Mathematics I - Syllabus

This topic covers the challenges faced by e-government in terms of security and the approaches to address them. It explores the importance of security in e-government and the ways to mitigate risks.

This topic introduces a security management model for e-government, outlining the key components and processes involved in ensuring the security of e-government systems.

This topic delves into the architecture of e-government security, including the design and implementation of secure systems and infrastructure for e-government services.

This topic covers the security standards and guidelines for e-government, including international standards and best practices for ensuring the security of e-government systems and data.

Security measures for protecting data during transactions in e-commerce.

Various security mechanisms used in e-commerce including cryptography, hash functions, digital signatures, authentication, access controls, intrusion detection systems, and secured socket layer (SSL).

Exploring the javax.servlet.http package, including key classes and interfaces. Understanding how to use the package to develop HTTP-based servlets.

Understanding how to handle HTTP requests and responses using servlets, including request and response objects.

Understanding how to use cookies in servlets, including setting and retrieving cookie values.

Understanding how to track user sessions using servlets, including session creation and management.

Introduction to JavaServer Pages (JSP), including their role in web development and key features.

Learn how to design relational databases using ER-to-relational mapping, including mapping of regular entities, weak entities, relationship types, multivalued attributes, and N-ary relationships.

Understand informal design guidelines for relational schemas, including semantics of attributes in relations, redundant information in tuples and update anomalies, NULL values in tuples, and generation of spurious tuples.

Study functional dependencies, including definition, inference rules, Armstrong's axioms, attribute closure, equivalence of functional dependencies, and minimal sets of functional dependencies.

Explore normal forms based on primary keys, including First Normal Form, Second Normal Form, Third Normal Form, and their general definitions.

Learn about Boyce-Codd Normal Form, a higher normal form that ensures a relational schema is in a good structure.

Understand multivalued dependency and Fourth Normal Form, which eliminates multivalued dependencies in a relational schema.

Study properties of relational decomposition, including attribute preservation, dependency preservation, and loss-less/non-additive join.

This topic explores the various applications of recursion in problem-solving, including tree traversals and dynamic programming.

This topic covers the challenges faced by e-government in terms of security and the approaches to address them. It explores the importance of security in e-government and the ways to mitigate risks.

This topic introduces a security management model for e-government, outlining the key components and processes involved in ensuring the security of e-government systems.

This topic delves into the architecture of e-government security, including the design and implementation of secure systems and infrastructure for e-government services.

This topic covers the security standards and guidelines for e-government, including international standards and best practices for ensuring the security of e-government systems and data.

Security measures for protecting data during transactions in e-commerce.

Various security mechanisms used in e-commerce including cryptography, hash functions, digital signatures, authentication, access controls, intrusion detection systems, and secured socket layer (SSL).

This topic introduces the concept of matrices, including their definition, notation, and basic operations. It lays the foundation for further study of matrices and their applications.

This topic covers the different types of matrices, including square matrices, diagonal matrices, identity matrices, and zero matrices. It explains their properties and characteristics.

This topic defines and explains the concept of equality of matrices, including the conditions for two matrices to be equal and the rules for comparing matrices.

This topic covers the basic algebraic operations of matrices, including addition, subtraction, multiplication, and scalar multiplication. It explains the rules and properties of these operations.

This topic introduces the concept of determinants, including their definition, calculation, and properties. It explains the importance of determinants in matrix theory and their applications.

This topic covers the concepts of transpose, minors, and cofactors of a matrix, including their definitions, calculations, and properties. It explains their relationships and applications.

This topic explains the various properties of determinants, including the multiplication property, addition property, and scalar multiplication property. It highlights their importance in matrix theory.

This topic defines and explains the concepts of singular and non-singular matrices, including their properties and characteristics. It highlights their importance in matrix theory and applications.

This topic covers the concepts of adjoint and inverse of matrices, including their definitions, calculations, and properties. It explains their relationships and applications.

This topic introduces the concept of linear transformations, including their definition, notation, and basic properties. It explains their importance in matrix theory and applications.

This topic covers the concept of orthogonal transformations, including their definition, properties, and applications. It highlights their importance in matrix theory and linear algebra.

This topic explains the concept of rank of matrices, including its definition, calculation, and properties. It highlights its importance in matrix theory and applications.

Understanding the different stages of an activity's life cycle, including creation, start, resume, pause, stop, and destroy. This topic covers the methods that are called during each stage.

Learning how to create multiple activities in an Android application, including defining and implementing separate activities for different tasks.

Introduction to the fundamental principle of counting, which is used to solve various counting problems in mathematics. This principle is essential in understanding permutation and combination.

Exploring the concept of permutation when all objects in a set are distinct and unique. This topic covers the formulas and techniques used to calculate the number of permutations in such cases.

Understanding permutation when a set contains objects that are not all distinct. This topic covers the modifications to the permutation formula to accommodate repeated objects.

Applying permutation concepts to circular arrangements, where the order of objects matters but the starting point is arbitrary. This topic covers the special considerations for circular permutations.

Examining permutation scenarios where objects can be reused, and the implications on the permutation formula. This topic covers the techniques used to calculate permutations in such cases.

Introducing the concept of combination, where the order of objects does not matter. This topic covers the formulas and techniques used to calculate the number of combinations when all objects are distinct.

Exploring the properties and characteristics of combinations, including the relationships between combinations and permutations. This topic covers the advanced concepts and applications of combination.