# Mathematics

## School

School of Science, Engineering and Technology

## School Dean

## Department

## Department Chair

Mathematics is more than just the theory of numbers. It discovers tools from which a quantitative understanding of our world is made possible. Moreover, the language of mathematics is truly a universal language, transcending ethnic, societal, and national boundaries. Finally, mathematics also is a critical filter, opening doors to exciting and high-paying careers in business, government, teaching and research.

Students majoring in mathematics at St. Mary's University are exposed to the theoretical foundations of mathematics and experience its applications in a variety of disciplines. Innovative teaching and learning environments allow students to develop critical thinking and general problem solving strategies. In addition, our mathematics graduates understand the power and usefulness of computers equipped with graphing and symbolic algebra. Classroom assignments enhance the students' abilities to communicate mathematics effectively- both orally and in writing. Students have the opportunity to hear about current research and present their own research at the undergraduate mathematics seminar.

Math courses cannot be transferred after enrolling as a student at St. Mary's University. Eligibility for enrollment in Math courses is based on SAT/ACT scores, COMPASS math placement scores or college transfer credit.

**Mathematics Placement Policy**

New students will be placed in the appropriate Math course based on their SAT or ACT Math score.

Students who do not satisfy either **SAT Math ≥ 470** or **ACT Math ≥ 17 **may only enroll in:

**MT0301 Intermediate Algebra**

Students with **SAT Math ≥ 470** or **ACT Math ≥ 17** may enroll in:

**MT 1301 Concepts I**

**MT 1302 Concepts II**

**MT 1303 College Algebra**

**MT 1305 Finite Mathematics**

Students with **SAT Math ≥ 520** or **ACT Math ≥ 22** may enroll in:

**MT 1301 Concepts I**

**MT 1302 Concepts II**

**MT 1303 College Algebra**

**MT 1305 Finite Mathematics**

**MT 1306 Calculus for Business **

**MT 1411 PreCalculus **

**MT 2303 Introduction to Probability & Statistics **

Students with **SAT Math ≥ 520 or ACT Math ≥ 22** may seek advanced placement into **MT 2412** **Calculus** by taking the COMPASS Trigonometry test. A score on the **COMPASS Trigonometry Test ≥ 46** is required to enroll in **MT 2412 Calculus**.

Students who do not have an ACT or SAT Math score will be required to take the COMPASS Math Test in order to be placed in a Math course.

Depending on the major, new students may fulfill the math requirement via IB, AP or Dual Credit.

**All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.**

**MT 0301. Intermediate Algebra. 3 Semester Hours.**

Development of algebraic skills necessary as a prerequisite for students not meeting standards for entry into credit courses. This is a non-credit course. (Fall;Spring).

**MT 0401. Math Skills. 4 Semester Hours.**

This non-credit course reviews fundamental mathematics and algebraic skills necessary for entry-level college math courses. Students are placed in the course based on their SAT/ACT Math scores. Weekly participation in a peer-led-team-learning (PLTL) group study session is required. (Fall;Spring).

**MT 1301. Mathematical Logic for the Humanities. 3 Semester Hours.**

A mathematics course designed for students in the humanities. A variety of concepts are covered. Topics will be drawn from the following areas: introductory treatments of sets, logic, number systems, number theory, geometry, relations, functions, graph theory, optimization algorithms, linear programming, and coding theory. Prerequisite: MT 0301 or MT 0401 or SAT Math ≥ 470 or ACT Math ≥ 17.
(Fall; Spring).

**MT 1302. Mathematical Topics in the Social Sciences. 3 Semester Hours.**

A mathematics course designed for students in the social sciences. A variety of mathematical topics will be covered, with an emphasis on civically-minded applications: personal finance, voting schemes, apportionment and other forms of resource distribution, introductory probability and statistics, and other topics to be selected by the instructor. The course will be project-oriented. The computational capabilities of Microsoft Excel will be explored. Prerequisite: MT0301 or MT0401 or SAT Math ≥ 470 or ACT Math ≥ 17. (Fall; Spring).

**MT 1303. College Algebra. 3 Semester Hours.**

Linear and quadratic functions, graphing, inverse functions. Polynomial, exponential, logarithmic functions and their graphs. Linear and exponential regression models. Systems of equations, matrices and determinants.
Prerequisite:MT 0301 or MT 0401 or SAT Math ≥ 470 or ACT Math ≥ 17. (Fall; Spring).

