Instructor resource file download The work is protected by local and international copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Coding of Binary Information and Error Detection.
Offers students a level of rigor appropriate for beginners or non-math majors. Enables instructors to sharpen their focus on key ideas and concepts. Representations of Special Grammars and Languages. Sign Up Already have an access code? Helps students develop the skills of building mathematical dicrete through abstraction. Helps students focus on fundamental concepts without becoming bogged down in special cases, weakly-motivated examples, and applications.
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Skip to content Mind Sculpt. Toggle navigation. Add a menu. This edition doesn't have a description yet. Can you add one? Previews available in: English. Add another edition? Copy and paste this code into your Wikipedia page. Need help? Discrete Mathematical Structures, Fifth Editi Bernard Kolman, Robert C. Donate this book to the Internet Archive library. If you own this book, you can mail it to our address below.
Not in Library. Want to Read. Check nearby libraries Library. Whereas the ideas of calculus were fundamental to the science and technology of the industrial revolution, the ideas of discrete mathematics underlie the science and technology of the computer age. The main themes of a first course in discrete mathematics are logic and proof, induction and recursion, discrete structures, combinatorics and discrete probability, algorithms and their analysis, and applications and modeling.
Logic and Proof Probably the most important goal of a first course in discrete mathematics is to help students develop the ability to think abstractly.
This means learning to use logically valid forms of argument and avoid common logical errors, appreciating what it means to reason from definitions, knowing how to use both direct and indirect arguments to derive new results from those already known to be true, and being able to work with symbolic representations as if they were concrete objects.
Such thinking is widely used in the analysis of algorithms, where recurrence relations that result from recursive thinking often give rise to formulas that are verified by mathematical induction. Those studied in this book are the sets of integers and rational numbers, general sets, Boolean algebras, functions, relations, graphs and trees, formal languages and regular expressions, and finite-state automata.
Discrete probability focuses on situations involving discrete sets of objects, such as finding the likelihood of obtaining a certain number of heads when an unbiased coin is tossed a certain number of times. Skill in using combinatorics and probability is needed in almost every discipline where mathematics is applied, from economics to biology, to computer science, to chemistry and physics, to business management.
To solve a problem on a computer, it is necessary to find an algorithm, or step-by-step sequence of instructions, for the computer to follow. Designing an algorithm requires an understanding of the mathematics underlying the problem to be solved. Determining whether or not an algorithm is correct requires a sophisticated use of mathematical induction.
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