The  main  objectives  of the  paper  are  to  train  the  students to  grasp  the  use  of mathematical techniques and operations to analyse economic problems and to  initiate students into various economic concepts which are amenable to mathematical treatment.

Static Equilibrium Analysis: Linear partial equilibrium market model; equilibrium of competitive market with indirect taxes; Equilibrium of a Non-linear market model; Economics application of matrix algebra: Partial equilibrium market model; Input-Output Model; Review of comparative static analysis using IS- LM model

Derivatives in elasticity of demand; Relationship between AR, MR and elasticity; relationship between AC and MC; Tax yield in competitive market; comparative static analysis of market model; 

General Structure, derivation of first order and second order conditions; envelope theorem

Applications: Profit maximization in different markets (Perfect competition, Monopoly, Duopoly, Monopolistic Competition)

General Structure with two independent variables, derivation of first order and second order conditions, envelope theorem.

Applications: Utility maximization and derivation of demand function and some extensions of consumer behaviour including consumption-labour choice and intertemporal choice; cost minimization and derivation of factor demand function;

Derivation of TC from MC, derivation of TR from MR function; Consumer surplus, Producer surplus; Investment, capital formation and Derivation of simple growth process

Cobweb Model; market model with inventory; Dynamic stability of market price; Harrod-Domar growth theory; Market equilibrium with price expectations

Two-person zero sum game, concept of pure strategy and mixed strategy; One shot game, concept of Nash equilibrium and method of dominance; Applications: Cournot model, problem of prisoners dilemma and cartel instability, The Commons problem; strategic trade; Sequential game and backward induction; Application: Stackelberg equilibrium, time consistent macroeconomic policy.

2.    Edward Dowling (latest edition), Introduction to Mathematical Economics, Schaums Outline Series

3.    Renshaw, G (Second Edition): Maths for Economics, Oxford University Press

4.     Prajit K Dutta -Strategies and Games, The MIT Press

2. Knut Sydsaeter and Peter J. Hammod: Mathematics for Economic Analysis (Pearson Education), Chapter 17, Chapter 18, sections 18.1-18.5.

 CIA II: mid-semester examination, 2hours, 50 marks

 CIA III: A class test will be consucted for 20 marks

 ESE: 3 hours, 100 marks

The nature, scope and significance of public economics –Public vs Private Finance- Principle of Maximum Social advantage: Approaches and Limitations- Functions of Government - Economic functions -allocation, distribution and stabilization; Regulatory functions of the Government and its economic significance

The nature, scope and significance of public economics –Public vs Private Finance- Principle of Maximum Social advantage: Approaches and Limitations- Functions of Government - Economic functions -allocation, distribution and stabilization; Regulatory functions of the Government and its economic significance

The nature, scope and significance of public economics –Public vs Private Finance- Principle of Maximum Social advantage: Approaches and Limitations- Functions of Government - Economic functions -allocation, distribution and stabilization; Regulatory functions of the Government and its economic significance

The nature, scope and significance of public economics –Public vs Private Finance- Principle of Maximum Social advantage: Approaches and Limitations- Functions of Government - Economic functions -allocation, distribution and stabilization; Regulatory functions of the Government and its economic significance

Concept of public goods-characteristics of public goods, national vs. local public goods; determination of provision of public good; Externality- concept of social versus private costs and benefits, merit goods, club goods; Provision versus production of public goods - Market failure and public Provision

Concept of public goods-characteristics of public goods, national vs. local public goods; determination of provision of public good; Externality- concept of social versus private costs and benefits, merit goods, club goods; Provision versus production of public goods - Market failure and public Provision

Concept of public goods-characteristics of public goods, national vs. local public goods; determination of provision of public good; Externality- concept of social versus private costs and benefits, merit goods, club goods; Provision versus production of public goods - Market failure and public Provision

Concept of public goods-characteristics of public goods, national vs. local public goods; determination of provision of public good; Externality- concept of social versus private costs and benefits, merit goods, club goods; Provision versus production of public goods - Market failure and public Provision

Structure and growth of public expenditure; Wagner’s Law of increasing state activities; Wiseman-Peacock hypothesis;  Trends of Public expenditure

Structure and growth of public expenditure; Wagner’s Law of increasing state activities; Wiseman-Peacock hypothesis;  Trends of Public expenditure

Structure and growth of public expenditure; Wagner’s Law of increasing state activities; Wiseman-Peacock hypothesis;  Trends of Public expenditure

Structure and growth of public expenditure; Wagner’s Law of increasing state activities; Wiseman-Peacock hypothesis;  Trends of Public expenditure

Concept of tax, types, canons of taxation-Incidence of taxes; Taxable capacity; Approaches to the principle of Equity in taxation -Ability to Pay principle, Benefit Approach; Sources of Public Revenue;  Goods and Services Tax.