**MT 1305. Finite Mathematics. 3 Semester Hours.**

Systems of linear equations and matrices, mathematics of finance, probability, probability distributions and statistics. Excel software package will be used. Prerequisite: MT 0301 or MT 0401 or SAT Math ≥ 470 or ACT Math ≥ 17. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 1306. Calculus for Business. 3 Semester Hours.**

Differential and integral calculus of algebraic, exponential, and logarithmic functions and models with applications to business. Excel software package will be used. Prerequisite: MT 1303 or MT 1411 or SAT Math ≥ 520 or ACT Math ≥ 22
(All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 1411. Precalculus. 4 Semester Hours.**

Functions, graphing, and inverse functions. Properties and graphs of exponential and logarithmic functions. Trigonometric functions of angles with right triangle applications. Trigonometric functions of real numbers, inverses, graphs. Trigonometric identities and equations, conic sections and polar coordinates. Prerequisite: MT 1303 or SAT Math ≥ 520 or ACT Math ≥ 22 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.)
(Fall; Spring).

**MT 2303. Introduction to Probability and Statistics. 3 Semester Hours.**

This is a non-calculus introduction to the basic principles and practices of statistics. The course begins with the description and display of one - variable and two variable data sets, including histograms, stemplots, and scatterplots, as well as the computation and interpretation of mean, standard deviation, and correlation. Sufficient probability theory is developed to provide the foundation for the simpler inferential methods treated in the course: confidence intervals and tests of significance for one and two populations. A statistical software package is used throughout the course, including student homework projects. Prerequisite: MT 1303 or MT 1306 or MT1411 or MT2412 or SAT Math ≥ 520 or ACT Math ≥ 22
(All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 2306. Business Statistics. 3 Semester Hours.**

This course is designed as an introduction to basic statistical concepts and their applications for business. Topics covered include organizing and displaying data, descriptive statistics, sampling distributions, confidence intervals and hypotheses testing, simple linear regression and correlation. Microsoft Excel is used to help with problem solving. Pre-requisites: MT 1305 or MT1411 or MT2412 or SAT Math ≥ 520 or ACT Math ≥ 22.

**MT 2412. Calculus I. 4 Semester Hours.**

Limits, continuity, derivatives, and integrals of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions; indeterminate forms; applications. Prerequisite: MT 1411 or COMPASS Trigonometry score ≥ 46.
(All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 2413. Calculus II. 4 Semester Hours.**

Applications of integrals; formal integration techniques; numerical integration; improper integrals; sequences; series; power series; Taylor series; applications of series. Prerequisite: MT 2412 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 3304. Essential Elements in Math I. 3 Semester Hours.**

A study of topics from elementary mathematics with a problem - solving approach. The course is designed for and is to be taken only by elementary education majors. Topics for the course include problem-solving, sets, numeration systems, the real numbers, number theory, probability, statistics, geometry, motion geometry, and concepts of measurement. Prerequisite: MT 1303 or MT 1411 or MT 2412 or SAT Math ≥ 470 or ACT Math ≥ 17 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall).

**MT 3305. Essential Elements in Math II. 3 Semester Hours.**

Strategies for teaching are developed concurrently with content from the elementary mathematics curriculum. National and state educational standards in mathematics will be addressed. An in-depth analysis of the state assessment standards for both teachers and students will be included. Students will learn and experience research based instructional strategies that promote mathematical excellence in the classroom. This course is intended for Elementary Education majors. (Fall).

**MT 3306. Essential Elements of Mathematics III. 3 Semester Hours.**

A study of topics from elementary mathematics with an inquiry-based learning approach. Topics for the course include foundations of geometry, measurement, area, volume, geometry of motion and change, probability and statistics, and pictorial representation of data. Technology will be integrated throughout the course. - Prerequisite: MT 1303 or MT 1411 or MT 2412 or SAT Math ≥ 470 or ACT Math ≥ 17 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring).

**MT 3311. Differential Equations. 3 Semester Hours.**

First-order differential equations; linear differential equations of second order and higher; applications; systems of linear differential equations; the Laplace Transform. (Fall; Spring).

