Axioms of Desarguesian geometry, principle of duality; projectivities, perspectivities, and the fundamental theorem; collineations (homologies and...
Euclidean isometry and similarity groups; geometry of circles; inversion; hyperbolic geometry: Poincare disk model of the hyperbolic plane. Precludes...
Axioms of set theory. Development of the systems of natural numbers and the real numbers. Axiom of choice, Zorn's lemma, well-ordering. The...
Congruences, distribution of primes, arithmetic functions, primitive roots, quadratic residues, quadratic reciprocity law, continued fractions,...
Series solutions of ordinary differential equations of second order about regular singular points; asymptotic solutions. Systems of ordinary...
Laplace transforms, series solutions of ordinary differential equations, the Frobenius method. Fourier series and Fourier transforms, solutions of...
Mathematical modeling in the experimental sciences: design, analysis and pitfalls. Computational methods directly applicable to problems in science...
Formulation of linear programming problems, the simplex method, duality theory, implementations, extensions and applications. Network flow problems...
Dijkstra's algorithm and Bellman-Ford algorithm for the minimum weight dipath problem, the minimum weight spanning tree problem, augmenting path...
An introduction to the design and analysis of algorithms. Topics include: recurrence relations, sorting and searching, divide-and-conquer, dynamic...
Elementary discussion of error, polynomial interpolation, quadrature, linear systems of equations and matrix inversion, non-linear equations,...
Incorporation of basic numerical methods into efficient, reliable software. The course includes examination of existing software systems, e.g., linear...
This course covers mathematics used in the modern casino gaming industry. The topics include probabilities, odds, house advantages, variance and...
Congruences, distribution of primes, general cryptographic systems, public key cryptographic systems and authentification using number theory,...
Linear recurrences; difference equations; graph theory and trees; heuristic and approximation algorithms; software tools; DNA sequencing methods;...
Population dynamics; evolutionary trees; predator-prey models; game theory; evolutionary genetics; nonlinear dynamics and chaos; pattern formation. ...
Algorithms for multiplication, division, greatest common divisors and factorization over the integers, finite fields and polynomial rings. Basic tools...
Enumeration: elementary methods, inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory and algorithms:...
Enumeration: inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory: connectivity, planarity, Hamilton...
Available only to students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.