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Bhupal Nobles' University, Udaipur Convocation | भूपाल नोबल्स विश्वविद्यालय, उदयपुर दीक्षांत समारोह

भूपाल नोबल्स विश्वविद्यालय दीक्षांत समारोह महाराणा प्रताप स्टेशन रोड, सेवाश्रम सर्कल, उदयपुर। भूपाल नोबल्स विश्वविद्यालय उदयपुर द्वारा वर्ष 2018 से 2024 तक की स्नातक एवं स्नातकोत्तर परीक्षा में उत्तीर्ण एवं विद्यावाचस्पति (Ph.D.) उपाधिधारियों के लिए दीक्षान्त समारोह 27 मार्च 2025 गुरूवार को प्रातः 10:30 बजे आयोजित करने का निश्चित हुआ है। दीक्षान्त समारोह में 2020 से 2025 तक की विद्यावाचस्पति की उपाधियों तथा स्नातक एवं स्नातकोत्तर परीक्षाओं में वर्ष 2024 तक प्रथम स्थान प्राप्त करने वाले छात्रों को उपाधि एवं स्वर्ण पदक प्रदान किए जायेंगे। अतः जो उपाधिधारी उक्त समारोह में उपाधि प्राप्त करने के इच्छुक हों, वे समारोह में उपस्थित होने की लिखित सूचना के साथ स्नातक एवं स्नातकोत्तर प्रथम वरीयता प्राप्त छात्रों हेतु, पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) एवं विद्यावाचस्पति (Ph.D.), शोधार्थी पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) नकद अथवा डिमाण्ड ड्राफ्ट भूपाल नोबल्स विश्वविद्यालय, उदयपुर के नाम बनाकर कुलसचिव, भूपाल नोबल्स विश्वविद्यालय, उदयपुर को दिनांक 17.03.2025 तक ...
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Algebra | Mathematics | BSc

Algebra

Matrices, Theory of Equation and Group Theory



Authors: Dr. Vimal Saraswat, Dr. Gajendrapal Singh Rathore 

ISBN : 978-93-94954-35-9 

Price: Rs. 385.00

Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi

E-mail : info@sacademy.co.in

Phone: +91 9664392614

To buy this book click on Algebra by Saraswat

This book includes the following topics 

Matrix and its Rank

  • Introduction
  • Types of matrices
  • Operation on matrices or matrix algebra
  • Properties of matrix addition
  • Properties of scalar multiplication of matrix
  • Trace of a matrix
  • Multiplication of matrices
  • Properties of matrix multiplication
  • Transpose matrix
  • Symmetric and skew symmetric matrix
  • Orthogonal matrix
  • Conjugate matrix
  • Conjugate transpose matrix or tranjugate matrix
  • Unitary matrix
  • Hermitian and skew-Hermitian matrices
  • Sub matrx of a matrix
  • Determinant of a square matrix
  • Properties of determinant
  • Singular and non-singular matrix
  • Adjoint or adjugate matrix
  • Inverse of a matrix
  • Adjoint method for finding the inverse of a matrix
  • Elementary transformation method for finding the inverse of a matrix
  • Vector
  • Linear combination
  • Linear independent and linear dependent vector
  • Rank of a matrix
  • Column rank and row rank of a matrix
  • Nullity of a matrix
  • Equivalent matrix
  • Normal or canonical form of a matrix

Linear Equations, Eigen Values and Eigen Vectors

  • Introduction
  • System of homogeneous linear equation and their solution
  • System of non-homogeneous linear equations and their solution
    • ramer's rule, Inverse matrix method, Elementary transformation method
  • Condition of consistency
  • Working method for finding the solution of system of non-homogeneous linear equations
  • Triangular or echelon form of a matrix
  • Characteristics equation of a matrix
  • Cayley-Hamilton theorem
  • Application of Cayley-Hamilton's theorem
  • Eigen values and eigen vectors
  • Properties of eigen values of any characteristic equation
  • Nature of characteristic root or eigen values of some special type of matrices

Theory of Equations

  • Introduction
  • Rational integral function or polynomials
  • Equation
  • Roots of an equation
  • सIdentity
  • Properties of equation
  • Relation between roots and coefficients of equation
  • Solution of equation using relations of roots and coefficients
  • Symmetric function of the roots
  • Transformation of equations
    • Equation whose roots are k times the roots of a given equation, Equation whose roots are oppositely signed of a given equation, Equation whose roots are the reciprocals of the roots of a given equation
  • Reciprocal equation
  • Synthesis division
    • To diminish the roots by a given number; To remove a particular terms of an equation

Cubic and Biquadratic Equations

  • Introduction
  • Descarte’s rule of sign
  • Solution of cubic equation by Cardon’s method
  • Solution of general cubic equation by Cardon’s methods
  • Nature of the roots of cubic equations
  • Solution of biquadratic equation by Ferrari’s method
  • Newton’s method of approximation/li>
  • Horner's method

Group

  • Introduction
  • Cartesian product
  • Algebraic structure
  • Binary operation
  • Group
  • Finite and infinite group
  • Groupoid or quasi group
  • Semi-group
  • Monoid
  • Commutative or abelian group
  • Order of a group
  • Modulo operation
  • Uniqueness property in group
  • Properties of inverse in group
  • Cancellation law in group
  • Left and right identity element
  • Left and right inverse
  • Theorems based on semi group
  • Integral power of an element of group
  • Order of an element of a group
  • Klein's 4-group
  • Theorems based on order of element of a group

Subgroup

  • Introduction
  • Subgroup
  • Examples of subgroup
  • Multiplication of complexes of a group
  • Inverse of a complex of a group
  • Necessary and sufficient condition for a subgroup
  • Necessary and sufficient condition for a finite subset to be a subgroup
  • Necessary and sufficient condition for union to be a subgrop
  • Coset
  • Lagrange's theorem
  • Index of subgroup
  • Relation of congruence modulo of a group with respect to a sugroup
  • Euler's ф function
  • Properties of Euler's ф function
  • Euler's theorem
  • Fermat's theorem

Cyclic Group

  • Introduction
  • Cyclic group
  • Theorems based on cyclic group

Normal Subgroup and Quotient Group

  • Introduction
  • Normal subgroup
  • Simple group
  • Theorem based on normal subgroup
  • Quotient group
  • Commutator subgroup

Permutation Group

  • Introduction
  • Permutation
  • Equivalent or equal permutation
  • Identity permutation)/li>
  • Product of permutation
  • Inverse permutation
  • Permutation group
  • Symmetric group
  • Cyclic permutation or cycles and the length of cyclic permutation
  • Inverse of cycle
  • Order of a cycle
  • Disjoint cycles
  • Order of permutation
  • Transposition
  • Even and odd permutation

Group Homomorphism

  • Introduction
  • Homomorphism
  • Types of homomorphism
    • Monomorphism, Epimorphism, Isomorphism, Endomorphism, Automorphism
  • Kernel of homomorphism
  • Theorem based on homomorphism
  • Natural homomorphism
  • Fundamental theorem of homomorphism
  • Three theorems on isomorphism
  • Cayley's theorem
  • Inner automorphism

Centre of group, Normalizer and Class equation

  • Introduction
  • Conjugate elements
  • Conjugate class
  • Self-conjugate element
  • Normalizer of an element
  • Centre of group
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