 Teacher: JAIMOLE CROSS
Syllabus
UNIT I 
Introduction to Databases: Introduction, Traditional FileBased Systems, Database Approach, Roles in the Database Environment, Advantages and Disadvantages of DBMSs, The ThreeLevel ANSISPARC Architecture, Database Languages, Data Models, Functions of a DBMS, Components of a DBMS. Relational Model: Introduction, Terminology, Integrity Constraints, Views. The Relational Algebra: Unary Operations, Set Operations, Join Operations, Division Operation, Aggregation and Grouping Operations.

UNIT II 
SQL: Introduction, Data Manipulation–Simple Queries, Sorting Results, Using the SQL Aggregate Functions, Grouping Results, Subqueries, ANY and ALL, Multitable Queries, EXISTS and NOT EXIST, Combining Result Tables, Database Updates. SQL: The ISO SQL Data Types, Integrity Enhancement Feature–Domain Constraints, Entity Integrity, Referential Integrity, General Constraints, Data Definition–Creating a Database, Creating a Table, Changing a Table Definition, Removing a Table, Creating an Index, Removing an Index, Views–Creating a View, Removing a View, View Resolution, Restrictions on Views, View Updatability, WITH CHECK OPTION, Advantages and Disadvantages of Views, View Materialization, Transactions, Discretionary Access Control–Granting Privileges to Other Users, Revoking Privileges from Users. Advanced SQL: The SQL Programming Language–Declarations, Assignments, Control Statements, Exceptions, Cursors, Subprograms, Stored Procedures, Functions, and Packages, Triggers, Recursion.

UNIT III 
Entity–Relationship Modeling: Entity Types, Relationship Types, Attributes, Keys, Strong and Weak Entity Types, Attributes on Relationships, Structural Constraints, Problems with ER Models–Fan Traps, Chasm Traps. Enhanced Entity–Relationship Modeling: Specialization/Generalization, Aggregation, Composition. Functional–Dependencies: Anomalies, Partial Functional Dependency, Transitive Functional Dependency, Multi Valued Dependency, Join Dependency. Normalization: The Purpose of Normalization, How Normalization Supports Database Design, Data Redundancy and Update Anomalies, Functional Dependencies in brief, The Process of Normalization,1NF, 2NF, 3NF, BCNF. The Database Design Methodology for Relational Databases (Appendix–D).

UNIT IV 
Transaction Management: Transaction Support–Properties of Transactions, Database Architecture, Concurrency Control–The Need for Concurrency Control, Serializability and Recoverability, Locking Methods, Deadlock, Time Stamping Methods, Multiversion Timestamp Ordering, Optimistic Techniques, Granularity of Data Items, Database Recovery–The Need for Recovery, Transactions and Recovery, Recovery Facilities, Recovery Techniques, Nested Transaction Model. Security: Database Security–Threats, ComputerBased Controls–Authorization, Access Controls, Views, Backup and Recovery, Integrity, Encryption, RAID.

Text References :
T1. Thomas M. Connolly, Carolyn E. Begg, Database Systems–A Practical Approach to Design, Implementation, and Management (6e). 
T2. Sharon Allen, Evan Terry, Beginning Relational Data Modelin. 
T3. Jeffrey A. Hoffer, V. Ramesh, HeikkiTopi, Modern Database Management. 
T4. Raghu Ramakrishnan, Johannes Gehrke, Database Management Systems. 
T5. RamezElmasri, Shamkant B. Navathe, Fundamentals of Database Systems 
T6. Abraham Silberschatz, Henry F. Korth, S. Sudarshan, Dat9abase System Concepts 
T7. C Coronel, S Morris, Peter Rob, Database Systems: Design, Implementation, and Management. 
 Teacher: APARNA VIJAYAN
Unit 
Content 
No. of Classes 
I 
Groups: Definition and Examples of Groups Elementary Properties of GroupsFinite Groups; Subgroups Terminology and Notation Subgroup Tests  Examples of Subgroups Cyclic Groups: Properties of Cyclic Groups  Classification of Subgroups Cyclic GroupsPermutation Groups: Definition and Notation Cycle NotationProperties of Permutations A Check Digit Scheme Based on D_{5}. 
21 
II 
Isomorphisms ; Motivation Definition and Examples Cayley’s Theorem Properties of Isomorphisms AutomorphismsCosets and Lagrange’s Theorem Properties of Cosets 138  Lagrange’s Theorem and ConsequencesAn Application of Cosets to Permutation Groups The Rotation Group of a Cube and a Soccer Ball Normal Subgroups and Factor Groups ; Normal SubgroupsFactor Groups Applications of Factor Groups Group Homomorphisms  Definition and Examples Properties of Homomorphisms The First Isomorphism Theorem. 
21 
III 
Introduction to Rings: Motivation and Definition Examples of Rings Properties of Rings Subrings Integral Domains : Definition and Examples –Characteristics of a Ring Ideals and Factor Rings; Ideals Factor Rings Prime Ideals and Maximal Ideals. 
17 
IV 
Ring Homomorphisms: Definition and ExamplesProperties of Ring Homomorphisms The Field of Quotients Polynomial Rings: Notation and Terminology. 
16 
TOTAL 
75 
Course Objective 

1 
To develop and understanding of the basic concepts of group theory and rings. 
2 
To encourage precision in the use of mathematical language, and to develop further the ability to understand and produce proofs in an algebraic context. 
Course Outcomes 


After the completion of the course the student will be able to 
CO1 
An exposure of well defined operations and recognise the algebraic structures. 
CO2 
Use the subgroup criterion to prove that various subsets are subgroups of some given group 
CO3 
Decide whether a given group is cyclic, and given a finite cyclic group, find a generator for a subgroup of a given order 
CO4 
Understand the notions of homomorphism and isomorphism in groups 
CO5 
Understand the notion of normal subgroup and determine whether a given subgroup is normal 
CO6 
Identifying the set of axioms that define the algebraic structure of a ring 
CO7 
Understand the notion of ideal and determine whether a given subset of a ring is an ideal 
CO8 
Identifying the properties that determine that a mapping between rings is a homomorphism. Understand polynomial rings and their use to construct finite fields 
 Teacher: RAM PRASAD D