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 (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

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 : 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

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



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

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 ….7.1


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