Mathematics

Courses Taught

• FYS 162-3 Traffic School
  Why do traffic jams on the highway seem to appear and disappear for no reason? How well do we understand traffic flow? Can technology and policy improve traffic congestion? This seminar is an introduction to automobile traffic flow modeling. Using a combination of mathematical analysis and computer simulation, we study three modeling problems: traffic jam formation on highways, the late merge, and optimal traffic light control. We explore how modeling can suggest solutions to traffic flow problems, and along the way draw connections to economics (congestion pricing, the cost of congestion), psychology (road rage and distracted driving), and policy (the formulation of traffic regulations).
• MATH 107 Applied Statistics
  Introduction to statistical methods with applications from social, biological, and health sciences. Topics include descriptive statistics, fundamentals of probability theory, probability distributions, hypothesis testing, linear regression and correlation, analysis of categorical data, and analysis of variance. Laboratory work is designed to utilize the computational power of a statistical computer package. Credit cannot be received for both this course and Biology 260, Economics 241, Health Sciences 232, or Psychology 205. No prerequisites.
• MATH 110 Calculus I Companion
  Supplement to Math 111 with a focus on supporting and enhancing calculus and precalculus content knowledge and problem-solving skills. Topics include basic algebraic concepts, equations and inequalities, functions, and other precalculus topics in support of study of Calculus I topics. No prerequisites. Must be enrolled in Math 111 in the same semester.
• MATH 111 Calculus I
  Differential and integral calculus of one real variable. Topics include introduction to limits, continuity, the derivative, the definite integral. Applications are drawn from the natural and social sciences. No prior experience with calculus is assumed. Students who have received credit for Mathematics 105-106 cannot also receive credit for Mathematics 111. No prerequisites.
• MATH 112 Calculus II
  Differential and integral calculus of one real variable. Topics include the definite integral, integration techniques, improper integrals, differential equations and sequences and series. Applications are drawn from the natural and social sciences. Prerequisite: Math 105 and 106 or Math 111 with a C- or better or First Year Standing with no credit for any other mathematics course at Gettysburg.
• MATH 211 Multivariable Calculus
  Vectors, vector functions, functions of several variables, partial differentiation, optimization, multiple integration, transformation of coordinates, line integrals and Green's Theorem. Prerequisite: Math 112 with a C- or better.
• MATH 212 Linear Algebra
  Systems of linear equations, algebra of matrices, determinants, abstract vector spaces, linear transformations, eigenvalues, and quadratic forms. Prerequisite: Math 112 with a C- or better.
• MATH 215 Abstract Mathematics I
  Introduction to abstract mathematical thinking, emphasizing mathematical reasoning and exposition. Students examine the concepts and methods of abstract mathematics, such as primitives and definitions, axioms and theorems, conjectures and proofs; study the topics of higher-level mathematics, such as logic, sets, quantifiers, and mathematical structures; learn the skills of reading, understanding, writing, and presenting rigorous mathematics; and gain an appreciation for the history and culture of mathematics. No prerequisites.
• MATH 225 Differential Equations
  Analysis of one and two-dimensional differential equations, with an emphasis on the qualitative behavior of solutions. Topics include graphical exploration, numerical approximation, separable and linear equations, phase line and phase plane analysis, conservative and dissipative systems, linearization, and applications to biology, chemistry, and physics. Prerequisite: Math 112 with a C- or better.
• MATH 315 Abstract Mathematics II
  Further development of the skills of abstract mathematical reasoning and writing proofs, as well as the rigorous development of the elements of advanced mathematics. Topics include a variety of advanced proof techniques, relations, functions, order, limits, finite enumeration, infinite cardinalities, and number systems. Prerequisite: Math 215 with a C- or better.
• MATH 321 Real Analysis
  Rigorous treatment of concepts studied in elementary calculus and an introduction to more advanced topics in analysis. Topics include elements of logic and set theory, properties of real numbers, elements of metric space topology, continuity, the derivative, the Riemann integral, sequences and series, and uniform convergence. Prerequisite: Math 215 with a C- or better.
• MATH 331 Abstract Algebra
  Study of basic structures of modern abstract algebra, including groups, rings, fields, and vector spaces. Prerequisite: Math 215 with a C- or better.
• MATH 342 Applied Linear Algebra
  Rigorous continuation of first-semester linear algebra, with applications both within mathematics and to the social and natural sciences. Topics, chosen by the instructor, may include matrix powers and exponentials, nonnegative matrices and Markov chains, coding theory, design theory, graph theory, the Perron-Frobenius theorem, ranking theory, data clustering, and max-plus algebra. Prerequisite: Math 212 with a C- or better.
• MATH 343 Geometry
  Study of both synthetic and analytic approaches to geometry. Topics include axiomatic systems, Euclidean geometry, non-Euclidean geometries, projective geometry, and subgeometries of projective geometry. Prerequisite: Math 215 with a C- or better.
• MATH 353 Probability and Statistics
  Study of topics in probability and statistics. Topics include discrete and continuous random variables and their distributions, expected value and variance, the Law of Large Numbers, the Central Limit Theorem, sampling distributions, theory and application of estimation, hypothesis testing, regression, correlation, and analysis of variance. Applications to problems in the social and natural sciences will also be considered. Prerequisites: Math 211 and Math 212 with a C- or better.
• MATH 361 Chaos and Dynamical Systems
  Dynamical systems and chaos theory. Topics include linear and nonlinear systems, mappings and orbits, bifurcations, stability theory and applications of dynamical systems. Prerequisite: Math 212 and 215, both with a C- or better
• MATH 364 Complex Analysis
  Complex numbers, analytic functions, complex integration, Cauchy's Theorem, Taylor and Laurent series, contour integrals, the residue theorem, and conformal mapping. Prerequisite: Math 211 with a C- or better.