PPT-Copyright © Peter

Cappello Mathematical Induction Goals Explain amp illustrate construction of proofs of a variety of theorems using mathematical induction Copyright Peter Cappello Motivation Mathematics uses 2 kinds of arguments. Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. Predicates & Quantifiers. Copyright © Peter Cappello 2011. The Limits of Propositional Logic. Consider the argument. . All. computer science courses are easy.. CS 40 is a computer science course.. Votkinsk. in 1840. . P. eter wrote his music during a time known as the Romanic period. He used his great imagination create beautiful music that was sometimes very happy and sometimes very sad.. Peter Tchaikovsky first became interested in music when he was four or five years old. One day Peter’s father brought home a large machine that played music called an . Selected Exercises. Goal:. Introduce fundamental . number . theory concepts: . T. he . division . algorithm. Congruences. Rules of modular arithmetic. Copyright © Peter . Cappello. 2. Exercise 10. Goal: . Show . how . propositional equivalences . are established . & introduce . the most . important such . equivalences.. Copyright © Peter . Cappello. 2. Equivalence. Name. p .  T . ≡ p; p . Selected Exercises. Goal. Explain & illustrate proof construction of . a variety of theorems using strong induction. Copyright © Peter Cappello. 2. Strong Induction. Domain of discussion is the . Structural Induction:. Selected Exercises. Copyright © Peter Cappello. 2. Exercise 10. Give a recursive definition of . S. m. (. n . ). , the sum of integer . m. + nonnegative integer . n. .. Copyright © Peter Cappello. Selected Exercises. Partial Order. Let R be a relation on A.. R is a . partial order . when it is:. Reflexive. Antisymmetric. Transitive.. Copyright © Peter Cappello. 2. Copyright © Peter . Cappello. Selected Exercises. Goals. . Introduce . big-O . & big. -. Omega. S. how . how . to estimate . the size of functions using this notation.. Copyright © Peter . Cappello. 2. Preface. You may use . The foundation stone of the . fortress. was laid on the 16. th. of May . in . 1703. This is the day of St. Petersburg’s foundation. It was decided to build fortress here, because of its location. . 5 . For this very reason, make every effort to add to your faith goodness; and to goodness, knowledge; . 6 . and to knowledge, self-control; and to self-control, perseverance; and to perseverance, godliness; . Thus, employees only stop being promoted once they can no longer perform effectively, so, "managers rise to the level of their incompetence.". The . Peter Principle. is a concept in management theory in which the selection of a candidate for a position is based on the candidate's performance in their current role . AD63. AD64. 1 PETER. July 19, AD64 . Neronian. fire begins. 1 Peter written sometime between AD62-64. Approximate time of Paul’s appearance before Nero. Dispersion. ~ . diaspora. 1 PETER. Pilgrims. Matthew 16:13-19. Matthew 16:18-19. 18.  And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. . 19.  And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven..