Maths (specialist)

Open Courseware and Resources (specialist)

- Mathematics: body of knowledge centered on such concepts as quantity, structure, space and change and also the academic discipline that studies them (Wikipedia).

Fourier Analysis - Theory and Applications

theory of the Lebesgue integral with applications to probability; Fourier series and Fourier integrals.

Principles of Discrete Applied Mathematics

illustrative topics in discrete applied mathematics, sorting algorithms, information theory, coding theory, secret codes, generating functions, Fourier Transforms, linear programming, game theory, applications

Differential Equations

solution of first-order by analytical, graphical & numerical methods, undetermined coefficients, exponential signals, oscillations, damping, resonance, Fourier series, delta functions, convolution & Laplace transform, matrix & linear systems, eigenvectors, non-linear autonomous systems, critical point analysis: recitations, course download, readings, tools
 

Combinatorics

What is, Subsets and binomial coefficients, Lucas' Theorem, Selections and arrangements, Power series, Recurrence relations, Partitions and permutations, The Principle of Inclusion and Exclusion, Families of sets, Erdös-Ko-Rado theorem, Systems of distinct representatives, Latin squares, Steiner triple systems, Kirkman's Theorem

Differential Analysis

foundation in theory of elliptic & parabolic linear partial differential equations, theory of harmonic functions, maximum principles for more general elliptic & parabolic equations, Schauder theory

Association Schemes and Partially Balanced Designs

links graphs with nice regularity properties, sets of real symmetric matrices which commute with each other, incomplete-block designs in designed experiments, finite groups: definitions, adjacency matrices, special association schemes, Bose-Mesner algebra, character tables, techniques, strongly regular graphs, block designs, statistics, efficiency, cyclic designs, families of partitions, orthogonal block structures: reading list

Algebra I

groups, vector spaces, linear transformations, symmetry groups, bilinear forms and linear groups: readings, practice quizzes

Finite Geometry and its Application

intensive course: embeddings of point-line geometries in projective spaces, matrix techniques for strongly regular graphs & related geometries, history of polar spaces & generalized polygons, nuclei in finite projective planes, partial spreads in finite projective space, collineation groups of finite planes, ovals and ovoids in projective spaces

Economic Applications of Game Theory

basic tools of game theoretic analysis, applications of game theory, primarily in economics and political science: readings

Uncertainty in Engineering

probability & statistics with emphasis on applications, events & probability, Bayes' theorem, random variables & vectors, distributions, Bernoulli trials & Poisson point processes, full-distribution uncertainty propagation, second-moment representation, propagation, conditional analysis, random sampling, estimation, hypothesis testing, linear regression

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