Covers basic methods and results in combinatorial theory. Includes enumeration methods, elementary properties of functions and relations and graph theory. Emphasizes applications. Requisites: Requires prerequisite course of MATH 2001 (minimum grade C-).
Axiomatic systems; Euclid's presentation of the elements of geometry; Hilbert's axioms; neutral, Euclidean and non-Euclidean geometries and their models. Requisites: Requires prerequisite courses of MATH 2001 and MATH 3130 or MATH 3135 (all minimum grade C-).
Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness, and numerical solutions. Requisites: Requires prerequisite courses of MATH 2400 or APPM 2350 and MATH 3130 or MATH 3135 or APPM 3310 (all minimum grade C-).
Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing. Credit not granted for this course and MATH 2510 or MATH 4510. Requisites: Requires prerequisite courses of MATH 2001 and 2300 or APPM 1360 (all minimum grade C-).
Provides Learning Assistants with an opportunity to analyze assessment data for formative purposes, and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students will gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to Learning Assistants in Math. Requisites: Requires a corequisite course of EDUC 4800.
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Same as MATH 5000. Requisites: Requires prerequisite courses of MATH 2001 and one of the following: MATH 3001, 3130, 3140 or 3210 or 3135 (all minimum grade C-).
Provides a rigorous treatment of infinite series, sequences of functions, and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral, or Fourier analysis). Same as MATH 5001. Requisites: Requires prerequisite courses of MATH 3001 and MATH 3130 or MATH 3135 (all minimum grade C-).
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation, and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Same as MATH 5120 and APPM 4120. Requisites: Requires prerequisite course of MATH 3130 or MATH 3135 or APPM 3310 (minimum grade C-).
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140. Requisites: Requires prerequisite course of MATH 3140 (minimum grade C-).
Introduces the basic concepts of point set topology. Includes topological spaces, metric spaces, homeomorphisms, connectedness, and compactness. Same as MATH 5200. Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-).
Introduces the modern differential geometry of plane curves, space curves, and surfaces in space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the Gauss-Bonnet theorem. Same as MATH 5230. Requisites: Requires prerequisite courses of MATH 2400 or APPM 2350 and MATH 3130 or MATH 3135 and MATH 2001 (all minimum grade C-).
The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth, and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics. Same as MATH 5330. Requisites: Requires prerequisite course of MATH 3001 (minimum grade C-).
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5682. Recommended prereqs., MATH 3310 and MATH 3140. Same as MATH 5440. Requisites: Requires prerequisite course of MATH 3130 or MATH 3135 (minimum grade C-).
Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Same as MATH 5450. Requisites: Requires prerequisite courses of MATH 2400 or APPM 2350 and MATH 3001 (all minimum grade C-).
Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470. Requisites: Requires prerequisite courses of MATH 3430 (minimum grade C-).
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Same as MATH 5510. Credit not granted for this course and APPM 3570, ECEN 3810, or MATH 3510. Requisites: Requires prerequisite course of MATH 2400 or APPM 2350 and MATH 3130 or MATH 3135 (all minimum grade C-).
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as MATH 5520 and APPM 4520. Requisites: Requires prerequisite course of MATH 4510 or APPM 3570 (minimum grade C-).
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Same as MATH 5540 and APPM 4540. Requisites: Requires prerequisite course of MATH 4520 or APPM 4520 (minimum grade C-).
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced restriction: knowledge of a programming language. Same as APPM 4650. Requisites: Requires prerequisite course of MATH 3130 or MATH 3135 or APPM 3310 (minimum grade C-).
Continuation of MATH 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving partial differential equations. Same as APPM 4660. Requisites: Requires prerequisite course of MATH 4650 (minimum grade C-).
Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic, and other topics chosen by the instructor. Same as MATH 5730. Requisites: Prereq. courses of MATH 2001 and one of the following: MATH 3001, 3110, 3120, 3130, 3140, 3170, 3210, 3510, 3850, 4000, 4001, 4120, 4140, 4200, 4210, 4230, 4320, 4330, 4430, 4440, 4450, 4710, 4510, 4520, 4540, 4650, 4660 or 4820 (all min grade C-).
Designed to train students to teach mathematics in an inclusive, multicultural environment. Students teach a math course within the McNeill Academic Program (Student Academic Services Center) meeting weekly with faculty and colleagues to learn to re-design curriculum, fine-tune pedagogical practices, create assessments, mentor undergraduate instructor assistants and create an inclusive classroom environment. May be repeated up to 4 total credit hours. Department enforced restriction: experience with college-level instruction. Requisites: Restricted to students with 87-180 credits (Seniors) or graduate students only.
Covers various topics not normally covered in the curriculum Requisites: offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 5810.
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820. Requisites: Prereq. courses of MATH 2001 and one of the following: MATH 3001, 3110, 3120, 3130, 3140, 3170, 3210, 3510, 3850, 4000, 4001, 4120, 4140, 4200, 4210, 4230, 4320, 4330, 4430, 4440, 4450, 4710, 4510, 4520, 4540, 4650, 4660 or 4820 (all min grade C-).
