THIS BOOK PROVIDES A BROAD INTRODUCTION TO SOME OF THE MOST FASCINATING AND BEAUTIFUL AREAS OF DISCRETE MATHEMATICAL STRUCTURES. IT STARTS WITH A CHAPTER ON SETS AND GOES ON TO PROVIDE EXAMPLES IN LOGIC, APPLICATIONS OF THE PRINCIPLE OF INCLUSION AND EXCLUSION AND FINALLY THE PIGEONHOLE PRINCIPAL. COMPUTATIONAL TECHNIQUES INCLUDING THE PRINCIPLE OF MATHEMATICAL INTRODUCTION ARE PROVIDED, AS WELL AS A STUDY ON ELEMENTARY PROPERTIES OF GRAPHS, TREES AND LATTICES. SOME BASIC RESULTS ON GROUPS, RINGS, FIELDS AND VECTOR SPACES ARE ALSO GIVEN, THE TREATMENT OF WHICH IS INTENTIONALLY SIMPLE SINCE SUCH RESULTS ARE FUNDAMENTAL AS A FOUNDATION FOR STUDENTS OF DISCRETE MATHEMATICS. IN ADDITION, SOME RESULTS ON SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS ARE DISCUSSED.SAMPLE CHAPTER(S)CHAPTER 1: SETS (313 KB)REQUEST INSPECTION COPY
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This book provides a broad introduction to some of the most fascinating and beautiful areas of discrete mathematical structures. It starts with a chapter on sets and goes on to provide examples in logic, applications of the principle of inclusion and exclusion and finally the pigeonhole principal. Computational techniques including the principle of mathematical introduction are provided, as well as a study on elementary properties of graphs, trees and lattices. Some basic results on groups, rings, fields and vector spaces are also given, the treatment of which is intentionally simple since such results are fundamental as a foundation for students of discrete mathematics. In addition, some results on solutions of systems of linear equations are discussed.
The book provides a broad introduction to some of the fascinating and beautiful areas of Discrete Mathematical Structures. It starts with a chapter on sets, gives some beautiful examples in logic, a nice presentation of the Principal of mathematical introduction, after giving some nice things about computational techniques goes on to study elementary propertities of graphs, trees and lattices. It also provides some basic results on groups, rings, fields and vector spaces- the treatment of these topics is extremely elementary and only such results are included as are absolutely necessary for the students. Some results on solutions of systems of linear equations are also discussed.
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