The student dedicated to becoming a mathematics teacher values the AQB MAT Program’s commitment to the discipline with its authentic research projects in mathematics (the academic research project) and in mathematics education (the classroom research project). MAT’s strong cohort model and small class size offer support to students over the course of the program and into the first years of their teaching career.

**Foundations of Mathematics (required) 9201560 (4 Credits)**

This course is required in the M.A.T program in mathematics education and is designed to introduce the fundamentals of mathematical history, logic and concepts of formal proof. This is an introductory course for the purpose of developing certain concepts and techniques that is fundamental in modern approaches to the solution of applied problems. An appropriate selection of topics is based on the concepts of metric spaces, compactness, sequences and convergence, continuity, differentiation and integration, function sequences, contraction mapping theorem. Strong emphasis on proofs and applications. Prerequisite: Consent of program department.

**Linear Algebra and Geometry 9201562 (4 Credits)**

The course emphasizes conceptual understanding and communication of mathematical topics through modeling, problem solving, and technology. The two main themes throughout the course are linear algebra and vector geometry. A course sequence on modern applications of mathematics that involve matrices, basic properties of vectors of R2 and R3, dot product, orthonormal basis, cross product, linear transformations of Euclidean 2- and 3-Space and the classification of its rigid motions, symmetric bilinear forms, conics and quadrics. Linear transformations covered include rotations, reflections, shears and projections. Students study the matrix representations of linear transformations along with their derivations. The curriculum also presents affine geometry and affine transformations along with connections to computer graphics. This course also includes a review of relevant algebra and trigonometry concepts. Prerequisite: Foundations of Applied Mathematics.

**Topics in analysis 9201561 (4 Credits)**

The course provides the bridge between the theory of functions of real and complex variables and the numerous examples in which this theory is used. The intent is to extend the understanding of analysis using real variables to the complex plane, as well as to introduce some of the unique characteristics of mathematics done in the complex plain, particularly as applied to foundational problems associated with real and numerical analysis.

Topics will include floating point arithmetic, root finding for nonlinear equations, fixed point analysis, stability, interpolation theory, least squares methods for function approximation and numerical methods for integration. Measure and integration with emphasis on the real line and the plane. Measures and measurable functions, Lusin and Egoroff theorems, Lebesgue integral. Complex numbers considered algebraically and geometrically, polar form, powers and roots, derivative of complex-valued functions, analyticity, Cauchy-Riemann equations. Prerequisite: Foundations of Applied Mathematics.

**Probability and Statistics 9201564 (4 Credits)**

Probability is an important and complex field of study. Fortunately, only a few basic issues in probability theory are essential for understanding statistics. These basic issues are covered in this course, including, sample space, discrete and continuous random variables, probability distributions, joint and conditional distributions, expectation, transformation of random variables, limit theorems.

This course will cover the sampling and analysis of various types of data from a statistical perspective. It is intended to give graduate students, who have some basic preparation in statistics, a deeper and richer understanding of how statistical methods are related to the science and how facility with statistics can help to answer many research questions.

This course will focus on designing sampling, data summaries and descriptive statistics; introduction to a statistical computer package; statistical inference of univariate data (Confidence Intervals and Testing of hypotheses); statistical inference for bivariate data: inference for intrinsically linear simple regression models.

**Geometry 9201522 (4 Credits)**

The course has the following goals:

- To learn new mathematics through inquiry, using open-ended problems, hands- on explorations, written and small group dialogs, and non-test based assessments.
- To develop an experiential understanding of the geometric properties of surfaces in 2 and 3-dimensional space, and use that understanding to devise their own mathematical arguments and proofs.
- To introduce students to many topics from geometry such as curve theory, spherical and hyperbolic geometry, detail of surfaces, curvature, torsion , and analytic geometry.

**Special topics in Mathematics 9201563 (4 Credits)**

This occasionally offered course will allow the student to be exposed to topics in mathematics that are not offered as part of our regular sequence of mathematics courses. It will allow students to gain appreciation for the breadth of fields that are part of modern mathematics.