Digital library
Textbooks, references and open learning resources.
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Combinatorics Through Guided Discovery
Kenneth P. Bogart · Dartmouth University
In the contents: 01: What is Combinatorics · 1.04: What is Combinatorics (Exercises) · 02: Induction and Recursion
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Elementary Number Theory
Wissam Raji · American University of Beirut
In the contents: 1.02: The Well Ordering Principle and Mathematical Induction · 1.03: Divisibility and the Division Algorithm · 2.06: The function x. the symbols O o and
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Discrete Mathematics
Oscar Levin · University of Northern Colorado
In the contents: 0: Introduction and Preliminaries · 0.1: What is Discrete Mathematics · 0.E: Introduction and Preliminaries (Exercises)
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Elementary Number Theory
Mike Barrus & W. Edwin Clark · University of Rhode Island
In the contents: 1.06: The Floor and Ceiling of a Real Number · 1.07: Greatest Common Divisor and Least Common Multiple · 1.14: Fermat Primes and Mersenne Primes
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A Spiral Workbook for Discrete Mathematics
Harris Kwong · State University of New York at Fredonia
In the contents: 01: Introduction to Discrete Mathematics · 1.01: An Overview of Discrete Mathematics · 1.03: How to Read and Write Mathematics
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Yet Another Introductory Number Theory Textbook - Cryptology Emphasis
Jonathan A. Poritz · Colorado State University – Pueblo
In the contents: 01: Well-Ordering and Division · 1.01: The Well-Ordering Principle and Mathematical Induction · 1.03: Divisibility and the Division Algorithm
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MCC: MTH 220 - Discrete Math
Judy Dean · Monroe Community College
In the contents: 1: Introduction to Discrete Mathematics · 1.1: An Overview of Discrete Mathematics · 1.3: How to Read and Write Mathematics
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Applied Combinatorics
Mitchel T. Keller & William T. Trotter · Georgia Tech & Morningside College
This book arose from our feeling that a text that met our approach to Applied Combinatorics was unavailable. Because of the diverse set of instructors assigned to the course, the standard text was one that covered every topic imaginable, but provided little depth. We took a different approach, attacking the central subjects of the course description to provide exposure, but taking the time to go into greater depth in select areas to give the students a better feel for how combinatorics works.
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A Cool Brisk Walk Through Discrete Mathematics
Stephen Davies · University of Mary Washington
In the contents: 2.3: Finite and infinite sets · 3.3: Relations between a set and itself · 3.4: Finite and infinite relations
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Combinatorics
Joy Morris · University of Lethbridge
In the contents: 01: What is Combinatorics · 03: Permutations Combinations and the Binomial Theorem · 04: Bijections and Combinatorial Proofs
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An Introduction to the Theory of Numbers
Leo Moser · University of Alberta
In the contents: 1.01: Compositions and Partitions
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Combinatorics and Graph Theory
David Guichard · Whitman College
In the contents: 1.03: Combinations and Permutations · 5.02: Euler Circuits and Walks · 5.03: Hamilton Cycles and Paths
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An Introduction to Number Theory
J. J. P. Veerman · Portland State University
In the contents: 1.01: Divisors and Congruences · 1.02: Rational and Irrational Numbers · 1.03: Algebraic and Transcendental Numbers
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Discrete Mathematics for Computer Science
Mark A. Fitch · University of Alaska Anchorage
In the contents: 1.05: Combinatorics- First Counts · 3.04: Combinatorics- Second Counts · 4.05: Combinatorics- Inclusion Exclusion
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Applied Discrete Structures
Al Doerr & Ken Levasseur · University of Massachusetts Lowell
In the contents: 1.01: Set Notation and Relations · 1.03: Cartesian Products and Power Sets · 1.05: Summation Notation and Generalizations
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Applied Combinatorics
Mitchel Keller; William Trotter · Mitchel T. Keller, William T. Trotter · 2017
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. Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom's MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book's source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book. Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics. Applied Combinatorics is open source and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA).
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Spiral Workbook for Discrete Mathematics
Harris Kwong · Open SUNY · 2015
This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students' problem-solving and writing skills.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.
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STAT C1000
Edward Pineda-Castro · Los Angeles City College
In the contents: 3.02: Parameter and Statistic · 3.04: Interpreting the Mean and Standard Deviation · 3.05: Measures of Relative Standing
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Interactive Lecture Notes for Introductory Statistics
Anton Butenko · Mt. San Jacinto College
In the contents: 3.02: Parameter and Statistic · 3.04: Interpreting the Mean and Standard Deviation · 3.05: Measures of Relative Standing
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Introductory Probability
Charles Grinstead & J. Laurie Snell · Dartmouth & Swarthmore Universities
In the contents: 01: Discrete Probability Distributions · 1.01: Simulation of Discrete Probabilities · 1.02: Discrete Probability Distribution