Vinayaka Mission University
Vinayaka Missions University (VMU) is a pioneering and vibrant school offering a multi-social experience with an atmosphere checked by the ideal congruity of living in differing qualities.
Years1
UNIT - 01
DEFINITION OF A GROUP - EXAMPLES OF GROUP - SOME PRELIMINARY LEMMAS.
UNIT - 02
SUB GROUPS - A COUNTING PRINCIPLE - NORMAL SUB GROUPS AND QUOTIENT
GROUPS.
UNIT - 03
HOMOMARPHISMS.
UNIT - 04
AUTO - MORPHISMS.
UNIT - 05
CAYLEYS `S THEORM - PERMUTATION GROUPS.
UNIT - 06
ANOLNES COUNTING PRINCIPLE AND AYLOUC`S THEORM.
UNIT - 07
DEFINITION AND EXAMPLES OF RING - SOME SPECIAL CLASSES OF RINGS.
UNIT - 08
HOMOMARPHISMS - IDEALS AND QUOTIENT RINGS - THE FIELD OF QUOTIENTS OF AN
INTEGRAL DOMAIN.
UNIT - 09
EUCLIDEAN RINGS - A PARTICULAR EUCLIDEAN RINGS - PLOYNOMIAL RINGS.
UNIT - 10
POLYNOMIALS OVER THE RATIONAL FIELD AND POLYNOMIAL RINGS OVER
COMMUTATIVE RINGS.
UNIT - 11
ELEMENTARY BASIC CONCEPTS OF VECTOR SPACES - LINEAR INDEPENDENCE AND
BASES DUAL SPACES
UNIT - 12
INTER PRODUCT SPACES AND MODULES.
Vinayaka Missions University,Directorate of Distance Education
Salem India
MASTER OF SCIENCE IN MATHEMATICS
1 Yr.
ALGEBRA-1(2030501)
INTRODUCTION - TRANSFORMATION OF CO-ORDINATES - SUMMATION CONVERSION
KRONECKER DEITA.
CO-VARIANT - CONTRA VARIANT VECTORS - SECOND - HIGHER ORDERS TENSORS -
SYMMETRIC - SKEW SYMMETRIC TENSOR.
CONTRACTION - OUTER & INNER PRODUCT - QUOTIENT LAW - CONJUGATE - RELATIVE
TENSORS.
CONJUGATE TENSOR - ASSOCIATE TENSOR - MAGNITUDE PHYSICAL COMPONENTS.
GENERAL ORTHOGONAL CO-ORDINATES CYLINDRICAL COORDINATED - SPHERICAL COORDINATES
- SKEW - SYMMETRIC CO-VARIANT TENSOR.
CHAPTER - 06
CHRISTOFFEL SYMBOLS - TRANSFORMATION LAW OF CHRISTOFFEL SYMBOLS - COVARIANT
DIFFERENTIATION.
LAW OF CO-VARIANT DIFFERENTIATION - INTRISIC DIFFERENTIATION - GRADIENT
DIVERGENCE - LAPLACIAN AND CURL - PARALLELISM.
GEODESIC - EULER`S EQUATIONS - DIFFERENTIAL EQUATION FOR GEODESICS - COORDINATES.
RIEMANN - CHRISTOFFEL TENSOR - CURVATURE TENSOR.
RICCI TENSOR AND EINSTEIN TENSOR - RIEMANN CURVATURE - CONSTANT
CURVATURE.
CO-ORDINATE TRANSFORMATION - CARTESIAN TENSOR - PERMUTATION TENSOR -
TENSOR ALGEBRA
SCALAR & VECTOR PRODUCT OF TOW VECTORS - GRADIENT DIVERGENCE - CURL AND
LAPLACIAN - GAUSS & STOKES THEOREM - ISOTROPIC TENSOR.
ANALYTICAL MECHANICS AND TENSER ANALYSIS(2030502)
INTRODUCTION - HIGHER ORDER EQUATIONS - LINEAR DEPENDENCE - WRONSKIAN
METHOD OF VARIATION OF PARAMETERS.
HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT CO-EFFICIENT - EQUATIONS
WITH VARIABLE CO-EFFICIENT.