Concept of tax, types, canons of taxation-Incidence of taxes; Taxable capacity; Approaches to the principle of Equity in taxation -Ability to Pay principle, Benefit Approach; Sources of Public Revenue;  Goods and Services Tax.

Concept of tax, types, canons of taxation-Incidence of taxes; Taxable capacity; Approaches to the principle of Equity in taxation -Ability to Pay principle, Benefit Approach; Sources of Public Revenue;  Goods and Services Tax.

Concept of tax, types, canons of taxation-Incidence of taxes; Taxable capacity; Approaches to the principle of Equity in taxation -Ability to Pay principle, Benefit Approach; Sources of Public Revenue;  Goods and Services Tax.

Different approaches to public debt; concepts of public debt; sources and effects of public debt; Methods of debt redemption- Growth of public debt in India. 

Different approaches to public debt; concepts of public debt; sources and effects of public debt; Methods of debt redemption- Growth of public debt in India. 

Different approaches to public debt; concepts of public debt; sources and effects of public debt; Methods of debt redemption- Growth of public debt in India. 

Different approaches to public debt; concepts of public debt; sources and effects of public debt; Methods of debt redemption- Growth of public debt in India. 

Government budget and its structure – Receipts and   expenditure - concepts of current and capital account, balanced, surplus, and deficit budgets, concepts of deficit , functional classification of budget- Budget, government policy and its impact

Government budget and its structure – Receipts and   expenditure - concepts of current and capital account, balanced, surplus, and deficit budgets, concepts of deficit , functional classification of budget- Budget, government policy and its impact

Government budget and its structure – Receipts and   expenditure - concepts of current and capital account, balanced, surplus, and deficit budgets, concepts of deficit , functional classification of budget- Budget, government policy and its impact

Government budget and its structure – Receipts and   expenditure - concepts of current and capital account, balanced, surplus, and deficit budgets, concepts of deficit , functional classification of budget- Budget, government policy and its impact

Federal Finance: Different layers of the government; Inter governmental Transfer; horizontal vs. vertical equity; Principle of federal finance; Finance Commission.

Federal Finance: Different layers of the government; Inter governmental Transfer; horizontal vs. vertical equity; Principle of federal finance; Finance Commission.

Federal Finance: Different layers of the government; Inter governmental Transfer; horizontal vs. vertical equity; Principle of federal finance; Finance Commission.

Federal Finance: Different layers of the government; Inter governmental Transfer; horizontal vs. vertical equity; Principle of federal finance; Finance Commission.

2. David Hyman: Public Finance: A Contemporary Application of Theory to Policy (11th Edition)

3. R.K.Lekhi &  Joginder Singh (2021) , Public Finance.Kalyani

Publishers.

4.  Das, S. (2017). Some concepts regarding the goods and services tax. Economic and Political Weekly, 52(9).

5. Government of India. (2017). GST - Concept and status - as on 3rd June, 2017. Central Board of Excise and Customs, Department of Revenue, Ministry of Finance

CIA II: 50 Marks (Mid-semester Examination)

CIA III: 20 Marks

End Semester Examination      : 100 Marks

This paper is designed to prepare the students with training in theoretical and practical aspects of Insurance Science. It also equip them to work in life and non-life insurance companies (designing insurance products, valuing financial contracts and investing funds); consultancy (offering advice to occupational pension funds and employee benefit plans); government service (supervising insurance companies and advising on the national insurance); and also in the stock exchange, industry, commerce and academia. This paper also develops the caliber of the students to understand the banking procedure with its command on money inflow in the market.

