Syllabus for Math 475 Introduction to Combinatorics Summer 2024

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Syllabus for Math 475

Introduction to Combinatorics

Summer 2024

        Texts: The course's lecture notes (will be uploaded to canvas). These notes are the only required text of the course. They follow closely the text "Introductory Combinatorics", 5th Edition, by Richard A. Brualdi. You do not need to buy this book, we have a .pdf copy of it on the course's canvas page.

For our course we will assume that you know (and I will recall in class what/when needed) the basic notions of set theory (sets, functions) such as,

 Appendices A & B in the book of "Linear Algebra" by S. Friedberg, A. Insel, and L. Spence (see our course's canvas page);

and the basic notions of linear algebra such as in,

 "Linear Algebra" by S. Friedberg, A. Insel, and L. Spence. In particular, notions from chapters 1-to-6.

        Content: We will study basic topics from combinatorics. We will cover roughly chapters 2, 8 and 14 in the Brualdi's text. The main topics include permutations and combinations; pigeon-hole principle; partial orders; Dilworthís theorem; the inclusion-exclusion principle; recurrence relations and generating functions; difference sequences; Catalan numbers; Stirling numbers; partition numbers; counting equivalence classes in the presence of symmetries.

        Your work: We will have nine homework assignments, one each Monday. You will need to upload them to Canvas every Sunday by 11:59pm. There will be a 10min quiz on the homework every Monday at 11:45, uploaded to canvas. The final grade will be based on the equal average of the HWs and quizzes. Each week you get a grade between 100-0, and the overall score will be A if you got between 100-80, B for 79-60, C for 59-50, or F if you got less than 50.

        Attitude: In our course we will study parts from the basics of combinatorics, which is one of the most important subjects of mathematics, and some of the motivating problems of this domain of knowledge. The goal is to help you to develop your way on how to think about some mathematical objects that appears in the formulations and solutions of these problems. You will get help to develop your abilities to express yourself mathematically, including formulating statements, obtain computational results, and write proofs. I expect you to be an integral part of the course i.e., to listen to lectures and their recordings, and to read their notes, to work hard on HWs and quizzes.