subjectId	Discipline Name	Subject Name	Coordinators	Type	Institute	Content
111101001	Mathematics	Algebra II	Prof. Jugal K. Verma	Web	IIT Bombay	Select Lecture 1 : Introduction and Overview Lecture 2 : Algebraic extensions I Lecture 3 : Algebraic Extensions II Problem Set 1 : Algebraic Extensions Lecture 4 : Ruler and Compass Constructions I Lecture 5 : Ruler and Compass Constructions II Problem Set 2 : Ruler and Compass Constructions Tutorial 1 : Algebraic Extensions and Ruler and Compass Constructions Lecture 6 : Symmetric Polynomials I Lecture 7 : Symmetric Polynomials II Problem set 3 : Symmetric Polynomials Lecture 8 : Algebraic Closure of a Field Problem set 4 : Splitting Fields Tutorial 2 : Symmetric Polynomials and Splitting Fields Lecture 9 : Separable Extensions I Lecture 10 : Separable Extensions II Problem set 5 : Separable Extensions Lecture 11 : Finite Fields I Tutorial 3 : Separable Extensions and Finite Fields Problem set 6 : Finite Fields Lecture 12 : The Primitive Element Theorem Problem set 7 : Primitive elements Tutorial 4 : Finite Fields and Primitive Elements Lecture 13 : Normal Extensions Lecture 14 : Galois group of a Galois Extension I Lecture 15 : Galois group of a Galois Extension II Problem set 8 : Fundamental Theorem of Galois Theory Tutorial 5 : Fundamental Theorem of Galois Theory Lecture 16 : Applications and Illustrations of the FTGT Lecture 17 : Cyclotomic Extensions I Lecture 18 : Cyclotomic Extensions II Problem Set 9 : Cyclotomic Extensions Lecture 19 : Abelian and Cyclic Extensions Lecture 20 : Cyclic Extensions and Solvable Groups Tutorial 6 : Cyclotomic Extensions Lecture 21 : Galois Groups of Composite Extensions Lecture 22 : Solvability by Radicals Problem Set 10 : Solvability by Radicals Lecture 23 : Solutions of Cubic and Quartic Equations Lecture 24 : Galois Groups of Quartic Polynomials Problem Set 11 : Galois groups of Quartic Polynomials. Tutorial 7 : Galois Groups of Quartics and Solvability by Radicals Lecture 25 : Norm, Trace and Hilbert's Theorem 90 Problem Set 12 : Cyclic Extensions Lecture 26 : Polynomials with Galois Group Sn:
111101002	Mathematics	Algebraic Topology	Prof. G.K. Srinivasan	Web	IIT Bombay	Select Lecture 1: Introduction Lecture 2 : Preliminaries from general topology Lecture 3 : More Preliminaries from general topology Lecture 4 : Further preliminaries from general topology Lecture 5 : Topological groups Lecture 6 : Test - 1 Lecture 7 : Paths, homotopies and the fundamental group Lecture 8 : Categories and Functors Lecture 9 : Functorial properties of the fundamental group Lecture 10 : Brouwers theorem and its applications Lecture 11 : Homotopies of maps. Deformation retracts Lecture 12 & 13 : The fundamental group of the circle. Lecture 14 : Test - II Lecture 15 : Covering Projections Lecture 16 : Lifting of paths and homotopies Lecture 17 : Action of the fundamental group on the fibers Lecture 18 : The lifting criterion Lecture 19 : Deck transformations Lecture 20 : Orbit Spaces Lecture 21 : Test - III Lecture 22 : Fundamental groups of certain orthogonal groups Lecture 23 & 24 : Coproducts and push-outs Lecture 25 : Adjunction Spaces Lecture 26 : Seifert Van Kampen theorem Lecture 27 : Test - IV Lecture 28 : Introductory remarks on homology theory Lecture 29 & 30 : The Singular chain complex and homology groups Lecture 31 : The homology groups and their functoriality Lecture 32 : The abelianization of the fundamental group Lecture 33 : Homotopy invariance of homology Lecture 34 : Small Simplicies Lecture 35 : The Mayer Vietoris sequence and its applications Lecture 36 : Maps of Spheres Lecture 37 : Test - V Lecture 38 : Relative homology Lecture 39 : Excisim Theorem Lecture 40 : Inductive limits Lecture 41 : The Jordan-Brouwer separation theorem
111101003	Mathematics	Elementary Numerical Analysis	Prof. Rekha P. Kulkarni	Video	IIT Bombay	Select L1- Introduction L2-Polynomial Approximation L3-Interpolating Polynomials L4-Properties of Divided Difference L5-Error in the Interpolating polynomial L6-Cubic Hermite Interpolation L7-Piecewise Polynomial Approximation L8-Cubic Spline Interpolation L9-Tutorial 1 L10-Numerical Integration: Basic Rules L11-Composite Numerical Integration L12-Gauss 2-point Rule: Construction L13-Gauss 2-point Rule: Error L14-Convergence of Gaussian Integration L15-Tutorial 2 L16-Numerical Differentiation L17-Gauss Elimination L18-L U decomposition L19-Cholesky decomposition L20-Gauss Elimination with partial pivoting L21-Vector and Matrix Norms L22-Perturbed Linear Systems L23-Ill-conditioned Linear System L24-Tutorial 3 L25-Effect of Small Pivots L26-Solution of Non-linear Equations L27-Quadratic Convergence of Newton's Method L28-Jacobi Method L29-Gauss-Seidel Method L30-Tutorial 4 L31-Initial Value Problem L32-Multi-step Methods L33-Predictor-Corrector Formulae L34-Boundary Value Problems L35-Eigenvalues and Eigenvectors L36-Spectral Theorem L37-Power Method L38-Inverse Power Method L39-Q R Decomposition L40-Q R Method
111101004	Mathematics	Introduction to Probability Theory	Dr. K. Suresh Kumar	Web	IIT Bombay	Select Chapter 1 : Introduction Chapter 2 : Random Variables Chapter 3 : Conditional Probability and Independence Chapter 4 : Distributions Chapter 5 : Random Vectors , Joined Distributions Chapter 6 : Expectation and Conditional Expectation Chapter 7 : Characteristic Functions Chapter 8 : Limit Theorems
111101005	Mathematics	Measure and Integration	Prof. Inder K Rana	Video	IIT Bombay	Select L1- Introduction ,Extended Real numbers L2-Algebra and Sigma Algebra of a subset of a set L3-Sigma Algebra generated by a class L4-Monotone Class L5-Set function L6-The Length function and its properties L7-Countably additive set functions on intervals L8-Uniqueness Problem for Measure L9-Extension of measure L10-Outer measure and its properties L11-Measurable sets L12-Lebesgue measure and its properties L13-Characterization of Lebesque measurable sets L14-Measurable functions L15-Properties of measurable functions L16-Measurable functions on measure spaces L17-Integral of non negative simple measurable functions L18-Properties of non negative simple measurable functions L19-Monotone convergence theorem & Fatou's Lemma L20-Properties of Integral functions & Dominated Convergence Theorem L21-Dominated Convergence Theorem and applications L22-Lebesgue Integral and its properties L23-Denseness of continuous function L24-Product measures, an Introduction L25-Construction of Product Measure L26-Computation of Product Measure-I L27-Computation of Product Measure-II L28-Integration on Product spaces L29-Fubini's Theorems L30-Lebesgue Measure and integral on R2 L31-Properties of Lebesgue Measure and integral on Rn L32-Lebesgue integral on R2 L33-Integrating complex-valued functions L34-Lp - spaces L35-L2(X,S,mue) L36-Fundamental Theorem of calculas for Lebesgue Integral-I L37-Fundamental Theorem of calculus for Lebesgue Integral-II L38-Absolutely continuous measures L39-Modes of convergence L40-Convergence in Measure
111102011	Mathematics	Linear Algebra	Dr. R. K. Sharma,Dr. Wagish Shukla	Web	IIT Delhi	Select Vectors Spaces Polynomials in one Variable Matrices and linear transformations Classical and Quantum Computation of dual basis1 More onVector Spaces and Linear transformations Eigenvalues and Eigenvectors Diagonalization Sesqui or Bi-Linear Forms More on sesqui or bi-linear forms Inner Product Space Orthogonal and Orthonormal Basis Generalized Inverse
111101080	Mathematics	Mathematics in India - From Vedic Period to Modern Times	Prof. M.D.Srinivas , Prof.M.S.Sriram, Prof.K.Ramasubramanian	Video	IIT Bombay	Select Indian Mathematics: An Overview Vedas and Sulbasutras - Part 1 Vedas and Sulbasutras - Part 2 Panini's Astadhyayi Pingala's Chandahsastra Decimal place value system Aryabhatiya of Aryabhata - Part 1 Aryabhatiya of Aryabhata - Part 2 Aryabhatiya of Aryabhata - Part 3 Aryabhatiya of Aryabhata - Part 4 and Introduction to Jaina Mathematics Brahmasphutasiddhanta of Brahmagupta - Part 1 Brahmasphutasiddhanta of Brahmagupta - Part 2 Brahmasphutasiddhanta of Brahmagupta - Part 3 Brahmasphutasiddhanta of Brahmagupta - Part 4 and The BakhshaliManuscript Mahaviras Ganitasarasangraha Mahaviras Ganitasarasangraha 2 Mahaviras Ganitasarasangraha 3 Development of Combinatorics 1 Development of Combinatorics 2 Lilavati of Bhaskaracarya 1 Lilavati of Bhaskaracarya 2 Lilavati of Bhaskaracarya 3 Bijaganita of Bhaskaracarya 1 Bijaganita of Bhaskaracarya 2 Ganitakaumudi of Narayana Pandita 1 Ganitakaumudi of Narayana Pandita 2 Ganitakaumudi of Narayana Pandita 3 Magic Squares - Part 1 Magic Squares - Part 2 Development of Calculus in India 1 Development of Calculus in India 2 Jyanayanam: Computation of Rsines Trigonometry and Spherical Trigonometry 1 Trigonometry and Spherical Trigonometry 2 Trigonometry and Spherical Trigonometry 3 Proofs in Indian Mathematics 1 Proofs in Indian Mathematics - Part 2 Proofs in Indian Mathematics 3 Mathematics in Modern India 1 Mathematics in Modern India 2
