ICT-MATHEMATICS

MATHEMATICS

Mathematics deals with exact measurement and is there a thing in the world that is not measurable? to be is to be measurable. If a thing cannot be measured, it cannot exist!

The world exists in relationship among variables and mathematics expresses that. Is it not then life? 

It is....................................................

We introduce mathematics in a different way. Instead of treating mathematics abstractly, we introduce all the concepts of mathematics with a link to life. We make it totally clear that mathematics is not a game but a way of grasping and handling the world in exact quantitative terms. 

We cover all the important concepts of mathematics that are needed to deal with the world powerfully!

Happy learning and discovery!

ABSTRACT ALGEBRA

DIRECT PRODEUCT OF GROUPS (EXTERNAL DIRECT PRODEUCT OF GROUPS) MODULE-I

DIRECT PRODEUCT OF GROUPS (INTERNAL DIRECT PRODEUCT OF GROUPS) MODULE-2

PRIMARY DECOMPOSITION THEOREM FOR FINITE ABELIAN GROUPS (DIRECT PRODEUCT OF GROUPS) MODULE-3

THE FUNDAMENTAL THEOREM OF FINITE ABELIAN GROUPS – EXISTENCE (DIRECT PRODEUCT OF GROUPS) MODULE-4

THE FUNDAMENTAL THEOREM OF FINITE ABELIAN GROUPS – UNIQUENESS (DIRECT PRODEUCT OF GROUPS) MODULE-5

CONJUGATION – CONJUGACY CLASS EQUATION - MODULE-I

CONJUGATION – CAUCHY’S THEOREM AND IT’S CONSEQUENCES - MODULE-2

SYLOW THEOREMS – GROUP ACTION - MODULE-I

SYLOW THEOREMS – SYLOW’S FIRST THEOREM - MODULE-2

SYLOW THEOREMS – SYLOW’S SECOND AND THIRD THEOREMS - MODULE-3

SYLOW THEOREMS – APPLICATIONS OF SYLOW THEOREMS - MODULE-4

NILPOTENT AND SOLVABLE GROUPS – NILPOTENT GROUPS - MODULE-I

NILPOTENT AND SOLVABLE GROUPS - SOLVABLE GROUPS(1) - MODULE-2

NILPOTENT AND SOLVABLE GROUPS - SOLVABLE GROUPS(2) - MODULE-3

NILPOTENT AND SOLVABLE GROUPS – JORDAN- HOLDER THEOREM - MODULE-4

POLYNOMIAL RINGS - INTRODUCTION TO POLYNOMIALS 

POLYNOMIAL RINGS - DIVISION ALGORITHM AND ITS CONSEQUENCES 

POLYNOMIAL RINGS - FROM ARITHMETIC TO POLYNOMIALS - MODULE-3

IRREDUCIBILITY OF POLYNOMIALS OVER A FIELD

MAXIMAL IDEALS

PRIME IDEALS

DIVISIBILITY IN COMMUTATIVE RINGS

PRIME AND IRREDUCIBILITY ELEMENTS

FACTORIZATIONS IN INTEGRAL DOMINS – EUCLIDEAN AND PRINCIPAL IDEAL DOMAINS - MODULE-3

FACTORIZATIONS IN INTEGRAL DOMINS - UNIQUE FACTORIZATION DOMAINS - MODULE-4

THE RING OF GAUSSIAN INTEGERS

FIELD EXTENSIONS – EXTENSIONS OF FIELDS - MODULE-I

FIELD EXTENSIONS - MINIMAL POLYNOMIALS - MODULE-2

FIELD EXTENSIONS – ALGEBRAIC EXTENSIONS - MODULE-3

SPLITTING FIELDS AND SEPARABILITY OF A POLYNOMIAL - SPLITTING FIELDS OF A POLYNOMIAL - MODULE-I

SPLITTING FIELDS AND SEPARABILITY OF A POLYNOMIAL - UNIQUENESS OF SPLITTING FIELDS - MODULE-2

SPLITTING FIELDS AND SEPARABILITY OF A POLYNOMIAL - SEPARABILITY OF A POLYNOMIAL - MODULE-3

APPLICATIONS OF FIELDS EXTENSIONS – EXISTENCE AND UNIQUENESS OF GALOIS FIELDS - MODULE-1

APPLICATIONS OF FIELDS EXTENSIONS – CHARACTERIZATIONS GALOIS FIELDS - MODULE-2

APPLICATIONS OF FIELDS EXTENSIONS – CONSTRUCTION WITH STRAIGHTEDGE AND COMPASS - MODULE-3

APPLICATIONS OF FIELDS EXTENSIONS – CONSTRUCTIBILITY OF REAL NUMBERS - MODULE-4

APPLICATIONS OF FIELDS EXTENSIONS – WEDDERBURN’S THEOREM ON FINITE DIVISION RINGS - MODULE-5

LINEAR ALGEBRA

LINEAR EQUATIONS-INTERDUCTION TO SYSTEMS OF LINEAR EQUATIONS-MODULE-1

LINEAR EQUATIONS-ROW REDUCTION AND THE GAUSSIAN ELIMINATION-MODULE-2

VECTOR SPACES- INTERDUCTION TO VECTOR SPACES- MODULE-1

VECTOR SPACES-SUB SPACES- MODULE-2

VECTOR SPACES – LINEAR COMBINATIONS AND SPANNING SETS - MODULE-3

VECTOR SPACES – LINEAR INDEPENDENCE AND DEPENDENCE OF VECTORS - MODULE-4

VECTOR SPACES –BASES AND DIMENSION OF A VECTOR SPACE - MODULE-5

VECTOR SPACES – MAXIMAL LINEARLY INDEPENDENT SUBSETS - MODULE-6

VECTOR SPACES – MAXIMAL LINEARLY INDEPENDENT SUBSETS(SUM&QUOTIENT) - MODULE-7

LINEAR TRANSFORMATIONS AND MATRICES - LINEAR TRANSFORMATIONS - MODULE-1

LINEAR TRANSFORMATIONS AND MATRICES – MATRIX REPRESENTATIONS - MODULE-2

LINEAR TRANSFORMATIONS AND MATRICES – INVERTIBILITY OF LINEAR MAPS - MODULE-3

LINEAR TRANSFORMATIONS AND MATRICES – THE RANK OF A MATRIX - MODULE-4

LINEAR TRANSFORMATIONS AND MATRICES – DETERMINANTS OF SQUARE MATRICES - MODULE-5

LINEAR TRANSFORMATIONS AND MATRICES – CHARACTERIZATION OF THE DETERMINANT FUNCTION - MODULE-6

DIAGONALIZATION OF A LINEAR OPERATOR – EIGENVALUES AND EIGENVECTORS OF A LINEAR OPERATOR - MODULE-1

DIAGONALIZATION OF A LINEAR OPERATOR – DIAGONALIZATION- MODULE-2

DIAGONALIZATION OF A LINEAR OPERATOR – CRITERION FOR DIAGONALIZATION OF A LINEAR OPERATOR – MODULE-3

DIAGONALIZATION OF A LINEAR OPERATOR – MINIMAL POLYNOMIAL OF A LINEAR OPERATOR – MODULE-4

INNER PRODUCT SPACES AND LINEAR OPERATOR - INNER PRODUCT SPACES - MODULE-1

INNER PRODUCT SPACES AND LINEAR OPERATOR – ORTHOGONALIZATION AND ORTHOGONAL COMPLEMENTS - MODULE-2

INNER PRODUCT SPACES AND LINEAR OPERATOR – PROJECTION OPERATOR - MODULE-3

INNER PRODUCT SPACES AND LINEAR OPERATOR – OPERATORS ON INNER PRODUCT SPACES - MODULE-4

INNER PRODUCT SPACES AND LINEAR OPERATOR – NORMAL AND SELF-ADJOINT OPERATORS - MODULE-5

INNER PRODUCT SPACES AND LINEAR OPERATOR – SPECTRAL DECOMPOSITION - MODULE-6

INNER PRODUCT SPACES AND LINEAR OPERATOR – UNITARY AND ORTHOGONAL OPERATORS - MODULE-7

INNER PRODUCT SPACES AND LINEAR OPERATOR - ORTHOGONAL OPERATORS - MODULE-8