INTRODUCTION - POWER SERIES SOLUTION - LEGENDRE EQUATION & LEGENDRE
POLYNOMIAL.
BESSELS EQUATION AND PROPERTIES.
INTRODUCTION - SYSTEMS OF FIRST ORDER EQUATIONS - MODEL FOR ARMS
COMPETITION BETWEEN TWO NATIONS - EXISTENCE AND UNIQUENESS THEOREM.
FUNDAMENTAL MATRIX.
INTRODUCTION - NON-HOMOGENEOUS LINEAR SYSTEMS - LINEAR SYSTEMS WITH
CONSTANT COEFFICIENTS - LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS.
INTRODUCTION - PRELIMINARIES - SUCCESSIVE APPROXIMATIONS - PICARDS THEOREM
- CONTINUATION AND DEPENDENCE ON INITIAL CONDITIONS.
INTRODUCTION - STURM LIOUVILLE PROBLEM - GREENS FUNCTION - APPLICATION OF
BOUNDARY VALUE PROBLEMS.
PICARDS THEOREM.
INTRODUCTION - LEARNING OBJECTIVES - FUNDAMENTAL RESULTS - STURMS
COMPARISION THEOREM - ELEMENTARY LINEAR OSCILLATIONS - COMPARISON
THEOREM OF HILLE - WINTNER.
INTRODUCTION - SYSTEM OF EQUATIONS WITH CONSTANT COEFFICIENTS - LINEAR
EQUATION WITH CONSTANT COEFFICIENTS - STABILITY OF QUASI-LINEAR SYSTEMS -
SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS.
THE THEORY OF SPACE CURVES - ARC LENGTH TANGENT - NORMAL BINORMAL -
DEFINITION OF SPACE CURVE - GEOMETRICAL INTERPRETATION OF - EQUATION OF
THE TANGENT LINE TO A CURVE AT A POINT - TANGENT LINE IN CARTESIAN FORM.
OSCULATING PLANE - PRINCIPAL NORMAL AND BINORMAL - CURVATURE OF THE CURVE
IN SPACE - SERRET - FRENET FORMULAE - EXPRESSION FOR TORSION.
DIFFERENT OF A SURFACE - CURVES ON A SURFACE - CONTACT BETWEEN CURVES
AND SURFACES - OSCULATING CIRCLE - OSCULATING SPHERE - LOCUS OF THE
CENTRE OF SPHERICAL CURVATURE.
TANGENT SURFACES - INVOLUTES AND EVOLUTES - INTRINSIC EQUATION OF SPACE
CURVES - FUNDAMENTALS EXISTENCE THEOREM FOR SPACE CURVES - HELICES - THE
SPHERICAL INDICARICES (OR) SPHERICAL IMAGES.
SURFACE REPRESENTATION - REGULAR AND SINGULAR POINTS - CHANGE OF
PARAMETERS - CURVILINEAR EQUATIONS OF THE CURVE ON THE SURFACE - TANGENT
PLANE AND NORMAL - SURFACES OF REVOLUTION.
ANCHOR RING - HELICOIDS - METRIC ON A SURFACE - THE FIRST FUNDAMENTAL FORM -
INVARIANCE OF THE METRIC - ELEMENT OF AREA - DIRECTION COEFFICIENTS ON A
SURFACE.
FAMILY OF CURVES - DIFFERENTIAL EQUATION OF THE FAMILY OF CURVES -
ORTHOGONAL TRAJECTORIES - DOUBLE FAMILY OF CURVES - ISOMETRIC
CORRESPONDENCE - INTRINSIC PROPERTIES.
GEODESICS AND THEIR DIFFERENTIAL EQUATION - CANONICAL GEODESIC EQUATIONS -
SECOND FUNDAMENTAL FORM - FUNDAMENTAL EQUATIONS OF SURFACE THEORY -
GEODESICS ON A SURFACE OF REVOLUTION - CURVATURE OF NORMAL SECTION OF
THE SURFACE - MENNIER`S THEOREM - CLAIRAUT`S THEOREM.
