The focus of the course is to give an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the power of techniques in algebraic combinatorics. Rigorous mathematical proofs, rational generating functions and Recurrence relations and Adjacency and Laplacian matrices of graphs are expected in this 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

Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers | 00:10:00 | ||

Partially ordered sets II Dilworth’s and Sperner’s theorem | 00:10:00 | ||

Partially ordered sets III the Mobius function | 00:10:00 | ||

Introduction to partitions and two proofs of Euler’s theorem | 00:15:00 | ||

Partitions II Euler Pentagonal theorem and other identities | 00:10:00 | ||

Proof of Schensted’s theorem | 00:10:00 | ||

An introduction to symmetric functions | 00:15:00 | ||

Symmetric functions II | 00:15:00 | ||

Polya theory III, intro to exponential generating functions | 00:10:00 | ||

Exponential generating functions and tree enumeration | 00:10:00 | ||

Tree enumeration II | 00:10:00 | ||

Eulerian tours II | 00:10:00 | ||

Chip firing games I | 00:20:00 | ||

Chip firing games II the critical group | 00:20:00 | ||

Chip firing games III proof of uniqueness | 00:20:00 | ||

Perfect matchings and Domino tilings | 00:10:00 | ||

Lattice path enumeration II | 00:20:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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