | Multi-Variable Calculus | 4 | |

Description of course Multi-Variable Calculus : | Vector algebra in two and three dimensions, partial derivatives, multiple integrals, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, divergence theorem. Offered Fall and Spring. Prerequisite: a grade of C- or higher in MATH 113 and 114 | ||

MATH 210 | Intro-Differ Equations & Syst | 4 | |

Description of course Intro-Differ Equations & Syst : | An introduction to ordinary differential equations (ODEs), with an emphasis on linear differential equations and linear systems, including applications. Topics covered include first-order equations, ODE models in the physical and biological sciences and engineering, numerical methods of solution, higher order linear equations, matrix tools, the role of eigenvalues and eigenvectors, and LaPlace transforms. Offered Fall and Spring. Prerequisite: a grade of C- or above in MATH 114 | ||

MATH 223 | Structures of Elem. Math III | 4 | |

Description of course Structures of Elem. Math III : | An advanced examination of the mathematical underpinnings of the K-8 school curriculum with an emphasis on the conceptual understanding of mathematics. Topics include counting, graph theory and other discrete topics, number theory, recursion, algebra and functions, probability and statistics. As the third course in a three-course sequence in mathematics for prospective elementary teachers, this course integrates uses of technology and problem solving in STEM applications appropriate for the K-8 classroom. Offered Fall and Spring. Prerequisites: A C‐ or above in MATH 121 and a C‐ or above in MATH 122 | ||

MATH 240 | Linear Algebra | 4 | |

Description of course Linear Algebra : | An introductory course in linear algebra, beginning with linear equations and matrix algebra. Subsequent topics include study of vector spaces, orthogonality, eigenvectors and inner products. The course combines theoretical and applied perspectives, including concepts of rigorous proof. Offered Fall and Spring. Prerequisite: A grade of C- or above in MATH 200, concurrent enrollment allowed. | ||

MATH 243 | Individual Study | 2 OR 4 | |

Description of course Individual Study : | No description is available. | ||

MATH 259 | Elements of Geometry & Stat | 4 | |

Description of course Elements of Geometry & Stat : | Intended for elementary education majors who plan a licensure endorsement in mathematics for grades 5-8. Includes intermediate concepts in geometry and statistics essential for a middle school teacher of mathematics. Topics will include: axiometric systems of geometry with emphasis on Books I and VI of Euclid's Elements; an introduction to non-Euclidean geometry; geometric and inductive reasoning, with applications; introduction to geometric probability and the geometric display of data; organization and analysis of data sets; statistical support of decisions, including applications in education; prediction; the role of randomness in both formal and empirical probability. Prerequisites: MATH 100 and 121 | ||

MATH 269 | Research | 2 OR 4 | |

Description of course Research : | No description is available. | ||

MATH 297 | Topics | 4 | |

Description of course Topics : | The subject matter of these courses will vary from year to year, but will not duplicate existing courses. Descriptions of these courses are available in the Searchable Class Schedule on Murphy Online, View Searchable Class Schedule NOTE: Depending on the subject matter of topics course, the course may or may not count towards a minor in Mathematics. | ||

MATH 298 | Topics | 4 | |

Description of course Topics : | The subject matter of these courses will vary from year to year, but will not duplicate existing courses. Descriptions of these courses are available in the Searchable Class Schedule on Murphy Online, View Searchable Class Schedule NOTE: Depending on the subject matter of topics course, the course may or may not count towards a minor in Mathematics. | ||

MATH 300 | Advanced Differential Equation | 4 | |

Description of course Advanced Differential Equation : | A second course in differential equations and their applications. Topics are selected from a continued study of linear differential equations and systems, Laplace transforms, series solution methods, non-linear equations and systems, partial differential equations and other topics chosen by the instructor. Offered spring of odd-numbered years. Prerequisite: A grade of C- or above in MATH 210 | ||

MATH 301 | Abstract Algebra I | 4 | |

Description of course Abstract Algebra I : | Properties of sets, relations and mappings; introduction to groups, rings and fields. Offered Spring. Prerequisite: A grade of C- or above in MATH 240 | ||

MATH 302 | Abstract Algebra II | 4 | |

Description of course Abstract Algebra II : | Topics in modern algebra with applications. Includes material selected from the theory of groups, rings, and fields; linear algebra; Boolean algebra and discrete structures. Offered fall of odd-numbered years. Prerequisite: A grade of C- or above MATH 301 | ||

MATH 303 | Statistics/Applied Sciences | 4 | |

Description of course Statistics/Applied Sciences : | Probability, Estimation, Hypothesis Testing, Analysis of Variance, Regression Analysis, Topics selected from Experimental Design, Statistical Process Control, Non-Parametric Methods, Factor Analysis as time permits. Offered Fall of even-numbered years. Prerequisite: A grade of C- or above in MATH 114 NOTE: Students who receive credit for MATH 303 may not receive credit for MATH 313 or STAT 314. | ||