NORMAL PROPERTY OF A GEODESIC - EXISTENCE THEOREM - GEODESIC PARALLELS -
GEODESIC POLARS - GEODESIC CURVATURE COMPONENTS OF GEODESIC CURVATURE
- GEODESIC CURVATURE OF THE PARAMETRIC CURVE - LIOUVILLE`S FORMULA GAUSS -
BONNET THEOREM - GAUSSIAN CURVATURE - MINDING`S THEOREM - CONFORMAL
MAPPING - COROLLARY.
DIFFERENTIAL GEOMETRY{MMAT.03}(2030504)
GEODESIC MAPPING - RULED SURFACE (DEVELOPABLE AND SKEW) - EQUATION OF THE
RULED SURFACES - NECESSARY CONDITION - LINES OF CURVATURE - DIFFERENTIAL
EQUATION OF LINES OF CURVATURE - PROPERTY OF LINES OF CURVATURES ON
DEVELOPABLE - CONJUGATE DIRECTION - ASYMPTOTIC LINES - ASYMPTOTIC LINES ON
A RULED SURFACE - PARAMETER OF DISTRIBUTION OF A RULED SURFACE -
PROPERTIES OF PARAMETER OF DISTRIBUTION - CENTRAL POINT AND THE EQUATION
OF THE LINE OF STRICTION.
JOACHIMSTHAL`S THEOREM - DUPIN`S INDICATRIX - TYPES OF POINT (ELLIPTIC,
HYPERBOLIC AND PARABOLIC) - THIRD FUNDAMENTAL FORM - FAMILY OF SURFACES -
ENVELOPE - THE EDGE OF REGRESSION - DEFINITION OF EDGE OF REGRESSION -
CHARACTERISTIC TOUCHES THE EDGE OF REGRESSION - MINIMAL SURFACES - GAUSS
CHARACTERISTIC EQUATION - MAINARDI - CODAZZI EQUATIONS.
COMPACT SURFACES - POINTS ARE UMBILICS - HILBERT`S LEMMA - COMPACT
SURFACES OF CONSTANT GAUSSIAN OR MEAN CURVATURE - COMPLETE SURFACES -
CHARACTERIZATION.
DERIVATIVES: DEFINITION OF DERIVATIVES - DERIVATIVES AND CONTINUITY - ALGEBRA
OF DERIVATIVES - THE CHAIN RULE - ONE SIDED DERIVATIVES AND INFINITE
DERIVATIVES FUNCTION WITH NON ZERO DERIVATIVES AND LOCAL EXTREMA.
ROLLER THEORM - THE MEAN VALUE THEORM FOR DERIVATIVES - INTERMEDIATE -
VALUE THEORM FOR DERIVATIVES AND TAYLOR`S FORMULA WITH REMAINDER.
THE RIEMANN - STIELTIES INTEGRAL - THE DEFINITION OF RIEMANN - STIELTIES
INTEGRAL - LINEOR PROPERTIES - INTEGRATION BY PARTS - CHANGE OF VARIABLES IN
A RIEMANN - STIELTJIES INTEGRAL - REDUCTION TO A RIEMAN STEP FUNCTION AS
INTEGRATORS.
REDUCTION OF A RIEMANN - STIELTJES INTEGRAL TO A FINITE SUM - EULER`S
SUMMATION FORMLA - MONOTONICALLY INCREASING INTEGRATIONS - UPPER AND
LOWER INTEGRALS - ADDITIVE AND LINEAR PROPERTIES OF UPPER AND LOWER
INTEGRALS - RIEMAN`S CONDITION.
COMPARISON THEORMS - INTEGRATORS OF BOUNDED VARIATION - SUFFICIENT
CONDITION - EXISTENCE OF RIEMAN - STIELTJES INTEGRALS AND NECESSARY
CONDITIONS FOR EXISTENCE OF RIEMANN - STIELTJES INTEGRAL.
RIEMANN - STIELTJES INTEGRALS CONDINUED: MEON - VALUE THEORMS FOR RIEMANN
- STIELTJES INTEGRALS - THE INTEGRAL AS A FUNCTION OF THE INTERVAL - SECOND
FUNDAMENTAL THEORM OF INTEGRAL CALCULUS.
RIEMANN INTEGRAL - SECOND MEAN - VALUE THEOREM FOR RIEMANN - INTEGRALS -
REMAN - STIELTJES INTEGRALS DEPENDING ON A PARAMETER - DIFFERENTIATION
UNDER THE INTEGRAL SIGN AND INTERCHANGING THE ORDER OF INTEGRATION.