Contingent Consumption; Utility Functions and Probabilities; Expected Utility Theory in Insurance Market; Risk pooling; risk spreading; risk transfer; Quality Choice – Choosing the Quality; Moral Hazard and Adverse Selection in Banking and Insurance Theories; Signaling - The Sheepskin Effect; Incentives; Asymmetric Information - Monitoring Costs Example: The Grameen Bank; Systems Competition; The Problem of Complements; Relationships among Complementors; Markets with Network Externalities.

The Monetary Policy of RBI – Bank Nationalisation and Credit Planning; Monetary Targeting; Multiple Indicator Approach and Liquidity Adjustment Facilities (LAFs); Theoretical Basis of Banking Operations; Liabilities of Banks – deposits, non-deposit resources, other liabilities; Banking Assets – Investments, Bank Credit; Concept of Lending and Portfolio Choice and Aspects; Banking Innovations; Risk Management in Banking; Non-Bank Financial Intermediaries (NBFIs) and Statutory Financial Organisation – Small Savings, Provident Funds and Pension Funds; NBFIs and Miscellaneous Financial Organisation – Loan Companies, Investment Companies, Hire-Purchase Finance; Lease Finance; Housing Finance.

Types of life insurance Contracts: Term and Cash Insurance; The Level Premium Concept; Life Insurance Products; Types of Term Insurance; Whole Life Insurance; Variation of Whole Life Insurance; Indeterminate Premium Whole Life Insurance; General Classifications of Life Insurance; Computation of Life Insurance Premium; Benefits-Certain and Benefits-Uncertain contracts.

Individual Health and Disability Income Insurance; Types of Individual Health Insurance Coverage: Hospital (Surgical Insurance, Major Medical Insurance); Disability Income Insurance; Need for Disability Income Insurance: Short Term Versus Long Term Disability Coverage; Health Insurance for the Elderly; Long Term Care Insurance; Employee Benefits: Group, Life and Health Insurance; Group Insurance: Group Life Insurance Plans, Group Health Insurance Plans, Group Disability - Income Insurance.

Insurance Company Operations: Rate Making, Underwriting, Production, Claim Settlement, Reinsurance; Life Insurance Industry in India; Government Insurance Units; Private Players; Emerging Scenario; Marketing Systems; Distribution Channels: Agents and Brokers; Changes in Distribution System; Government regulation of Insurance; Rationale of Regulation; Function of IRDA, IITDA Regulations; Issues in Insurance Regulation.

CIA II (Mid Semester): Out of 50 Marks

CIA III: Out of 20 Marks

End Semester Examination: Out of 100 Marks

Analytical and Logical Training Skills is an add-on course. This course is designed in a way that inculcates the habit of application of concepts thereby paving way for effective learning and optimal utilization of time. It is specially designed for high performance in Quantitative, reasoning and general knowledge sections of various examinations.

Course Objective: This course will the learner to 

COBJ1, enhance aptitude and reasoning skills

COBJ2. quickly answer the questions on quantitative, reasoning and general knowledge

 COBJ3. face competitive examinations boldly and be successful also.

Arithmetic Aptitude, Logical reasoning and analytical ability, Basic numeracy, Pattern completion, Rule Detection etc.,

English Usage, Sentence Correction, Reading Comprehension, etc.,

Current Affairs, Basic General Knowledge, General Science, etc.

1. The GMAT®Official Guide 2019 for Verbal Review Wiley (2018)
2. The GMAT®Official Guide 2019 for Quantitative Review. Wiley (2018)
3. Pearson Guide to Quantitative Aptitude and Data Interpretation Pearson Education
4. How to Prepare for Verbal Ability and Reading Comprehension for the CAT McGraw Hill Education
5. https://knappily.com/ for Current Events and General Awareness

• Weekly Assignments to check the conceptual understanding of the covered topics.
• Online module consists of practice questions and study materials.
• After 20 hours of classes - a Multiple Choice Questions based test of 50 marks, similar in pattern to competitive examinations will be conducted. There will be 2 tests of 50 marks each that will be considered for internal evaluation and grading purposes.

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 aims at providing a solid foundation upon the fundamental theories on Fourier and Laplace transforms.

