Mathematics

College Algebra is the introductory course in algebra. The course is designed to familiarize learners with fundamental mathematical concepts such as inequalities, polynomials, linear and quadratic equations, and logarithmic and exponential functions.

This is an introductory course in Number Theory for students interested in mathematics and the teaching of mathematics. The course begins with the basic notions of integers and sequences, divisibility, and mathematical induction. It also covers standard topics such as Prime Numbers; the Fundamental Theorem of Arithmetic; Euclidean Algorithm; the Diophantine Equations; Congruence Equations and their Applications (e.g. Fermat's Little Theorem); Multiplicative Functions (e.g. Euler's Phi Function); Application to Encryption and Decryption of Text; The Law of Quadratic Reciprocity.

The complex number system, analytic functions, the Cauchy integral theorem, series representation, residue theory, and conformal mapping.

In this elementary introductory course, we develop much of the language and many of the basic concepts of differential geometry in the simpler context of curves and surfaces in ordinary 3 dimensional Euclidean space. Our aim is to build both a solid mathematical understanding of the fundamental notions of differential geometry and sufficient visual and geometric intuition of the subject.

Probability & Statistics introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods.

Covers linear, quadratic, exponential, and logarithmic functions; systems of linear equations; elementary linear programming; matrix algebra; inverse; and mathematics of finance.

Covers limits, continuity, derivatives, indefinite and definite integrals, and applications.

This course is an introduction to abstract algebra and will survey basic algebraic systems-groups, rings, and fields. Although these concepts will be illustrated by concrete examples, the emphasis will be on abstract theorems, proofs, and rigorous mathematical reasoning.

The course offers a solid introduction in modern algebra by covering basic concepts that are at the foundation of modern mathematics. It continues the first course in algebra which introduced groups. This course will emphasize the understanding of the concepts, through examples and proof writing. The course will discuss the foundations of ring and field theory: notion of ideals, fundamental theorems of isomorphism for rings, polynomial rings, divisibility in rings, field extensions, algebraic extensions, vector spaces, module theory and other topics if time permits.

This course introduces topology, covering topics fundamental to modern analysis and geometry.

A continuation of MATH-197. This course is an introduction to abstract algebra and will survey basic algebraic systems-groups, rings, and fields. Although these concepts will be illustrated by concrete examples, the emphasis will be on abstract theorems, proofs, and rigorous mathematical reasoning.

A continuation of MATH-198. The course offers a solid introduction in modern algebra by covering basic concepts that are at the foundation of modern mathematics. It continues the first course in algebra which introduced groups. This course will emphasize the understanding of the concepts, through examples and proof writing. The course will discuss the foundations of ring and field theory: notion of ideals, fundamental theorems of isomorphism for rings, polynomial rings, divisibility in rings, field extensions, algebraic extensions, vector spaces, module theory and other topics if time permits.

Algebra 1 introduces students to variables, algebraic expressions, equations, inequalities, functions, and all their multiple representations. In this class, students will develop the ability to explore and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. This course lays the foundation for mathematical literacy that will help students be successful in every subsequent course in mathematics.

Algebra II is a second-year algebra course with an overall theme of problem solving. The overriding themes of the course are: algebraic manipulation, equation solving, graphing, and probability. This Algebra II course is designed to prepare students for college level mathematics.

This course covers standard topics such as Prime Numbers; the Fundamental Theorem of Arithmetic; Euclidean Algorithm; the Diophantine Equations; Congruence Equations and their Applications (e.g. Fermat's Little Theorem); Multiplicative Functions (e.g. Euler's Phi Function); Application to Encryption and Decryption of Text; The Law of Quadratic Reciprocity.

A continuation of MATH-195. Covers linear, quadratic, exponential, and logarithmic functions; systems of linear equations; elementary linear programming; matrix algebra; inverse; and mathematics of finance.

A continuation of MATH-196. Covers limits, continuity, derivatives, indefinite and definite integrals, and applications.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations.

A continuation of MATH-222. This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations.

This course will cover various techniques for solving linear and nonlinear partial differential equations (PDEs) arising from physical and engineering applications; this includes both analytical and numerical methods.

Complex Analysis, in a nutshell, is the theory of differentiation and integration of functions with complex-valued arguments z = x +i y , where i = (-1)1/2 . While the course will try to include rigorous proofs for many - but not all - of the material covered, emphasize will be placed on applications and examples.

A continuation of MATH-229. Complex Analysis, in a nutshell, is the theory of differentiation and integration of functions with complex-valued arguments z = x +i y , where i = (-1)1/2 . While the course will try to include rigorous proofs for many - but not all - of the material covered, emphasize will be placed on applications and examples.