**MT 3312. Advanced Math for Engineers. 3 Semester Hours.**

Linear algebra; fundamental concepts of classical optimization; vector differential calculus, vector fields; complex variables; calculus of several variables. Prerequisite: MT 3311 or MT 3324 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) ( Spring).

**MT 3313. Advanced Math for Industrial Engineers. 3 Semester Hours.**

Multidimensional differential calculus with emphasis on real-valued functions. Fundamental concepts of classical optimization, non-linear programming and elementary linear algebra. Prerequisites: MT 3311 or MT 3324. Students can not receive credit for both MT 3313 and MT 3315. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring).

**MT 3315. Advanced Math for Electrical Engineers. 3 Semester Hours.**

Vector differential calculus with emphasis on gradient, divergence and curl. Vector integral calculus with emphasis on Green's theorem, Stoke's theorem and the divergence theorem of Gauss. Elementary complex algebra and functions, Elementary linear algebra. Prerequisites: MT 2413. Students cannot receive credit for both MT 3313 and MT 3315. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring).

**MT 3321. Introduction to Modern Algebra. 3 Semester Hours.**

Algebraic structures with emphasis on the theory of groups. Prerequisite: MT 2413 and MT 3323. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring).

**MT 3323. Discrete Math Structures. 3 Semester Hours.**

Logic, argument forms, methods of proof, proof writing, set theory, counting principles, recursion relations, graphs and trees. Prerequisite: MT 1303 or MT 1411 or MT2412 or SAT Math ≥ 520 or ACT Math ≥ 22 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 3324. Linear Algebra. 3 Semester Hours.**

Linear systems and matrices; determinants; vectors and vector spaces; linear transformations and matrices, eigenvalues and eigenvectors; applications. A computer software package is integrated throughout the course. (Spring).

**MT 3361. History of Math. 3 Semester Hours.**

The history of Mathematics is covered from the time of Pythagoras to the creation of non- Euclidean geometries in the mid- 19th century. This course could be taken by non- Majors.

**MT 3372. Math Modeling. 3 Semester Hours.**

Creative model construction and the modeling process, model fitting and models requiring optimization, empirical model construction, modeling dynamic behavior. Prerequisite: MT 3311 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring only).

**MT 3375. Theory of Interest. 3 Semester Hours.**

An introductory course covering topics related to interest theory and financial derivatives. Topics will include the growth of money, equations of value and yield rates, annuities, amortizations, bonds, and stocks. Additional advanced topics from financial derivatives may also be included. This course is suitable for students intending to take professional actuarial exams. (Odd-year Fall only).

**MT 3384. Topics in Applied Statistics. 3 Semester Hours.**

One semester courses currently available under the following titles: 1) Introduction to Non- parametric Statistical Inference; 2) Introduction to Applied Regression and Correlation; 3) Fundamentals of Sampling; 4) Analysis of Variance. Prerequisite: MT 2303. When different topics are treated, the number may be repeated for additional credit. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.).

**MT 3392. Elementary Math Analysis. 3 Semester Hours.**

Sequences, subsequences, convergence, Heine-Borel Theorem, functions, limits, continuity, uniform continuity, compactness, derivatives, Mean-Value Theorem, L'Hospital's Rule, Inverse Function Theorem, Riemann integration, and Fundamental Theorem of Calculus. Emphasis is on rigorous proof and communicating mathematics in verbal and written form. Prerequisite: MT 2413 and MT 3323 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Even-year Fall Only).

**MT 3414. Calculus III. 4 Semester Hours.**

Partial derivatives, multiple integration, three-dimensional vector calculus. Prerequisite: MT 2413. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Spring only).

**MT 4311. Complex Variables. 3 Semester Hours.**

Complex numbers, analytic functions, elementary functions, mapping by elementary functions, integrals, series, residues and poles. Prerequisite: MT 3414 and 3323 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) ( Odd-year Fall only).

**MT 4312. Boundary Value Problems. 3 Semester Hours.**

Fourier Series, Fourier and Laplace transforms and boundary value problems of partial differential equations. Prerequisite: MT3311 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.).

**MT 4331. Probability Theory. 3 Semester Hours.**

Discrete and continuous probability spaces; random variables and their distribution. Prerequisite: MT 2413 or consent of instructor (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 4332. Statistics. 3 Semester Hours.**

Descriptive statistics. Sampling distributions, estimation, tests of hypotheses, regression and correlation. Prerequisite: MT 2413 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall; Spring).

