ABSTRACT ALGEBRA 

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

DIRECT PRODEUCT OF GROUPS (EXTERNAL 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 - MODULE-I

POLYNOMIAL RINGS - DIVISION ALGORITHM AND ITS CONSEQUENCES - MODULE-2

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

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  - MODULE-4

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 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

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

BESSELS 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 HYPERGEOMETRICFUNCTION- 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

TOPOLOGY

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

INTRODUCTION TO TOPOLOGICAL SPACES – BASE OF TOPOLOGICAL SPACES – MODULE-2

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

DIFFERENTIAL GEOMETRY

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

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

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

5 and 6 not there ….

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