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Note for Discrete Mathematics - DMS by Vssut Rulers

  • Discrete Mathematics - DMS
  • Note
  • Veer Surendra Sai University Of Technology VSSUT -
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References: 1. “Discrete Mathematical Structures”: Tremblay and Manohar, Tata McGraw Hill 2. “Discrete Mathematics”: 1st edition by Maggard Thomson 3. “Discrete M a t h e m a t i c s ”: Semyour Lipschutz, Varsha Patil IInd Edition Schaum’s Series, TMH 4. “Discrete M a t h e m a t i c a l Structures”: Kolman, B u s b y a n d R o s s , Prentice Hall India, Edition 3 5. “Discrete Mathematics and its application” – Mott Kendle 6. “Discrete Mathematical Structure” : G. Shankar Rao, New Age Publisher. 7. “Fundamental Approach to Discrete Mathematics” Acharjaya D. P. Sreekumar, New Age Publisher.

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Disclaimer This document does not claim any originality and cannot be used as a substitute of prescribed text books. The information presented here is merely a collection by the committee members for their respective teaching assignments. Various sources as mentioned references at the beginning of the document as well as freely available materials from the internet were constituted for preparing this document. The ownership of the information lies with respective authors or institutions. Further this document is not intended to be used for commercial purposes and the committee members are not accountable for any issues, legal or otherwise, arising out of this document. The committee members make no representations or warranties with respect to the accuracy or completeness of the contents of the document and disclaim any implied warranties of merchantability or fitness for a particular purpose. The committee members shall not be liable for any loss or profit or any other commercial, incidental, consequential or any other damages.

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Acknowledgement The committee members gratefully acknowledge Google, NPTEL and different reference books for getting help for preparation of this lecture note. The committee members also want to express their gratitude to the persons those who thinks knowledge should be free and be accessible and sharable without any restrictions so that every individual on this world has the same opportunity to explore and become enlightened by the collective gift of mankind. This lecture note being first draft so there may be some error. Also detail proofs and some graphs are omitted; however details discussion has been made in the class. Thus apart from this lecture note students/readers are strongly recommended following the mentioned books in the references and above all conferring with the faculty members for thorough knowledge in the subject.       

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 Justification of Learning the Subject: What is Discrete Mathematics? Consider an analog clock (One with hands that continuously rotate and show time in continuous fashion) and a digital clock (It shows time in discrete fashion). The former one gives the idea of Continuous Mathematics whereas the later one gives the idea of Discrete Mathematics. Thus, Continuous Mathematics deals with continuous functions, differential and integral calculus etc. whereas discrete mathematics deals with mathematical topics in the sense that it analyzes data whose values are separated (such as integers: Number line has gaps) Example of continuous math – Given a fixed surface area, what are the dimensions of a cylinder that maximizes volume? Example of Discrete Math – Given a fixed set of characters, and a length, how many different passwords can you construct? How many edges in graph with n vertices? How many ways to choose a team of two people from a group of n?  Why do you learn Discrete Mathematics? This course provides some of the mathematical foundations and skills that you need in your further study of Information Technology and Computer Science & Engineering. These topics include: Logic, Counting Methods, Relation and Function, Recurrence Relation and Generating Function, Introduction to Graph Theory And Group Theory, Lattice Theory and Boolean Algebra etc. .

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