Syllabus for

Academic Year  (2024)

This course is designed to introduce some branches of mathematics used to understand microeconomic theory and macroeconomic theory in a lucid manner. The course begins by introducing students to the idea of basic concepts of linear algebra and its application in economics. The course then systematically introduces students to the higher level of mathematics such as, differential equation and difference equations; and their applications in the field of microeconomics and macroeconomics at the intermediate level.

Course Objectives:

On completion of the course the students will be able to:

(1) understand linear algebra, differential equations and difference equations; and its application in economics. 

(2) apply the mathematical tools and techniques that are commonly applied to understand and analyse economic models like the Leontief model, growth model, cobweb model etc.

Matrix; Matrix Operations: Addition, Subtraction, Scalar Multiplication and Multiplication; Laws of Matrix Algebra: Commutative, Associative and Distributive; Matrix expression of a System of Linear Equations.

Matrix; Matrix Operations: Addition, Subtraction, Scalar Multiplication and Multiplication; Laws of Matrix Algebra: Commutative, Associative and Distributive; Matrix expression of a System of Linear Equations.

Determinants; Rank of a Matrix; Minors, Cofactors, Adjoint and Inverse Matrices; Laplace Expansion; Solving Linear Equations with the Inverse; Cramer’s Rule for Matrix Solutions; Application in Economics: Input-Output Analysis using Matrices, IS-LM analysis using Matrices

Determinants; Rank of a Matrix; Minors, Cofactors, Adjoint and Inverse Matrices; Laplace Expansion; Solving Linear Equations with the Inverse; Cramer’s Rule for Matrix Solutions; Application in Economics: Input-Output Analysis using Matrices, IS-LM analysis using Matrices

Introduction to Differential Equations: Definitions and Concepts; Exact Differential Equation; Integrating Factor; First-Order Linear Differential Equations-Homogeneous Equation with variable Coefficient, Homogeneous Equation with Constant Coefficient, Non-homogeneous equation with constant coefficient; Economic Application of First-Order Differential Equations: Domar’s growth Model, Dynamic of Market Price-Time Path and Dynamic Stability of Equilibrium.

Introduction to Differential Equations: Definitions and Concepts; Exact Differential Equation; Integrating Factor; First-Order Linear Differential Equations-Homogeneous Equation with variable Coefficient, Homogeneous Equation with Constant Coefficient, Non-homogeneous equation with constant coefficient; Economic Application of First-Order Differential Equations: Domar’s growth Model, Dynamic of Market Price-Time Path and Dynamic Stability of Equilibrium.

Introduction to Difference Equations: Definitions and Concepts; Finite differences; First-Order Linear Difference Equation- Solution of Homogeneous Equations, Solution of Non- homogeneous Equations, Nature of Time Path-A Graphical Approach; Application in Economics: The Cobweb Model; Harrod Model, Dynamic Multiplier.

Introduction to Difference Equations: Definitions and Concepts; Finite differences; First-Order Linear Difference Equation- Solution of Homogeneous Equations, Solution of Non- homogeneous Equations, Nature of Time Path-A Graphical Approach; Application in Economics: The Cobweb Model; Harrod Model, Dynamic Multiplier.

Sydsaeter, K. & Hammond, P. (2016). Mathematics for Economic Analysis. New Delhi: Pearson Education Inc.

Dowling, E. T. (2012). Schaum’s Outlines-Introduction to Mathematical Economics. (3rd ed.). New York: McGraw Hill

Roser, M. (2003). Basic Mathematics for Economists.  (2nd ed.). New York: Routledge. 

This course exposes students to theory and functioning of the monetary and banking sectors of the economy, with exclusive discussions on the Indian context. It discusses the monetary institutions, determinants of money supply, interest rates, banking reforms, policies for economic stability and Basel norms.

Money: Definition, features, functions, kinds of money, kinds of deposits and measures of money supply; Demand for money: classical, neo classical, Keynesian, Baumol’s and Tobins; Supply of money: H theory of money supply, money multiplier process. The Functioning of Gold Standard and Its Breakdown; Bretton Woods System and New Developments in International Monetary System; Monetary Theories – Keynesian, Monetarist, Austrian and Modern Monetary Theory

Money: Definition, features, functions, kinds of money, kinds of deposits and measures of money supply; Demand for money: classical, neo classical, Keynesian, Baumol’s and Tobins; Supply of money: H theory of money supply, money multiplier process. The Functioning of Gold Standard and Its Breakdown; Bretton Woods System and New Developments in International Monetary System; Monetary Theories – Keynesian, Monetarist, Austrian and Modern Monetary Theory

Relevance of Money and Monetary Policy (objectives, targets, indicator, instruments of monetary policy) in Economy, Budget Deficit; Monetary Base, Money and Inflation (Deflation); Inflation Targeting – History and Relevance in Indian Context

Relevance of Money and Monetary Policy (objectives, targets, indicator, instruments of monetary policy) in Economy, Budget Deficit; Monetary Base, Money and Inflation (Deflation); Inflation Targeting – History and Relevance in Indian Context

Development of Banking since independence; increase in effectiveness of Reserve Bank of India; shortcomings of Indian banking system; commercial Banks; Classification functions, organisation, structure and credit creation; progress of commercial banks and failures of commercial banks in India.

Development of Banking since independence; increase in effectiveness of Reserve Bank of India; shortcomings of Indian banking system; commercial Banks; Classification functions, organisation, structure and credit creation; progress of commercial banks and failures of commercial banks in India.

Nationalization of Banks; Narasimham Committee, Chakravarty Committee and Urjit Patel Committee Recommendations; Recent Developments in Banking Sector: Bank Mergers and Acquisitions; Demonetization; Non-performing assets, Basel I; Basel II; Basel III; Issues and Challenges for Indian Banks

Nationalization of Banks; Narasimham Committee, Chakravarty Committee and Urjit Patel Committee Recommendations; Recent Developments in Banking Sector: Bank Mergers and Acquisitions; Demonetization; Non-performing assets, Basel I; Basel II; Basel III; Issues and Challenges for Indian Banks

Burton, M., & Brown, B. (2014). Financial System of the Economy: Principles of Money and Banking: Principles of Money and Banking. Routledge.