111102012	Mathematics	Linear Programming Problems	Dr. Aparna Mehra	Web	IIT Delhi	Select Linear programming modeling, Optimal solutions and grap Notion of convex set, convex function, their prope Preliminary definitions (like convex combination, Optimal hyper-plane and existence of optimal solut Basic feasible solutions: algebraic interpretation Relationship between extreme points and correspond Adjacent extreme points and corresponding BFS alo Fundamental theorem of LPP and its illustration th LPP in canonical form to get the initial BFS & meth Case of unbounded LPP, Simplex algorithm and illustrati Artificial variables and its interpretation in co Two phase method and illustration Degeneracy and its consequences including cases of cycl Introduction to duality & formulation of dual LPP for d Duality theorems and their interpretations Complementary slackness theorem, Farkas Lemma, Ex Economic interpretation & applications of duality Dual simplex method and its illustration Post optimality analysis: the cases of change in re Sensitivity analysis for addition and deletion of Lecture 3 Karmarkar's interior point method How to model the given LPP in Karmarkar's framewo Complexity issue of Karmarkar's method Integer programming: modeling & a look at its feasi Gomory cut algorithm and derivation of cut equatio Examples Branch and Bound algorithm Special LPPs: Transportation programming problem, m Initial BFS and optimal solution of balanced TP pr Other forms of TP and requisite modifications Assignment problems and permutation matrix Hungarian Method Duality in Assignment Problems Network Problems and LPP Formulation Network Simplex Method:
111102014	Mathematics	Stochastic Processes	Dr. S. Dharmaraja	Video	IIT Delhi	Select Introduction to Stochastic Processes Introduction to Stochastic Processes (Contd.) Problems in Random Variables and Distributions Problems in Sequences of Random Variables Definition, Classification and Examples Simple Stochastic Processes Stationary Processes Autoregressive Processes Introduction, Definition and Transition Probability Matrix Chapman-Kolmogrov Equations Classification of States and Limiting Distributions Limiting and Stationary Distributions Limiting Distributions, Ergodicity and Stationary Distributions Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing Models Reducible Markov Chains Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix Limiting and Stationary Distributions, Birth Death Processes Poisson Processes M/M/1 Queueing Model Simple Markovian Queueing Models Queueing Networks Communication Systems Stochastic Petri Nets Conditional Expectation and Filtration Definition and Simple Examples Definition and Properties Processes Derived from Brownian Motion Stochastic Differential Equations Ito Integrals Ito Formula and its Variants Some Important SDE`s and Their Solutions Renewal Function and Renewal Equation Generalized Renewal Processes and Renewal Limit Theorems Markov Renewal and Markov Regenerative Processes Non Markovian Queues Non Markovian Queues Cont,, Application of Markov Regenerative Processes Galton-Watson Process Markovian Branching Process
111103016	Mathematics	Formal Languages and Automata Theory	Dr. Diganta Goswami, Dr. K.V. Krishna	Video	IIT Guwahati	Select Introduction Alphabet, Strings, Languages Finite Representation Grammars (CFG) Derivation Trees Regular Grammars Finite Automata Nondeterministic Finite Automata NFA <=> DFA Myhill-Nerode Theorem Minimization RE => FA FA => RE FA <=> RG Variants of FA Closure Properties of RL Homomorphism Pumping Lemma Simplification of CFG Normal Forms of CFG Properties of CFLs Pushdown Automata PDA <=> CFG Turing Machines Turing Computable Functions Combining Turing Machines Multi Input Turing Decidable Languages Varients of Turing Machines Structured Grammars Decidability Undecidability1 Undecidability2 Undecidability3 Time Bounded Turing Machines P and NP NP-Completeness NP-Complete Problems1 NP-Complete Problems2 NP-Complete Problems3 Chomsky Hierarchy
111103020	Mathematics	Number Theory	Dr. Anupam Saikia	Web	IIT Guwahati	Select Introduction Decimal Expansion of a Positive Integer Euclid's Algorithm Coprime Integers Prime Numbers Prime Number Theorem Congruence Linear Congruence Simultaneous Linear Congruences System of Congruences with Non-coprime Moduli Linear Congruences Modulo Prime Powers Fermat's Little Theorem Pseudo-primes Greatest Integer Function Euler's function RSA Cryptosystem Arithmetic Functions Mobius Function Dirichlet Product Units Modulo an Integer Existence of Primitive Roots for Primes Primitive Roots for Powers of 2 Definition and Examples Gauss Lemma Quadratic Reciprocity Quadratic Residues of Powers of an Odd Prime The Jacobi Symbol Definition and Examples . Discriminant of a Quadratic Form Proper Representation and Equivalent Forms Uniqueness of Equivalent Reduced Form Class Number Fermat Primes Primes Expressible as a Sum of Two Squares Sum of Three Squares Finite Continued Fractions Euler's Rule Infinite Continued Fractions Periodic Continued Fractions Conjugate of a Quadratic Irrational Continued Fractions of Reduced Quadratic Irrationals Best Rational Approximation to an Irrational Pell's Equation Riemann Zeta Function Dirichlet Series Lucas Test for Primality Pollard's Method for Factorization Fermat's Factorization Fermat's Conjecture Exercise-1 Exercise-2 Exercise-3 Exercise-4 Exercise-5 Exercise-6 Exercise-7 Exercise-8 Exercise -9 Bibliography Index
111103021	Mathematics	Partial Differential Equations	Dr. Rajen Kumar Sinha	Web	IIT Guwahati	Select A Review of Multivariable Calulus Essential Ordinary Differential Equations Surfaces and Integral Curves Solving Equations dx/P = dy/Q = dz/R First-Order Partial Differential Equations Linear First-Order PDEs Quasilinear First-Order PDEs Nonlinear First-Order PDEs Compatible Systems and Charpit�s Method Some Special Types of First-Order PDEs Jacobi Method for Nonlinear First-Order PDEs Classification of Second-Order PDEs Canonical Forms or Normal Forms Superposition Principle and Wellposedness Introduction to Fourier Series Convergence of Fourier Series Fourier Cosine and Sine Series Modeling the Heat Equation The Maximum and Minimum Principle Method of Separation of Variables Time-Independent Homogeneous BC Time-Dependent BC Mathematical Formulation and Uniqueness Result The Infinite String Problem The Semi-Infinite String Problem The Finite Vibrating String Problem The Inhomogeneous Wave Equation Basic Concepts and The Maximum/Minimum Principle Green�s Identity and Fundamental Solutions The Dirichlet BVP for a Rectangle The Mixed BVP for a Rectangle The Dirichlet Problems for Annuli The Dirichlet Problem for the Disk Fourier Transform Fourier Sine and Cosine Transformations Heat Flow Problems Vibration of an Infinite String Laplace�s Equation in a Half-Plane The Laplace Equation The Wave Equation The Heat Equation Bibliography
111103070	Mathematics	Complex Analysis	Prof. P. A. S. Sree Krishna	Video	IIT Guwahati	Select Introduction Introduction to Complex Numbers de Moivre's Formula and Stereographic Projection Topology of the Complex Plane Part-I Topology of the Complex Plane Part-II Topology of the Complex Plane Part-III Introduction to Complex Functions Limits and Continuity Differentiation Cauchy-Riemann Equations and Differentiability Analytic functions; the exponential function Sine, Cosine and Harmonic functions Branches of Multifunctions; Hyperbolic Functions Problem Solving Session I Integration and Contours Contour Integration Introduction to Cauchy's Theorem Cauchy's Theorem for a Rectangle Cauchy's theorem Part - II Cauchy's Theorem Part - III Cauchy's Integral Formula and its Consequences The First and Second Derivatives of Analytic Functions Morera's Theorem and Higher Order Derivatives of Analytic Functions Problem Solving Session II Introduction to Complex Power Series Analyticity of Power Series Taylor's Theorem Zeroes of Analytic Functions Counting the Zeroes of Analytic Functions Open mapping theorem – Part I Open mapping theorem – Part II Properties of Mobius Transformations Part I Properties of Mobius Transformations Part II Problem Solving Session III Removable Singularities Poles Classification of Isolated Singularities Essential Singularity & Introduction to Laurent Series Laurent's Theorem Residue Theorem and Applications Problem Solving Session IV