INFINITE PRODUCTS: INFINITE PRODUCTS TEST FOR CONVERGENCE OF PRODUCT -
ABSOLUTE CONVERGENCE - REARRANGEMENT OF FACTORS IN A PRODUCT -
TANNERYS THEORM - INFINITE PRODUCT FOR TRIGONOMETRIC FUNCTIONS AND
HYPER BOLIC FUNCTIONS AND BERNOULLIS NUMBERS.
LEBESQUE MEASURE: OUTER MEASURE - MEASURABLE SETS AND LEBESQUE
MEASURE - A NON MESURABLE SET - MEASURABLE FUNCTIONS AND LITTLE WOODS
THREE PRINCIPLES.
REAL ANALYSIS{MMAT.02}(2030507)
LEBSEQUE INTEGRAL: LEBESQUE INTEGRAL OF BOUNDED MEASURABLE FUNCTION
OVER A SET OF FINITE MEASURE INTEGRAL OF A NON NEGATIVE FUNCTION.
GENERAL LEBSEQUE INTEGRAL - DERIVATIVE OF MONOTONIC FUNCTION - FUNCTIONS
OF BOUNDED VARIATION.
DERIVATION OF AND INTEGRAL - ABSOLUTE CONTINUITY.
TOPOLOGICAL SPACE - DEFINITION - DIRECT TOPOLOGY - FINER THEN BASIS FOR A
TOPOLOGY - STANDARD TOPOLOGY - SUB BASIS TOPOLOGY - ORDER TOPOLOGY -
RAYS - PRODUCT OF TWO TOPOLOGY - SUBSPACE TOPOLOGY - IF A IS SUBSPACE OF X
AND B IS SUBSPACE OF Y THEN PRODUCT OF TWO TOPOLOGY.
A X B IS SAME - CONVEX - LET X BE AN IN THE ORDERED TOPOLOGY LET Y BE A SET OF
X THAT IS CONVEX IN X THEN THE ORDERED TOPOLOGY ON Y IS THE SAME AS THE
TOPOLOGY ON Y IS THE SAME.
AS THE TOPOLOGY Y-CLOSED SETS - LIMIT POINTS - LET Y BE A SUBSPACE OF X THEN
A SET A IS CLOSED IN Y IF IT EQUALS THE INTERSECTION OF CLOSED SETS OF X WITH
Y.
CLOSURE SETS - INTERIOR SETS - LIMIT POINTS - HAUSDORFF - EVERY FINITE POINT IN
A SET IN A HAUSDORFF SPACE IS CLOSED - IF X IS HAUSDORFF SPACE THEN
SEWUENCE OF POINTS OF X CONVERGES TO AT MOST ONE POINTS.
A SUBSPACE OF HAUSDORFF SPACE IS HAUSDORFF - CONTINUES FUNCTION -
HOMOMRPHISM - UNIT CIRCLE - CONSECRATING CONTINUES FUNCTION.
PASTING LEMMA - MAPS INTO PRODUCTS - PRODUCT TOPOLOGY - CARTESIAN
PRODUCT - BOX TOPOLOGY -COMPARISON OF BOX AND PRODUCT TOPOLOGY.
METRIC TOPOLOGY - DISTANCE - BALL - METRIZABLE - BOUNDED DIAMETER -
SLANDERED BOUNDED METRIC - EUCLIDEAN - UNIFORMETRIC.
SEQUENCE LEMMA - FIRST COUNTABLE AXIOM - SECOND COUNTABLE AXIOM -
UNIFORM LIMIT THEOREM - QUOTIENT TOPOLOGY - CONNECTED SPACE - COLLECTION
OF CONNECTED SUBSPACE COMMON POINT.
THE IMAGE OF CONNECTED SPACE CONTINUOUS MAPPING - A FINITE CARTESIAN
PRODUCT OF CONNECTED SPACE - SUBSPACE OF REAL LINE - INTERMEDIATE VALUE
THEOREM.