Durlauf, S. N., and Blume, L. (2010). Monetary Economics. Palgrave McMillan.

Mishkin, F. S. (2007). The Economics of Money, Banking, and Financial Markets. Pearson Education. 

Handa, J. (2009). Monetary Economics. Routledge.

Jayadev, M. (2013). Basel III Implementation: Issues and Challenges for Indian banks. IIMB Management Review, 25(2), 115-130.

Reinhart, C. M., & Rogoff, K. S. (2009). This Time is Different: Eight Centuries of Financial Folly. Princeton University Press.

Sen, S., & Ghosh, S. K. (2005). Basel Norms, Indian Banking Sector and Impact on Credit to SMEs and the Poor. Economic and Political Weekly, 40(12), 1167-1180.

Course Description

The course aims to explain the principles and methods of behavioral economics while contrasting them with standard economic models. It highlights the importance of cognitive ability, social interaction, moral incentives and emotional responses in explaining human behaviour and economic outcomes.

 Course Objectives

The course aims to help students to:

1. Understand the scope of interaction between psychological phenomena and economic variables.

2. analyse the perspectives about economic phenomena outside the spectrum of core economic theories

Nature of Behavioural economics; Methodological approach; Origins of behavioral economics; Neo-classical and behavioral approaches to studying economics.

Nature of Behavioural economics; Methodological approach; Origins of behavioral economics; Neo-classical and behavioral approaches to studying economics.

Values; Preferences and Choices; the standard model; The neuro scientific basis of utility Beliefs; Heuristics and Biases; The standard model; Probability estimation; Self-evaluation bias- Projection bias- Causes of irrationality Decision making under risk and uncertainty; Risk based assessment; Prospect theory; Reference points; Loss Aversion; Shape of utility function; Decision weighting Mental accounting; Nature and components of mental accounting; Framing and editing; Budgeting and fungibility; Choice bracketing and dynamics.

Values; Preferences and Choices; the standard model; The neuro scientific basis of utility Beliefs; Heuristics and Biases; The standard model; Probability estimation; Self-evaluation bias- Projection bias- Causes of irrationality Decision making under risk and uncertainty; Risk based assessment; Prospect theory; Reference points; Loss Aversion; Shape of utility function; Decision weighting Mental accounting; Nature and components of mental accounting; Framing and editing; Budgeting and fungibility; Choice bracketing and dynamics.

Nature of behavioural game theory; mixed strategies; Bargaining; Social Preferences: Altruism, envy, fairness and justice.

Nature of behavioural game theory; mixed strategies; Bargaining; Social Preferences: Altruism, envy, fairness and justice.

Wilkinson, N., &Klaes, M. (2012). An Introduction to Behavioral Economics. New York: Palgrave Macmillan

Camerer, C. F., Loewenstein, G., & Rabin, M. (eds.). (2011). Advances in Behavioral Economics. Princeton: Princeton University Press.

Cartwright, E. (2017). Behavioral Economics. London: Routledge.

Jalan, B. (1997). India's Economic Policy. New Delhi: Penguin Books India. Kahneman, D., & Tversky, A. (2013). Choices, Values, and Frames. In Handbook

Of The Fundamentals Of Financial Decision Making: Part I (pp. 269-278).

Kahneman, D., & Tversky, A. (Eds.). (2000). Choices, Values, and Frames.

Cambridge: Cambridge University Press.

Kapila, U. (Eds.). (2009). Indian Economy since Independence. New Delhi: Academic Foundation.

Thaler, R. H., & Sunstein, C. R. (1975). Nudge: Improving Decisions about Health, Wealth, and Happiness. London: Penguin Books

*Mid Semester Examination   ** End Semester Examination

Course Description

This course provides an introduction to basic econometric concepts and techniques of econometric analysis. The course begins with an introduction to the definitions and scope of econometrics. Then students will be introduced to simple as well as multiple linear regression models and the fundamental assumptions of Classical Linear Regression Modelling. The causes, consequences and remedies for the assumption violations viz. Heteroskedasticity, Autocorrelation and Multicollinearity are then discussed.

Course Objectives

This course aims to:

1. Understand the basic econometric concepts and techniques.

2. Demonstrate simple as well as multiple linear regression models.

3. Analyse and examine the CLRM assumption violations.

Definition and scope of econometrics; Methodology of econometric research; Historical origin of the term regression and its modern interpretation; Statistical vs. deterministic relationship; regression vs. causation, regression vs. correlation; Terminology and notation; The nature and sources of data for econometric analysis.

Definition and scope of econometrics; Methodology of econometric research; Historical origin of the term regression and its modern interpretation; Statistical vs. deterministic relationship; regression vs. causation, regression vs. correlation; Terminology and notation; The nature and sources of data for econometric analysis.

Two Variable Case Estimation of model by OLS method: Assumptions; Properties of Least Square Estimators: Gauss-Markov Theorem; Testing of regression coefficient; Test for regression as a whole: Coefficient of determination.

Two Variable Case Estimation of model by OLS method: Assumptions; Properties of Least Square Estimators: Gauss-Markov Theorem; Testing of regression coefficient; Test for regression as a whole: Coefficient of determination.

Multiple Regression Analysis: The problem of estimation, notation and assumptions; meaning of partial regression coefficients; the multiple coefficients of determination:R-square and adjusted R-square; interpretation of multiple regression equation.

Multiple Regression Analysis: The problem of estimation, notation and assumptions; meaning of partial regression coefficients; the multiple coefficients of determination:R-square and adjusted R-square; interpretation of multiple regression equation.

Introduction to Multicollinearity, Heteroscedasticity & Autocorrelation: the nature of the problem; its detection and corrective measures.

Introduction to Multicollinearity, Heteroscedasticity & Autocorrelation: the nature of the problem; its detection and corrective measures.

Gujarati, D. N. (2016). Econometrics by Example (2 ed.). New Delhi: Palgrave.

Gujarati, D. N., Porter, D.C., & Gunasekar, S. (2017). Basic Econometrics. (5 nd ed.). New Delhi: McGraw-Hill.

Studenmund, A. H. (2016). Using Econometrics: A Practical Guide. (7 ed.). New Delhi: Pearson.

Koutsoyiannis, A. (1973). Theory of Econometrics (2nd ed.). New York: Harper & Row.