BILINEAR FORMS – DEFINITION AND BASIC PROPERTIES - MODULE-1

BILINEAR FORMS – SYMMETRIC BILINEAR FORMS - MODULE-2

BILINEAR FORMS – QUADRATIC FORMS - MODULE-3

CANONICAL FORMS – JORDAN CANONICAL FORMS 1 - MODULE-1

CANONICAL FORMS – JORDAN CANONICAL FORMS 2 - MODULE-2

CANONICAL FORMS – JORDAN CANONICAL FORMS 3 - MODULE-3

MODULES – DEFINITIONSAND BASIC PROPERTIES - MODULE-1

MODULES – FREE MODULES - MODULE-2

REAL ANALYSIS AND MEASURE THEORY

LEBESGUE OUTER MEASURE - DEFINITION AND PROPERTIES OF LEBESGUE OUTER MEASURE – MODULE-1

LEBESGUE OUTER MEASURE - LEBESGUE MEASURABLE SETS AND THEIR PROPERTIES - MODULE-2

LEBESGUE OUTER MEASURE - EXAMPLES AND SOME FURTHER OBSERVATIONS ON MEASURABLE SETS - MODULE-3

LEBESGUE MEASURE – NOTION OF LEBESGUE MEASURE AND IT’S BASIC PROPERTIES - MODULE-1

LEBESGUE MEASURE - CHARACTERIZATION OF MEASURABLE SETS AND FURTHER OBSERVATIONS - MODULE-2

LEBESGUE MEASURE - EXISTENCE OF A NON-MEASURABLE SET - MODULE-3

LEBESGUE MEASURE - NOTION OF INNER MEASURE - MODULE-4

LEBESGUE MEASURABLE FUNCTIONS - LEBESGUE MEASURABLE FUNCTIONS AND BASIC PROPERTIES - MODULE-1

LEBESGUE MEASURABLE FUNCTIONS - ALMOST EVERYWHERE CONCEPT AND ITS IMPLICATIONS - MODULE-2

LEBESGUE MEASURABLE FUNCTIONS - SIMPLE FUNCTIONS AS BUILDING BLOCKS OF LEBESGUE MEASURABLE FUNCTIONS - MODULE-3

CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS - CONVERGENCE ALMOST EVERYWHERE AND CONVERGENCE IN MEASURE - MODULE-1

CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS - RELATION BETWEEN ALMOST EVERYWHERE CONVERGENCE AND CONVERGENCE IN MEASURE - MODULE-2

CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS - ALMOST UNIFORM CONVERGENCE AND EGOROFF'S THEOREM - MODULE-3

CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS - CONVERGENCE OF SEQUENCES OF MEASURABLE FUNCTIONS LUSIN’S THEOREM 

LEBESGUE INTEGRATION OF BOUNDEDMEASURABLE FUNCTIONS - MOTIVATION AND INTRODUCTION OF THENOTION OF LEBESGUE INTEGRATION OFBOUNDED FUNCTIONS - MODULE-1

LEBESGUE INTEGRATION OF BOUNDEDMEASURABLE FUNCTIONS - EQUIVALENCE OF MEASURABILITY AND INTEGRABILITY AND BOUNDED CONVERGENCE THEOREM- MODULE-2

LEBESGUE INTEGRATION OF BOUNDEDMEASURABLE FUNCTIONS - RIEMANN INTEGRATION AND LEBESGUE INTEGRATION - MODULE-3

LEBESGURE INTEGRATION OF ARBITRARY MEASURABLE FUNCTIONS - LEBESGUE INTEGRAL OF NON-NEGATIVE FUNCTIONS AND MONOTONE CONVERGENCE THEOREM - MODULE-1

LEBESGURE INTEGRATION OF ARBITRARY MEASURABLE FUNCTIONS - FATOU'S LEMMA AND NOTION OF LEBESGUE INTEGRABLE FUNCTIONS - MODULE-2

LEBESGURE INTEGRATION OF ARBITRARY MEASURABLE FUNCTIONS - MOST GENERAL NOTION OF LEBESGUE INTEGRABILITY AND OMINATED CONVERGENCE THEOREM - MODULE-3

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - FUNCTIONS OF BOUNDED VARIATIONS - MODULE-1

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - VITALI COVERING THEOREM - MODULE-2

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - ABSOLUTELY CONTINUOUS FUNCTIONS- MODULE-3

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - FURTHER RESULTS ON ABSOLUTELY CONTINUOUS FUNCTIONS AND DINI'S DERIVATES - MODULE-4

FUNCTIONS OF BOUNDED VARIATIONS ANDASSOCIATED CONCEPTS - DIFFERENTIABILITY OF NON-DECREASING FUNCTIONS - MODULE-5

MORE ON LEBESGUE INTEGRATION: EXISTENCE OF INDENITE INTEGRAL ANDFUNDAMENTAL THEOREM OF INTEGRAL CALCULUS - SOME USEFUL RESULTS OF LEBESGUE INTEGRATION - MODULE-1

MORE ON LEBESGUE INTEGRATION: EXISTENCE OF INDENITE INTEGRAL ANDFUNDAMENTAL THEOREM OF INTEGRAL CALCULUS - FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS FOR RIEMANN INTEGRATION AND IT'S DEFICIENCY- MODULE-2

MORE ON LEBESGUE INTEGRATION: EXISTENCE OF INDENITE INTEGRAL ANDFUNDAMENTAL THEOREM OF INTEGRAL CALCULUS - FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS FOR LEBESGUE INTEGRATION - MODULE-3

ABSTRACT MEASURE THEORY - RINGS AND Σ-RINGS - MODULE-1

ABSTRACT MEASURE THEORY - MONOTONE CLASSES- MODULE-2

ABSTRACT MEASURE THEORY - ABSTRACT MEASURE AND ABSTRACT OUTER MEASURE- MODULE-3

ABSTRACT MEASURE THEORY - EXTENSION OF MEASURE AND THE NOTION MEASURABLE COVERS - MODULE-4

ABSTRACT MEASURE THEORY - COMPLETE MEASURE AND THE NOTION OF COMPLETION - MODULE-5

RIEMANN-STIELTJES INTEGRAL - RIEMANN-STIELTJES INTEGRAL AND ITS BASIC PROPERTIES - MODULE-1

RIEMANN-STIELTJES INTEGRAL - NOTION OF DARBAUX STIELTJES INTEGRAL AND ITS IMPLICATIONS - MODULE-2

ORDINARY DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS 

ORDINARY DIFFERENTIAL EQUATIONS : INTRODUCTION –INTRODUCTION – MODULE – 1

FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS : LINEAR DIFFERENTIAL EQUATIONS - MODULE - 1

FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS : EXISTENCE AND UNIQUENESS THEOREM - MODULE – 2

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS - GENERAL PROPERTIES OF SOLUTIONS - MODULE – 1

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS - METHOD OF VARIATION OF PARAMETERS - MODULE – 2

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS - POWER SERIES SOLUTIONS - MODULE – 3

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS - ORDINARY AND SINGULAR POINTS - MODULE – 4

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS -FROBENIUS SERIES METHOD-I - MODULE – 5

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS -FROBENIUS SERIES METHOD-II - MODULE – 6

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS -FROBENIUS SERIES METHOD-III - MODULE – 7