COMPACT SPACE - COVER - OPEN COVER - COMPACT - EVERY CLOSED SUBSPACE OF A
COMPACT SPACE IS COMPACT - EVERY COMPACT SUBSPACE OF A HAUSDORFF OF
SPACE IS CLOSED - THE IMAGE OF COMPACT SPACE UNDER A CONTINUES MAP IS
SET TOPOLOGY AND THEORY OF RELATIVITY{MMAT.05}(2030508)
COMPACT - A PRODUCT OF FINITELY MINING COMPACT SPACE IS COMPACT - TUBE
LEMMA - FINITE INTERSECTION PROPERTY - COMPACT SUBSPACE OF REAL LINE
EXTREME VALUE THEOREM - LEBESGUE NUMBER LEMMA.
UNIFORM CONTINUITY THEOREM - CONTINUES COMPACT REAL LINE - COUNT ABILITY
ACTION - FIRST COUNTABLE - SECOND - DENSE - LINDALE SPACE - SEPARABLE -
SEPARATION ACTIONS - REGULAR - NORMAL - A PRODUCT OF HAUSDORFF SPACE IS
HAUSDORFF - SUBSPACE OF HAUSDORFF SPACE - A SUB APACE OF REGULAR SPACE
IS REGULAR - A PRODUCT OF REGULAR SPACES REGULAR - EVERY REGULAR SPACE
WITH A COUNTABLE BASIS IS NORMAL - EVERY COMPACT- HAUSDORFF SPACE IS
NORMAL - EVERY WELL ORDERED SET X IS NORMAL IF THE ORDERED TOPOLOGY -
URYSOHN LEMMA - COMPLETELY REGULAR -A SUBSPACE OF COMPLETELY REGULAR
SPACE COMPLETERLY REGULAR - A PRODUCT OF COMPLETELY REGULAR SPACE IS
COMPLETELY REGULAR.
URYSOHN METRIZATION THEOREM - IMBEDDING THEOREM - THE TIETZE EXTENSION
THEOREM - MINIMAL UNCOUNTABLE WELL ORDERED SET - COMPONENTS AND LOCAL
CONNECTED.
Years2
EXTENSION FIELDS - ROOTS OF POLYNOMIALS AND MORE ABOUT ROOTS.
TREATMENTS OF GALOIS THEORY.
SOLVABILITY RADICALS.
THE ALGEBRA OF LINEAR TRANSFORMATION.
CHARACTERISTIC ROOTS - MATRICES CANONICAL FORMS AND TRIANGULAR FORMS.
NIL POTENT TRANSFORMATION AND THEIR CANONICAL FORMS.
RATIONAL CANTICLE FORMS TRACE AND TRANSPOSE.
DETERMINANTS, HERMIT IAN, UNITARY AND NORMAL TRANSFORMATION.
QUADRATIC FORMS FINITE FIELDS.
WEDDER BURN`S THEOREM.
THE FINITE DIVISION RINGS.
2 Yr.
ALGEBRA II(2030509)
FUNDAMENTAL THEOREMS - LINE INTEGRALS - RECTIFIABLE ARCS - LINE INTEGRALS AS
FUNCTIONS OF ARCS.
CAVHY`S THEOREM FOR A RECTANGLE AND CAVCHY`S THEOREM FOR A CIRCULAR
DISK - CAVCHY`S INTEGRAL FORMULA - THE INDEX OF A POINT WITH RESPECT TO A
CLOSED CURVE - THE INTEGRAL FORMULA AND HIGHER DERIVATIVES.
LOCAL PROPERTIES OF ANALYTIC FUNCTIONS - REMOVABLE SINGULARITIES - TAYLORS
THERMO - ZEROS AND POLES - THE LOCAL MAPPING AND THE MAXIMUM PRINCIPLES.
THE GENERAL FORM OF CAVCHY`S THEOREM - CHAINS AND CYCLES - SIMPLE
CONNECTIVITY - EXACT DIFFERENTIALS IN SIMPLY CONNECTED REGIONS AND
MULTIPLY CONNECTED REGIONS - THE CALCULUS OF RESIDUES - THE RESIDUE
THEOREM, THE ARGUMENT PRINCIPLE AND THE EVALUATION OF DEFINITE INTEGRALS.