Wooldridge, J. M. (2014). Introductory Econometrics: A Modern Approach (4 ed.). New Delhi: Cengage Learning.

Economic activities tend to cluster together, while economic growth is more localized. Cities play a vital role in driving the structural transformation process in developing countries by acting as engines of economic growth. They offer various benefits of co-location to firms, households, and institutions, including external economies of agglomeration. However, cities also face numerous challenges, such as unregulated development, soaring land prices, housing shortages, inadequate civic infrastructure and services, traffic congestion, slums, poverty, pollution, environmental degradation, weak local governance, etc. This course aims to provide a comprehensive understanding of urban economics. We will also examine some contemporary urban issues in India, their underlying causes, and how urban economics can aid in designing public policies to address them. Urban economics introduces space into economic analysis. It studies urban phenomena using tools of economics. The field of urban economics is vast. It has a rich and growing body of research literature, including recent contributions from new economic geography. 

In this course, we will explore the fundamental theoretical models of urban economics to gain an understanding of why cities form, grow, or decline. We will also investigate what makes cities the engines of economic growth and how urban problems can be studied from an economic perspective. Moreover, we will refer to empirical studies that test some significant urban economic theories, particularly those related to agglomeration externalities.

The course aims to help students to:

1. understand the concepts and theories of urbanisation.
2. Compare and contrast the problems of India and the Global South.

Introduction to Urban Economics - Scope and Dimensions; Urbanization Trends and Patterns: World and India; Why study Urban Economics? Why do Cities exist? Why do Cities grow or decline? Agglomeration Externalities; Models of Rural-Urban Migration; Migration and Public Policy; Empirical Evidence on Agglomeration Economies.

Introduction to Urban Economics - Scope and Dimensions; Urbanization Trends and Patterns: World and India; Why study Urban Economics? Why do Cities exist? Why do Cities grow or decline? Agglomeration Externalities; Models of Rural-Urban Migration; Migration and Public Policy; Empirical Evidence on Agglomeration Economies.

Concept of Spatial Equilibrium; The von Thunen Model; The Basic Alonso-Muth-Mills Model; Extensions of the Basic Model; Spatial Equilibrium in Cities; Spatial Equilibrium across Cities; Contribution from New Economic Geography

Concept of Spatial Equilibrium; The von Thunen Model; The Basic Alonso-Muth-Mills Model; Extensions of the Basic Model; Spatial Equilibrium in Cities; Spatial Equilibrium across Cities; Contribution from New Economic Geography

Trading Cities, Factory Cities, Innovation Cities; 21st-century Urbanization in India; The Economics of Zoning and Land Use Regulations; Agglomeration Economies, Location Decisions of Firms, Why Do Firms Cluster? Benefits and Costs of Bigger Cities, Urban Growth; The Politics of Change: Urbanization and Urban Governance; Provision and Pricing of Amenities (Public Utility Pricing); Property Tax and Municipal Finances. Urban Local Bodies, Sources of Revenue and Pattern of Expenditure of Urban Local Bodies. 

Trading Cities, Factory Cities, Innovation Cities; 21st-century Urbanization in India; The Economics of Zoning and Land Use Regulations; Agglomeration Economies, Location Decisions of Firms, Why Do Firms Cluster? Benefits and Costs of Bigger Cities, Urban Growth; The Politics of Change: Urbanization and Urban Governance; Provision and Pricing of Amenities (Public Utility Pricing); Property Tax and Municipal Finances. Urban Local Bodies, Sources of Revenue and Pattern of Expenditure of Urban Local Bodies. 

Pull and Push Factors for Urbanization in India; Rural-Urban Migration Process; Growth of Formal and Informal Economic Activities in Urban Space; Skilling in the Informal Economy; Labor Force Participation and Distribution of Workers; Street Children and Street Vendors; The Role of Human Capital in Shrinking Cities.

Pull and Push Factors for Urbanization in India; Rural-Urban Migration Process; Growth of Formal and Informal Economic Activities in Urban Space; Skilling in the Informal Economy; Labor Force Participation and Distribution of Workers; Street Children and Street Vendors; The Role of Human Capital in Shrinking Cities.

Sullivan, A. (2014). Urban Economics, 8th Edition (McGraw Hill/Irwin).

Knox. Paul L. (2011). Urbanisation: an introduction to urban geography, 3rd Edition, Pearson.

Henderson, V. (2002). Urbanization in developing countries. The World Bank Research Observer, 17(1), 89-112.

Bahl, R. W., & Linn, J. F. (1992). Urban public finance in developing countries. The World Bank.

Harris, R., & Vorms, C. (2017). What's in a name? Talking about urban peripheries. Toronto: University of Toronto Press.

Henderson, J.V. and J.F. Thisse .(eds.). (2006). Handbook of Urban and Regional Economics, Elsevier. 

Misra, R.P. (2019). Million cities of India: Growth dynamics, internal structure, quality of life, and planning perspectives. New Delhi: Concept Publishing pvt ltd.

Sassen, S. (2006). Cities in a world economy (3rd ed.). Thousand Oaks, Calif.: Pine Forge Press.

Sing Kumar Amit. (2010). Patterns and Process of Urban Development. New Delhi: Abhijeet Publications.

Singh, K., & Ta'i, B. (2000).  Financing and Pricing of Urban Infrastructure. New Age International (P) Limited Publishers.

Sivaramakrishnan, K. C., Kundu, A., & Singh, B. N. (2007). Handbook of urbanization in India: An analysis of trends and processes (2nd ed.). New Delhi; New York: Oxford Univ. Press.

Students have to undertake an internship in any of their interested sectors during the semester break at the end of the second or fourth semester. Students will be attached to various agencies where they will be trained and supervised in acquiring skills and competencies. They will also be mentored by the supervisor/class teacher at the department. Students have to periodically meet their supervisors and submit a report at the end of their practicum period. The format of the report and the type of cases to be presented will be decided by the Department.

Course Objectives:

• To gain hands-on experience in various sub-fields of economics.
• To witness various ethical guidelines in practice.
• To explore areas of interest in economics.

