Books, articles, software, and activities to support the MATH311W course

This guide is intended to help students in Discrete Mathematics (MATH 311W) find books on proofs and proof writing, information sources on discrete math topics, and learn to evaluate information on the web. Please visit the **Mathematics Research Guide** for more sources of books, research articles, and information.

- Numbers, Groups and Codes by J. F. Humphreys; M. Y. PrestISBN: 052154050XPublication Date: 2004-05-13The textbook for Discrete Mathematics

Your Physical & Mathematical Sciences Library (PAMS)!

- MathOverflowa Q&A website for mathematicians where anyone can post a question and the answers are voted on by members of the community.
- ProofWikian open project for the collection, collaboration and classification of mathematical proofs.

- Proofs 101 by Joseph KirtlandISBN: 9781003082927Publication Date: 2020-11-21The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies.
- How to Solve It by George PolyaISBN: 069111966XPublication Date: 2015-09-25demonstrates how a proof can be "reasoned" out from building a bridge to winning a game of anagrams.
- How to Think Like a Mathematician by Kevin HoustonISBN: 9780521895460Publication Date: 2009-02-12All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions.
- Proofs and Fundamentals by Ethan D. BlochISBN: 9781441971265Publication Date: 2011-02-21introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis.
- Problems and Proofs in Numbers and Algebra by Richard S. Millman; Peter J. Shiue; Eric Brendan KahnISBN: 9783319144276Publication Date: 2015-02-09Focusing on an approach of solving rigorous problems and learning how to prove more complex topics in analysis, advanced number theory, and abstract algebra.
- Charming Proofs by Claudi Alsina; Roger B. NelsenISBN: 0883853485Publication Date: 2010-08-01Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct.
- Number Theory by James Pommersheim; Tim Marks; Erica Flapan; PommersheimISBN: 9780470424131Publication Date: 2010-02-15Every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section.
- A Logical Introduction to Proof by Daniel W. CunninghamISBN: 9781461436317Publication Date: 2013-01-01One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof.

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