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# Database Management Systems CS 623

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This 15 page Class Notes was uploaded by Kylee VonRueden on Wednesday September 30, 2015. The Class Notes belongs to CS 623 at Pace University - New York taught by Staff in Fall. Since its upload, it has received 69 views. For similar materials see /class/217102/cs-623-pace-university-new-york in ComputerScienence at Pace University - New York.

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Date Created: 09/30/15

A little of mathematics 0 Set of rows no duplicates 0 Each row describes a different entity 0 Each column states a particular fact about each entity Has an associated domain 0 We will be particu arly interested in relational databases 0 Data are stored in tables 0 Wh mathemat Relational databases are inspired of relations 7 mathe matics 0 Sets are the basic data structures of mathematics 0 Intuitiyely any welledefined collection of mathe matical objects can be grouped together to form a single object a set 0 Welleknown examples of sets from mathematics are the set of integers N the set of rational numbers Q and the set of real numbers R In computer science one often deals with sets of strings also called quotformal languagesquot or trees 0A Description of Sets set with no elements is called an empty set It is denoted Q or It is unique The number of element of a set S is denoted S We say also the cardinal of S Finite sets can in principle be described by listing their elements That we w te 901 NM to denote the set consisting of elements 501 Ame amehanmf de bngaetfi nite or infinite is to characterize via a logical for m t t t eement satisfy For every set S and formula Pav there exists a set denoted by ac 6 5 Pm that consists of all elements of S for which P is true Set Theory The basic concepts of sets theory are sets and the elementsrelationship The symbol 6 is commonly used to denote the membership relation and one writes so 6 to denote the proposition so is an element ofA which may be true or false Intuitively sets are unordered collections of ob jects where the multiplicities of elements don t atter Examples 12 21 12 1 222 123 1113 Examples of Sets o w 1 4 5 quotbommm o The finite set of integers between 2 and 5 nEZ 2ltnlt5 The open interval of real numbers between 2 and 5 wER 2ltwlt5 The infinite set of even integers nEZEkn2k 0 From a general description it may not always be obvious what the elements of the set are wayez6NgtltNgtltNlzwy Why 6 NgtltNgtltN I Eln e N n gt 2Aavnyn z Ordered Pairs and Tuples 0 Sets are unordered collections of elements Pairs m e gene a tuples a e ordered lections of elements Examples 12 is a pair a tuple of length 2 1245 is a tuple of length 4 o Tuples of different lengths are never equal 0 E amples 12 21 123 132 123 132 12 122 12 122 Subsets g 0 Definition Proper subsets A set A is a subset of another set 5 written 0 Definition A C B if and ony if every element of A is 33956 an element 0 A IS a proper subset of 5 written A C B if A is a subset of B but not equal to B 4 0 Examples E amples 12 g 123 1122 2 12 leacugza 1 2357 12cl1122 o The subset relation is often used to establish equale ity of sets based on the following lemma Lemma If A g B and 13 g A then A 13 Membership and subset relations Property of the Empty Set 0 Be careful about the distinction between the ele ment relation and the subset relation 0 Examples 0 Theorem If 9 is an empty set then g A for all sets A 2 6 123 2 6 123 2 g 1237 2 g 123 2 E 1e2 2 E 1e2 Cartesian Products Pairs and tuples provide us with a way of constructe ing new sets from given ones Definition If A and B are sets then there exists a set A x 13 read A cross 8quot called the Cartee sian product of A and B that consists of all ordered pairs ab where a 6 A an Symbolically Agtlt B abaEAAbEB For example if A 12 and B 45 then A X B 14 15 24 25 Properties of the Empty Set O Theorems Aui A Aw i More Set Operations Other operations for constructing sets include set union LJ set intersection 1 relative campiementatian or set difference campiementatian They are defined as follows Let A and B be subsets of some set U We define AuB wemweAVaceB A F avEUavEAAavEI 3 B wemweBAng weulwng Note that set difference can also be defined as fole lows A F A Ff For example let R be the set of real numbers Atheset wER 1 ltwgo B the set av EROSwlt 1 What are ALJ B A 1 B B A and A Set Identities 1 Set union and intersection are commutative M Set union and intersection are associative A Distributivity Au 5 q a Au 5 3 Au 0 A Double complement A j A U Idempotency A 1 A A LJ A A 6 De Morgan39s Laws Au 5 a B and An 13 Au 5 7 Absorption ALJA WB A and A 1ALJB A Sets can often be conveniently represented by Venn s diagram The union ALJ B of A and B is represented by The intersection Ad 13 is represented by u The set difference 13 A i s represented by u Powersets P Powerset Axiom If A is a set then there exists a set called the powerset of A and denoted by the syme bol 79A whose elements are exactly all the subsets of A Example If A is the set 123 then 79 A 1 1 Do we have 1 E 79A or NO because 1 1 etc If A has n elements how in its powerset Answer 2quot Why 2 2 9 1M H 2 3 717372737 3 2 679A or 3 673A many elements are there sjoint Sets Two sets A and B are said to be disjoint if they have no elements in common ie A B l E amples Is Q 1 9 N0 ENE 7 9 ll ls l 6 a l 9 Yes because A 1 l l Apartition fa etA a etnfpawe disjoint sets Al An such that A AlLJ2LJLJn For example at the end of the semester I will pare tition the class into subsets with grades of A A etc It wull be a partition since each student gets he and n he g a e Relations use ordered tuples to represent relatione ts ships among obJec Examples quotX is a parent ofy quot Morris Steve Rm Steve x is a number less than yquot 342 4243 Student number x is named y and majors in zquot 124324443 Mary 05E 563565426 Mary PSY x is an even numberquot 2 Essentially a