The focus of this course is the foundational ideas of grades K-8 mathematics. The purpose is to engage prospective teachers in (re)discovering the real number system in order to develop a deep understanding of number meanings, representation, operations, algorithms, and properties. Through intuition and imagination, rather than rigidly following prescribed methods, students will explore models for arithmetic, consideration of children’s thinking about numbers, and investigations with technology.
This course investigates foundational ideas of grades K-8 mathematics. The focus is on thinking about mathematical concepts that are currently prominent in elementary schools from the perspective of teaching. Mathematical tasks include a deep analysis of concepts, consideration of children’s thinking, and investigations with technology. Topics include two and three dimensional geometry, transformations,area, volume, surface area, measurements, statistics, and probability.
For students with one or two years of high school algebra. This course is at the level of college algebra, but is not focused on algebra. It stresses application of mathematics in careers of non-scientists and in the everyday lives of educated citizens, covering basic mathematics, logic, and problem solving in the context of real-world applications.
Algebra review, functions and graphs, logarithmic and exponential functions, analytic geometry, trigonometric functions, trigonometric identities and equations, mathematical induction, complex numbers. Students completing this course are prepared to enter calculus.
Limits and continuity for functions of one real variable. Derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions. Applications of the derivative. Introduction to related numerical methods.
Techniques of integration, numerical integration, and applications of integrals. Infinite series including Taylor series. Introduction to differential equations. Calculus in polar coordinates.
The calculus of vector-valued functions, functions of several variables, and vector fields. Includes vector operations, equations of curves and surfaces in space, partial derivatives, multiple integrals, line integrals, surface integrals, and applications.
Bridges the gap between computational, algorithmic mathematics courses and more abstract, theoretical courses. Emphasizes the structure of modern mathematics: axioms, postulates, definitions, examples conjectures, counterexamples, theorems, and proofs. Builds skill in reading and writing proofs. Includes careful treatment of sets, functions, relations, cardinality, and construction of the integers, and the rational, real, and complex number systems.
Vector spaces, linear independence, basis and dimension, linear mappings, matrices, linear equations, determinants, Eigen values, and quadratic forms.
Methods of solving first and second order differential equations, applications, systems of equations, series solutions, existence theorems, numerical methods, and partial differential equations.
Probability as a mathematical system, random variables and their distributions, limit theorems, statistical inference, estimation, decision theory and testing hypotheses.
Topics to be selected from counting techniques, mathematical logic, set theory, data structures, graph theory, trees, directed graphs, algebraic structures, Boolean algebra, lattices, and optimization of discrete processes.
This course explores the mathematical foundations of algorithms used in the field of Data Science, typically taken after a course in mathematical statistics. It includes the study of classification and regression techniques, robust regression, decision trees, support vector machines, neural networks, cross-validation techniques, forecasting models, and Topological data analysis. The course includes a data-driven project that requires the student to propose a question and gather, clean, and analyze data to present a response to a real-world problem.
The history of mathematics from ancient to modern times. The mathematicians, their times, their problems, and their tools. Major emphasis on the development of geometry, algebra, and calculus.
A review of Euclidean geometry, an examination of deficiencies in Euclidean geometry, and an introduction to non-Euclidean geometrics. Axiomatic structure and methods of proof are emphasized.
A survey of the classical algebraic structures taking an axiomatic approach. Deals with the theory of groups and rings and associated structures, including subgroups, factor groups, direct sums of groups or rings, quotient rings, polynomical rings, ideals, and fields.
An introduction to topological structures from point-set, differential, algebraic, and combinatorial points of view. Topics include continuity, connectedness, compactness, separation, dimension, homeomorphism, homology, homotopy, and classification of surfaces.
This course develops the logical foundations underlying the calculus of real-valued functions of a single real variable. Topics include limits, continuity, uniform continuity, derivatives and integrals, sequences and series of numbers and functions, convergence, and uniform convergence.
A study of the concepts of calculus for functions with domain and range in the complex numbers. The concepts are limits, continuity, derivatives, integrals, sequences, and series. Topics include Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formulas, Taylor and Laurent series, and special functions.
This course reviews and correlates the courses in the mathematics major. Each student is responsible for preparing the review of one area. Students also read papers from contemporary mathematics journals and present them to the class. The course uses the ETS mathematics major exam.