111104024	Mathematics	Applied Multivariate Analysis	Dr. Amit Mitra,Dr. Sharmishtha Mitra	Video	IIT Kanpur	Select Prologue Lecture-01 Basic concepts on multivariate distribution. Lecture - 02 Basic concepts on multivariate distribution. Lecture - 03 Multivariate normal distribution. � I Lecture - 04 Multivariate normal distribution. � II Lecture - 05 Multivariate normal distribution. � III Lecture - 06 Some problems on multivariate distributions. � I Lecture - 07 Some problems on multivariate distributions. � II Lecture - 08 Random sampling from multivariate normal distribution and Wishart distribution. � I Lecture - 09 Random sampling from multivariate normal distribution and Wishart distribution. � II Lecture - 10 Random sampling from multivariate normal distribution and Wishart distribution. � III Lecture - 11 Wishart distribution and it�s properties. �I Lecture - 12 Wishart distribution and it�s properties.- II Lecture -13 Hotelling�s T2 distribution and it�s applications. Lecture - 14 Hotelling�s T2 distribution and various confidence intervals and regions. Lecture- 15 Hotelling�s T2 distribution and Profile analysis. Lecture - 16 Profile analysis.-I Lecture - 17 Profile analysis. �II Lecture - 18 MANOVA.-I Lecture - 19 MANOVA.- II Lecture - 20 MANOVA .- III Lecture -21 MANOVA & Multiple Correlation Coefficient Lecture -22 Multiple Correlation Coefficient Lecture 23 Principal Component Analysis Lecture -24 Principal Component Analysis Lecture -25 Principal Component Analysis Lecture -26 Cluster Analysis Lecture -27 Cluster Analysis Lecture -28 Cluster Analysis Lecture -29 Cluster Analysis Lecture -30 Discriminant Analysis and Classification Lecture -31 Discriminant Analysis and Classification Lecture -32 Discriminant Analysis and Classification Lecture -33 Discriminant Analysis and Classification Lecture -34 Discriminant Analysis and Classification Lecture -35 Discriminant Analysis and Classification Lecture -36 Discriminant Analysis and Classification Lecture -37 Factor_Analysis Lecture 38 Factor_Analysis Lecture -39 Factor_Analysis Lecture -40 Cannonical Correlation Analysis Lecture -41 Cannonical Correlation Analysis Lecture -42 Cannonical Correlation Analysis Lecture -43 Cannonical Correlation Analysis
111104025	Mathematics	Calculus of Variations and Integral Equations	Prof. D. Bahuguna,Dr. Malay Banerjee	Video	IIT Kanpur	Select Lecture-01-Calculus of Variations and Integral Equations Lecture-02-Calculus of Variations and Integral Equations Lecture-03-Calculus of Variations and Integral Equations Lecture-04-Calculus of Variations and Integral Equations Lecture-05-Calculus of Variations and Integral Equations Lecture-06-Calculus of Variations and Integral Equations Lecture-07-Calculus of Variations and Integral Equations Lecture-08-Calculus of Variations and Integral Equations Lecture-09-Calculus of Variations and Integral Equations Lecture-10-Calculus of Variations and Integral Equations Lecture-11-Calculus of Variations and Integral Equations Lecture-12-Calculus of Variations and Integral Equations Lecture-13-Calculus of Variations and Integral Equations Lecture-14-Calculus of Variations and Integral Equations Lecture-15-Calculus of Variations and Integral Equations Lecture-16-Calculus of Variations and Integral Equations Lecture-17-Calculus of Variations and Integral Equations Lecture-18-Calculus of Variations and Integral Equations Lecture-19-Calculus of Variations and Integral Equations Lecture-20-Calculus of Variations and Integral Equations Lecture-21-Calculus of Variations and Integral Equations Lecture-22-Calculus of Variations and Integral Equations Lecture-23-Calculus of Variations and Integral Equations Lecture-24-Calculus of Variations and Integral Equations Lecture-25-Calculus of Variations and Integral Equations Lecture-26-Calculus of Variations and Integral Equations Lecture-27-Calculus of Variations and Integral Equations Lecture-28-Calculus of Variations and Integral Equations Lecture-29-Calculus of Variations and Integral Equations Lecture-30-Calculus of Variations and Integral Equations Lecture-31-Calculus of Variations and Integral Equations Lecture-32-Calculus of Variations and Integral Equations Lecture-33-Calculus of Variations and Integral Equations Lecture-34-Calculus of Variations and Integral Equations Lecture-35-Calculus of Variations and Integral Equations Lecture-36-Calculus of Variations and Integral Equations Lecture-37-Calculus of Variations and Integral Equations Lecture-38-Calculus of Variations and Integral Equations Lecture-39-Calculus of Variations and Integral Equations Lecture-40-Calculus of Variations and Integral Equations
111104026	Mathematics	Discrete Mathematics	Prof. A.K. Lal	Web	IIT Kanpur	Select Contents Basic Set Theory Well Ordering Principle and the Principle of Mathematical Induction Strong Form of the Principle of Mathematical Induction Division Algorithm and the Fundamental Theorem of Arithmetic Relations, Partitions and Equivalence Relation Functions Distinguishable Balls Binomial Theorem Onto Functions and the Stirling Numbers of Second Kind Indistinguishable Balls and Distinguishable Boxes Indistinguishable Balls in Indistinguishable Boxes Lattice Paths and Catalan Numbers Catalan Numbers Continued Generalizations Pigeonhole Principle Pigeonhole Principle Continued Principle of Inclusion and Exclusion Formal Power Series Formal Power Series Continued Application to Recurrence Relation Application to Recurrence Relation Continued Application to Recurrence Relation Continued Applications to Generating Functions Continued Groups Example of Groups SubGroups Lagrange�s Theorem Applications of Lagrange�s Theorem Group Action Group Action Continued The Cycle Index Polynomial Polya Inventory Theorem Basic Graph Theory Graph Operations Matrices related with Graphs Matrix Tree Theorem Eulerian graphs Planar Graphs Euler�s Theorem for Planar Graphs Stereographic Projection
111104027	Mathematics	Linear programming and Extensions	Prof. Prabha Sharma	Video	IIT Kanpur	Select Lecture_01_Introduction to Linear Programming Problems. Lecture_02_ Vector space, Linear independence and dependence, basis. Lec_03_Moving from one basic feasible solution to another, optimality criteria. Lecture_04_Basic feasible solutions, existence & derivation. Lecture_5_Convex sets, dimension of a polyhedron, Faces, Example of a polytope. Lecture_6_Direction of a polyhedron, correspondence between bfs and extreme points. Lecture_7_Representation theorem, LPP solution is a bfs, Assignment 1. Lecture_08_Development of the Simplex Algorithm, Unboundedness, Simplex Tableau. Lecture_9_ Simplex Tableau & algorithm ,Cycling, Bland�s anti-cycling rules, Phase I & Phase II. Lecture_10_ Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs. Lecture_11_Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP. Lecture_12_LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem. Lecture_13_Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality. Lecture_14_Examples of writing the dual, complementary slackness theorem. Lecture_15_Complementary slackness conditions, Dual Simplex algorithm, Assignment 3. Lecture_16_Primal-dual algorithm. Lecture_17_Problem in lecture 16, starting dual feasible solution, Shortest Path Problem. Lecture_18_Shortest Path Problem, Primal-dual method, example. Lecture_19_Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vector. Lecture_20_ Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysis. Lecture_21_Parametric LPP-Right hand side vector. Lecture_22_Parametric cost vector LPP. Lecture_23_Parametric cost vector LPP, Introduction to Min-cost flow problem. Lecture_24_Mini-cost flow problem-Transportation problem. Lecture_25_Transportation problem degeneracy, cycling Lecture_26_ Sensitivity analysis. Lecture_27_ Sensitivity analysis. Lecture_28_Bounded variable transportation problem, min-cost flow problem. Lecture_29_Min-cost flow problem Lecture_30_Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solution Lecture_31_Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cycles. Lecture_32_ Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis. Lecture_33_Min-cost flow changes in arc capacities , Max-flow problem, assignment 7 Lecture_34_Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm. Lecture_35_Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem. Lecture_36_Improved Max-flow algorithm. Lecture_37_Critical Path Method (CPM). Lecture_38_Programme Evaluation and Review Technique (PERT). Lecture_39_ Simplex Algorithm is not polynomial time- An example. Lecture_40_Interior Point Methods .