Working in various organizational setups for a period of 30 days (one month-100 Hours)

Working in various organizational setups for a period of 30 days (one month-100 Hours)

Course Description:

This course aims at developing the ability to write the mathematical proofs. It helps the students to understand and appreciate the beauty of the abstract nature of mathematics and also to develop a solid foundation of theoretical mathematics.

Course Objectives : This course will help the learner to

COBJ1. understand the theory of matrices, concepts in vector spaces and Linear Transformations.

COBJ2. gain problems solving skills in solving systems of equations using matrices, finding eigenvalues and eigenvectors, vector spaces and linear transformations.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Elementary row operations, rank, inverse of a matrix using row operations, Echelon forms, normal forms, system of homogeneous and non-homogeneous equations, Cayley Hamilton theorem, eigenvalues and eigenvectors, diagonalization of square matrices.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Vector space-examples and properties, subspaces-criterion for a subset to be a subspace, linear span of a set, linear combination, linear independent and dependent subsets, basis and dimensions, and standard properties.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, rank-nullity theorem, non-singular linear transformation, eigenvalues and eigenvectors of a linear transformation.

2. V. Krishnamurthy, V. P. Mainra, and J. L. Arora, An introduction to linear algebra. New Delhi, India: Affiliated East East-West Press Pvt Ltd., 2003.

2. S. Lang, Introduction to Linear Algebra, 2nd ed., New York: Springer-Verlag, 2005.

3. S. H. Friedberg, A. Insel, and L. Spence, Linear algebra, 4th ed., Pearson, 2015.

4. Gilbert Strang, Linear Algebra and its Applications, 4th ed., Thomson Brooks/Cole, 2007.

5. K. Hoffmann and R. A. Kunze, Linear algebra, 2nd ed., PHI Learning, 2014.

Course Description: This course is concerned with the fundamentals of mathematical modeling. It deals with finding solution to real world problems by transforming into mathematical models using differential equations. The coverage includes mathematical modeling through first order, second order and system of ordinary differential equations.

 Course objectives​: This course will help the learner to

This course will help the learner to

COBJ1.  interpret the real-world problems in the form of first and second order differential equations. 

COBJ2.  familiarize with some classical linear and nonlinear models. 

COBJ3.  analyse the solutions of systems of differential equations by phase portrait method.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

Population Dynamics, Carbon dating, Newtons law of cooling, Epidemics, Economics, Medicine, mixture problem, electric circuit problem, Chemical reactions, Terminal velocity, Continuously compounding of interest.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

The vibrations of a mass on a spring, free damped motion, forced motion, resonance phenomena, electric circuit problem, Nonlinear-Pendulum.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Phase plane analysis: Phase Portrait for Linear and Non-Linear Systems, Stability Analysis of Solution, Applications, Predator prey model: Lotka-Volterra Model, Kermack-McKendrick Model, Predator-Prey Model and Harvesting Analysis, Competitive-Hunter Model, Combat models: Lanchester Model, Battle of IWO Jima, Battle of Vietnam, Battle of Trafalgar., Mixture Models, Epidemics-SIR model, Economics.

Course Description: This course is an introductory course to the basic concepts of Graph Theory. This includes a definition of graphs, types of graphs, paths, circuits, trees, shortest paths, and algorithms to find shortest paths.

Course objectives: This course will help the learner to

COBJ 1. gain conceptual knowledge on terminologies used in graph theory.

COBJ 2. understand the results on graphs and their properties.

COBJ 3. gain proof writing and algorithm writing skills.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Graphs, connected graphs, classes of graphs, regular graphs, degree sequences, matrices, isomorphic graphs.

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Bridges, trees, minimum spanning trees, cut-vertices, blocks, traversability, Eulerian and Hamiltonian graphs, digraphs. 

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Matching, factorizations, decompositions, graceful labeling, planar graphs, Embedding graphs on surfaces.

Course description: Operations research deals with the problems on optimization or decision making that are affected by certain constraints / restrictions in the environment. This course aims at teaching solution techniques of solving linear programming models, simple queuing model, two-person zero sum games and Network models.

Course objectives: This course will help the learner to

COBJ1. gain an insight executing the algorithms for solving linear programming problems including transportation and assignment problems.

COBJ2. learn about the techniques involved in solving the two person zero sum game.

COBJ3. calculate the estimates that characteristics the queues and perform desired analysis on a network.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Introduction to simplex algorithm –Special cases in the Simplex Method –Definition of the Dual Problem – Primal Dual relationships – Dual simplex methods. Transportation Models: Determination of the starting solution – iterative computations of the transportation algorithm. Assignment Model: The Hungarian Method.

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Elements of a queuing Model – Pure Birth Model – Pure Death Model –Specialized Poisson Queues – Steady state Models: (M/M/1):(GD/∞/∞) – (M/M/1):(FCFS/∞/∞) - (M/M/1):(GD/N/∞) – (M/M/c):(GD/∞/∞) –  (M/M/∞):(GD/∞/∞).

Game Theory: Optimal solution of two person zero-sum games – Solution of Mixed strategy Games (only Linear programming solution).

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Linear programming formulation of the shortest-route Problem. Maximal Flow model:- Enumeration of cuts – Maximal Flow Algorithm – Linear Programming Formulation of Maximal Flow Model. CPM and PERT:- Network Representation – Critical path computations – Construction of the Time Schedule – Linear Programming formulation of CPM – PERT calculations.

Course description: This course aims at providing hands on experience in using Python functions to illustrate the notions vector space, linear independence, linear dependence, linear transformation and rank.

Course objectives: This course will help the learner to

COBJ1. The built in functions required to deal with vectors and Linear Transformations.

COBJ2. Python skills to handle vectors using the properties of vector spaces and linear transformations

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

1. Operations on matrices
2. Finding rank of matrices
   
3. Reducing a matrix to Echelon form
4. Inverse of a matrix by different methods
5. Solving system of equations using various methods
6. Finding eigenvalues and eigenvectors of a matrix
7. Expressing a vector as a linear combination of given set of vectors
8. Linear span, linear independence and linear dependence
9. Linear transformations and plotting of linear transformations
10. Applications of Rank-Nullity Theorem

Course description: This course provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary differential equations (ODEs) using Python programming.

Course objectives:

This course will help the learner to 

COBJ1. various models spanning disciplines such as physics, biology, engineering, and finance. 