LEGENDRE POLYNOMIALS - LEGENDRE EQUATION AND ITS SOLUTION- MODULE – 1

LEGENDRE POLYNOMIALS - GENERATING FUNCTION FOR LEGENDRE POLYNOMIALS - MODULE – 2

LEGENDRE POLYNOMIALS - RECURRENCE RELATIONS - MODULE – 3

LEGENDRE POLYNOMIALS - ORTHOGONAL PROPERTIES OF LEGENDRE - MODULE – 4

LEGENDRE POLYNOMIALS - LEGENDRE FUNCTION OF SECOND KIND - MODULE – 5

BESSEL'S FUNCTION - BESSEL'S EQUATION AND ITS SOLUTION - MODULE – 1

BESSEL'S FUNCTION - RECURRENCE RELATIONS AND ORTHOGONAL PROPERTY- MODULE – 2

HYPERGEOMETRIC FUNCTION - HYPERGEOMETRIC EQUATION AND ITS SOLUTION- MODULE – 1

HYPERGEOMETRIC FUNCTION - CONFLUENT HYPERGEOMETRIC FUNCTION- MODULE – 2

HYPERGEOMETRIC FUNCTION - PROBLEMS ON HYPERGEOMETRIC FUNCTION- MODULE – 3

LAGUERRE’S POLYNOMIALS - SOLUTION OF LAGUERRE'S EQUATION - MODULE – 1

LAGUERRE’S POLYNOMIALS - RECURRENCE RELATIONS AND ORTHOGONAL PROPERTY OF LAGUERRE'S POLYNOMIALS - MODULE – 2

HERMITE POLYNOMIALS - SOLUTION OF HERMITE EQUATION- MODULE – 1

HERMITE POLYNOMIALS - GENERATING FUNCTION AND RECURRENCE RELATIONS- MODULE – 2

HERMITE POLYNOMIALS - ORTHOGONAL PROPERTY OF HERMITE POLYNOMIALS- MODULE – 3

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - INTRODUCTION TO HIGHER ORDER ORDINARY DIFFERENTIAL - MODULE – 1

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - LINEAR HOMOGENEOUS AUTONOMOUS SYSTEM - MODULE – 2

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - SOLUTION OF HOMOGENEOUS EQUATIONS: EQUAL ROOTS - MODULE – 3

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - FUNDAMENTAL MATRIX SOLUTIONS - MODULE – 4

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - FUNDAMENTAL SOLUTIONS IN EXPONENTIAL FORM - MODULE – 5

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATION - NONHOMOGENEOUS SYSTEM OF EQUATIONS - MODULE – 6

QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS - INTRODUCTION TO QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS - MODULE – 1

QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS - LINEAR DIFFERENTIAL EQUATIONS- MODULE – 2

QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS - STABILITY OF LINEAR SYSTEMS - MODULE – 3

QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS - STABILITY OF EQUILIBRIUM SOLUTIONS - MODULE – 4

TOPOLOGY

INTRODUCTION TO TOPOLOGICAL SPACES - INTRODUCTION TO TOPOLOGICAL SPACES – MODULE-1

INTRODUCTION TO TOPOLOGICAL SPACES – BASE OF TOPOLOGICAL SPACES

INTRODUCTION TO TOPOLOGICAL SPACES – NEW SPACES FROM OLD ONE – MODULE-3

INTRODUCTION TO TOPOLOGICAL SPACES – INTRODUCTION OF CONTINUITY – MODULE-4

INTRODUCTION TO TOPOLOGICAL SPACES – HOMEOMORPHISM – MODULE-5

INTRODUCTION TO TOPOLOGICAL SPACES – PRODUCT TOPOLOGY – MODULE-6

COUNTABILITY AXIOMS – METRIZABLE SPACES – MODULE - 1

COUNTABILITY AXIOMS – FIRST COUNTABILITY AND SECOND COUNTABILITY – MODULE - 2

COUNTABILITY AXIOMS – LINDELFOFNESS – MODULE - 3

SEPARATION AXIOMS - SEPARATION AXIOMS - MODULE – 1

SEPARATION AXIOMS - SEPARATION AXIOMS, NORMALITY - MODULE – 2

SEPARATION AXIOMS – PROPERTIES OF NORMALITY SPACES - MODULE – 3

SEPARATION AXIOMS – URYSHON’S LEMMA - MODULE – 4

SEPARATION AXIOMS – TIETZE EXTENSION THEOREM - MODULE – 5

CONNECTEDNESS – INTRODUCTION TO CONNECTED SPACES - MODULE – 1

CONNECTEDNESS – EXAMPLES OF CONNECTED SPACES - MODULE – 2

CONNECTEDNESS – PATH CONNECTED SPACES - MODULE – 3

CONNECTEDNESS – COMPONENTS - MODULE – 4

CONNECTEDNESS – MATRIX LIE GROUPS - MODULE – 5

COMPACTNESS – INTRODUCTION TO COMPACT TOPOLOGICAL SPACES - MODULE – 1

COMPACTNESS –FINITE PRODUCT OF COMPACT SPACES - MODULE – 2

COMPACTNESS –ALEXANDER SUB-BASE THEOREM - MODULE – 3

COMPACTNESS – COMPACT IN MATRIC SPACES- MODULE – 4

COMPACTNESS - LOCAL COMPACTNESS- MODULE – 5

COMPACTNESS- TYCHONO PRODUCT THEOREM- MODULE – 6

COMPACTNESS - COMPACTNESS IN METRIC SPACES, SOME ADVANCED PROPERTIES - MODULE – 7

COMPACTNESS – EQUICONTINUITY AND CLASSICAL VERSION OF ASCOLI’S THEOREM - MODULE – 8

COMPACTNESS- POINTWISE AND COMPACT CONVERGENCE - MODULE – 9

COMPACTNESS – COMPACT OPEN TOPOLOGY - MODULE – 10

COMPACTNESS – BAIRE SPACES - MODULE – 11

COMPACTNESS –STONE WEIERSTRASS THEOREM - MODULE – 12

COMPACTNESS –STONE WEIERSTRASS CECH COMPACTIFICATION - MODULE – 13

QUOTIENT TOPOLOGY – QUOTIENT SPACES - MODULE – 1

QUOTIENT TOPOLOGY – A QUICK REVIEW ON TOPOLOGICAL GROUP - MODULE – 2

QUOTIENT TOPOLOGY – ORBIT SPACE - MODULE – 3 

CALCULUS OF SERVERAL VERIABLES 

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - MEANING OF Rn

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - SCALAR AND VECTOR FIELDS

CALCULUS OF SERVERAL VERIABLES – FUNCTIONS ON Rn - LINEAR TRANSFORMATIONS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - LIMITS AND CONTINUITY OF SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - PARTIAL DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - VECTOR DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - PROPERTIES OF VECTOR DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - TOTAL DERIVATIVE

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - DISCUSSIONS ON DIFFERENTIABILITY

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - GRADIENT OF A SCALAR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - SUFFICIENT CONDITIONS FOR DIFFERENTIABILITY

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - CHAIN RULE FOR DERIVATIVES OF SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - HOMOGENEOUS FUNCTIONS AND EULER'S THEOREM

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF SCALAR FIELDS - ON EQUALITY OF MIXED PARTIAL DERIVATIVES

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – TAYLOR SERIES FOR SCALAR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – LIMITS AND CONTINUITY OF VECTOR FIELDS

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – VECTOR DERIVATIVE OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – TOTAL DERIVATIVE OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – DISCUSSIONS ON DIFFERENTIABILITY OF A VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – JACOBIAN MATRIX OF A DIFFERENTIABLE VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – CALCULUS OF VECTOR FIELDS – MEAN VALUE THEOREM FOR A DIFFERENTIABLE VECTOR FIELD

