Notes on Discrete Mathematics So why do I need to learn all this nasty mathematics? 1. But isn't . Functions on recursive structures. single gigantic PDF file at aracer.mobi Basic Structures: Sets, Functions, Sequences, and Sums .. .. Discrete Structures: A course in discrete mathematics should teach students how to work. 2 Peano Axioms and Countability. Peano Axioms and the set of Natural Numbers Addition.

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Schaum's Outline of Discrete Mathematics, Third Edition (Schaum's Page 1 DISCRETE MATHEMATICAL STRUCTURES Theory ond Applications Page 2. Discrete mathematics deals with objects that come in discrete bundles, e.g.,. 1 or 2 babies. Why study discrete mathematics in computer science? It does not. Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. This tutorial has an ample amount of both theory and mathematics. The readers are PART 6: DISCRETE STRUCTURES.

CC identifies a computer science body of knowledge, a set of knowledge units "for which there is a broad consensus that the material is essential to an undergraduate degree in computer science. This fifth edition of Mathematical Structuresfor Computer Science covers all the topics in the CC discrete structures core and quite a bit more. All topics suggested for a onesemester version and virtually everything suggested for a two-semester version of a discrete structures course are covered here. Themes of the importance of logical thinking, the power of mathematical notation, and the usefulness of abstractions continue to bind together what otherwise appears to be a collection of disjointed topics. Of all computer science courses, discrete structures is probably the least appreciated in real time-and the most appreciated, given more perspective. Two years after the fact, students report back, "Every course I had after that used material from discrete structures. Answers to all Practice Problems are given at the back of the book, as are answers to all starred Exercises. A complete Solutions Manual is available to instructors from the publisher. Web Site A Web site for the book may be found at www.

Thank you to Forrest B. Rothman, C. Try reading with pencil and paper at hand and work the Practice problems as you encounter them. They are intended to reinforce or clarify some new terminology or method just introduced; answers are given at the back of the book.

Pay attention also to the Reminders that point out common pitfalls or provide helpful hints. You may find at first that the thought processes required to solve the exercises in the book are new and difficult. Your biggest attribute for success will be perseverance.

Here's what I tell my students: "If you do not see at first how to solve a problem, don't give up, think about it some more; be sure you understand all the terminology used in the problem, play with some ideas. If no approach presents itself, let it be and think about it again later.

Repeat this process for days on end. When you finally wake up in the middle of the night with an idea, you'll know you are putting in the right amount of effort for this course.

A Web site for the book may be found at www. Each Technique that has a corresponding Web page example is marked with the icon By. Then succeeding pages develop the solution, much as you would be expected to write it.

As you navigate the pages, the solution unfolds step by step. The audio file contains a first-person stream-of-consciousness thought process about that step of the solution-why it occurred to the narrator to try this step, why it looked promising, what knowledge was being called on to suggest that this step should come next, and so on. The point is, you see perfect and complete worked-out proofs in the textbook and often see them performed by the instructor.

Yet when you go home and try to produce such a solution by yourself, you are unsure where to start or how to think about the problem or how to see any pattern to enable a guess as to what to do next. Consequently you give up in frustration.

Time to get started! You have been selected to serve on jury duty for a criminal case. The attorney for the defense argues as follows: If my client is guilty, then the knife was in the drawer. Either the knife was not in the drawer or Jason Pritchard saw the knife. If the knife was not there on October 10, it follows that Jason Pritchard did not see the knife. Furthermore, if the knife was there on October 10, then the knife was in the drawer and also the hammer was in the barn.

But we all know that the hammer was not in the bam.

Therefore, ladies and gentlemen of the jury, my client is innocent. Question:Is the attorney's argument sound? How should you vote? Formal logic strips away confusing verbiage and allows us to concentrate on the underlying reasoning being applied. In fact, formal logic-the subject of this chapter-provides the foundation for the organized, careful method of thinking that characterizes any reasoned activity-a criminal investigation, a scientific experiment, a sociological study.

In addition, formal logic has direct applications in computer science. The last two sections of this chapter explore a programming language based on logic and the use of formal logic to verify the correctness of computer programs.

Also, circuit logic the logic governing computer circuitry is a direct analog of the statement logic of this chapter. We shall study circuit logic in Chapter 7. Section 1. A statement or proposition is a sentence that is either true or false. Consider the following: Ten is less than seven.

How are you? She is very talented. Posted 8th October Graph Theory: Matchings. Posted 2nd November Graph Theory: Connectivity.

Posted 9th November Semester review. Posted 19th November Homework Assignments Homework 1. Posted 28th July Due: 4th August at the start of class. Homework 2. Posted 3rd August Due: 11th August at the start of class. Homework 3. Due: 18th August at the start of class. Note: Notes which can help with this homework have been posted.

Homework 4. Due: 25th August at the start of class. Homework 5. Due: 14th September at the start of class. Homework 6. Due: 21st September at the start of class.

Homework 7. Due: 29th September at the start of class. Homework 8. Due: 6th October at the start of class. Homework 9. Due: 20th October at the start of class. Homework Due: 10th November at the start of class. Due: 17th November at the start of class. Posted 15th November Due: 24th November at the start of class.

Posted 24th November Due: 2nd December before the major exam begins.