111104030	Mathematics	Numerical Solution of ODEs	Prof. M.K. Kadalbajoo	Web	IIT Kanpur	Select Preliminaries Existence, Uniqueness, and Wellposedness Stability and Asymptotic Stability The Euler Method Convergence of Euler�s Method Improvement of the error bound Stability Higher Order Methods Runge-Kutta Methods Error bounds for Runge-Kutta methods Absolute Stability for Runge-Kutta Methods Systems of Equations Direct Methods For Higher Order Equations General Single Step Methods Convergence of General One-Step Methods Derivation of Implicit Runge-Kutta methods Derivation of Implicit Runge-Kutta Methods(Contd.) Multistep Methods Multistep Methods(Contd.) Multistep Methods(Contd..) The local error of the formulas based on integration Local Error of Nystrom & Milne-Simpson Methods Multistep Methods for Special Equations of the Second Order Special 2nd order equations(Contd.) Linear Multistep Methods Linear Multistep Methods(Contd) Consistency and Zero-Stability of Linear Multistep Methods Convergence of Linear Multistep Methods Necessary & Sufficient Conditions for Convergence Absolute Stability and Relative Stability General methods for finding intervals of absolute and relative stability Some more methods for Absolute & Relative Stability First order linear systems with constant coefficient Stiffness and Problem of Stiffness The problem of implicitness for Stiff systems Linear multistep methods for Stiff systems Finite Difference Methods Analysis of Difference System Analytic Expression of the Error Nonlinear second order equations Special Boundary Value Problems Special Boundary Value Problems(Contd.)
111104031	Mathematics	Ordinary Differential Equations	Prof. V. Raghavendra	Web	IIT Kanpur	Select Preliminaries Picard's Successive Approximations Picard's Theorem Continuation and Dependence on Initial conditions Existence of Solutions in the Large Existence and Uniqueness of Solutions of Systems Cauchy-Peano theorem Introduction Linear Dependence and Wronskian Basic Theory for Linear Equations Method of Variation of Parameters Homogeneous Linear Equations with Constant Coefficients Introduction- module 3 Systems of First Order Equations Fundamental Matrix Non-homogeneous linear Systems Linear Systems with Constant Coefficients Phase Portraits-Introduction Phase Portraits (continued) Introduction - module 4 Sturm's Comparison Theorem Elementary Linear Oscillations Boundary Value Problems Sturm-Liouville Problem Green's Functions Introduction -Module 5 Linear Systems with Constant Coefficient (module5) Linear Systems with Variable Coefficients Second Order Linear Differential Equations Stability of Quasi-linear Systems Stability of Autonomous Systems Stability of Non-Autonomous Systems A Particular Lyapunov Function
111104068	Mathematics	Convex Optimization	Dr. Joydeep Dutta	Video	IIT Kanpur	Select Lecture-01 Convex Optimization Lecture-02 Convex Optimization Lecture-03 Convex Optimization Lecture-04 Convex Optimization Lecture-05 Convex Optimization Lecture-06 Convex Optimization Lecture-07 Convex Optimization Lecture-08 Convex Optimization Lecture-09 Convex Optimization Lecture-10 Convex Optimization Lecture-11 Convex Optimization Lecture-12 Convex Optimization Lecture-13 Convex Optimization Lecture-14 Convex Optimization Lecture-15 Convex Optimization Lecture-16 Convex Optimization Lecture-17 Convex Optimization Lecture-18 Convex Optimization Lecture-19 Convex Optimization Lecture-20 Convex Optimization Lecture-21 Convex Optimization Lecture-22 Convex Optimization Lecture-23 Convex Optimization Lecture-24 Convex Optimization Lecture-25 Convex Optimization Lecture-26 Convex Optimization Lecture-27 Convex Optimization Lecture-28 Convex Optimization Lecture-29 Convex Optimization Lecture-30 Convex Optimization Lecture-31 Convex Optimization Lecture-32 Convex Optimization Lecture-33 Convex Optimization Lecture-34 Convex Optimization Lecture-35 Convex Optimization Lecture-36 Convex Optimization Lecture-37 Convex Optimization Lecture-38 Convex Optimization Lecture-39 Convex Optimization Lecture-40 Convex Optimization Lecture-41 Convex Optimization Lecture-42 Convex Optimization
111104072	Mathematics	Econometric Theory	Prof. Shalabh	Web	IIT Kanpur	Select main Lecture1 Lecture2 Lecture3 Lecture4 Lecture5 Lecture6 Lecture7 Lecture8 Lecture9 Lecture10 Lecture11 Lecture12 Lecture13 Lecture14 Lecture15 Lecture16 Lecture17 Lecture18 Lecture19 Lecture20 Lecture21 Lecture22 Lecture23 Lecture24 Lecture25 Lecture26 Lecture27 Lecture28 Lecture29 Lecture30 Lecture31 Lecture32 Lecture33 Lecture34 Lecture35 Lecture36 Lecture37 Lecture38 Lecture39 Lecture40 Lecture41 Lecture42 Lecture43 Lecture44 Lecture45 Bibliography
111104073	Mathematics	Sampling Theory	Prof. Shalabh	Web	IIT Kanpur	Select Lecture1 Lecture2 Lecture3 Lecture4 Lecture5 Lecture6 Lecture7 Lecture8 Lecture9 Lecture10 Lecture11 Lecture12 Lecture13 Lecture14 Lecture15 Lecture16 Lecture17 Lecture18 Lecture19 Lecture20 Lecture21 Lecture22 Lecture23 Lecture24 Lecture25 Lecture26 Lecture27 Lecture28 Lecture29 Lecture30 Lecture31 Lecture32 Lecture33 Lecture34 Lecture35 Lecture36 Lecture37 Lecture38 Lecture39 Lecture40 Lecture41 Exercises
111104074	Mathematics	Linear Regression Analysis	Prof. Shalabh	Web	IIT Kanpur	Select main Lecture1 Lecture2 Lecture3 Lecture4 Lecture5 Lecture6 Lecture7 Lecture8 Lecture9 Lecture10 Lecture11 Lecture12 Lecture13 Lecture14 Lecture15 Lecture16 Lecture17 Lecture18 Lecture19 Lecture20 Lecture21 Lecture22 Lecture23 Lecture24 Lecture25 Lecture26 Lecture27 Lecture28 Lecture29 Lecture30 Lecture31 Lecture32 Lecture33 Lecture34 Lecture35 Lecture36 Lecture37 Lecture38 Lecture39 Lecture40 Lecture41 Lecture42 Lecture43 Lecture44 Bibliography-RegressionAnalysis
111104075	Mathematics	Analysis of variance and design of experiment-I	Prof. Shalabh	Web	IIT Kanpur	Select main Lecture1 Lecture2 Lecture3 Lecture4 Lecture5 Lecture6 Lecture7 Lecture8 Lecture9 Lecture10 Lecture11 Lecture12 Lecture13 Lecture14 Lecture15 Lecture16 Lecture17 Lecture18 Lecture19 Lecture20 Lecture21 Lecture22 Lecture23 Lecture24 Lecture25 Lecture26 Lecture27 Lecture28 Lecture29 Lecture30 Lecture31 Lecture32 Lecture33 Lecture34 Lecture35 Lecture36 Lecture37 Exercises References