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – INTRODUCTION TO INTEGRATION

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – ON CURVES AND THEIR LENGTHS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – ON LINE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS – FUNDAMENTAL THEOREMS OF CALCULUS ON LINE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – LINE INTEGRALS NECESSARY AND SUFFICIENT CONDITIONS FOR A VECTOR FIELD TO BE GRADIENT

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – DOUBLE INTEGRALS-I

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – DOUBLE INTEGRALS-II

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – GREEN'S THEOREM

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS – CHANGE OF VARIABLES IN DOUBLE INTEGRAL

CALCULUS OF SERVERAL VERIABLES – MULTIPLE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – INTRODUCTION TO SURFACES

CALCULUS OF SERVERAL VERIABLES – SURFACE INTEGRALS

CALCULUS OF SERVERAL VERIABLES – SURFACE INTEGRALS - STOKES THEOREM AND DIVERGENCE THEOREM

CALCULUS OF SERVERAL VERIABLES – INVERSE FUNCTION THEOREM AND IMPLICIT FUNCTION THEOREM 

COMPLEX ANALYSIS 

COMPLEX ANALYSIS – COMPLEX NUMBERS – BASIC IDEAS

COMPLEX ANALYSIS – COMPLEX NUMBERS – STEREOGRAPHIC PROJECTION

COMPLEX ANALYSIS – COMPLEX NUMBERS – STRAIGHT LINE AND CIRCLE IN THE COMPLEX PLANE

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – BASIC DEFINITIONS

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – LIMIT OF A FUNCTION

COMPLEX ANALYSIS – CONCEPT OF FUNCTIONS, LIMIT AND CONTINUITY – CONTINUITY OF A FUNCTION

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – COMPLEX DIFFERENTIATION

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – ANALYTIC FUNCTIONS-I

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – ANALYTIC FUNCTIONS-II

COMPLEX ANALYSIS – ANALYTIC FUNCTIONS – HARMONIC FUNCTIONS

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – EXPONENTIAL FUNCTION

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – TRIGONOMETRIC FUNCTIONS AND HYPERBOLIC FUNCTIONS

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – MULTIVALUED FUNCTIONS-I

COMPLEX ANALYSIS – ELEMENTARY FUNCTIONS – MULTIVALUED FUNCTIONS-II

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – LINE INTEGRALS

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S FUNDAMENTAL THEOREM

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S INTEGRAL FORMULA

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – WINDING NUMBER

COMPLEX ANALYSIS – COMPLEX INTEGRATIONS – CAUCHY'S INEQUALITY AND APPLICATION

COMPLEX ANALYSIS – SERIES EXPANSION – SEQUENCE AND SERIES

COMPLEX ANALYSIS – SERIES EXPANSION – SEQUENCE OF FUNCTIONS

COMPLEX ANALYSIS – SERIES EXPANSION – POWER SERIES

COMPLEX ANALYSIS – SERIES EXPANSION – LAURENT'S THEOREM

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES – RIEMANN'S THEOREM

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES - ZEROS OF AN ANALYTIC FUNCTION

COMPLEX ANALYSIS – CLASSIFICATION OF SINGULARITIES - UNIQUENESS THEOREM AND ITS APPLICATIONS

COMPLEX ANALYSIS – CALCULUS RESIDUES - RESIDUE THEOREM

COMPLEX ANALYSIS – CALCULUS RESIDUES - ARGUMENT PRINCIPLE

COMPLEX ANALYSIS – CALCULUS RESIDUES - SCHWARZ LEMMA AND ITS APPLICATIONS

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - CONFORMAL MAPPING

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION BASIC PROPERTIES

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION NORMAL FORM

COMPLEX ANALYSIS – CONFORMAL MAPPING AND BILINEAR TRANSFORMATION - BILINEAR TRANSFORMATION AND INVERSE POINTS

COMPLEX ANALYSIS – CONTOUR INTEGRATION-I

COMPLEX ANALYSIS – CONTOUR INTEGRATION-II 

NUMERICAL ANALYSIS 

NUMERICAL ANALYSIS - NUMERICAL ERRORS - ERROR IN NUMERICAL COMPUTATIONS

NUMERICAL ANALYSIS - NUMERICAL ERRORS - PROPAGATION OF ERRORS AND COMPUTER ARITHMETIC

NUMERICAL ANALYSIS - NUMERICAL ERRORS - OPERATORS IN NUMERICAL ANALYSIS

NUMERICAL ANALYSIS - INTERPOLATION - LAGRANGE'S INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - NEWTON'S INTERPOLATION METHODS

NUMERICAL ANALYSIS - INTERPOLATION - CENTRAL DIFFERENCE INTERPOLATION FORMULAE

NUMERICAL ANALYSIS - INTERPOLATION - AITKEN'S AND HERMITE'S INTERPOLATION METHODS

NUMERICAL ANALYSIS - INTERPOLATION - SPLINE INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - INVERSE INTERPOLATION

NUMERICAL ANALYSIS - INTERPOLATION - BIVARIATE INTERPOLATION

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTIONS - LEAST SQUARE METHOD

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTION BY LEAST SQUARES METHOD

NUMERICAL ANALYSIS - APPROXIMATION OF FUNCTION BY CHEBYSHEV POLYNOMIALS

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – NEWTON’S METHOD TO SOLVE TRANSCENDENTAL EQUATION

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – ROOTS OF A POLYNOMIAL EQUATION

NUMERICAL ANALYSIS – SOLUTION OF NON-LINEAR EQUATION – SOLUTION OF SYSTEM OF NON- LINEAR EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – MATRIX INVERSE METHOD

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – ITERATION METHODS TO SOLVE SYSTEM OF LINEAR EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – METHODS OF MATRIX FACTORIZATION

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – GAUSS ELIMINATION METHOD AND TRI-DIAGONAL EQUATIONS

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – GENERALIZED INVERSE OF MATRIX

NUMERICAL ANALYSIS – SOLUTION OF SYSTEM OF LINEAR EQUATION – SOLUTION OF INCONSISTENT AND ILL CONDITIONED SYSTEMS

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – CONSTRUCTION OF CHARACTERISTIC EQUATION OF A MATRIX

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – EIGENVALUE AND EIGENVECTOR OF ARBITRARY MATRICES

NUMERICAL ANALYSIS – EIGENVALUES AND EIGENVECTORS OF MATRIX – EIGENVALUES AND EIGENVECTORS OF SYMMETRIC MATRICES

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – NUMERICAL DIFFERENTIATION

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – NEWTON-COTES QUADRATURE

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – GAUSSIAN QUADRATURE

NUMERICAL ANALYSIS – NUMERICAL DIFFERENTIATION AND INTEGRATION – MONTE-CARLO METHOD AND DOUBLE INTEGRATION

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – RUNGE-KUTTA METHODS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – PREDICTOR-CORRECTOR METHODS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – FINITE DIFFERENCE METHOD AND ITS STABILITY

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS – SHOOTING METHOD AND STABILITY ANALYSIS

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATION: PARABOLIC

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATIONS: HYPERBOLIC

NUMERICAL ANALYSIS – NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS – PARTIAL DIFFERENTIAL EQUATIONS: ELLIPTIC 

FUNCTIONAL ANALYSIS 

FUNCTIONAL ANALYSIS - METRIC SPACES - FUNDAMENTAL INEQUALITIES

FUNCTIONAL ANALYSIS - METRIC SPACES - SOME PROPERTIES ON METRIC SPACES

FUNCTIONAL ANALYSIS - METRIC SPACES - METRIC SUBSPACES

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - COMPLETION OF METRIC SPACES

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - COMPACTNESS OF C[A,B]

