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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

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix

equations Ax = b, Applications of linear system, Linear independence


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


Binary Operations, Groups, Subgroups, Cyclic Groups


Rings and Fields, Integral domains


Lab works