relation is the set of assignments which makes a predicate true Examples IsParent Morm39s Steve Rm Steve LessThtm 342 42 43 MajorIn 124324443 Mary SSE 563565426 Mary PSY IsE ven n n 2k inary Relations Binary relations have two blanks relating two ob jects More formally suppose A and B are sets A binary relation f m A t B a et R g A 13 Thus R is a set of ordered pairs ab where a 6 A and b E 5 Notation If ab E R then we sometimes write aRb Example A 267 13 125 R1 is x in A is an integer multiple ofy in B quot so R1 21226 162 71 The Parent Of Relation The parent of relations x is a parent of yquot is a binary relation between pairs of people Table R Gene Joan William Sue Myrtle OrmondePaula Gene Joan W x x S Myrtle Orm Paula Graph Which representation is better for testing whether the pair 504 is in the relation Which representation is better for capturing the overall structure Presenting Binary Relations o Binary relations are particularly useful because they have two kinds of compact visual representation tables and graphs 0 Tables R R a b c 1 b 1 1 2 2 C ac ac C 3 3 b 3 c 0 Graphs are composed of vertices or nodes cone nected by edges or arcs There is an arc from a to b if ab E R CD CD CD General n ary Relations 0 Suppose Al Ag An are sets A relation of Al A is a set Rg Al x Agx gtlt An 0 Thus R is a set of ordered netuples a1a2 where a 6 A an 0 Example 41 N A names A3 majors tudent numbe named and ma n 2quot 124324443 Mary 03E 563565426 Mary PSY are tuples of the relation 0 Such structures are modeled by hypergraphs a graph structure where each quotedgequot represents a subset of more than two yertices Ov rviw o The most important commercial database systems today employ the relational model meaning that the data is stored as tab es of tuples ie relations A relation is a mathematical entity corresponding to a table row 7 tuple column attribute o A Shakespearian killed relation would be Killer Victim NJ US aesar Hamlet aertes Hamlet Polonius Laertes mlet Brutus Brutus Cassius Caesar 0 Requests for information from the database is made in a query language like SQL which is based on the notations of set theory and the predicate calculus 0 Example 1 Who killed Caesar 0 Example 2 Who was both a killer and a victim In SQL SELECT Killer from Killed INTERSECT SE LECT Victim from Killed 0 Much of the power of relational databases comes from the fact that we can combine different re lations o For example suppose we also have a diedby rela tion Victim Method We can combine the two tables with a J39oin opere ation which the tables based on common fields For example the join of killed and diedby is Killer Victim Method Hamlet Laer t s word Hamlet Polonlus Sword Laertes am word B u Bru s rd Cassius Caesar Daggers In SQL SELECT Killer from Killed where victimz Caesar This reads select from relation killed39 all tuples where the victim was Caesar and report only the killer field from each o Example 3 Which killers used daggers In SQL SELECT Killer FROM Killed Diedby WHERE KilledvictimdiedJyvictim AND Method Da ers 0 Note that this database design assumes that each tm an n be edb neweapn Rasputin C8623 Database management systems Dr Christelle Scharff PhD from France 1999 Research Automated deduction and theorem prov ing Verification of hardware and software Data mining New technologies in education French accent Teaching in France in Cambodia in USA State University of New York at Stony Brook cscharff paceedu httpwwwcsis paceeduscharff Prerequisites What do you know background operating sys tems software DBMS Oracle SQL JDBC XML PostgreSQL Highlevel language programming JAVA Data structures and algorithms Trees pointers searching sorting Discrete mathematical structures Sets relations graphs Formal logic Propositional logic truth table predicates What is cs623 0 Course description C5623 looks at the design of database management systems to obtain consis tency integrity and availability of data and at con ceptual models and schemas of data relational hierarchical and network It also discusses trans action processing systems Topics covered include models of transactions architectures of transaction processing systems and concurrent transactions Students undertake a semester project that includes the design and implementation of a database sys tem and of transactions 0 Goals By the end of this course students will be able to design and implement a database system and will have some practice using JDBC to imple ment a set of transactions They will also develop independent learning skills and will be aware of the research going on in databases 0 Tools Oracle SQL JDBC XML Description httpwwwcsispaceeduscharffcs623 Everything iswill be on the web Class time Office Hours When Where Textbooks Assignments Homeworks Project Research paper Exam Grades Academic integrity Guidelines for assignments Research Hierarchical network and object oriented models of data February 12 PostgreSQL February 12 XML Client Server Data mining Datawarehouse Internet and databases CORBA UML Distributed databases January 22 Presentation Overview of databases and transactions Chapter 1 and 2 January 29 The entity relationship model chap ter 5 February 5 Relational data model chapter 4 February 12 Relational algebra and SQL chapter 6 February 19 Advanced SQL chapter 6 Subjects of research papers due subject abstract and list of references February 26 Relational normalization theory chap ter 8 March 5 SQL in the real world JDBC chapter 10 March 12 No class Semester break March 19 Advanced topics in databases chapter 16171819 Research papers due and last research presentations March 26 Physical data organization and indexing chapter 9 April 2 Models of transactions chapter 21 April 9 Architectures of transaction processing systems chapter 22 April 16 Security and Internet protocols chapter 27 April 23 Presentations and demonstrations of the projects Last day of class April 30 Last presentations and review

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