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR METRIC SPACES - FIXED POINT OF CONTRACTION MAPPING

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - LINEAR SPACES

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - BASIC PROPERTIES OF NORMED LINEAR SPACES

FUNCTIONAL ANALYSIS - NORMED LINEAR SPACES AND BANACH SPACES - EXAMPLES OF BANACH SPACES

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - CONVEX SET

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - EQUIVALENT NORMS AND SERIES IN BANACH SPACES

FUNCTIONAL ANALYSIS - CHARACTERIZATION OF BANACH SPACES - QUOTIENT SPACES

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - NORM OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - BOUNDED LINEAR OPERATORS - CONVERGENCE OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - OPEN MAPPING THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - CLOSED GRAPH THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR OPERATORS - EXTENSION OF BOUNDED LINEAR OPERATORS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - LINEAR FUNCTIONALS

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - HAHN BANACH THEOREM

FUNCTIONAL ANALYSIS - FUNDAMENTAL THEOREMS FOR BOUNDED LINEAR FUNCTIONALS - APPLICATIONS OF HAHN BANACH THEOREM

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - FIRST CONJUGATE SPACES

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - SECOND CONJUGATE SPACES

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - STRONG CONVERGENCE AND WEAK CONVERGENCE OF A SEQUENCE OF OPERATORS

FUNCTIONAL ANALYSIS - CONJUGATE SPACES - CONJUGATES OPERATORS ON NORMED LINEAR SPACES….

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - INNER PRODUCT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - ORTHOGONAL AND ORTHONORMAL VECTORS

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SOME FUNDAMENTAL RESULTS ON INNER PRODUCT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SOME RESULTS ON HILBERT SPACES

FUNCTIONAL ANALYSIS - INNER PRODUCT SPACES AND HILBERT SPACES - SERIES IN HILBERT SPACES AND ISOMETRIC ISOMORPHISM BETWEEN HILBERT SPACES

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - ADJOINT OPERATORS ALGEBRA OF ADJOINT OPERATORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - SELF ADJOINT OPERATORS OVER HILBERT SPACES AND ITS EIGEN VALUES AND EIGEN VECTORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES - NORMAL OPERATORS AND UNITARY OPERATORS

FUNCTIONAL ANALYSIS - CLASSIFICATION OF OPERATORS OVER HILBERT SPACES PROJECTION OPERATORS

INTEGRAL EQUATIONS AND INTEGRAL TRANSFORM 

INTEGRAL EQUATIONS: AN INTRODUCTION - CLASSIFICATIONS OF INTEGRAL EQUATIONS

INTEGRAL EQUATIONS: AN INTRODUCTION - OCCURRENCE OF VOLTERRA INTEGRAL EQUATIONS

INTEGRAL EQUATIONS: AN INTRODUCTION - OCCURRENCE OF FREDHOLM INTEGRAL EQUATIONS

FREDHOLM ALTERNATIVE EQUATIONS OF SECOND KIND WITH DEGENERATE KERNEL - THE THEORY OF FREDHOLM ALTERNATIVE

HOMOGENEOUS FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH DEGENERATE KERNEL

SOLUTION OF FREDHOLM INTEGRAL EQUATION WITH DEGENERATE KERNEL: EXAMPLES

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: SOLUTION BY THE METHOD

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: SOLUTION BY THE METHOD

METHOD OF SUCCESSIVE APPROXIMATIONS APPLIED TO VOLTERRA INTEGRAL EQUATION OF SECOND KIND

FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND WITH CONTINUOUS KERNEL: ITERATED KERNEL

INTEGRAL EQUATIONS OF SECOND KIND WITH MORE GENERAL FORM OF KERNEL

FREDHOLM INTEGRAL EQUATION OF SECOND KIND WITH SQUARE INTEGRABLE KERNEL AND FORCING TERM

PROPERTIES OF INTEGRAL EQUATIONS WITH SYMMETRIC KERNEL

HILBERT SCHMIDT THEOREM

SOLUTION OF ABEL INTEGRAL EQUATION: METHOD BASED ON ELEMENTARY INTEGRATION

SOLUTION OF ABEL INTEGRAL EQUATION: METHOD BASED ON LAPLACE TRANSFORM

INTRODUCTION TO FOURIER TRANSFORM

FOURIER TRANSFORMS OF SOME SIMPLE FUNCTIONS

PROPERTIES OF FOURIER TRANSFORM

CONVOLUTION THEOREM AND PARSEVAL RELATION

APPLICATION OF FOURIER TRANSFORMS IN SOLVING LINEAR ORDINARY DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER SINE AND COSINE TRANSFORMS IN SOLVING LINEAR ORDINARY DIFFERENTIAL

APPLICATION OF FOURIER TRANSFORM IN SOLVING PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER SINE AND COSINE TRANSFORMTO THE SOLUTION OF PARTIAL DIFFERENTIAL

AN INTRODUCTION TO LAPLACE TRANSFORM

OPERATIONAL PROPERTIES OF LAPLACE TRANSFORM

CONVOLUTION OF LAPLACE TRANSFORM

METHOD OF EVALUATION OF INVERSE LAPLACE TRANSFORM

APPLICATION OF LAPLACE TRANSFORM TO DIFFERENTIAL EQUATIONS

AN INTRODUCTION TO MELLIN TRANSFORM

OPERATIONAL PROPERTIES OF MELLIN TRANSFORM

EVALUATION OF MELLIN TRANSFORM OF SOME FUNCTIONS

HANKEL TRANSFORM AND ITS PROPERTIES

HANKEL TRANSFORM OF SOME KNOWNFUNCTIONS AND APPLICATIONS

INTRODUCTION TO Z TRANSFORM

INVERSION OF Z TRANSFORM 

DIFFERENTIAL GEOMETRY

INTRODUCTION OF TENSORS: CONTRAVARIANT AND COVARIANT VECTORS –MODULE-1 

INTRODUCTION OF TENSORS: HIGHER ORDER TENSORS–MODULE-2 

ALGEBRA OF TENSORS: ALGEBRAIC OPERATIONS ON TENSORS –MODULE-1 

ALGEBRA OF TENSORS: SYMMETRICNESS OF TENSORS AND QUOTIENT LAW–MODULE-2 

RIEMANNIAN SPACE: FUNDAMENTAL METRIC TENSOR- MODULE-1 

RIEMANNIAN SPACE: APPLICATIONS OF FUNDAMENTAL METRIC TENSORS- MODULE-2
DERIVATIVES OF TENSORS: CHRISTOFFEL SYMBOLS- MODULE-1 

DERIVATIVES OF TENSORS: COVARIANT DIFFERENTIATION- MODULE-2 

GEOMETRY OF SPACE CURVE: INTRINSIC DERIVATIVE AND CURVILINEAR COORDINATE SYSTEM IN SPACE- MODULE-1 

GEOMETRY OF SPACE CURVE: SERRET-FRENET FORMULII FOR SPACE CURVE- MODULE-2 

GEOMETRY OF SPACE CURVE: SOME PARTICULAR TYPE OF SPACE CURVES - MODULE-3
GEOMETRY OF SPACE CURVE: FUNDAMENTAL THEOREM FOR SPACE CURVE - MODULE-4 

