Combinatorial Commutative Algebra, Ezra Miller and Sturmfels

Combinatorial Commutative Algebra PDF Download Ebook. Ezra Miller and Bernd Sturmfels provide a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings.

The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.

Each chapter begins with an overview and ends with Notes on references and pointers to the literature. Theorems are, for the most part, attributed only in the Notes. When an exercise is based on a specific source, that source is credited in the Notes. For the few exercises used in the proofs of theorems in the main body of the text, solutions to the non routine ones are referenced in the Notes. The References list the pages on which each source is cited.

The mathematical notation throughout the book is kept as consistent as possible, making the glossary of notation particularly handy, although some of our standard symbols occasionally moonlight for brief periods in nonstandard ways, when we run out of letters. The exposition mainly concerns combinatorially defined ideals and their quotients, with a focus on numerical invariants and resolutions, especially under gradings more refined than the standard integer grading.

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Discrete Mathematics with Graph Theory 3rd Edition, Goodaire

Discrete Mathematics with Graph Theory 3rd Edition PDF Download Ebook. Edgar G. Goodaire and Michael M. Parmenter make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique reader interest and bring clarity to even the most complex concepts.

Above all, the book is designed to engage today's readers in the interesting, applicable facets of modern mathematics. More than 200 worked examples and problems, as well as over 2500 exercises are included. Full solutions are provided in the back of the book. More than 150 Pauses—short questions inserted at strategic points—are included. Full solutions to Pauses are included at the end of each section.

The most common (negative) criticism of our first edition was the short treatment of logic and the absence of truth tables. This problem has been remedied with Chapter 1 (previously Chapter 0) completely rewritten and expanded significantly to include new sections on truth tables, the algebra of propositions, and logical arguments.

The text now includes more than enough material for instructors who wish to include a substantial unit on formal logic, while continuing to permit a shorter treatment dealing exclusively with the major points and jargon of proofs in mathematics. The second most common complaint—and every student's favorite—was the shortage of answers in the back of the book. In fact, the first edition contained over 500 solved problem. For the second edition, however, this number has been increased to over 800.

Graph theory is the subject of Chapters 9 through 15, and again we find that there is more material here than can be successfully treated in thirty-three lectures. Chapter 13 (Depth-First Search and Applications) can also be omitted without difficulty. In fact, most of the last half of this book is self-contained and can be treated to whatever extent the instructor may desire.

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Discrete and Combinatorial Mathematics 5th Edition, Grimaldi

Discrete and Combinatorial Mathematics: An Applied Introduction 5th Edition PDF Download Ebook. Ralph P. Grimaldi continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications.

Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making it the ideal text for preparing students for advanced study. This text has an enhanced mathematical approach, with carefully thought out examples, including many examples with computer sciences applications.

Historical reviews and biographies bring a human element to their assignments. Chapter summaries allow students to review what they have learned. There is expanded treatment of discrete probability in Chapter 3 with new material on cryptology, private-key cryptosystems in Chapter 14; public-key RSA cryptosystems in Chapter 16.

Interest in graphs and their applications has grown exponentially in the past two decades, largely due to the usefulness of graphs as models for computation and optimizations. This book targets the need for a fresh approach to the theory. Students will be able to develop the techniques of research used in theoretical areas of CS such as algorithms.

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Discrete Mathematical Structures 6th Edition, Kolman

Discrete Mathematical Structures 6th Edition PDF Download Ebook. Bernard Kolman, Robert Busby and Sharon C. Ross have woven in a thread of coding in all its aspects, efficiency, effectiveness, and security. Two new sections, Other Mathematical Structures and Public Key Cryptology are the major components of this thread, but smaller related insertions begin in Chapter 1.

The number of exercises for this edition has been increased by more than 25%. Whatever changes we have made, our objective has remained the same as in the first four editions: to present the basic notions of discrete mathematics and some of its applications in a clear and concise manner that will be understandable to the student.

Chapters 1 through 10 each end with a student experiment. These provide opportunities for discovery and exploration, or a more in-depth look at topics discussed in the text. They are designed as extended-time, out-of-class experiences and are suitable for group work. Each experiment requires significantly more writing than section exercises do. Some additional experiments are to be found in Appendix B. Content, prerequisites, and goals for each experiment are given in the Instructor's Solutions Manual.

Chapter 1 contains material that is fundamental to the course. This includes sets, subsets, and their operations; sequences; properties of the integers, including base n representations; matrices; and mathematical structures. A goal of this chapter is to help students develop skills in identifying patterns on many levels. Chapter 2 covers logic and related material, including methods of proof and mathematical induction.

Although the discussion of proof is based on this chapter, the commentary on proofs continues throughout the book. Chapter 3, on counting, deals with permutations, combinations, the pigeonhole principle, elements of probability, and recurrence relations.

Chapter 4 presents basic types and properties of relations, along with their representation as directed graphs. Connections with matrices and other data structures are also explored in this chapter. Chapter 5 deals with the notion of a function and gives important examples of functions, including functions of special interest in computer science.

An introduction to the growth of functions is developed. Chapter 6 covers partially ordered sets, including lattices and Boolean algebras. A symbolic version for finding a Boolean function for a Boolean expression joins the pictorial Kamaugh method. Chapter 7 introduces directed and undirected trees along with applications of these ideas. Elementary graph theory with applications to transport networks and matching problems is the focus of Chapter 8.

In Chapter 9 we return to mathematical structures and present the basic ideas of semigroups, groups, rings, and fields. By building on work in previous chapters, only a few new concepts are needed. Chapter 10 is devoted to finite-state machines. It complements and makes effective use of ideas developed in previous chapters.