COBJ2. develop the basic understanding of differential equations and skills to implement numerical algorithms to solve mathematical problems using Python.

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

1. Growth of a population – Linear growth, Exponential growth, Logistic growth
2. Decay Model - Radioactive Decay
3. Numerical Methods
4. A Simple Pendulum
5. Spreading of a Disease
6. Mixture problems
7. Trajectory of a ball
8. Spring mass system
9. Electrical Circuits

Course description: The course graph theory using Python is aimed at enabling the students to appreciate and understand core concepts of graph theory with the help of technological tools. It is designed with a learner-centric approach wherein the students will understand the concepts of graph theory using programming tools and develop computational skills.

Course objectives: This course will help the learner to

COBJ1. gain familiarity in Python language using jupyter interface and NetworkX package

COBJ2. construct graphs and analyze their structural properties.

COBJ3. implement standard algorithms for shortest paths, minimal spanning trees and graph searching..

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

1. Introduction to NetworkX package
2. Construction of graphs
3. Degree and distance related parameters
4. In-built functions for different graph classes
5. Computation of graph parameters using in-built functions
6. Graph Operations and Graph Connectivity
7. Customization of Graphs
8. Digraphs
9. Matrices and Algorithms of Graphs
10. Graph as models.

Course description: Operations research deals with the problems on optimization or decision making that are affected by certain constraints / restrictions in the environment. This course aims to enhance programming skills in Python to solve problems chosen from Operations Research.

Course objectives: This course will help the learner to

COBJ1. gain a familiarity in using Python to solve linear programming problems, calculate the estimates that characteristics the queues and perform desired analysis on a network.

COBJ2. use Python for solving problems on Operations Research.

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

1. Simplex method
2. Dual simplex method
3. Balanced transportation problem
4. Unbalanced transportation problem
5. Assignment problems
6. (M/M/1) queues
7. (M/M/c) queues
8. Shortest path computations in a network
9. Maximum flow problem
10. Critical path computations

This course initiates discussion on some of the key issues of the Indian economy. It provides an overview of the role of state and market, planning process, macroeconomic challenges, and policy management in India, with special reference to Karnataka. The course exposes the students to the data on various economic aspects and policies in India and Karnataka.

Major features of the economy at independence; growth and development under different policy regimes—goals, constraints, institutions, and policy framework; Roles of State and Market; The Role of the State in Economic Development; Goals of Economic Planning, Planning Commission and NITI Ayog; five-year plans and economic development.

Major features of the economy at independence; growth and development under different policy regimes—goals, constraints, institutions, and policy framework; Roles of State and Market; The Role of the State in Economic Development; Goals of Economic Planning, Planning Commission and NITI Ayog; five-year plans and economic development.

Historical background and current status, Land Reforms, New Agricultural Strategy, and Green Revolution, Issues related to direct and indirect farm subsidies and minimum support prices, Framers Distress; Industrial development in India, public sector undertaking in India, privatization of the public sector enterprises, Economic Reforms.

Historical background and current status, Land Reforms, New Agricultural Strategy, and Green Revolution, Issues related to direct and indirect farm subsidies and minimum support prices, Framers Distress; Industrial development in India, public sector undertaking in India, privatization of the public sector enterprises, Economic Reforms.

An introduction to Karnataka Economy SGDP and demography; Comparison of Karnataka economy with other Indian states; Agriculture and Industry; Poverty, Health, Education, Unemployment and Inequality; Rural development. 

An introduction to Karnataka Economy SGDP and demography; Comparison of Karnataka economy with other Indian states; Agriculture and Industry; Poverty, Health, Education, Unemployment and Inequality; Rural development. 

2.Drèze, J., & Sen, A. (2013). An Uncertain Glory: India and its Contradictions. NJ: Princeton University Press.

3.Dyson, T. (2013). Population and Development: The Demographic Transition. New York: Zed Books Ltd. 

4.Khilnani, S. (1999). The Idea of India, Farrar, Straus and Giroux, Ch. 1‐2. 

5.Mohan, R. (2008). Growth record of the Indian economy, 1950-2008: A story of sustained savings and investment. Economic and Political Weekly, 43 (19), 61-71.

6.Datt, G., & Mahajan, A. (2016). Indian Economy. (72nd ed.). New Delhi: S. Chand & Company Pvt. Ltd. 

7.Kapila, U. (2016). Indian Economy – Performance and Policies (17th ed.). New Delhi: Academic Foundation. 

8.Misra, S. K., & Puri, V. K. (2011). Indian Economy (34th ed.). Delhi: Himalaya Publishing House

9.Iteshamul, H. (2015). A Handbook of Karnataka. Bangalore: Government of Karnataka. 

2.Film: The Story of India, PBS documentary, Part 6. (An HD version is also available on Netflix). 

3.Luce, Edward. 2008. In Spite of the Gods: The Rise of Modern India. First Anchor Books—Read Chapter 2.

4.Economic Survey of Karnataka 2016-17. Government of Karnataka

5.Karnataka Development Report, Karnataka: Institute for Social and Economic Change

6.Meti, T. K. (1976). The Economy of Karnataka: An Analysis of Development and Planning. New Delhi: Oxford & IBH Publishing Company

Course Description

Anyone with an analytical mind and a basic knowledge of economics should be able to complete this course. Since economic activity is the root cause of many environmental issues, such as carbon emissions, over-harvesting of renewable resources, and pollution of the air and water as a result of industrial activity, this course looks at various strategies for changing behaviour through economic institutions like markets and incentives as well as through regulation, etc. By using techniques for the practical assessment of environmental products and services as well as the measurement of environmental damages, it also discusses the economic effects of environmental regulations. However, under the umbrella of sustainable development, the effects of economic expansion on the environment are also covered. The course's principles and methodologies are shown through environmental challenges and issues from the Indian and worldwide context, with a particular focus on global warming.

Course Objectives:

The course aims to help students to:

1. understand the theories of environmental economics;

2. analyse the fiscal tools and policy options in managing the environmental issues

Introduction to environmental economics; Definition, Nature and Scope; Nexus between environment and economy; Key environmental issues and problems (Karnataka state, National wise and International wise), Material balance principle, Renewable and non-renewable energy sources, Tragedy of commons, common pooled resources, Hotelling’s rule; Pareto optimality and market failure in the presence of externalities.