SURFACE: PARAMETRIC REPRESENTATION OF SURFACES AND FIRST FUNDAMENTAL FORM- MODULE-1 

SURFACE: GEODESIC ON A SURFACE- MODULE-2 

CURVATURE ON SURFACE: PARALLEL VECTOR FIELD AND GAUSSIAN CURVATURE-- MODULE-1 

CURVATURE ON SURFACE: INTRINSIC GEOMETRY OF CURVES ON SURFACE-(1)- MODULE-2 

CURVATURE ON SURFACE: INTRINSIC GEOMETRY OF CURVES ON SURFACE-(2)- MODULE-3 

SURFACE EMBEDDED IN SPACE: SECOND FUNDAMENTAL FORM AND ITS APPLICATIONS- MODULE-1 

SURFACES EMBEDDED IN SPACE: GAUSS AND WEINGARTEN FORMULAS AND THIRD FUNDAMENTAL FORM OF A SURFACE - MODULE-1 

SURFACE EMBEDDED IN SPACE: GAUSS AND CODAZZI- MAINARDI EQUATIONS - MODULE-2 

SURFACE EMBEDDED IN SPACE: GAUSS AND CODAZZI- MAINARDI EQUATIONS(2) - MODULE-2.2 

SURFACE EMBEDDED IN SPACE: PRINCIPAL CURVATURE - MODULE-3 

SURFACE EMBEDDED IN SPACE: LINES OF CURVATURE AND RODRIGUE’S FORMULA - MODULE-4 

SURFACE EMBEDDED IN SPACE: ASYMPTOTIC LINES, EULER’S THEOREM ON NORMAL CURVATURE AND DUPIN INDICATRIX - MODULE-5 

SURFACE EMBEDDED IN SPACE: PROBLEMS ON SURFACE EMBEDDED IN SPACE - MODULE-6 

SURFACE EMBEDDED IN SPACE: PROBLEMS ON SURFACE EMBEDDED IN SPACE(2) - MODULE-7 

SURFACE EMBEDDED IN SPACE: GAUSS-BONNET THEOREM WITH SOME APPLICATIONS - MODULE-8 

SURFACE EMBEDDED IN SPACE: GAUSS-BONNET THEOREM WITH SOME APPLICATIONS (2) - MODULE-9 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – APPLICATIONS OF TENSORS IN PHYSICAL LAWS AND EQUATIONS - MODULE-1 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – MAPPINGS ON SURFACE S AND SPACES - MODULE-2 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – MAPPINGS ON SURFACE S AND SPACES(2) - MODULE-3 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – THE INSIDE GEOMETRY OF THE SPECIAL THEORY OF RELATIVITY - MODULE-4 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – APPLICATIONS OF DIFFERENTIAL GEOMETRY IN GENERAL THEORY OF RELATIVITY AND COSMOLOGY(1) - MODULE-5 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – APPLICATIONS OF DIFFERENTIAL GEOMETRY IN GENERAL THEORY OF RELATIVITY AND COSMOLOGY (2) - MODULE-6 

SOME APPLICATIONS OF DIFFERENTIAL GEOMETRY – APPLICATIONS OF DIFFERENTIAL GEOMETRY IN GENERAL THEORY OF RELATIVITY AND COSMOLOGY (3) - MODULE-7 

CLASSICAL MECHANICS

ROTATING FRAME OF REFERENCE - ROTATING COORDINATE SYSTEM – MODULE -1 

ROTATING FRAME OF REFERENCE - EQUATION OF MOTION OF A FREE PARTICLE RELATIVE TO THE ROTATING EARTH – MODULE -2

ROTATING FRAME OF REFERENCE - EFFECTS OF EARTH’S ROTATION – MODULE -3

CONSTRAINED MOTION - CONSTRAINTS AND ITS CLASSIFICATION – MODULE -1

CONSTRAINED MOTION - LAGRANGE’S EQUATION OF MOTION OF FIRST KIND – MODULE -2

CONSTRAINED MOTION - GENERALIZED PRINCIPLE OF D’ALEMBERT– MODULE -3

LAGRANGIAN MACHANICS - LAGRANGE’S EQUATION OF MOTION OF SECOND KIND - MODULE -1

LAGRANGIAN MACHANICS - LAGRANGE’S EQUATION OF MOTION FOR A NONHOLONOMIC DYNAMICAL SYSTEM - MODULE -2

LAGRANGIAN MACHANICS - RAYLEIGH’S DISSIPATION FUNCTION - MODULE -3

LAGRANGIAN MACHANICS - APPLICATIONS OF LAGRANGE’S EQUATIONS OF MOTION- MODULE -4

HAMILTONIAN MECHANICS - ROUTH’S PROCESS FOR THE IGNORATION OF COORDINATES – MODULE-1

HAMILTONIAN MECHANICS - HAMILTONIAN OF A DYNAMICAL SYSTEM – MODULE-2

HAMILTONIAN MECHANICS - HAMILTON’S EQUATIONS OF MOTION– MODULE-3

HAMILTONIAN MECHANICS - APPLICATIONS OF HAMILTONIAN MECHANICS– MODULE-4

VARIATIONAL PRINCIPLES - VARIATION OF A FUNCTIONAL – MODULE-1

VARIATIONAL PRINCIPLES - HAMILTON’S PRINCIPLE AND USES – MODULE-2

VARIATIONAL PRINCIPLES - EXTENDED HAMILTON’S PRINCIPLE AND ITS USE– MODULE-3

VARIATIONAL PRINCIPLES - PRINCIPLE OF LEAST ACTION– MODULE-4

CANONICAL TRANSFORMATIONS - ASPECTS OF CANONICAL TRANSFORMATION – MODULE-1

CANONICAL TRANSFORMATIONS - GENERATING FUNCTION– MODULE-2

CANONICAL TRANSFORMATIONS - CANONICALITY– MODULE-3

BRACKETS- POISSON BRACKETS AND LAGRANGE BRACKETS – MODULE-1

BRACKETS- PROPERTIES OF POISSON BRACKETS – MODULE-2

BRACKETS- CONSTANTS OF MOTION– MODULE-3

CALCULUS OF VARIATIONS - EULER-LAGRANGE EQUATION - MODULE-1

CALCULUS OF VARIATIONS - APPLICATIONS OF EULER-LAGRANGE EQUATION- MODULE-2

CALCULUS OF VARIATIONS - ISOPERIMETRIC PROBLEMS - MODULE-3

MOTION OF A RIGID BODY - MOTION OF A SYSTEM OF PARTICLES- MODULE-1

MOTION OF A RIGID BODY - ASPECTS OF MOTION OF A RIGID BODY - MODULE-2

MOTION OF A RIGID BODY - EULER’S EQUATIONS OF MOTION- MODULE-3

MOTION OF A RIGID BODY - MOTION OF A TOP - MODULE-4

APPLICATION S OF CLASSICAL MECHANICS IN SPECIAL THEORY - APPLICATIONS OF LORENTZ TRANSFORMATION - MODULE-1

APPLICATION S OF CLASSICAL MECHANICS IN SPECIAL THEORY - APPLICATIONS OF LORENTZ TRANSFORMATION - MODULE-2

APPLICATION S OF CLASSICAL MECHANICS IN SPECIAL THEORY - VELOCITY AND ACCELERATION IN RELATIVISTIC MECHANICS - MODULE-3

APPLICATION S OF CLASSICAL MECHANICS IN SPECIAL THEORY - FORCE AND ENERGY IN RELATIVISTIC MECHANICS - MODULE-4

NUMBER THEORY AND GRAPH THEORY 

FUNDAMENTALS AND DIVISIBILITY - WELL ORDERING PRINCIPLE AND ITS EQUIVALENCE TO MATHEMATICAL INDUCTION

FUNDAMENTALS AND DIVISIBILITY - PROPERTIES OF DIVISION OF INTEGERS AND DIVISION ALGORITHM

FUNDAMENTALS AND DIVISIBILITY - POLYGONAL NUMBERS

FUNDAMENTALS AND DIVISIBILITY - GCD, EUCLIDEAN ALGORITHM AND BEZOUT’S IDENTITY

PRIME NUMBERS AND CONGRUENCES - PRIMES AND THEIR PROPERTIES

PRIME NUMBERS AND CONGRUENCES - THERE ARE INFINITE NUMBER OF PRIMES

PRIME NUMBERS AND CONGRUENCES - IS THERE ANY FORMULA FOR PRIME NUMBERS?