HARMONIC FUNCTIONS - DEFINITIONS AND BASIC PROPERTIES THE MEAN-VALUE
PROPERTY - POISSION`S FORMULA SCHWARY THEOREM AND THE REFLECTION
PRINCIPLE.
POWER SERIES EXPANSIONS - WEIERSTRASS`S THEOREM - THE TAYLOR SERIES AND
THE LAURENT SERIES - PARTIAL FRACTIO NS AND FACTORIZATION - PARTIAL
FRACTIONS.
INFINITE RODUCTS AND CANONICAL PRODUCTS - ENTIRE FUNCTIONS - JENSEN`S
FORMULA AND HADAMARD`S THEOREM.
NORMAL FAMILIES - EQICONTINUITY - NORMALLY AND COMPACTNESS - ARZELA`S
THEOREM - FAMILIES OF ANALYTIC FUNCTIONS AND THE CLASSICAL DEFINITION.
THE RIEMANN MAPPING THEOREM - STATEMENT AND THE PROOF A CLOSER LOOK AT
HARMONIC FUNCTIONS - FUNCTIONS WITH THE MEAN VALUE PROPERTY AND
HARNACK`S PRINCIPLE.
ELLIPTIC FUNCTION - SIMPLY PERIODIC FUNCTIONS AND DOUBLY PERIODIC FUNCTIONS
- THE PERIODIC MODULE - UNOMIDULAR TRANSFORMATIONS.
COMPLEX ANALYSIS(2030510)
THE CANONICAL BASIS AND THE GENERAL PROPERTIES OF ELLIPTIC FUNCTIONS.
THE WEIERSTRASS THEORY - THE WEIERSTRASS - FUNCTION, THE FUNCTION? (Z) AND?
(Z) AND THE DIFFERENTIAL EQUATION.
BANACH SPACES - DEFINITION AND EXAMPLES - HOLDER`S AND MINKOWSKI`S
INEQUALITIES (*) CONTINUOUS LINEAR TRANSFORMATIONS - EQUIVALENCE OF
VARIOUS NORMS IN 1NP.
LOCALLY COMPACT NORMAL LINEAR SPACE IN FINITE SEPARABLE IF N* IS SOCONJUGATE
SPACES 1NP AN 1N ? (*) NATURAL IMBEDDING OF N INTO N** ANY FINITE
DIMENSIONAL NORMAL LINEAR SPACE IS REFLEXIVE.
THE OPEN MAPPING THEOREM - THE CLOSED GRAPH THEOREM - CONJUGATE OF AN
OPERATOR.
HILBERT SPACES - SOME EXAMPLES - ORTHOGONAL COMPLEMENTS - ORTHONORMAL
RESULTS - A HILLERT SPACE H IS SEPARABLE IF AND ONLY IF EVERY ORTHONORMAL
SET IS COUNTABLE (*) ORTHOGONAL DIMENSION OF H (*).
THE CONJUGATE SPACE H* AD JOINT OF AN OPERATOR - SELF AD JOINT OPERATORS -
NORMAL AND UNITARY OPERATOR PROJECTIONS.
FNITE DIMENSIONAL SPECTRAL THEORY - MATRIUS - DETERMINANTS AND THE
SPECTRUM OF AN OPERATOR - THE SPECTRAL THEOREM
THE STRUCTURE OF COMMUTATIVE BONANCH ALGELUAS.
THE CRELFAND MAPPING APPLICATION OF THE FORMULAE R(X) = L1MLLXNLL1/N.
INVOLUTIONS IN BANACH ALGELUA.
THE GELFAND NEUMARK REPRESENTATIONS THEOREM.
FUNCTIONAL ANALYSIS(2030511)
GRAPHS AND SUB-GRAPS AND SIMPLE GRAPHS - GRAPH ISOMORPHISM - THE INCIDENE
AND ADJACENCY MATRICES.
SUB-GRAPHS - VERTEXDEGREES - PATH PROBLEMS.
TREES - CUT EDGES AND BOUNDS - CUT VERTICES - CAYLEY`S FORMULA AND THE
CONNECTOR PROBLEM.
CONNECTIVITY - BLOCKS AND CONSTRUCTION OF RELIABLE COMMUNICATION
NETWORK - EULER TOURS - HAMILTON CYCLES.