This will be a basic Functional Analysis course covering the three major theorems, the Hahn- Banach theorem, Uniform boundedness principle and the Open mapping-Closed Graph theorem. We shall also do Fredholm theory as it is useful to people doing PDE and also the Spectral theory of self-adjoint and bounded operators. The course will emphasize applications of Functional Analysis to PDE via illustrations in the use of Sobolev spaces.

A continuation of MATH-231. This will be a basic Functional Analysis course covering the three major theorems, the Hahn-Banach theorem, Uniform boundedness principle and the Open mapping-Closed Graph theorem. We shall also do Fredholm theory as it is useful to people doing PDE and also the Spectral theory of self-adjoint and bounded operators. The course will emphasize applications of Functional Analysis to PDE via illustrations in the use of Sobolev spaces.

First-order scalar equations: geometry of integral curves, symmetries and exactly soluble equations; existence, uniqueness and dependence on parameters with examples. Systems of first-order equations, Hamilton's equations and classical mechanics, completely integrable systems. Higher-order equations. Initial value problems for second order linear equations, series solutions and special functions. Boundary value problems with applications. Introduction to perturbation theory and stability.

A continuation of MATH-234. First-order scalar equations: geometry of integral curves, symmetries and exactly soluble equations; existence, uniqueness and dependence on parameters with examples. Systems of first-order equations, Hamilton's equations and classical mechanics, completely integrable systems. Higher-order equations. Initial value problems for second order linear equations, series solutions and special functions. Boundary value problems with applications. Introduction to perturbation theory and stability.

Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series.

A continuation of MATH-236. Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series.

Fourier series and integrals. The Laplace, heat, and wave equations: Solution by separation of variables. D'Alembert's solution of the wave equation. Boundary-value problems.

This course cover selected topics in statistical methods and research workflow related to statistical analysis. The topics covered are typically not included in statistical methods courses at the Master's Level. In academic and applied research in sociology and allied disciplines, methods knowledge is key. The same holds for individuals with sociology degrees in business and government roles for. Statistical social science is moving forward at high speed, and this course delivers practical and theoretical knowledge that allow students to do cutting-edge analyses and implement efficient workflows.

Theory and applications of mathematical models of dynamical systems (discrete and continuous). Topics include linear and non-linear equations, linear and non-linear systems of equations, bifurcation, chaos and fractals.

Continuation of MATH-243. Theory and applications of mathematical models of dynamical systems (discrete and continuous). Topics include linear and non-linear equations, linear and non-linear systems of equations, bifurcation, chaos and fractals

A survey of mathematical methods for the solution of problems in the applied sciences and engineering. Topics include: ordinary differential equations and elementary partial differential equations. Fourier series, Fourier and Laplace transforms, and eigenfunction expansions.

Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics.

This course is an introduction to the numerical analysis. The primary objective of the course is to develop the basic understanding of numerical algorithms and skills to implement algorithms to solve mathematical problems on the computer. a) Basic concepts: round-off errors, floating point arithmetic, Convergence.

A continuation of MATH-247. This course is an introduction to the numerical analysis. The primary objective of the course is to develop the basic understanding of numerical algorithms and skills to implement algorithms to solve mathematical problems on the computer. a) Basic concepts: round-off errors, floating point arithmetic, Convergence.

This first course will cover the basics of point-set topology. Meeting Time The course meets on MWF at 12, in Science Center 507. Topological spaces, continuous maps, and convergence.

Algebraic topology uses techniques from abstract algebra to study how (topological) spaces are connected. Most often, the algebraic structures used are groups (but more elaborate structures such as rings or modules also arise).

A continuation of MATH-252. Algebraic topology uses techniques from abstract algebra to study how (topological) spaces are connected. Most often, the algebraic structures used are groups (but more elaborate structures such as rings or modules also arise).

This course will introduce the theory of the geometry of curves and surfaces in threedimensional space using calculus techniques, exhibiting the interplay between local and global quantities.

A continuation of MATH-259. This course will introduce the theory of the geometry of curves and surfaces in three-dimensional space using calculus techniques, exhibiting the interplay between local and global quantities.

A survey of the historical development of mathematics. The emphasis will be on mathematical concepts, problem solving, and pedagogy from a historical perspective. Graduate students will be required to do some additional work beyond what is expected of the undergraduate members of the class.

Thesis guidance for M.A. students. See note on page 577 related to thesis hours.

Dissertation guidance for doctoral students. See note on page 577 related to research and dissertation hours.

Dissertation guidance for doctoral students. See note on page 577 related to research and dissertation hours.