Stanford CS161 Handouts
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Lecture notes on matchings in algorithms course
More resources on Matching Theory
Wikipedia: Matching (graph theory)
Comprehensive overview with references
Algorithms: Design and Analysis, Part 1
This course covers the essential information that every serious programmer needs to know about algorithms and data structures, with emphasis on applications and scientific performance analysis of Java implementations. Part I covers elementary data structures, sorting, and searching algorithms. Part II focuses on graph- and string-processing algorithms. All the features of this course are available for free. People who are interested in digging deeper into the content may wish to obtain the textbook Algorithms, Fourth Edition (upon which the course is based) or visit the website algs4.cs.princeton.edu for a wealth of additional material. This course does not offer a certificate upon completion.
mathworld.wolfram.com
MathWorld is a comprehensive online mathematics encyclopedia from Wolfram that provides detailed articles, definitions, and examples across math topics. It includes graph theory entries relevant to Matching Theory, such as matchings, bipartite graphs, and related algorithms.
Matching Theory
Matching Theory - A book resource
ocw.mit.edu
MIT OpenCourseWare is a free, openly accessible repository of MIT course materials, including lecture notes, assignments, exams, and often video lectures, spanning a wide range of subjects. You can browse by course to study foundational topics relevant to matching theory, such as graph theory, combinatorial optimization, algorithms, and game theory.
Introduction to Graph Theory
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this online course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.