This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds:

Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations.
Discrete structures: graphs, state machines, modular arithmetic, counting.
Discrete probability theory.

On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.
This course is part of the Open Learning Library, which is free to use. You have the option to sign up and enroll in the course if you want to track your progress, or you can view and use all the materials without enrolling.

This course is an introduction to electromagnetism and electrostatics. Topics include: electric charge, Coulomb’s law, electric structure of matter, conductors and dielectrics, concepts of electrostatic field and potential, electrostatic energy, electric currents, magnetic fields, Ampere’s law, magnetic materials, time-varying fields, Faraday’s law of induction, basic electric circuits, electromagnetic waves, and Maxwell’s equations. The course has an experimental focus, and includes several experiments that are intended to illustrate the concepts being studied.
Acknowledgements
Prof. Roland wishes to acknowledge that the structure and content of this course owe much to the contributions of Prof. Ambrogio Fasoli.

This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.