111104078	Mathematics	Analysis of variance and design of experiment-II	Prof. Shalabh	Web	IIT Kanpur	Select main Lecture1 Lecture2 Lecture3 Lecture4 Lecture5 Lecture6 Lecture7 Lecture8 Lecture9 Lecture10 Lecture11 Lecture12 Lecture13 Lecture14 Lecture15 Lecture16 Lecture17 Lecture18 Lecture19 Lecture20 Lecture21 Lecture22 Lecture23 Lecture24 Lecture25 Lecture26 Lecture27 Lecture28 Lecture29 Lecture30 Lecture31 Lecture32 Lecture33 Lecture34 Lecture35 Lecture36 Lecture37 Lecture38 Exercise
111104079	Mathematics	Probability Theory and Applications	Prof. Prabha Sharma	Video	IIT Kanpur	Select Lecture-01-Basic principles of counting Lecture-02-Sample space , events, axioms of probability Lecture-03-Conditional probability, Independence of events. Lecture-04-Random variables, cumulative density function, expected value Lecture-05-Discrete random variables and their distributions Lecture-06-Discrete random variables and their distributions Lecture-07-Discrete random variables and their distributions Lecture-08-Continuous random variables and their distributions. Lecture-09-Continuous random variables and their distributions. Lecture-10-Continuous random variables and their distributions. Lecture-11-Function of random variables, Momement generating function Lecture-12-Jointly distributed random variables, Independent r. v. and their sums Lecture-13-Independent r. v. and their sums. Lecture-14-Chi � square r. v., sums of independent normal r. v., Conditional distr. Lecture-15 Conditional disti, Joint distr. of functions of r. v., Order statistics Lecture-16-Order statistics, Covariance and correlation. Lecture-17-Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation. Lecture-18-Conditional expectation, Best linear predictor Lecture-19-Inequalities and bounds. Lecture-20-Convergence and limit theorems Lecture-21-Central limit theorem Lecture-22-Applications of central limit theorem Lecture-23-Strong law of large numbers, Joint mgf. Lecture-24-Convolutions Lecture-25-Stochastic processes: Markov process. Lecture-26-Transition and state probabilities. Lecture-27-State prob., First passage and First return prob Lecture-28-First passage and First return prob. Classification of states. Lecture-29-Random walk, periodic and null states. Lecture-30-Reducible Markov chains Lecture-31-Time reversible Markov chains Lecture-32-Poisson Processes Lecture-33-Inter-arrival times, Properties of Poisson processes Lecture-34-Queuing Models: M/M/I, Birth and death process, Little�s formulae Lecture-35-Analysis of L, Lq ,W and Wq , M/M/S model Lecture-36-M/M/S , M/M/I/K models Lecture-37-M/M/I/K and M/M/S/K models Lecture-38-Application to reliability theory failure law Lecture-39-Exponential failure law, Weibull law Lecture-40-Reliability of systems
111105035	Mathematics	Advanced Engineering Mathematics	Prof. Somesh Kumar,Prof. P.D. Srivastava,Prof. J. Kumar,Dr. P. Panigrahi	Video	IIT Kharagpur	Select Review Groups, Fields and Matrices Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Basis, Dimension, Rank and Matrix Inverse Linear Transformation, Isomorphism and Matrix Representation System of Linear Equations, Eigenvalues and Eigenvectors Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Jordan Canonical Form, Cayley Hamilton Theorem Inner Product Spaces, Cauchy-Schwarz Inequality Orthogonality, Gram-Schmidt Orthogonalization Process Spectrum of special matrices,positive/negative definite matrices Concept of Domain, Limit, Continuity and Differentiability Analytic Functions, C-R Equations Harmonic Functions Line Integral in the Complex Cauchy Integral Theorem Cauchy Integral Theorem (Contd.) Cauchy Integral Formula Power and Taylor's Series of Complex Numbers Power and Taylor's Series of Complex Numbers (Contd.) Taylor's, Laurent Series of f(z) and Singularities Classification of Singularities, Residue and Residue Theorem Laplace Transform and its Existence Properties of Laplace Transform Evaluation of Laplace and Inverse Laplace Transform Applications of Laplace Transform to Integral Equations and ODEs Applications of Laplace Transform to PDEs Fourier Series Fourier Series (Contd.) Fourier Integral Representation of a Function Introduction to Fourier Transform Applications of Fourier Transform to PDEs Laws of Probability - I Laws of Probability - II Problems in Probability Random Variables Special Discrete Distributions Special Continuous Distributions Joint Distributions and Sampling Distributions Point Estimation Interval Estimation Basic Concepts of Testing of Hypothesis Tests for Normal Populations
111105037	Mathematics	Functional Analysis	Prof. P.D. Srivastava	Video	IIT Kharagpur	Select Metric Spaces with Examples Holder Inequality and Minkowski Inequality Various Concepts in a Metric Space Separable Metrics Spaces with Examples Convergence, Cauchy Sequence, Completeness Examples of Complete and Incomplete Metric Spaces Completion of Metric Spaces + Tutorial Vector Spaces with Examples Normed Spaces with Examples Banach Spaces and Schauder Basic Finite Dimensional Normed Spaces and Subspaces Compactness of Metric/Normed Spaces Linear Operators-definition and Examples Bounded Linear Operators in a Normed Space Bounded Linear Functionals in a Normed Space Concept of Algebraic Dual and Reflexive Space Dual Basis & Algebraic Reflexive Space Dual Spaces with Examples Tutorial - I Tutorial - II Inner Product & Hilbert Space Further Properties of Inner Product Spaces Projection Theorem, Orthonormal Sets and Sequences Representation of Functionals on a Hilbert Spaces Hilbert Adjoint Operator Self Adjoint, Unitary & Normal Operators Tutorial - III Annihilator in an IPS Total Orthonormal Sets And Sequences Partially Ordered Set and Zorns Lemma Hahn Banach Theorem for Real Vector Spaces Hahn Banach Theorem for Complex V.S. & Normed Spaces Baires Category & Uniform Boundedness Theorems Open Mapping Theorem Closed Graph Theorem Adjoint Operator Strong and Weak Convergence Convergence of Sequence of Operators and Functionals LP - Space LP - Space (Contd.)