PRIME NUMBERS AND CONGRUENCES - INTRODUCTION TO CONGRUENCES

PRIME NUMBERS AND CONGRUENCES - WILSON’S AND CHINESE REMAINDER THEOREM

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - INTRODUCTION TO ARITHMETIC FUNCTIONS

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - PROPERTIES OF EULER’S PHI-FUNCTION

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - EULER’S THEOREM AND DIRICHLET PRODUCT

ARITHMETIC FUNCTIONS AND ROOTS OF UNITY - NTH ROOTS OF UNITY

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - PRIMITIVE ROOTS

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - QUADRATIC RESIDUES/NON-RESIDUES

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - GAUSS LEMMA

PRIMITIVE ROOTS AND QUADRATIC RESIDUES - QUADRATIC RECIPROCITY LAW

ADDITIONAL TOPICS - THE GAUSSIAN INTEGERS

ADDITIONAL TOPICS - PYTHAGOREAN TRIPLES

ADDITIONAL TOPICS - PELL’S EQUATION

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - INTRODUCTION TO GRAPH THEORY

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - SOME KNOWN GRAPH FAMILIES AND THEIR PROPERTIES

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - CONSTRUCTION OF NEW GRAPHS FROM OLD GRAPHS

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - CONNECTEDNESS OF A GRAPH

BASIC CONCEPTS AND DEFINITIONS OF GRAPH THEORY - GRAPH ISOMORPHISM AND AUTOMORPHISM GROUP OF A GRAPH

GRAPH PROPERTIES – TREES

GRAPH PROPERTIES – EULERIAN AND HAMILTONIAN GRAPHS

GRAPH PROPERTIES – PLANAR GRAPHS AND COLORING

GRAPH PROPERTIES – MATCHING AND COVERING

GRAPH PROPERTIES – NETWORK FLOWS

SPECTRAL GRAPH THEORY – REVIEW OF EIGENVALUES AND EIGENVECTORS OF A SQUARE MATRIX

SPECTRAL GRAPH THEORY – ADJACENCY MATRIX OF A GRAPH

SPECTRAL GRAPH THEORY – BOUNDS OF EIGENVALUES OF SUBGRAPHS AND EIGENVALUES OF REGULAR GRAPHS

SPECTRAL GRAPH THEORY – EIGENVALUES OF SOME KNOWN GRAPHS/DIGRAPHS

SPECTRAL GRAPH THEORY – AUTOMORPHISMS OF GRAPHS AND ADJACENCY MATRIX

ADDITIONAL TOPICS – NONNEGATIVE MATRICES

ADDITIONAL TOPICS – INCIDENCE MATRIX OF A GRAPH

ADDITIONAL TOPICS – LAPLACIAN MATRIX OF A GRAPH 

OPERATIONS RESEARCH

LINEAR PROGRAMMING PROBLEM - MATHEMATICAL FORMULATION OF LPP AND GRAPHICAL METHOD FOR SOLVING LPP – MODULE-1

LINEAR PROGRAMMING PROBLEM - SIMPLEX METHOD FOR SOLVING LPP AND BIG-M METHOD – MODULE-2

LINEAR PROGRAMMING PROBLEM - SOME SPECIAL CASES IN LPP – MODULE-3

LINEAR PROGRAMMING PROBLEM - DUALITY AND SOLVING LPP USING, DUALITY IN SIMPLEX METHOD – MODULE-4

LINEAR PROGRAMMING PROBLEM - DUAL SIMPLEX METHOD AND REVISED SIMPLEX METHOD – MODULE-5

TRANSPORTATION AND ASSIGNMENT PROBLEMS - MATHEMATICAL FORMULATION AND INITIAL BFS OF TRANSPORTATION PROBLEM – MODULE-1

TRANSPORTATION AND ASSIGNMENT PROBLEMS - OPTIMALITY TEST BY STEPPING STONE METHOD AND MODI METHOD, AND SOME SPECIAL CASES OF TRANSPORTATION PROBLEM – MODULE-2

TRANSPORTATION AND ASSIGNMENT PROBLEMS ASSIGNMENT PROBLEM AND ITS, SOLUTION BY HUNGARIAN METHOD, AND TRAVELLING SALESMAN PROBLEM – MODULE-3

GAME THEORY - BASIC CONCEPT AND TERMINOLOGIES, TWO-PERSON ZERO-SUM GAME, AND GAME WITH PURE AND MIXED STRATEGIES - MODULE-1

GAME THEORY - DOMINANCE PRINCIPLE, ARITHMETIC METHOD, AND GRAPHICAL METHOD FOR SOLVING A (2× N) GAME - MODULE-2

GAME THEORY - GRAPHICAL METHOD FOR SOLVING A(M×2) GAME AND SOLUTION OF A GAME BY SIMPLEX METHOD- MODULE-3

JOB SEQUENCING AND REPLACEMENT THEORY – BASIC TERMINOLOGIES AND ASSUMPTIONS OF JOB SEQUENCEING, AND PROCESSING OF n JOBS THROUGH 2 AND 3 MACHINES - MODULE-1

JOB SEQUENCING AND REPLACEMENT THEORY –PROCESSING n JOBS THROUGH m MACHINES PROCESSING 2 JOBS THROUGH m MACHINES – GRAPHICAL METHOD - MODULE-2

JOB SEQUENCING AND REPLACEMENT THEORY –INTRODUCTION TO REPLACEMENT THEORY AND DETERMINATION OF OPTIMAL REPLACEMENT TIME - MODULE-3

JOB SEQUENCING AND REPLACEMENT THEORY – SELECTION OF THE BEST MACHINE, AND INDIVIDUAL AND GROUP REPLACEMENT POLICIES - MODULE-4

INVENTORY THEORY – ECONOMIC ORDER QUANTITY AND EOQ MODELS WITHOUT SHORTAGE - MODULE-1

INVENTORY THEORY –EOQ MODELS WITH SHORTAGE AND EPQ MODELS WITH AND WITHOUT SHORTAGES - MODULE-2

INVENTORY THEORY –MULTI-ITEM INVENTORY MODELS, PURCHASE INVENTORY MODEL AND INVENTORY MODELS WITH PRICE BREAKS - MODULE-3

INVENTORY THEORY –NEWSBOY PROBLEM AND PROBALILISTIC INVENTORY MODEL WITH INSTANTANEOUS DEMAND AND NO SET UP COST - MODULE-4

INVENTORY THEORY – PROBALILISTIC INVENTORY MODEL WITH UNIFORM DEMAND AND NO SET UP COST, AND BUFFER STOCK IN PROBALILISTIC INVENTORY MODEL - MODULE-5

QUEUEING THEORY – BASIC CHARACTERISTICS OF QUEUEING SYSTEM AND PROBABILITY DISTRIBUTION OF ARRIVALS - MODULE-1

QUEUEING THEORY –PROBABILITY DISTRIBUTION OF DEPARTURES MODEL-1 - MODULE-2

QUEUEING THEORY –PROBABILITY DISTRIBUTION OF DEPARTURES MODEL-2 - MODULE-3

QUEUEING THEORY –PROBABILITY DISTRIBUTION OF DEPARTURES MODEL-3 and 4 - MODULE-4

NETWORK ANALYSIS – BASIC COMPONENTS OF NETWORK AND CRITICAL PATH METHOD (CPM) –MODULE-1 

NETWORK ANALYSIS – TOTAL FLOAT AND FREE FLOAT OF ACTIVITY, AND CPM MODEL: TIME COST OPTIMIZATION –MODULE-2

NETWORK ANALYSIS – PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)–MODULE-3