**MT 4333. Applied Statistical Methods. 3 Semester Hours.**

This course will cover regression analysis and time series. The topics in regression will include: single and multiple linear regression, hypothesis testing and confidence intervals, testing of models, data analysis and appropriateness of models. The topics in time series/forecasting will include: linear time series models, moving average, regression-based and/or ARIMA models, estimation, data analysis and forecasting with time series models, forecast errors and confidence intervals. Prerequisite: MT4332 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Even-year Fall only).

**MT 4341. Modern Geometry. 3 Semester Hours.**

A study of elementary geometry from an advanced point of view. Topics include the history of geometry, the axiomatic method and theorem proving, Euclidean constructions, non- Euclidean geometries, curriculum and learning issues involving geometry, and technology and the use of software in the teaching of geometry. ( Most semesters, but Spring course).

**MT 4342. Topics in Advanced Mathematics. 3 Semester Hours.**

Topics to be chosen by instructor. When different topics are treated, MT 4342 may be repeated for additional credit on approval of the Chairperson. Prerequisite: MT 2413, MT 3323, and consent of instructor.

**MT 4351. Numerical Analysis I. 3 Semester Hours.**

Roots of equations, interpolation and approximation, numerical differentiation and integration, solutions of linear systems of equations and matrix inversion. Prerequisite: MT 2413 and MT 3311 (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Fall only).

**MT 4352. Numerical Analysis II. 3 Semester Hours.**

The numerical solution of ordinary differential equations; introduction to partial differential equations; numerical solutions of nonlinear systems of equations. Prerequisite: MT 3311 and MT 4351. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.).

**MT 4395. Senior Mathematics Seminar. 3 Semester Hours.**

A capstone course for mathematics majors in the Bachelor of Sciences programs. Each student selects a mathematical area of interest, researches the selected area, generates a reference list and research paper, and presents the paper to a seminar of faculty and students. Advanced mathematical topics will also be convered (topics may vary). Prerequisite: MT3324 and either MT3321 or MT3392 or MT4331. (All courses serving as prerequisites in the School of Science, Engineering and Technology must be completed with a “C” or better in order to advance to the next sequenced course.) (Odd-year Fall only).

**MT 4396. Actuarial Exam Preparation. 3 Semester Hours.**

This course will prepare students in the actuarial sciences concentration for either the professional actuarial Exam P/1 (Spring semester, odd years), or the professional actuarial Exam FM/2 (Spring semester, even years). Exam P/1: Topics reviewed will cover calculus, general probability, random variables with univariate probability distributions, random variables with multivariate probability distributions, moment generating functions, transformations, and other topics typically encountered on Exam P/1. Exam FM/2: Topics reviewed will cover the time value of money, annuities, loans, bonds, general cash flows and portfolios, immunization, interest rate swaps, determinants of interest rates, and other topics typically encountered on Exam FM/2. Can only be taken by students seeking the B.A. in Mathematics with a concentration in Actuarial Science degree or students with a strong interest in passing actuary exams.
Prerequisite: MT 3375 or MT 4331, and consent of instructor. (Spring).

**MT 5160. Independent Study. 1 Semester Hour.**

Prerequisite: Consent of instructor and Chairperson.

**MT 5260. Independent Study. 2 Semester Hours.**

Prerequisite: Consent of instructor and Chairperson.

**MT 5311. Topics in Analysis. 3 Semester Hours.**

When different topics are treated, MT 5311 may be repeated for additional credit on approval of the Chairperson. Prerequisite: MT 3414 or consent of instructor.

**MT 5360. Independent Study. 3 Semester Hours.**

Prerequisite: Consent of instructor and Chairperson.

Ryan Dunning, Ph.D.

Associate Professor

Michael Lecocke, Ph.D.

Associate Professor

Kathryn Lemons, M.S.

Instructor

Anna Lurie, Ph.D.

Associate Professor

Ian Martines, Ph.D.

Associate Professor

Jason Shaw, Ph.D.

Associate Professor

Paul Uhlig, Ph.D.

Professor

Mary Wagner-Krankel, Ph.D.

Professor