111105038	Mathematics	Numerical methods of Ordinary and Partial Differential Equations	Dr. G.P. Raja Sekhar	Video	IIT Kharagpur	Select Motivation with few Examples Single - Step Methods for IVPs Analysis of Single Step Methods Runge - Kutta Methods for IVPs Higher Order Methods/Equations Error - Stability - Convergence of Single Step Methods Tutorial - I Tutorial - II Multi-Step Methods (Explicit) Multi-Step Methods (Implicit) Convergence and Stability of multi step methods General methods for absolute stability Stability Analysis of Multi Step Methods Predictor - Corrector Methods Some Comments on Multi - Step Methods Finite Difference Methods - Linear BVPs Linear/Non - Linear Second Order BVPs BVPS - Derivative Boundary Conditions Higher Order BVPs Shooting Method BVPs Tutorial - III Introduction to First Order PDE Introduction to Second Order PDE Finite Difference Approximations to Parabolic PDEs Implicit Methods for Parabolic PDEs Consistency, Stability and Convergence Other Numerical Methods for Parabolic PDEs Tutorial - IV Matrix Stability Analysis of Finite Difference Scheme Fourier Series Stability Analysis of Finite Difference Scheme Finite Difference Approximations to Elliptic PDEs- I Finite Difference Approximations to Elliptic PDEs - II Finite Difference Approximations to Elliptic PDEs - III Finite Difference Approximations to Elliptic PDEs - IV Finite Difference Approximations to Hyperbolic PDEs - I Finite Difference Approximations to Hyperbolic PDEs - II Method of characteristics for Hyperbolic PDEs - I Method of characterisitcs of Hyperbolic PDEs - II Finite Difference Approximations to 1st order Hyperbolic PDEs Summary, Appendices, Remarks
111105041	Mathematics	Probability and Statistics	Prof. Somesh Kumar	Video	IIT Kharagpur	Select Algebra of Sets - I Algebra of Sets - II Introduction to Probability Laws of Probability - I Law of Probability - II Problems in Probability Random Variables Probability Distributions Characteristics of Distribution Special Distributions - I Special Distributions - II Special Distributions - III Special Distributions - IV Special Distributions - V Special Distributions - VI Special Distributions - VII Functions of a Random Variable Joint Distributions - I Joint Distributions - II Joint Distributions - III Joint Distributions - IV Transformations of Random Vectors Sampling Distributions - I Sampling Distributions - II Descriptive Statistics - I Descriptive Statistics - II Estimation - I Estimation - II Estimation - III Estimation - IV Estimation - V Estimation - VI Testing of Hypothesis - I Testing of Hypothesis - II Testing of Hypothesis - III Testing of Hypothesis - IV Testing of Hypothesis - V Testing of Hypothesis - VI Testing of Hypothesis - VII Testing of Hypothesis - VIII
111105042	Mathematics	Regression Analysis	Dr. Soumen Maity	Video	IIT Kharagpur	Select Simple Linear Regression Simple Linear Regression (Contd.) Simple Linear Regression (Contd. ) Simple Linear Regression ( Contd.) Simple Linear Regression ( Contd. ) Multiple Linear Regression Multiple Linear Regression (Contd.) Multiple Linear Regression (Contd. ) Multiple Linear Regression ( Contd.) Selecting the BEST Regression Model Selecting the BEST Regression Model (Contd.) Selecting the BEST Regression Model (Contd. ) Selecting the BEST Regression Model ( Contd.) Multicollinearity Multicollinearity (Contd.) Multicollinearity ( Contd.) Model Adequacy Checking Model Adequacy Checking (Contd.) Model Adequacy Checking ( Contd.) Test for Influential Observations Transformation and Weighting to correct model inadequacies Transformation and Weighting to correct model inadequacies (Contd.) Transformation and Weighting to correct model inadequacies ( Contd.) Dummy Variables Dummy Variables (Contd.) Dummy Variables (Contd. ) Polynomial Regression Models Polynomial Regression Models (Contd.) Polynomial Regression Models (Contd. ) Generalized Linear Models Generalized Linear Models (Contd.) Non-Linear Estimation Regression Models with Autocorrelated Errors Regression Models with Autocorrelated Errors (Contd.) Measurement Errors and Calibration Problem Tutorial - I Tutorial - II Tutorial - III Tutorial - IV Tutorial - V
111105043	Mathematics	Statistical Inference	Prof. Somesh Kumar	Video	IIT Kharagpur	Select Introduction and Motivation Basic Concepts of Point Estimations - I Basic Concepts of Point Estimations - II Finding Estimators - I Finding Estimators - II Finding Estimators - III Properties of MLEs Lower Bounds for Variance - I Lower Bounds for Variance - II Lower Bounds for Variance - III Lower Bounds for Variance - IV Sufficiency Sufficiency and Information Minimal Sufficiency, Completeness UMVU Estimation, Ancillarity Invariance - I Invariance - II Bayes and Minimax Estimation - I Bayes and Minimax Estimation - II Bayes and Minimax Estimation - III Testing of Hypotheses : Basic Concepts Neyman Pearson Fundamental Lemma Applications of NP lemma UMP Tests UMP Tests (Contd.) UMP Unbiased Tests UMP Unbiased Tests (Contd.) UMP Unbiased Tests : Applications Unbiased Tests for Normal Populations Unbiased Tests for Normal Populations (Contd.) Likelihood Ratio Tests - I Likelihood Ratio Tests - II Likelihood Ratio Tests - III Likelihood Ratio Tests - IV Invariant Tests Test for Goodness of Fit Sequential Procedure Sequential Procedure (Contd.) Confidence Intervals Confidence Intervals (Contd.)
111105069	Mathematics	A Basic Course in Real Analysis	Prof. P.D. Srivastava	Video	IIT Kharagpur	Select Rational Numbers and Rational Cuts Irrational numbers, Dedekind's Theorem Continuum and Exercises Continuum and Exercises (Contd.) Cantor's Theory of Irrational Numbers Cantor's Theory of Irrational Numbers (Contd.) Equivalence of Dedekind and Cantor's Theory Finite, Infinite, Countable and Uncountable Sets of Real Numbers Types of Sets with Examples, Metric Space Various properties of open set, closure of a set Ordered set, Least upper bound, greatest lower bound of a set Compact Sets and its properties Weiersstrass Theorem, Heine Borel Theorem, Connected set Tutorial - II Concept of limit of a sequence Some Important limits, Ratio tests for sequences of Real Numbers Cauchy theorems on limit of sequences with examples Fundamental theorems on limits, Bolzano-Weiersstrass Theorem Theorems on Convergent and divergent sequences Cauchy sequence and its properties Infinite series of real numbers Comparison tests for series, Absolutely convergent and Conditional convergent series Tests for absolutely convergent series Raabe's test, limit of functions, Cluster point Some results on limit of functions Limit Theorems for functions Extension of limit concept (one sided limits) Continuity of Functions Properties of Continuous Functions Boundedness Theorem, Max-Min Theorem and Bolzano's theorem Uniform Continuity and Absolute Continuity Types of Discontinuities, Continuity and Compactness Continuity and Compactness (Contd.), Connectedness Differentiability of real valued function, Mean Value Theorem Mean Value Theorem (Contd.) Application of MVT , Darboux Theorem, L Hospital Rule L'Hospital Rule and Taylor's Theorem Tutorial - III Riemann/Riemann Stieltjes Integral Existence of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral (Contd.) Definite and Indefinite Integral Fundamental Theorems of Integral Calculus Improper Integrals Convergence Test for Improper Integrals
111106044	Mathematics	An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves	DDr. T.E. Venkata Balaji	Video	IIT Madras	Select The Idea of a Riemann Surface Simple Examples of Riemann Surfaces Maximal Atlases and Holomorphic Maps of Riemann Surfaces A Riemann Surface Structure on a Cylinder A Riemann Surface Structure on a Torus Riemann Surface Structures on Cylinders and Tori via Covering Spaces Moebius Transformations Make up Fundamental Groups of Riemann Surfaces Homotopy and the First Fundamental Group A First Classification of Riemann Surfaces The Importance of the Path-lifting Property Fundamental groups as Fibres of the Universal covering Space The Monodromy Action The Universal covering as a Hausdorff Topological Space The Construction of the Universal Covering Map Completion of the Construction of the Universal Covering: Universality of the Universal Covering Completion of the Construction of the Universal Covering: The Fundamental Group of the base as the Deck Transformation Group The Riemann Surface Structure on the Topological Covering of a Riemann Surface Riemann Surfaces with Universal Covering the Plane or the Sphere Classifying Complex Cylinders: Riemann Surfaces with Universal Covering the Complex Plane Characterizing Moebius Transformations with a Single Fixed Point Characterizing Moebius Transformations with Two Fixed Points Torsion-freeness of the Fundamental Group of a Riemann Surface Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental Groups Classifying Annuli up to Holomorphic Isomorphism Orbits of the Integral Unimodular Group in the Upper Half-Plane Galois Coverings are precisely Quotients by Properly Discontinuous Free Actions Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations Quotients by Kleinian Subgroups give rise to Riemann Surfaces The Unimodular Group is Kleinian The Necessity of Elliptic Functions for the Classification of Complex Tori The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the Plane The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-function The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-Plane The Construction of a Modular Form of Weight Two on the Upper Half-Plane The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-Plane The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-plane The Weight Two Modular Form Vanishes at Infinity The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-Plane The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant The Fundamental Region in the Upper Half-Plane for the Unimodular Group A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once Moduli of Elliptic Curves Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two Complex Tori are the same as Elliptic Algebraic Projective Curves
