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).

Calculus

Review of Pre-Calculus, Trigonometry, Inverse Functions, Exponential & Logarithmic Functions, Limits, Inverse Sine, Cosine, and Tangent
 

Partial Differential Equations

ordinary differential equations in Banach spaces, implicit and Inverse functions theorems, First order nonlinear partial differential equations, Cauchy-Darboux-Kovalevskaya theorem, elliptic ODE boundary valued problems, heat and Wave Equation, Spectral Theorem for self-adoint operators, Fourier Transform, solutions to Laplace heat and wave equations, Sobolev spaces, Non-constant coefficient elliptic, heat and wave equations, Non-Linear PDE's and Techniques

Mathematical Coding Theory

fundamentals of coding theory, linear, Reed-Muller, Golay, cyclic and BCH codes: Supplements, Bibliography

First order differential equations

lays the foundations of Newtonian mechanics and procedure for solving dynamics problems
 

Calculus on the Web

internet utility for learning and practicing: books (precalculus, calculus), linear algebra, number theory, abstract algebra

Linear Algebra

matrix theory and linear algebra, emphasis on topics useful in other disciplines including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices: Readings, Tools, Study Materials, Related Resources

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

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