PPT-Congruence

Geometry for Teachers Von Christopher G Chua LPT MST Instructor Geometry for Teachers Chapter Objectives For this chapter in the course on Statistical Methods graduate students are expected to develop the following learning competencies. Congruence Relations Youre young Myrtle Mae Youve got a lot to learn and I hop e you never learn it Vita in Harvey You are doubtless familiar with the connection between homo morphisms and normalsubgroupsofgroup If am 1 then the congruence ax mod phas exactly one solution modulo Constructive Solve the linear system sa tm 1 Then sba tbm b So sba mod gives the solution sb If and are solutions then au mod and au mod au au mod mod since a If we assume that gcd am 1 then the equation has in64257nitely many solutions We can 64257nd all solutions as follows 1 Using Euclids extended algorithm we 64257nd an integer such that ax 1 mod 1 Such an is called an inverse of modulo 2 Multiplyin for 3D memory systems. CAMEO. 12/15/2014 MICRO. Cambridge, UK. Chiachen Chou, Georgia Tech. Aamer. . Jaleel. , Intel. Moinuddin. K. . Qureshi. , Georgia Tech. Executive Summary. How to use . S. tacked DRAM: Cache or Memory. Chapter 4. With Question/Answer Animations. Chapter Motivation. Number theory . is the part of mathematics devoted to the study of the integers and their properties. . Key ideas in number theory include divisibility and the . 1.People are types. 2. Environments are types. 3. Birds of a feather flock together. 4. Behavior = ƒ(congruence). Holland’s five key concepts. 1. Calculus. 2. Consistency. 3. Differentiation. Tom Sallee. University of California, Davis. BE SURE TO ASK QUESTIONS . This talk is for you—not me.. Most basic geometric question . What does it mean to say that two geometric figures or objects are “the same”. Side-Angle-Side (SAS) Congruence Postulate. If two sides and the included angle are congruent to the corresponding sides and angles on another triangle, then the triangles are congruent. . EXAMPLE 1. Helpful websites. http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm. http://www.mathwarehouse.com/geometry/congruent_triangles/. http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html. Postulates. Postulate: a rule that is accepted without proof. Theorem: a rule that can be proved. Postulate 1 – Ruler Postulate. . The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is he coordinate of the point.. Review Quiz . #10. Proving Theorems about . Parallelograms. Question 1. Determine whether these four vertices form a parallelogram: . A . (–3, 0), . B . (6, 0), . C . (1, 1), . D . (–2, –2).. No, because both pairs of opposite sides are not parallel.. The Back Story. Aptly named Deputy Nick Crimes has just woken from a coma to discover that Earth is in the midst of a zombie apocalypse. The "shufflers" and "nibblers", as the zombies are known, are continually looking for "fresh meat" in the form of human flesh.. Chapter 4. Objective. List corresponding parts.. Prove triangles congruent (ASA, SAS, AAS, SSS, HL). Prove corresponding parts congruent (CPCTC). Examine overlapping triangles.. Key Vocabulary - Review. Nikolaj Bj. ø. rner. Microsoft Research. Lecture 2. Overview of the lectures. Day. Topics. Lab. 1. Overview of SMT and applications. . SAT solving,. Z3. Encoding combinatorial problems with Z3. 2. Congruence closure.