Chapter 11 finishes our discussion of coding for error detecting and correction and for security purposes. Appendix A discusses algorithms and pseudocode. The simplified pseudocode presented here is used in some text examples and exercises; these may be omitted without loss of continuity. Appendix B gives some additional experiments dealing with extensions or previews of topics in various parts of the course.

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A Walk Through Combinatorics 3rd Edition, Miklos Bona

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory 3rd Edition PDF Download Ebook. Miklos Bona encourages students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time.

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate.

The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.

The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.

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Introductory Combinatorics 5th Edition, Richard Brualdi

Introductory Combinatorics 5th Edition PDF Download Ebook. Richard A. Brualdi emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).

Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents.

The book has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. It is valuable book for any reader interested in learning more about combinatorics. It clarifies the exposition throughout and adds a wealth of new exercises, appropriate for one- or two-semester, junior- to senior-level combinatorics courses.

A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles. An excellent treatment of Polya's Counting Theorem that does not assume students have studied group theory. Use of the term “combination” as it applies to a set has been de-emphasized; the author now uses the essentially equivalent term of “subset” for clarity.

A new section (Section 1.6) on mutually overlapping circles has been moved from Chapter 7 to illustrate some of the counting techniques covered in later chapters. Chapter 2 now contains a short section (Section 3.6) on finite probability. Chapter 3 now contains a proof of Ramsey’s theorem in the case of pairs as well as Pascal’s formula.

An extensively revised Chapter 7 moves up generating functions and exponential generating functions to Sections 7.2 and 7.3, giving them a more central treatment. Coverage of more topics of graph theory and digraphs and networks has been reversed. Chapter 12 now covers more topics of graph theory and Chapter 13 now covers digraphs and networks.

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Principles and Techniques in Combinatori Ebook

Principles and Techniques in Combinatori PDF Download Ebook. Chen Chuan-Chong and Koh Khee-Meng offer wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises. It is textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read.

Moreover, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book has solid introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.

Author assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty students have devised (being trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking.

Contents include: Permutations and Combinations, Binomial Coefficients and Multinomial Coefficients, The Pigeonhole Principle and Ramsey Numbers, The Principle of Inclusion and Exclusion, Generating Functions and Recurrence Relations.

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Applied Combinatorics 6th Edition by Alan Tucker

Applied Combinatorics 6th Edition PDF Download Ebook. Alan Tucker offers 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 new sixth edition has new examples, expanded discussions, and additional exercises throughout the text.

The game of Mastermind that appeared at the beginning of the first edition has been brought back to this edition. New material is added including: chromatic polynomials, the transportation problem, and NP-completeness. The chapter on formal languages and finite-state machines from the second edition is back in abbreviated form.

A closing postlude about crytoanalysis has been added. A greater emphasis on underlying reasoning in combinatorial problem-solving has been stressed throughout the text. Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems. Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.

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Combinatorics and Graph Theory 2nd Edition, John Harris

Combinatorics and Graph Theory 2nd Edition PDF Download Ebook. John Harris, Jeffry L. Hirst and Michael Mossinghoff offer wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics.

In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features new sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. New material on partitions, multinomial coefficients, and the pigeonhole principle is presented with expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors.

There are topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. This book also offers expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable with numerous new exercises throughout the book.

The narrative and proofs are well written, and the authors are given to frequent uses of humor. Students should find this book as easy to read as any other good-quality text written with them in mind. Each of the three chapters concludes with several paragraphs describing an excellent selection of more advanced texts or papers to consider for further study.

There is a short section on References in each chapter introducing briefly other books dealing with the topics covered in the respective chapter. A full list of 293 references, about 550 exercises and an index with 13 pages are also provided.

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Combinatorics Topics, Techniques, Algorithms by Peter Cameron

Combinatorics: Topics, Techniques, Algorithms PDF Download Ebook. Peter J. Cameron stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof.

The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics. Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra.

This book gives number brief case studies. Its 18 chapters (not counting intro and closing) span a variety of interesting topics. Cameron doesn't write down to the reader - it takes serious thought and some mathematical background to get full value from the reading. The examples are nowhere near as concrete as you'd expect in a popularized version. Still, the author avoids opaque references to specialist terms, and keeps the text approachable.

The book is divided into two parts corresponding roughly to undergraduate material and graduate. The selection of topics is robust; the writing is clear and consise. The level is senior and above. The reader should have some knowledge of advanced math such as group theory, and analysis of algorithms.

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A Course in Combinatorics 2nd Edition, van Lint and Wilson

A Course in Combinatorics 2nd Edition PDF Download Ebook. J. H. van Lint and R. M. Wilson describe subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. There are also many applications, so workers in many scientific fields need some familiarity with the subject.

The extensive depth and breadth of the coverage make the book a unique guide to the whole of the subject, so that it is ideal for courses at the advanced undergraduate or beginning graduate level and also for working mathematicians and scientists. The authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as graph theory, extremal problems, designs, colorings, and codes.

The depth and breadth of the coverage make the book a unique guide to the whole of the subject. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.

The writing is very clear and there is a lot of explanation. Exercises are mixed in with the text, which I like very much; it makes them seem more natural, and it makes the book well-suited for self-study. I would say the difficulty level of this book is a bit inconsistent--but this is more a function of the material than of the writing style. The authors make everything as clear as possible, but they choose to include some difficult topics which require more thought.

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