and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, coun...
In this article, we present computerized proof techniques of Gosper, WilfZeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete mathematics. We demonstrate by examples how one can use these computerized proof techniques to raise students'' interests...
Penner, R. C.Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific Pub. Co., 1999. 19. Polya, G.How to Solve It: A New Aspect ofMathematical Methods. Ishi Press, 2009. 20. Rodgers, N.Learning to Reason: an Introduction to Logic, Sets and Relations. Wiley ...
Discrete mathematics. Proof techniques and mathematical structures The textbook is written as an introductory course of discrete mathematics (DM) for university students of the first and second year of education. The book ... RC Penner - WORLD SCIENTIFIC 被引量: 6发表: 1999年 ...
"To address this situation and establish certainty, Hales turned to computers, using techniques of formal verification. He and a team of collaborators wrote out the entire proof in extraordinary detail using strict formal logic, which a computer program then checked with perfect rigor. This paper ...
TE Simos,G Psihoyios - 《Journal of Computational & Applied Mathematics》 被引量: 64发表: 2005年 Selected papers of the 4th International Conference on "Applications of stable Isotope Techniques to Ecological Studies", April 19–23, 2004, Wellington, N... In this paper an exponentially-fitted...
In this paper, we propose a novel Chines... JC Patra,JE Phua,C Bornand - 《Digital Signal Processing》 被引量: 225发表: 2010年 A chaotic system based fragile watermarking scheme for image tamper detection In the past few years, various fragile watermarking techniques have been proposed for ...
Despite various attempts that have been made in this regard, security and privacy are long-standing open problems in VANETs [1], [5]. Researchers have tried employing some cryptography techniques to alleviate these challenges. However, many researchers tried to come out of the privacy issues ...
Matrix mechanics, having had a 6-month head start, also tackled the Stark and Zeeman effects as well as dispersion theoryFootnote 14 and developed the necessary approximation schemes (like perturbation theory) and formal techniques (like coordinate transformations, action-angle variables) for the ...
The course focused on basic proof techniques such as if-then and if-and-only-if but also introduced more advanced proof techniques, including induction, contradiction, contraposition, and smallest counterexample. The final weeks of the course focused on applying these techniques to set-based function...