MATH 313 | Probability | 4 | |

Description of course Probability : | Probability theory in discrete and continuous sample spaces; random variables and distribution functions; moments; the moment-generating function; functions of random variables; law of large numbers; central limit theorem. Offered Fall and Spring. Prerequisites: A grade of C- or above in MATH 200 (may be taken concurrently with consent of instructor) NOTE: Students who receive credit for MATH 313 may not receive credit for MATH 303. | ||

MATH 315 | Applied Math & Modeling I | 4 | |

Description of course Applied Math & Modeling I : | This is a topics course in applied mathematics. Course content will be drawn from topics that coincide with expertise of department members. Recent topics include finite element methods, techniques in scientific computing, wavelets and applications, mathematical biology, and weather modeling. Offered Fall. Prerequisites: A grade of C- or above in MATH 210 and 240, or permission of instructor. | ||

MATH 316 | Applied Math & Modeling II | 4 | |

Description of course Applied Math & Modeling II : | This is a second topics course in applied mathematics. It does not require MATH 315 as a prerequisite. Course content will be drawn from the topics listed under MATH 315. Offered Spring. Prerequisites: A grade of C- or above in MATH 210 and MATH 240, or permission of instructor. | ||

MATH 317 | Real Analysis | 4 | |

Description of course Real Analysis : | Topology of the real numbers. Functions of one real variable. Rigorous development of continuity and uniform continuity; differentiability; uniform convergence. Sequences and series. Offered Fall. Prerequisites: A grade of C- or above in MATH 240 | ||

MATH 325 | Geometry | 4 | |

Description of course Geometry : | Axioms for geometries; geometrical transformations and their invariants; non-Euclidean geometries; additional topics. Offered Spring of even-numbered years. Prerequisites: A grade of C- or above in MATH 114; MATH 128 or MATH 240 recommended. | ||

MATH 385 | Math Meths/Numerical Anal | 4 | |

Description of course Math Meths/Numerical Anal : | Rigorous mathematical treatment of standard topics in numerical analysis including solutions to linear and nonlinear systems, interpolation, numerical integration and differentiation, differential equations, and iterative techniques in matrix algebra. This course provides a theoretical foundation for the numerical solution of mathematical problems. Offered Fall of even-numbered years. Prerequisites: A grade of C- or above in MATH 210 and 240, or permission of instructor | ||

MATH 389 | Research | 2 OR 4 | |

Description of course Research : | No description is available. | ||

MATH 393 | Individual Study | 2 OR 4 | |

Description of course Individual Study : | No description is available. | ||

MATH 400 | Dynamical Systems & Chaos | 4 | |

Description of course Dynamical Systems & Chaos : | An introduction to discrete and continuous dynamical systems and applications with topics including: iterated mappings in one and two dimensions, phase-plane theory, nonlinear differential equations, and chaos. Additional topics will be chosen from among bifurcations, stability, attractors, Lyapunov functions, Julia sets and Mandelbrot sets. Offered Spring of even-numbered years. Prerequisite: A grade of C- or above in MATH 210 or MATH 240, or permission of instructor | ||

MATH 419 | Complex Variables | 4 | |

Description of course Complex Variables : | Analytic functions; theorems of Cauchy; Laurent series; residue calculus; entire and meromorphic functions; conformal mapping. Offered in Fall of odd-numbered years. Prerequisite: A grade of C- or above in MATH 210 and MATH 240, or permission of instructor | ||

MATH 420 | Topology | 4 | |

Description of course Topology : | Properties of Euclidean spaces; general spaces; mappings; separation properties; connectedness; compactness; metrizable spaces. Prerequisite: A grade of C- or above in MATH 240, or permission of instructor | ||

MATH 450 | Adv Math:Explor & Exposition | 4 | |

Description of course Adv Math:Explor & Exposition : | A capstone mathematics course for students seeking to teach secondary mathematics. Students make substantial oral and written presentations. Topics are included from discrete and continuous mathematics. Students use publications, e.g. The American Mathematical Monthly, Mathematics Magazine, Mathematical intelligencer and Scientific American, as well as standard texts, as sources for their work. Offered in Fall of even-numbered years. Prerequisite: one of MATH 301 or 317 (a C‐ or above in the completed course) with concurrent registration in the other; or permission of instructor. | ||

MATH 476 | Experiential Learning | 2 | |

Description of course Experiential Learning : | No description is available. | ||

MATH 484 | Seminar | 2 | |

Description of course Seminar : | No description is available. | ||

MATH 489 | Topics | 4 | |

Description of course Topics : | The subject matter of these courses will vary from year to year, but will not duplicate existing courses. Descriptions of these courses are available in the Searchable Class Schedule on Murphy Online, View Searchable Class Schedule | ||

MATH 495 | Individual Study | 2 OR 4 | |

Description of course Individual Study : | No description is available. |