Mathematics

Every field of inquiry that deals with data uses methods of descriptive statistics to summarize and describe their data.  Every field of inquiry that deals with data seeks to draw inference beyond the available data.  This course introduces widely-used methods of descriptive statistics and methods of statistical inference through the lens of applied mathematics.  This course is not recommended to students who have taken and passed BIO 205.

An introduction to probability theory with applications to statistics:  basic combinatorics, permutations and combinations, sample space, events, mutual exclusivity, independence, conditional probability, Bayes’ theorem, random variables, distribution, expectation, variability, Chebyshev’s theorem, joint distribution, binomial distribution, normal distribution, Central Limit Theorem, estimation of and confidence intervals for binomial parameter, Bayesian approach to inference.  Further topics may include theory of sampling, covariance, correlation, least squares, regression.  Note: this is not a statistical methods course of the type that may be expected in areas such as health or social sciences, though it provides a good foundation for such courses.

Computer science is the study of problem-solving strategies called algorithms.  In this course, students will develop the essential skills of programming, examine select algorithms and data structures, and learn the broad strokes of the theory of computing, which includes formal languages, Turing machines, and the notions of universality, computability, and intractability regarding computational problems. 

This course is an introduction to the field of network science with an emphasis on the mathematical aspects and properties of networks. A network is an accessible yet powerful structure used to represent and study relationships. In practice, networks model different phenomena arising in fields such as biology, economics, sociology, computer science, and physics. In this class, we’ll look rigorously at the mathematical structure of networks (this field is often referred to as graph theory), while also considering real world models, such as spread of disease, web link analysis, and financial networks. This course has no prerequisites.

Linear algebra is the study of linear equations, matrices, vectors, linear functions, and vector spaces, as well as the theory and applications of linearity. The central ideas in linear algebra are so powerful that their influence seeps into many other branches of mathematics and statistics, the sciences, engineering, and economics. In this course we will develop a mastery of the particular tools of linear algebra, while making a dedicated effort to understand the concepts behind these tools and the relationships between them.

This course is an introduction to multivariable calculus. Topics include vectors in the plane and in space, limits and continuity, partial derivatives, directional derivatives, gradient, tangent planes, multivariable optimization and Lagrange multipliers, multiple integration, vector fields, line integrals, divergence, curl, and the theorems of Green, Gauss and Stokes.

Basic ideas of mathematical modeling; first order differential equations, first order systems, and linearity.  Other topics selected from Second order equations, forcing, nonlinear systems, Laplace transforms, numerical methods.

Through the lens of discrete mathematics, this course will serve as an introduction to formal proof writing techniques and advanced mathematics. Proof writing is the powerful process of demonstrating through formal argument that a statement or claim is correct in mathematical language. Topics covered in this class include combinatorics (methods of counting things), number theory (study of integers and prime numbers), and graph theory (theoretical study of networks), with an emphasis on creative problem solving and learning to read and write rigorous proofs. While no formal prerequisite is required, a previous math class at SUA or high school equivalent is strongly encouraged.