Discrete Mathematics Using a Computer

__Discrete Mathematics Using a Computer__ offers a new, "hands-on" approach to teaching Discrete Mathematics. Using software that is freely available on Mac, PC and Unix platforms, the functional language Haskell allows students to experiment with mathematical notations and concepts -- a practical approach that provides students with instant feedback and allows lecturers to monitor progress easily. This second edition of the successful textbook contains significant additional material on the applications of formal methods to practical programming problems. There are more examples of induction proofs on small programs, as well as a new chapter showing how a mathematical approach can be used to motivate AVL trees, an important and complex data structure. Designed for 1st and 2nd year undergraduate students, the book is also well suited for self-study. No prior knowledge of functional programming is required; everything the student needs is either provided or can be picked up easily as they go along. Key features include: • Numerous exercises and examples • A web page with software tools and additional practice problems, solutions, and explanations, as well as course slides • Suggestions for further reading Complete with an accompanying instructor's guide, available via the web, this volume is intended as the primary teaching text for Discrete Mathematics courses, but will also provide useful reading for Conversion Masters and Formal Methods courses. Visit the book’s Web page at: http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/ Discrete Mathematics Using A Computer Offers A New, Hands-on Approach To Teaching Discrete Mathematics. Using Software That Is Freely Available On Mac, Pc And Unix Platforms, The Functional Language Haskell Allows Students To Experiment With Mathematical Notations And Concepts -- A Practical Approach That Provides Students With Instant Feedback And Allows Lecturers To Monitor Progress Easily. This Second Edition Of The Successful Textbook Contains Significant Additional Material On The Applications Of Formal Methods To Practical Programming Problems. There Are More Examples Of Induction Proofs On Small Programs, As Well As A New Chapter Showing How A Mathematical Approach Can Be Used To Motivate Avl Trees, An Important And Complex Data Structure. Designed For 1st And 2nd Year Undergraduate Students, The Book Is Also Well Suited For Self-study. No Prior Knowledge Of Functional Programming Is Required; Everything The Student Needs Is Either Provided Or Can Be Picked Up Easily As They Go Along. Key Features Include: • Numerous Exercises And Examples • A Web Page With Software Tools And Additional Practice Problems, Solutions, And Explanations, As Well As Course Slides • Suggestions For Further Reading Complete With An Accompanying Instructor's Guide, Available Via The Web, This Volume Is Intended As The Primary Teaching Text For Discrete Mathematics Courses, But Will Also Provide Useful Reading For Conversion Masters And Formal Methods Courses. Visit The Book’s Web Page At: Http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/ Programming And Reasoning With Equations -- To Haskell -- Equational Reasoning -- Recursion -- Trees -- Logic -- Propositional Logic -- Predicate Logic -- Set Theory -- Set Theory -- Inductively Defined Sets -- Relations -- Functions -- Applications -- The Avl Tree Miracle -- Discrete Mathematics In Circuit Design. By John O’donnell, Cordelia Hall, Rex Page.

Discrete Mathematics Using a Computer offers a new, "hands-on" approach to teaching Discrete Mathematics. Using software that is freely available on Mac, PC and Unix platforms, the functional language Haskell allows students to experiment with mathematical notations and concepts — a practical approach that provides students with instant feedback and allows lecturers to monitor progress easily.

This second edition of the successful textbook contains significant additional material on the applications of formal methods to practical programming problems. There are more examples of induction proofs on small programs, as well as a new chapter showing how a mathematical approach can be used to motivate AVL trees, an important and complex data structure.

Designed for 1st and 2nd year undergraduate students, the book is also well suited for self-study. No prior knowledge of functional programming is required; everything the student needs is either provided or can be picked up easily as they go along.

Key features include:

• Numerous exercises and examples


• A web page with software tools and additional practice problems, solutions, and explanations, as well as course slides


• Suggestions for further reading

Complete with an accompanying instructor's guide, available via the web, this volume is intended as the primary teaching text for Discrete Mathematics courses, but will also provide useful reading for Conversion Masters and Formal Methods courses.

Visit the book’s Web page at: http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/

Computer science abounds with applications of discrete mathematics, yet s- dents of computer science often study discrete mathematics in the context of purely mathematical applications. They have to ?gure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad success in this enterprise, which is not surprising, since many of the most important advances in science and engineeringhavebeen, precisely, applicationsofmathematicstospeci?cscience and engineering problems. Tobesure,mostdiscretemathtextbooksincorporatesomeaspectsapplying discrete math to computing, but it usually takes the form of asking students to write programs to compute the number of three-ball combinations there are in a set of ten balls or, at best, to implement a graph algorithm. Few texts ask students to use mathematical logic to analyze properties of digital circuits or computer programs or to apply the set theoretic model of functions to understand higher-order operations. A major aim of this text is to integrate, tightly, the study of discrete mathematics with the study of central problems of computer science. Front Matter....Pages 1-1 Introduction to Haskell....Pages 3-35 Equational Reasoning....Pages 37-46 Recursion....Pages 47-60 Introduction....Pages 61-81 Trees....Pages 83-106 Front Matter....Pages 107-107 Propositional Logic....Pages 109-162 Predicate Logic....Pages 163-185 Front Matter....Pages 187-187 Set Theory....Pages 189-206 Inductively Defined Sets....Pages 207-222 Relations....Pages 223-265 Functions....Pages 267-309 Front Matter....Pages 311-311 The AVL Tree Miracle....Pages 313-353 Discrete Mathematics in Circuit Design....Pages 355-375