This is a graduate-level course in combinatorial theory. The content varies year to year, the topic of this course changes. It is hyperplane arrangements, including background material from the theory of posets and matroids. Some of the topics covered involve with topology, representation theory, and commutative algebra. Those with insufficient backgrounds in these topics should still be able to follow most of the course.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Chapter 1 Basic Definitions, the Intersection Poset and the Characteristic Polynomial | 00:20:00 | ||
| Chapter 2 Properties of the Intersection Poset and Graphical Arrangements | 00:30:00 | ||
| Chapter 3 Matroids and Geometric Lattices | 00:15:00 | ||
| Chapter 4 Broken Circuits, Modular Elements, and Supersolvability | 00:30:00 | ||
| Chapter 5 Finite Fields | 00:30:00 | ||
| Chapter 6 Separating Hyperplanes (Preliminary Version) | 00:30:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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