Introduction to environmental economics; Definition, Nature and Scope; Nexus between environment and economy; Key environmental issues and problems (Karnataka state, National wise and International wise), Material balance principle, Renewable and non-renewable energy sources, Tragedy of commons, common pooled resources, Hotelling’s rule; Pareto optimality and market failure in the presence of externalities.

Concepts of environmental value; Total economic value; Valuation of non-market goods and services-theory and practice; measurement methods; Revealed preference methods – travel cost, hedonic pricing; Stated preference methods – Contingent valuation, choice experiment; Cost-benefit analysis of environmental policies and regulations.

Concepts of environmental value; Total economic value; Valuation of non-market goods and services-theory and practice; measurement methods; Revealed preference methods – travel cost, hedonic pricing; Stated preference methods – Contingent valuation, choice experiment; Cost-benefit analysis of environmental policies and regulations.

Concepts; Measurement; Rules for sustainable development, Indicators of sustainable development; Perspectives from Indian experience; Ecosystem services and human well-being; Trade-off between environmental protection and economic growth; Environmental Kuznets’ curve. Pigouvian taxes and effluent fees, tradable permits; Liability Rules; Pollution Control Boards; Legislative measures of environmental protection in India, Economics of climate change.

Concepts; Measurement; Rules for sustainable development, Indicators of sustainable development; Perspectives from Indian experience; Ecosystem services and human well-being; Trade-off between environmental protection and economic growth; Environmental Kuznets’ curve. Pigouvian taxes and effluent fees, tradable permits; Liability Rules; Pollution Control Boards; Legislative measures of environmental protection in India, Economics of climate change.

Perman, R., Yue, M., Common, M., Maddison, D. &McGilvray, J. (2011). NaturalResource and Environmental Economics. (4th ed.). Boston: Pearson Education/Addison Wesley.

Kolstad, C D (2012). Environmental Economics. (2nd ed.). Oxford: Oxford University Press.

Kolstad, C D, (2010). Intermediate Environmental Economics. (2nd ed.). Oxford: Oxford University Press.

Conrad John : Resource Economics, Cambridge University Press, 2003

Stern, N., The economics of climate change – The Stern Review, Cambridge University Press, 2006.

This course introduces to some of the advanced econometric concepts and techniques. The course begins with an introduction to lag modeling and covers distributed as well as dynamic models. The students will then be introduced to the analysis of two major types of data used in econometric analysis viz. time series and panel data. The course also covers different approaches to econometric forecasting. Some of the important testing procedures such as Unit root tests, Seasonality tests, Structural break tests, Cointegration tests, and Model stability tests will be introduced to the students during this course. The modules will be delivered using econometric software applications such as EViews, Gretl, or STATA.

The course aims at providing students with: 

1. an introduction to some of the advanced econometric concepts and techniques.
2. the ability to apply advanced econometric techniques in the investigation of complex economic relationships using time series and panel data.
3. the skills to make economic forecasting.
4. hands-on training in econometric packages such as EViews, Gretl, or STATA.

Lags in econometric models: Distributed lag model, Autoregressive lag model; Reasons for lags; Estimation of distributed-lag model, The Koyck Approach to distributed-lag model; Estimation of autoregressive models; Causality in economics: The Granger causality test.

Lags in econometric models: Distributed lag model, Autoregressive lag model; Reasons for lags; Estimation of distributed-lag model, The Koyck Approach to distributed-lag model; Estimation of autoregressive models; Causality in economics: The Granger causality test.

Introduction to time series; Stationary and nonstationary time series; Spurious regression; Unit root tests: Dickey fuller and Augmented dickey fuller tests; Transforming non-stationary time series; Cointegration: Testing for cointegration, error correction mechanism.

Introduction to time series; Stationary and nonstationary time series; Spurious regression; Unit root tests: Dickey fuller and Augmented dickey fuller tests; Transforming non-stationary time series; Cointegration: Testing for cointegration, error correction mechanism.

Approaches to economic forecasting; ARIMA models; The Box-Jenkins methodology; Vector autoregression; Forecasting with VAR; Testing causality using VAR.

Approaches to economic forecasting; ARIMA models; The Box-Jenkins methodology; Vector autoregression; Forecasting with VAR; Testing causality using VAR.

Introduction to panel data; Constant coefficient model; Fixed effect LSDV model; Fixed effect WG model; Random effects model, Properties of estimators.

Introduction to panel data; Constant coefficient model; Fixed effect LSDV model; Fixed effect WG model; Random effects model, Properties of estimators.

Gujarati, D. N. (2016). Econometrics by Example (2nd ed.). New Delhi: Palgrave.

Gujarati, D. N., Porter, D.C., & Gunasekar, S. (2017). Basic Econometrics. (5th ed.). New Delhi: McGraw-Hill.

Studenmund, A. H. (2016). Using Econometrics: A Practical Guide.  (7th ed.). New Delhi:  Pearson.

Hamilton, J. D. (1994). Time Series Analysis. Princeton: Princeton University Press.

Koutsoyiannis, A. (1973). Theory of Econometrics. New York: Harper & Row.

Pindyck, R. S., & Rubinfeld, D. L. (1990). Econometric Models and Econometric Forecasts (4th ed.). New York: McGraw-Hill.

Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data. Massachusetts: MIT Press.

This course provides an introduction to neuroeconomics, an interdisciplinary field that integrates economic, psychological, and neuroscientific perspectives on decision-making. The course will explore the current state of knowledge regarding the neural mechanisms underlying decision-making processes and how they can be applied to refine or expand existing economic and psychological theories of decision-making.

The course aims at providing students with: 

1. an introduction to neuroeconomic models.
2. foundations on the concepts of values, preferences, choices, heuristics, and biases.
3. an introduction to the brain and neuroimaging tools.
4. understanding of Consumer Neuroscience and Neuromarketing.

Key concepts and terminologies in Neuroeconomics: Classical economic models vs. Neuroeconomic models. 

Key concepts and terminologies in Neuroeconomics: Classical economic models vs. Neuroeconomic models. 

