PPT-Introduction to Proofs

Section 17 Section Summary Mathematical Proofs Forms of Theorems Direct Proofs Indirect Proofs Proof of the Contrapositive Proof by Contradiction Proofs of Mathematical Statements A proof. J Hildebrand Evenodd proofs Practice problems Solutions The problems below illustrate the various proof techniques direct proof proof by contraposition proof by cases and proof by contradiction see the separate handout on proof techniques Perhaps youve already seen such proofs in your linear algebra course where a vector space was de64257ned to be a set of objects called vectors that obey certain properties Your text proved many things about vector spaces such as the fact that the in Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. Ranjit Jhala . Ken McMillan. Array Abstractions. From Proofs. The Problem: Reasoning about Data. for(i=0;i!=n;i++). M[i]=0;. for(j=0;j!=n;j. ++) . . . assert(M[j]==0);. All cells from . 0. to . Madhu Sudan. . MIT CSAIL. 09/23/2009. 1. Probabilistic Checking of Proofs. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. Can Proofs Be Checked Efficiently?. Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Dominique Unruh. University of Tartu. Tartu, April 12, 2012. Why quantum ZK?. Zero-knowledge:. Central tool in crypto. Exhibits many issues “in the small case”. Post-quantum crypto:. Classical protocols. But, pictures are not proofs in themselves, but may offer . inspiration. and . direction. . . Mathematical proofs require rigor, but mathematical ideas benefit from insight. . Speaker: . Karl Ting, . IIT-Bombay: Math, Proofs, Computing. 1. Mathematics, Proofs and Computation. Madhu. . Sudan. Harvard. Logic, Mathematics, Proofs. Reasoning:. Start with body of knowledge.. Add to body of knowledge by new observations, and new deductions. . Iddo Tzameret. Royal Holloway, University of London . Joint work with Fu Li (Tsinghua) and Zhengyu Wang (Harvard). . Sketch. 2. Sketch. : a major open problem in . proof complexity . stems from seemingly weak results. 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. To prove an argument is valid or the conclusion follows . Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Guy Katz. Schloss. . Dagstuhl. , October 2016. Acknowledgements . Based on joint work with Clark Barrett, Cesare . Tinelli. , Andrew Reynolds and Liana . Hadarean. (. FMCAD’16. ). 2. Stanford . University.