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Tribhuvan university CSIT 2074 Syllabus Mathematics II

Mathematics II - Syllabus

Course Overview and Structure
Syllabus Notes Old Questions Unit Wise Questions Question Bank

Embark on a profound academic exploration as you delve into the Mathematics II course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2074 Syllabus, this course (MTH163) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 80+20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.


 

Units

Key Topics

  • System of Linear Equations
    LI-01

    A system of linear equations is a collection of linear equations involving two or more variables. It is a fundamental concept in linear algebra, and its solution is crucial in various fields such as physics, engineering, and computer science.

  • Row Reduction and Echelon Forms
    LI-02

    Row reduction is a method of transforming a matrix into its echelon form, which is a simplified form of the matrix. This process is essential in solving systems of linear equations and finding the inverse of a matrix.

  • Vector Equations
    LI-03

    Vector equations are equations involving vectors and scalars. They are used to represent systems of linear equations in a compact and expressive form, and are essential in linear algebra and its applications.

  • Matrix Equations Ax = b
    LI-04

    Matrix equations of the form Ax = b are a fundamental concept in linear algebra. They represent systems of linear equations, and their solution is crucial in various fields such as physics, engineering, and computer science.

  • Applications of Linear Systems
    LI-05

    Linear systems have numerous applications in various fields such as physics, engineering, computer science, and economics. They are used to model real-world problems, make predictions, and optimize systems.

  • Linear Independence
    LI-06

    Linear independence is a concept in linear algebra that determines whether a set of vectors is independent or dependent. It is essential in finding the basis of a vector space and solving systems of linear equations.

Key Topics

  • Introduction to Transaction Processing
    TR-1

    This topic introduces the concept of transaction processing, highlighting the differences between single user and multi-user systems, read/write operations, and the need for concurrency control to avoid problems such as lost update, temporary update, incorrect summary, and unrepeatable read.

  • Transaction and System Concepts
    TR-2

    This topic covers the fundamental concepts of transactions, including transaction states, system log, and commit point of transaction.

  • Desirable Properties of Transactions
    TR-3

    This topic discusses the desirable properties of transactions, namely atomicity, consistency, isolation, and durability (ACID).

  • Schedules and Concurrency Control
    TR-4

    This topic explores schedules, conflicting operations, and characterizing schedules based on recoverability and serializability, including serial, non-serial, and conflict serializable schedules.

  • Concurrency Control Techniques
    TR-5

    This topic introduces concurrency control techniques, including two-phase locking and timestamp ordering.

Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Partitioned

matrices, Matrix factorization, The Leontief input output model, Subspace of Rn, Dimension and

rank


Introduction, Properties, Cramer’s rule, Volume and linear transformations


Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly

independent sets: Bases, Coordinate systems


Dimension of vector space and Rank, Change of basis, Applications to difference equations,

Applications to Markov Chains


Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and

linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to

differential equations


Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The Gram-

Schmidt process, Least squares problems, Application to linear models, Inner product spaces,

Applications of inner product spaces


Key Topics

  • Optimization Problems and Greedy Algorithms
    GR-1

    Introduction to optimization problems and the concept of optimal solutions, with an overview of greedy algorithms and their elements.

  • Greedy Algorithm Applications
    GR-2

    Exploration of various applications of greedy algorithms, including fractional knapsack, job sequencing with deadlines, Kruskal's algorithm, Prim's algorithm, and Dijkstra's algorithm.

  • Huffman Coding
    GR-3

    Introduction to Huffman coding, including its purpose, prefix codes, and the Huffman coding algorithm, along with its analysis.

  • Social Network Analysis
    GR-4

    Social network analysis is the process of examining social structures, relationships, and interactions within a network. It involves using graph theory and statistical methods to understand social behavior and patterns.

Key Topics

  • Introduction to Risk Management
    RI-1

    Overview of risk management in software project management, importance and objectives.

  • Nature of Risk
    RI-2

    Understanding the nature of risk, types of risks, and risk characteristics.

  • Risk Identification
    RI-3

    Techniques and methods for identifying risks in software projects.

Lab works