111106046	Mathematics	Fourier Analysis	Dr. R. Radha,Dr. S. Thangavelu	Web	IIT Madras	Select Course Title Contents Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Appendix Biblography Mathematicians at a glance
111106047	Mathematics	Functional Analysis	Prof. M.T. Nair	Web	IIT Madras	Select Course title Contents Preface Chapter 1 Chapter 2 Chapter 3 Chapter 4 References
111106050	Mathematics	Graph Theory	Prof. S.A. Choudum	Web	IIT Madras	Select Course Contents Preliminaries Connected graphs and shortest paths Trees Special classes of graphs Eulerian Graphs Hamilton Graphs Independent sets, coverings and matchings Vertex-colorings Edge colorings Planar Graphs Directed Graphs List of Books
111106051	Mathematics	Linear Algebra	Dr. K.C. Sivakumar	Video	IIT Madras	Select 1. Introduction to the Course Contents. 2. Linear Equations 3a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matrices 3b. Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples 4. Row-reduced Echelon Matrices 5. Row-reduced Echelon Matrices and Non-homogeneous Equations 6. Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations 7. Invertible matrices, Homogeneous Equations Non-homogeneous Equations 8. Vector spaces 9. Elementary Properties in Vector Spaces. Subspaces 10. Subspaces (continued), Spanning Sets, Linear Independence, Dependence 11. Basis for a vector space 12. Dimension of a vector space 13. Dimensions of Sums of Subspaces 14. Linear Transformations 15. The Null Space and the Range Space of a Linear Transformation 16. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces 17. Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I 18. Equality of the Row-rank and the Column-rank II 19. The Matrix of a Linear Transformation 20. Matrix for the Composition and the Inverse. Similarity Transformation 21. Linear Functionals. The Dual Space. Dual Basis I 22. Dual Basis II. Subspace Annihilators I 23. Subspace Annihilators II 24. The Double Dual. The Double Annihilator 25. The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose 26. Eigenvalues and Eigenvectors of Linear Operators 27. Diagonalization of Linear Operators. A Characterization 28. The Minimal Polynomial 29. The Cayley-Hamilton Theorem 30. Invariant Subspaces 31. Triangulability, Diagonalization in Terms of the Minimal Polynomial 32. Independent Subspaces and Projection Operators 33. Direct Sum Decompositions and Projection Operators I 34. Direct Sum Decomposition and Projection Operators II 35. The Primary Decomposition Theorem and Jordan Decomposition 36. Cyclic Subspaces and Annihilators 37. The Cyclic Decomposition Theorem I 38. The Cyclic Decomposition Theorem II. The Rational Form 39. Inner Product Spaces 40. Norms on Vector spaces. The Gram-Schmidt Procedure I 41. The Gram-Schmidt Procedure II. The QR Decomposition. 42. Bessel's Inequality, Parseval's Indentity, Best Approximation 43. Best Approximation: Least Squares Solutions 44. Orthogonal Complementary Subspaces, Orthogonal Projections 45. Projection Theorem. Linear Functionals 46. The Adjoint Operator 47. Properties of the Adjoint Operation. Inner Product Space Isomorphism 48. Unitary Operators 49. Unitary operators II. Self-Adjoint Operators I. 50. Self-Adjoint Operators II - Spectral Theorem 51. Normal Operators - Spectral Theorem
111106052	Mathematics	Mathematical Logic	Prof. Arindama Singh	Video	IIT Madras	Select Sets and Strings Syntax of Propositional Logic Unique Parsing Semantics of PL Consequences and Equivalences Five results about PL Calculations and Informal Proofs More Informal Proofs Normal forms SAT and 3SAT Horn-SAT and Resolution Resolution Adequacy of Resolution Adequacy and Resolution Strategies Propositional Calculus (PC) Some Results about PC Arguing with Proofs Adequacy of PC Compactness & Analytic Tableau Examples of Tableau Proofs Adequacy of Tableaux Syntax of First order Logic (FL) Symbolization & Scope of Quantifiers Hurdles in giving Meaning Semantics of FL Relevance Lemma Validity, Satisfiability & Equivalence Six Results about FL Laws in FL Quantifier Laws and Consequences Examples of Informal Proofs and Calculation Prenex Form Conversion Skolem Form Syntatic Interpretation Herbrand's Theorem Most General Unifiers Resolution Rules Resolution Examples Axiomatic System FC FC, Semidecidability of FL, and Tableau Analytic Tableau for FL Goedel's Incompleteness Theorems
111106053	Mathematics	Real Analysis	Prof. S.H. Kulkarni	Video	IIT Madras	Select Introduction Functions and Relations Finite and Infinite Sets Countable Sets Uncountable Sets, Cardinal Numbers Real Number System LUB Axiom Sequences of Real Numbers Sequences of Real Numbers - continued Sequences of Real Numbers - continued... Infinite Series of Real Numbers Series of nonnegative Real Numbers Conditional Convergence Metric Spaces: Definition and Examples Metric Spaces: Examples and Elementary Concepts Balls and Spheres Open Sets Closure Points, Limit Points and isolated Points Closed sets Sequences in Metric Spaces Completeness Baire Category Theorem Limit and Continuity of a Function defined on a Metric space Continuous Functions on a Metric Space Uniform Continuity Connectedness Connected Sets Compactness Compactness - Continued Characterizations of Compact Sets Continuous Functions on Compact Sets Types of Discontinuity Differentiation Mean Value Theorems Mean Value Theorems - Continued Taylor's Theorem Differentiation of Vector Valued Functions Integration Integrability Integrable Functions Integrable Functions - Continued Integration as a Limit of Sum Integration and Differentiation Integration of Vector Valued Functions More Theorems on Integrals Sequences and Series of Functions Uniform Convergence Uniform Convergence and Integration Uniform Convergence and Differentiation Construction of Everywhere Continuous Nowhere Differentiable Function Approximation of a Continuous Function by Polynomials: Weierstrass Theorem Equicontinuous family of Functions: Arzela - Ascoli Theorem
111107063	Mathematics	Numerical Solution of Ordinary and Partial Differential Equations	Dr. Rama Bhargava,Dr. Sunita Gakkhar	Web	IIT Roorkee	Select Numerical solution of first order ordinary differential equations Numerical Methods: Euler method Modified Euler Method Runge Kutta Method Fourth Order Runge Kutta Methods Higher order Runge Kutta Methods Multi Step Methods Predictor corrector Methods Multi Step Methods Predictor corrector Methods Contd� Multi Step Methods Adams Bashforth method Multi Step Methods Adams Moulton method Systems of Differential Equations Higher Order Equations Stiff Differential equations Finite Difference Methods: Dirichlet type boundary condition Finite Difference Methods: Mixed boundary condition Shooting Method Shooting Method contd� Solution by Finite Difference Methods Shooting Methods Shooting Methods Contd� Introduction of PDE, Classification and Various type of conditions Finite Difference representation of various Derivatives Parabolic Partial Differential Equations : One dimensional equation : Explicit method. Crank Nicolson method and Fully Implicit method Three Time Level Schemes Extension to 2d Parabolic Partial Differential Equations Compatibility and Stability of 1d Parabolic PDE Stability of one-dimensional Parabolic PDE Convergence of one?dimensional Parabolic PDE Elliptic Partial Differential Equations : Solution in Cartesian coordinate system Successive Over Relaxation Method Elliptic Partial Differential Equation in Polar System Alternating Direction Implicit Method Treatment of Irregular Boundaries Methods for Solving tridiagonal System Explicit Method for Solving Hyperbolic PDE Implicit Method to Hyperbolic PDE Convergence & Stability Method of Characteristics Examples and conclusions
