Syllabus

UNIT I

 

Introduction to Databases: Introduction, Traditional File-Based Systems, Database Approach, Roles in the Database Environment, Advantages and Disadvantages of DBMSs, The Three-Level ANSI-SPARC 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, Sub-queries, ANY and ALL, Multi-table 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, Multi-version 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, Computer-Based 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.



SYLLABUS

Unit

Content

No. of Classes

I

Groups: Definition and Examples of Groups- Elementary Properties of Groups-Finite Groups; Subgroups -Terminology and Notation -Subgroup Tests - Examples of Subgroups Cyclic Groups: Properties of Cyclic Groups - Classification of Subgroups Cyclic Groups-Permutation Groups: Definition and Notation -Cycle Notation-Properties of Permutations -A Check Digit Scheme Based on D5.

21

II

Isomorphisms ; Motivation- Definition and Examples -Cayley’s Theorem Properties of Isomorphisms -Automorphisms-Cosets and Lagrange’s Theorem Properties of Cosets 138 - Lagrange’s Theorem and Consequences-An Application of Cosets to Permutation Groups -The Rotation Group of a Cube and a Soccer Ball -Normal Subgroups and Factor Groups ; Normal Subgroups-Factor 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 Examples-Properties 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