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Gatech Math3012: Applied Combinatorics

Gatech Math3012: Applied Combinatorics

Gatech Math3012: Applied Combinatorics

Gatech Math3012: Applied Combinatorics

Applied Combinatorics  is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. Available at the Open Textbook Library:  https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=339

Applied Combinatorics  is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. Available at the Open Textbook Library:  https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=339

Applied Combinatorics  is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. Available at the Open Textbook Library:  https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=339

During this workshop there will be lectures and informal exchanges and discussions on recent advances in Design Theory and Differences sets (t- designs without repeated blocks, (s, r, mu)- nets and their automorphisms, quasi-symmetric designs, Fourier transforms of difference sets, Design on partially ordered sets etc.). Interactions between Design Theory and Coding Theory will be emphasized. Combinatorial and graph-theoretical methods are increasingly important in the social sciences. This workshop will emphasize mathematical techniques and open mathematical problems arising in such fields as anthropology, economics, political science, psychology, and sociology. Combinatorial models and methods also play a fundamental role in modern biology. A major portion of this workshop will focus on the combinatorics of sequence analysis. The presentations will emphasize open mathematical questions arising from biological modeling in the hope of enriching both mathematics and biology. Workshops.

During this workshop there will be lectures and informal exchanges and discussions on recent advances in Design Theory and Differences sets (t- designs without repeated blocks, (s, r, mu)- nets and their automorphisms, quasi-symmetric designs, Fourier transforms of difference sets, Design on partially ordered sets etc.). Interactions between Design Theory and Coding Theory will be emphasized. Combinatorial and graph-theoretical methods are increasingly important in the social sciences. This workshop will emphasize mathematical techniques and open mathematical problems arising in such fields as anthropology, economics, political science, psychology, and sociology. Combinatorial models and methods also play a fundamental role in modern biology. A major portion of this workshop will focus on the combinatorics of sequence analysis. The presentations will emphasize open mathematical questions arising from biological modeling in the hope of enriching both mathematics and biology. Workshops.

Pages: 496 Publisher: Wiley Published: May 1, 2012 The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games. This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used. Chapter 1 Elements Of Graph Theory Chapter 2 Covering Circuits And Graph Coloring Chapter 3 Trees And Searching Chapter 4 Network Algorithms Chapter 5 General Counting Methods For Arrangements And Selections Chapter 6 Generating Functions Chapter 7 Recurrence Relations Chapter 8 Inclusion-exclusion Chapter 9 Polya’s Enumeration Formula Chapter 10 Games With Graphs