Values; Preferences and Choices; The standard model; The neuroscientific basis of utility Beliefs; Heuristics and Biases; The standard model; Probability estimation; Self-evaluation bias- Projection bias- Causes of irrationality Decision making under risk and uncertainty; Risk-based assessment; Prospect theory; Reference points; Loss Aversion; Shape of utility function; Decision weighting Mental accounting; Nature and components of mental accounting; Framing and editing; Budgeting and fungibility; Choice bracketing and dynamics

Values; Preferences and Choices; The standard model; The neuroscientific basis of utility Beliefs; Heuristics and Biases; The standard model; Probability estimation; Self-evaluation bias- Projection bias- Causes of irrationality Decision making under risk and uncertainty; Risk-based assessment; Prospect theory; Reference points; Loss Aversion; Shape of utility function; Decision weighting Mental accounting; Nature and components of mental accounting; Framing and editing; Budgeting and fungibility; Choice bracketing and dynamics

Sensory Systems of the Human Brain, Motor Systems of the Primate Brain, Eye Movements, Body Movements; Overview of Neuroscience Methods in Neuroeconomics.: fMRI, EEG, and other imaging techniques.

Sensory Systems of the Human Brain, Motor Systems of the Primate Brain, Eye Movements, Body Movements; Overview of Neuroscience Methods in Neuroeconomics.: fMRI, EEG, and other imaging techniques.

Consumer Neuroscience and Neuromarketing.

Consumer Neuroscience and Neuromarketing.

Glimcher, P. W., & Fehr, E. (Eds.). 2014. Neuroeconomics: Decision Making and the Brain. Netherlands: Elsevier Science.

Montag, C. & Reuter, M. (Eds). 2016. Neuroeconomics. Germany: Springer Berlin Heidelberg.

Wilkinson, N., &Klaes, M. 2012. An Introduction to Behavioral Economics. New York: Palgrave Macmillan.

Camerer, C. F., Loewenstein, G., & Rabin, M. (eds.). 2011. Advances in Behavioral Economics. Princeton: Princeton University Press.

Cartwright, E. 2017. Behavioral Economics. London: Routledge.

Jalan, B. 1997. India's Economic Policy. New Delhi: Penguin Books India. Kahneman, 

Kahneman, D., & Tversky, A. (Eds.). 2013. Choices, Values, and Frames. In Handbook of The Fundamentals Of Financial Decision Making: Part I (pp. 269-278).

Financial economics is the branch of economics concerned with the working of financial markets, such as the stock market and the finances of companies. The course focuses equally on the theoretical framework as well as the practical aspects of the functioning of financial markets.

Course Objectives:

The course aims to help students to:

1.understand the basic concepts related to financial economics.

2.understand the attitude towards risk and decision making under uncertainties

3.apply the concepts of risk and return to compute the optimal portfolio

Investment Environment, Process, Alternatives and Criteria for Evaluation; Measuring Return and Risk: Historical and Expected; Time Value of Money: Future and Present Value Methods; von Neumann – Morgenstern Utility Index and Application-Risk and Insurance.

Investment Environment, Process, Alternatives and Criteria for Evaluation; Measuring Return and Risk: Historical and Expected; Time Value of Money: Future and Present Value Methods; von Neumann – Morgenstern Utility Index and Application-Risk and Insurance.

Efficient Set/Frontier; Portfolio Diversification and Portfolio Risk: Markowitz Approach: Calculation of Portfolio Return and Risk, Portfolio Risk-2-security case, Mean-Variance Portfolio, Optimal Portfolio Choice; Capital Asset Pricing Model (CAPM): Central idea of CAPM, Basic assumptions, Security Market Line, Calculation of Beta; Arbitrage Pricing Theory (APT): Basic Concept; Efficient Market Hypothesis (EMH): Three Forms of EMH.

Efficient Set/Frontier; Portfolio Diversification and Portfolio Risk: Markowitz Approach: Calculation of Portfolio Return and Risk, Portfolio Risk-2-security case, Mean-Variance Portfolio, Optimal Portfolio Choice; Capital Asset Pricing Model (CAPM): Central idea of CAPM, Basic assumptions, Security Market Line, Calculation of Beta; Arbitrage Pricing Theory (APT): Basic Concept; Efficient Market Hypothesis (EMH): Three Forms of EMH.

Bond Characteristics; Bond Prices: Price-Yield Relationship; Bond Yields: Current Yield, Yield to Maturity, Yield to Call, Realized Yield to Maturity; Dividend Discount Model-Single Period.

Bond Characteristics; Bond Prices: Price-Yield Relationship; Bond Yields: Current Yield, Yield to Maturity, Yield to Call, Realized Yield to Maturity; Dividend Discount Model-Single Period.

Sharpe, W., Alexander, G. and Bailey, J. (2003). Investments, Prentice Hall of India, 6th edition.

Roser, M. (2003). Basic Mathematics for Economists.  (2nd ed.). New York: Routledge.

The primary aim of this course is to introduce students to the concept of institutions and their role in economics and society. This course introduces theoretical and empirical studies examining the role of formal and informal institutions that make economic interaction possible. This course also survey different types of institutions from formal contracts and property rights to informal institutions such as culture, informal norms, traditions and beliefs - that all influence human behaviour and economic interactions. Together all these rules and enforcement mechanisms are called institutions. We will discuss historical examples and analyse the modern institutions and their evolutions. How these formal and informal institutions are working in the Indian context, and what are the possibilities of improvement in formal institutions that may help the economic growth with more inclusiveness in nature? This course also delves into modern institutional theory, its current state, its methods and approaches. Special focus is made on how these instruments and approaches can be applied in modern days problems such as climate change, disaster management and economic growth

The emergence of institutional theory as a direction of economic science. The theoretical content of early institutionalism. Institutional concepts of T. Veblen. Economic - legal theory of J. Commons and others prominent thinkers in this discipline. The main prerequisites of the new institutional economic theory. Methodological comparativistics: an institutional and neoclassical approach to building models. The structure of institutionalism and levels of analysis. Neoinstitutional economic theory, its main directions. New institutional economic theory. Traditional institutionalism and new institutional economic theory: a comparative analysis. The subject field of the new institutional economic theory. Prospects for the development of a new institutional economic theory. The practical applicability of institutional theories.