NETWORK ANALYSIS – LP AND DUAL LP SOLUTIONS TO NETWORK PROBLEM –MODULE-4

DYNAMIC PROGRAMMIMG – BASIC CONCEPT AND TERMINOLOGY, AND DYNAMIC PROGRAMMING MODELS I AND II - MODULE-1

DYNAMIC PROGRAMMIMG – DP MODEL III, SOLUTION OF DISCRETE DP PROBLEM AND SOLUTIONOF LPP BY DP - MODULE-2

INTEGER PROGRAMMING – INTRODUCTION TO INTEGER PROGRAMMING AND GOMORY’S CUTTING PLANE METHOD FOR ALL IPP - MODULE-1

INTEGER PROGRAMMING –GOMORY’S CUTTING PLANE METHOD FOR MIXED IPP, AND BRANCH AND BOUND METHOD - MODULE-2

NON- LINEAR PROGRAMMING – NLLP WITH EQUALITY CONSTRAINTS: LAGRANGE MULTIPLIER METHOD - MODULE-1

NON- LINEAR PROGRAMMING – NLLP WITH INEQUALITY CONSTRAINTS: KUHN – TUCKER CONDITIONS AND QUADRATIC PROGRAMMING - MODULE-2

NON- LINEAR PROGRAMMING – WOLFUS MODIFIED SIMPLEX METHODS AND BEALE’S METHOD - MODULE-3

PARTIAL DIFFERENTIAL EQUATIONS 

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: BASIC IDEAS

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: SIMULTANEOUS DIFFERENTIAL EQUATIONS

BASIC CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS: PFAFFIAN DIFFERENTIAL EQUATIONS

FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS: FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS: QUASI-LINEAR EQUATIONS OF FIRST ORDER

CHARPIT'S AND JACOBI'S METHODS OF SOLVING FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS

NONLINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

SOLUTION SATISFYING GIVEN CONDITIONS

ORIGIN OF SECOND ORDER EQUATIONS

LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

ELLIPTIC DIFFERENTIAL EQUATIONS

SOLUTION OF TWO DIMENSIONAL LAPLACE EQUATION BY SEPERATION OF VARIABLES

SOLUTION OF THREE DIMENSIONAL LAPLACE EQUATION BY SEPERATION OF VARIABLES

INTRODUCTION TO PARABOLIC DIFFERENTIAL EQUATIONS

SOLUTION OF ONE DIMENSIONAL HEAT EQUATION

SOLUTION OF TWO DIMENSIONAL HEAT EQUATION

SOLUTION OF THREE DIMENSIONAL HEAT EQUATION

INTRODUCTION TO HYPERBOLIC DIFFERENTIAL EQUATIONS

ONE DIMENSIONAL WAVE EQUATION

TWO DIMENSIONAL WAVE EQUATION

THREE DIMENSIONAL WAVE EQUATION

INTEGRAL TRANSFORMS AND THEIR INVERSION FORMULAE

APPLICATION OF LAPLACE TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF FOURIER TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

APPLICATION OF HANKEL AND MELLIN TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS

FINITE INTEGRAL TRANSFORM AND THEIR APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS

GREEN'S FUNCTION

SOLUTIONS OF PROBLEMS

EIGEN FUNCTION METHOD OF SOLVING PARTIAL DIFFERENTIAL EQUATIONS

NONLINEAR ONE-DIMENSIONAL WAVE EQUATION

DISPERSION AND DISSIPATION

THE KORTEWEG -DE VRIES EQUATION AND SOLUTIONS

BURGERS' EQUATION

SCHRODINGER EQUATION AND SOLITARY WAVES 

SET THEORY AND ELEMENTARY ALGEBRAIC TOPOLOGY

FINITE AND INFINITE SETS - FINITE AND COUNTABLY INFINITE SETS – MODULE-1

FINITE AND INFINITE SETS – UNCOUNTABLY SETS AND AXIOM OF CHOICE – MODULE-2

FINITE AND INFINITE SETS – ORDER RELATION ON A SET AND FUNDAMENTAL PRINCIPLES – MODULE-3

EQUIVALENCE OF FUNDAMENTAL PRINCIPLES AND CARDINAL NUMBER - EQUIVALENCE OF FUNDAMENTAL PRINCIPLES - MODULE-1

EQUIVALENCE OF FUNDAMENTAL PRINCIPLES AND CARDINAL NUMBER – CARDINAL NUMBER - MODULE-2

REVIEW OF PREVIOUS KNOWLEDGE – SET TROPOLOGY -1 - MODULE-1

REVIEW OF PREVIOUS KNOWLEDGE – SET TROPOLOGY -2 - MODULE-2

REVIEW OF PREVIOUS KNOWLEDGE – CATEGORIES AND FREE GROUPS - MODULE-3

QUOTIENT TOPOLOIGY – QUOTIENT SPACES AND QUOTIENT MAPS - MODULE-1

QUOTIENT TOPOLOIGY – ADJUNCTION SPACES AND ORBIT SPACES - MODULE-2

INTRODUCTION TO ALGEBRAIC TOPOLOGY AND HOMOTOPY THEORY

HOMOTOPY AND RELATIVE HOMOTOPY

CONTRACTIBLE SPACES AND HOMOTOPY EQUIVALENCE

RETRACTS AND DEFORMATION RETRACTS

PATH HOMOTOPY

CONSTRUCTION OF FUNDAMENTAL GROUPS AND INDUCED HOMOMORPHISMS

FUNDAMENTAL GROUPS HOMEOMORPHIC AND CONTRACTIBLE SPACES

EXPONENTIAL MAP AND ITS PATH LIFTING PROPERTY

FUNDAMENTAL GROUP OF CIRCLE AND TORUS

FUNDAMENTAL GROUPS OF SURFACES

FUNDAMENTAL GROUP AND ITS BASIC PROPERTIES – APPLICATIONS

COVERING SPACES AND COVERING MAPS - COVERING SPACES - MODULE-1

COVERING SPACES AND COVERING MAPS – PROPERTIES OF COVERING MAPS - MODULE-2

COVERING SPACES AND COVERING MAPS – UNIVERSAL COVERING SPACES AND LIFTING THEOREM - MODULE-3

COVERING SPACES AND COVERING MAPS – FUNDAMENTAL GROUPS COVERING SPACES - MODULE-4

SIMPLICIAL HOMOLOGY – GEOMETRIC SIMPLEX AND SIMPLICIAL COMPLEX - MODULE-1

SIMPLICIAL HOMOLOGY – TRIANGULABLE SPACES AND ORIENTED SIMPLICIAL COMPLEX - MODULE-2

SIMPLICIAL HOMOLOGY –CHAIN COMPLEX AND SIMPLICIAL HOMOLOGY GROUP - MODULE-3

SIMPLICIAL HOMOLOGY – SIMPLICIAL HOMOLOGY GROUPS AND INDUCED HOMOMORPHISM - MODULE-4

SINGULAR HOMOLOGY - SINGULAR HOMOLOGY GROUPS – MODULE-1

SINGULAR HOMOLOGY - SINGULAR HOMOLOGY GROUPS AND INDUCED HOMOMORPHISM – MODULE-2

SINGULAR HOMOLOGY - HOMOLOGY GROUP OF HOMEOMORPHIC AND HOMOTOPY EQUIVALENT SPACES – MODULE-3

SINGULAR HOMOLOGY GROUPS – COMPUTATION AND APPLICATION – MAYER VIETORIS THEOREM - MODULE-1

SINGULAR HOMOLOGY GROUPS – COMPUTATION AND APPLICATION - COMPUTATION AND APPLICATION OF HOMOLOGY GROUPS - MODULE-2

SINGULAR HOMOLOGY GROUPS – COMPUTATION AND APPLICATION – RELATION BETWEEN FUNDAMENTAL GROUP AND 1ST HOMOLOGY GROUP - MODULE-3