THE CHINESE POSTMAN PROBLEM AND THE TRAVELING SALESMAN PROBLEM.
MATCHINGS AND COVERINGS IN BIPARTITE GRAPHS - PERFECT MATCHINGS - THE
PERSONNEL ASSIGNMENT PROBLEM AND THE OPTIMAL ASSIGNMENT PROBLEM - EDGE
- COLORINGS.
EDGE CHROMATIC NUMBER - VIZINGS`S THEOREM AND THE TABLING PROBLEM.
INDEPENDENT SETS - RAMSEY`S THEOREM - TURAN`S THEOREM - SCHUR`S THEOREM
AND A GEOMETRY PROBLEM VERTEX COLORINGS.
CHROMATIC NUMBERS - BROOK`S THEOREM - HAJO`S CONJECTURE - CHROMATIC
POLYNOMIALS - GIRTH AND CHROMATIC NUMBER AND A STORAGE PROBLEM.
PLAN GRAPHS - PLANE AND PLANER GRAPHS - DUAL GRAPHS - EULER`S FORMULA -
BRIDGES - KURATOWSKI`S THEOREM.
THE FIVE COLOR THEOREM AND THE FOUR COLOR CONJUNCTIONS NON-HAMILTONIAN
PLANER GRAPHS AND A PLANARITY ALGORITHM.
DIRECTED GRAPHS - DIRECTED PATH - DIRECTED CYCLES - A JOB SEQUENCING
PROBLEM - DESIGNING AN EFFICIENT COMPUTER DRUM - MAKING A ROAD SYSTEM ONE
WAY AND RANKING THE PARTICIPANTS IN A TREATMENT.
GRAPH THEORY(2030512)
THE GENERAL LINEAR PROGRAMMING PROBLEM - THE LINEAR - PROGRAMMING
PROBLEM - PROPERTIES OF A SOLUTION TO THE LINEAR PROGRAMMING PROGRAM
AND GENERATING EXTREME POINT SOLUTIONS.
THE SIMPLEX COMPUTATIONAL PROCEDURES - DEVELOPMENT OF A MINIMUM
FEASIBLE SOLUTION - COMPUTATIONAL PROCEDURE - THE ARTIFICIAL BASIS
TECHNIQUES - A FIRST FEASIBLE SOLUTION USING SLACK VARIABLES - GEOMETRIC
INTERPRETATION OF THE SIMPLEX PROCEDURE.
THE REVISED SIMPLEX METHOD - THE GENERAL FORM OF THE INVERSE AND THE
PRODUCT FROM OF THE INVERSE.
THE DUALITY PROBLEMS OF LINEAR PROGRAMMING - THE UN-SYMMETRIC PRIMAL
DUAL PROBLEMS - THE SYMMETRIC PRIMAL - DUAL PROBLEM - ECONOMIC
INTERPRETATION OF THE PRIMAL - DUAL PROBLEMS.
DEGENERACY PROBLEMS - PERTURBATION TECHNIQUES AND EXAMPLE OF CYCLING.
ADDITIONAL COMPUTATION TECHNIQUES - DETERMINING A FIRST FEASIBLE SOLUTION -
THE DUAL SIMPLEX METHOD AND INTEGER PROGRAMMING.
THE TRANSPORTATION PROBLEM - THE GENERAL TRANSPORTATION PROBLEM -
COMPUTATIONAL PROCEDURE FOR SOLVING THE TRANSPORTATION PROBLEM -
VARIATION OF TRANSPORTATIONS.
DECISION ANALYSIS AND GAMES - DECISION ENVIRONMENTS - DECISION MAKING
UNDER CERTAINTY - DECISION MAKING UNDER RISK.
DECISION UNDER UNCERTAINTY AND GAME THEORY.
PROBABILISTIC INVENTORY MODEL - INTRODUCTION - CONTINUOUS REVIEW MODELS.
SINGLE PERIOD MODELS.
MULTI - PERIOD MODELS.
OPTIMIZATION TECHNIQUES(2030513)
To buy books pls click on the link below:
Copyright © 2013 - All Rights Reserved - Distance-edu.co.in Google
Powered by Nasbar Infotech