The emergence of institutional theory as a direction of economic science. The theoretical content of early institutionalism. Institutional concepts of T. Veblen. Economic - legal theory of J. Commons and others prominent thinkers in this discipline. The main prerequisites of the new institutional economic theory. Methodological comparativistics: an institutional and neoclassical approach to building models. The structure of institutionalism and levels of analysis. Neoinstitutional economic theory, its main directions. New institutional economic theory. Traditional institutionalism and new institutional economic theory: a comparative analysis. The subject field of the new institutional economic theory. Prospects for the development of a new institutional economic theory. The practical applicability of institutional theories.

Routine Rule (norm) as a basic element of institutions. Institutional structure of society. Informal rules, their role in society. Classification of sanctions for noncompliance with informal rules. Conditions for the effectiveness of informal rules. Formal institutions. Hierarchy of rules according to D. North. Supraconstitutional rules. Constitutional (political) rules. Economic rules. The rights. Property rights. Classification of rights and rules E. Ostrom. The relationship between formal rules and informal norms. Types of interrelation of formal rules and informal norms. The role of enforcement mechanisms is to enforce the rules. Classification of sanctions. Self-fulfilling rules. The impact of institutions on the effectiveness of the economic system. 

The concept of "transaction costs". Sources of transaction costs and their scope. Types of transaction costs. Market transaction costs. Corporate Transaction, Costs Political Transaction Costs. Non-market transaction costs. Non-measurable transaction costs. Transaction costs and basic types of economic exchange: personalized exchange, non-personalized exchange without third-party contract protection, nonpersonalized exchange with third-party protection by the state

Routine Rule (norm) as a basic element of institutions. Institutional structure of society. Informal rules, their role in society. Classification of sanctions for noncompliance with informal rules. Conditions for the effectiveness of informal rules. Formal institutions. Hierarchy of rules according to D. North. Supraconstitutional rules. Constitutional (political) rules. Economic rules. The rights. Property rights. Classification of rights and rules E. Ostrom. The relationship between formal rules and informal norms. Types of interrelation of formal rules and informal norms. The role of enforcement mechanisms is to enforce the rules. Classification of sanctions. Self-fulfilling rules. The impact of institutions on the effectiveness of the economic system. 

The concept of "transaction costs". Sources of transaction costs and their scope. Types of transaction costs. Market transaction costs. Corporate Transaction, Costs Political Transaction Costs. Non-market transaction costs. Non-measurable transaction costs. Transaction costs and basic types of economic exchange: personalized exchange, non-personalized exchange without third-party contract protection, nonpersonalized exchange with third-party protection by the state

Different approaches to the definition of the contract. Legal and economic approaches to the concept of "contract." The role of contracts in the coordination of economic agents. Types of contracts. The concept of a perfect contract. Limited rationality and the inability to conclude a perfect contract. Problems caused by incomplete real contracts. Adverse selection: the mechanism of occurrence and how to prevent it. Moral hazard: conditions of its occurrence and ways to prevent. Extortion as a form of opportunistic behaviour. 

Different approaches to the definition of the contract. Legal and economic approaches to the concept of "contract." The role of contracts in the coordination of economic agents. Types of contracts. The concept of a perfect contract. Limited rationality and the inability to conclude a perfect contract. Problems caused by incomplete real contracts. Adverse selection: the mechanism of occurrence and how to prevent it. Moral hazard: conditions of its occurrence and ways to prevent. Extortion as a form of opportunistic behaviour. 

North, Douglass C., John Joseph Wallis, and Barry R. Weingast, Violence and Social Orders: A Conceptual Framework for Interpreting Recorded Human History, Cambridge University Press, 2009.

Acemoglu, Daron and James A. Robinson, Why Nations Fail: The Origins of Power, Prosperity, and Poverty, New York: Crown, 2012.

Alston, Eric, Lee J. Alston, Bernardo Mueller, and Tomas Nonnenmacher, Institutional and Organizational Economics: Concepts and Applications, Cambridge, UK: Cambridge University Press, 2018.

Ménard, Claude and Mary M. Shirley, A Research Agenda in New Institutional Economics, Cheltenham: Edward Elgar, 2018.

Alston, L. J., Eggertsson, P., Eggertsson, T., & North, D. C. (Eds.). (1996). Empirical Studies in Institutional Change. Cambridge University Press.

Guha-Khasnobis, B., Kanbur, R., & Ostrom, E. (Eds.). (2006). Linking the Formal and Informal Economy: Concepts and Policies. Oxford University Press.

North, D. (1990). Institutions, Economic Theory and Economic Performance. Institutions, Institutional Change and Economic Performance. New York: Cambridge University Press.

Rodrik, Dani, Subramanian, Arvind, and Trebbi, Francesco, “Institutions Rule: The Primacy of Institutions over Geography and Integration in Economic Development,” NBER Working Paper 9305, 2002.

Furubotn, Eirik G. and Rudolf Richter, Institutions and Economic Theory: The Contribution of the New Institutional Economics, Ann Arbor: The University of Michigan Press, 1997.

Persson, Torsten and Guido Tabellini, Political Economics: Explaining Economic Policy (Zeuthen Lectures), MIT Press, 2000.

Acemoglu, Daron and James A. Robinson, Economic Origins of Dictatorship and Democracy, Cambridge University Press, 2005.

Shirley, Mary M.,  Institutions and Development, Cheltenham, UK and Northampton, MA: Edward Elgar, 2008.

To explore complex world problems physicists, engineers, financiers and mathematicians require certain methods. These practical problems can rarely be solved analytically. Their solutions can only be approximated through numerical methods. This course deals with the theory and application of numerical approximation techniques.

This course will help the learner to

1. learn about error analysis, solution of nonlinear equations, finite differences, interpolation, numerical integration and differentiation, numerical solution of differential equations, and matrix computation.

2. emphasis the development of numerical algorithms to provide solutions to common problems formulated in science and engineering.

Errors and their analysis, Floating point representation of numbers, solution of algebraic and Transcendental Equations: Bisection method, fixed point Iteration method, the method of False Position, Newton Raphson method and Mullers method. Solution of linear systems, matrix inversion method, Gauss elimination method, Gauss-Seidel and Gauss-Jacobi iterative methods, modification of the Gauss method to compute the inverse, LU decomposition method.