111108066	Mathematics	Advanced Matrix Theory and Linear Algebra for Engineers	Prof. Vittal Rao	Video	IISc Bangalore	Select Prologue Part 1 Prologue Part 2 Prologue Part 3 Linear Systems Part 1 Linear Systems Part 2 Linear Systems Part 3 Linear Systems Part 4 Vector Spaces Part 1 Vector Spaces Part 2 Linear Independence and Subspaces Part 1 Linear Independence and Subspaces Part 2 Linear Independence and Subspaces Part 3 Linear Independence and Subspaces Part 4 Basis Part 1 Basis Part 2 Basis Part 3 Linear Transformations Part 1 Linear Transformations Part 2 Linear Transformations Part 3 Linear Transformations Part 4 Linear Transformations Part 5 Inner Product and Orthogonality Part 1 Inner Product and Orthogonality Part 2 Inner Product and Orthogonality Part 3 Inner Product and Orthogonality Part 4 Inner Product and Orthogonality Part 5 Inner Product and Orthogonality Part 6 Diagonalization Part 1 Diagonalization Part 2 Diagonalization Part 3 Diagonalization Part 4 Hermitian and Symmetric matrices Part 1 Hermitian and Symmetric matrices Part 2 Hermitian and Symmetric matrices Part 3 Hermitian and Symmetric matrices Part 4 Singular Value Decomposition (SVD) Part 1 Singular Value Decomposition (SVD) Part 2 Back To Linear Systems Part 1 Back To Linear Systems Part 2 Epilogue
111108081	Mathematics	Ordinary Differential Equations and Applications	A. K. Nandakumaran, P. S. Datti, Raju K. George	Video	IISc Bangalore	Select General Introduction Examples Examples Continued I Examples Continued II Linear Algebra Linear Algebra Continued I Linear Algebra Continued II Analysis Analysis Continued First Order Linear Equations Exact Equations Second Order Linear Equations Second Order Linear Equations Continued I Second Order Linear Equations Continued II Well-posedness and Examples of IVP Gronwall's Lemma Basic Lemma and Uniqueness Theorem Picard's Existence and Uniqueness Theorem Picard's Existence and Uniqueness Continued Cauchy Peano Existence Theorem Existence using Fixed Point Theorem Continuation of Solutions Series Solution General System and Diagonalizability 2 by 2 systems and Phase Plane Analysis 2 by 2 systems and Phase Plane Analysis Continued General Systems General Systems Continued and Non-homogeneous Systems Basic Definitions and Examples Stability Equilibrium Points Stability Equilibrium Points Continued I Stability Equilibrium Points Continued II Second Order Linear Equations Continued III Lyapunov Function Lyapunov Function Continued Periodic Orbits and Poincare Bendixon Theory Periodic Orbits and Poincare Bendixon Theory Continued Linear Second Order Equations General Second Order Equations General Second Order Equations Continued
111104032	Mathematics	Probability and Distributions	Prof. Neeraj Misra	Web	IIT Kanpur	Select Lec1 Lec2 Lec3 Lec4 Lec5 Lec6 Problem1 Lec7 Lec8 Lec9 Lec10 Lec11 Problem2 Lec12 Lec13 Lec14 Lec15 Lec16 Problem3 Lec17 Lec18 Lec19 Problem4 Lec20 Lec21 Lec22 Lec23 Lec24 Problem5 Lec25 Lec26 Lec27 Lec28 Lec29 Lec30 Lec31 Lec32 Lec33 Lec34 Lec35 Lec36 Problem6 Lec37 Lec38 Lec39 Lec40 Lec41 Lec42 Problem7
111104071	Mathematics	Foundations of Optimization	Dr. Joydeep Dutta	Video	IIT Kanpur	Select Lecture-01 Lecture-02 Lecture-03 Lecture-04 Lecture-05 Lecture-06 Lecture-07 Lecture-08 Lecture-09 Lecture-10 Lecture-11 Lecture-12 Lecture-13 Lecture-14 Lecture-15 Lecture-16 Lecture-17 Lecture-18 Lecture-19 Lecture-20 Lecture-21 Lecture-22 Lecture-23 Lecture-24 Lecture-25 Lecture-26 Lecture-27 Lecture-28 Lecture-29 Lecture-30 Lecture-31 Lecture-32 Lecture-33 Lecture-34 Lecture-35 Lecture-36 Lecture-37 Lecture-38
111105039	Mathematics	Optimization	Prof. A. Goswami Dr. Debjani Chakraborty	Video	IIT Kharagpur	Select Lecture-01 Lecture-02 Lecture-03 Lecture-04 Lecture-05 Lecture-06 Lecture-07 Lecture-08 Lecture-09 Lecture-10 Lecture-11 Lecture-12 Lecture-13 Lecture-14 Lecture-15 Lecture-16 Lecture-17 Lecture-18 Lecture-19 Lecture-20 Lecture-21 Lecture-22 Lecture-23 Lecture-24 Lecture-25 Lecture-26 Lecture-27 Lecture-28 Lecture-29 Lecture-30 Lecture-31 Lecture-32 Lecture-33 Lecture-34 Lecture-35 Lecture-36 Lecture-37 Lecture-38 Lecture-39 Lecture-40
111107058	Mathematics	Discrete Mathematics	Dr. Aditi Gangopadhyay, Dr. Sugata Gangopadhyay	Video	IIT Roorkee	Select Introduction to the theory of sets Set operation and laws of set operation The principle of inclusion and exclusion Application of the principle of inclusion and exclusion Fundamentals of logic Logical Inferences Methods of proof of an implication First order logic(1) First order logic(2) Rules of influence for quantified propositions Mathematical Induction(1) Mathematical Induction(2) Sample space, events Probability, conditional probability Independent events, Bayes theorem Information and mutual information Basic definition Isomorphism and sub graphs Walks, paths and circuits operations on graphs Euler graphs, Hamiltonian circuits Shortest path problem Planar graphs Basic definition. Properties of relations Graph of relations Matrix of relation Closure of relaton(1) Closure of relaton(2) Warshall's algorithm Partially ordered relation Partially ordered sets Lattices Boolean algebra Boolean function(1) Boolean function(2) Discrete numeric function Generating function Introduction to recurrence relations Second order recurrence relation with constant coefficients(1) Second order recurrence relation with constant coefficients(2) Application of recurrence relation
111106083	Mathematics	NOC:An invitation to mathematics	Prof. Sankaran Vishwanath	Video	IIT Madras	Select Introduction Long division Applications of Long division Lagrange interpolation The 0-1 idea in other contexts - dot and cross product Taylors formula The Chebyshev polynomials Counting number of monomials - several variables Permutations, combinations and the binomial theorem. Combinations with repetition, and counting monomials. Combinations with restrictions, recurrence relations Fibonacci numbers; an identity and a bijective proof. Permutations and cycle type The sign of a permutation, composition of permutations Rules for drawing tangle diagrams Signs and cycle decompositions Sorting lists of numbers, and crossings in tangle diagrams Real and integer valued polynomials Integer valued polynomials revisited. Functions on the real line, continuity The intermediate value property. Visualizing functions. Functions on the plane, Rigid motions. More examples of functions on the plane, dilations. Composition of functions Affine and Linear transformations Length and Area dilation, the derivative Examples-I Examples-II Linear equations, Lagrange interpolation revisited Completed Matrices in combinatorics Polynomials acting on matrices Divisibility, prime numbers Congruences, Modular arithmetic The Chinese remainder theorem The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem
111106084	Mathematics	Advanced Complex Analysis - Part 1:Zeros of Analytic Functions,Analytic continuation, Monodromy, Hyperbolic Geometry and the Reimann Mapping Theorem	Dr. T.E. Venkata Balaji	Video	IIT Madras	Select Fundamental Theorems Connected with Zeros of Analytic Functions The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra Morera's Theorem and Normal Limits of Analytic Functions Hurwitz's Theorem and Normal Limits of Univalent Functions Local Constancy of Multiplicities of Assumed Values The Open Mapping Theorem Introduction to the Inverse Function Theorem Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function Univalent Analytic Functions have never-zero Derivatives and are Analytic Isomorphisms Introduction to the Implicit Function Theorem Proof of the Implicit Function Theorem: Topological Preliminaries Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function Doing Complex Analysis on a Real Surface: The Idea of a Riemann Surface F(z,w)=0 is naturally a Riemann Surface Constructing the Riemann Surface for the Complex Logarithm Constructing the Riemann Surface for the m-th root function The Riemann Surface for the functional inverse of an analytic mapping at a critical point The Algebraic nature of the functional inverses of an analytic mapping at a critical point The Idea of a Direct Analytic Continuation or an Analytic Extension General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence Analytic Continuation Along Paths via Power Series Part A Analytic Continuation Along Paths via Power Series Part B Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along Paths Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy Theorem Maximal Domains of Direct and Indirect Analytic Continuation: SecondVersion of the Monodromy Theorem Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) Version Existence and Uniqueness of Analytic Continuations on Nearby Paths Proof of the First (Homotopy) Version of the Monodromy Theorem
112104189	Mathematics	NOC:Basic Calculus for Engineers, Scientists and Economists	Dr. Joydeep Dutta	Video	IIT Kanpur	Select Numbers Functions-1 Sequence-1 Sequence-2 Limits and Continuity-1 Limits and Continuity-2 Limits And Continuity- 3 Derivative- 1 Derivative- 2 Maxima And Minima Mean-Value Theorem And Taylors Expansion-1 Mean-Value Theorem And Taylors Expansion-2 Integration -1 Integration - 2 Integration By Parts Definite Integral Riemann Integration -1 Riemann Integration - 2 Functions Of Two Or More Variables Limits And Continuity Of Functions Of Two Variable Differentiation Of Functions Of Two Variables - 1 Differentiation Of Functions Of Two Variables - 2 Unconstrained Minimization Of Funtions Of Two Variables Constrained Minimization And Lagrange Multiplier Rules Infinite Series - 1 Infinite Series - 2 Infinite Series - 3 Multiple Integrals - 1 Multiple Integrals - 2 Muliple Integrals - 3