Course objectives​: This course will help the learner to

COBJ1. gain familiarity in fundamental theories of the Fourier series, Fourier Integrals, Fourier and Laplace transforms.
COBJ2. acquire problem solving skills in using Fourier Series, Fourier and Laplace transforms.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier series and Fourier transform of some common functions. The Fourier integral, complex Fourier transforms, basic properties, transform of the derivative, convolution theorem, and Parseval’s identity. The applications of Fourier transform to ordinary differential equations.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Fourier cosine and sine transforms with examples, properties of Fourier Cosine and Sine Transforms, applications of Fourier sine and cosine transforms with examples.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

Laplace Transform of standard functions, Laplace transform of periodic functions, Inverse Laplace transform, solution of ordinary differential equation with constant coefficient using Laplace transform, solution of simultaneous Ordinary differential equations.

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​: This course aims to enlighten students with the fundamental concepts of vectors, geometry of space, partial differentiation and vector analysis such as gradient, divergence, curl, and the evaluation of line, surface and volume integrals. The three classical theorems, viz., Green’s theorem, Gauss divergence theorem and Stoke’s theorem are also covered.

Course objectives​: This course will help the learner to 

COBJ 1. gain familiarity with the fundamental concepts of vectors and geometry of space  Curves.

COBJ 2. illustrates and interprets differential and integral calculus of vector fields 

COBJ 3. demonstrate the use Green’s Theorem, Stokes Theorem, and Gauss’ divergence Theorem

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Fundamentals: Three-dimensional coordination systems, Vectors and vector operations, Line and planes in space, Curves in space and their tangents, Integrals of vector functions, Arc length in space, Curvature and normal vectors of a space, TNB frame, Directional derivatives and gradient  vectors, Divergence and curl of vector valued functions.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Double Integrals- Areas, Moments, and Centres of Mass – Double Integrals in Polar Form –Triple Integrals in Rectangular Coordinates, Masses and Moments in Three Dimensions, Triple Integrals in Cylindrical and Spherical Coordinates, Substitutions in Multiple Integrals.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

Line Integrals, Vector Fields, Work, Circulation and Flux, Path Independence, Potential Functions, and Conservative Fields, Green’s Theorem in the Plane, Surface Area and Surface  Integrals, Parametrized Surfaces, Stokes’ Theorem, The Divergence Theorem.

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

This course will help students to gain skills in using Python to illustrate Fourier transforms, Laplace transforms for some standard functions and implementing Laplace transforms in solving ordinary differential equations of first and second order with constant coefficient.

Course Objectives​: This course will help the learner to

COBJ1. code python language using jupyter interface.

COBJ2. use built in functions required to deal with Fourier and Laplace transforms.

COBJ3. calculate Inverse Laplace transforms and the inverse Fourier transforms of standard functions using sympy.integrals

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

1.  Fourier series using sympy and numpy.
2.  Practical harmonic analysis using math, sympy and numpy.
3.  Fourier cosine and Fourier sine transforms using sympy and math.
4.  Discrete Fourier transform using Python.
5.  Laplace transforms using sympy, sympy.integrals and sympy.abc.
6.  Inverse Laplace transforms using sympy, sympy.integrals and sympy.abc.
7. Inverse Fourier transforms using sympy, sympy.integrals and sympy.abc.

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: The course calculus of several variables using python is aimed at enabling the students to explore and study the calculus with several variables in a detailed manner with the help of the mathematical packages available in Python. This course is designed with a learner-centric approach wherein the students will acquire mastery in understanding multivariate calculus using Python modules.

Course objectives: This course will help the learner to gain a familiarity with

COBJ1. skills to implement Python language in calculus of several variables

COBJ2. the built-in functions available in library to deal with problems in multivariate calculus

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

1. Introduction to basic commands and plotting of graph using matplotlib
2. Vectors-dot and cross products, plotting lines in two and three-dimensional space, planes and surfaces.
3. Arc length, curvature and normal vectors.
4. Curves in sphere: Tangent vectors and velocity- circular helix with velocity vectors.
5. Functions of two and three variables: graphing numerical functions of two Variables.
6. Graphing numerical functions in polar coordinates. Partial derivatives and the directional derivative.
7. The gradient vector and level curves- the tangent plane -the gradient vector field.
8. Vector fields: Normalized vector fields- two-dimensional plot of the vector field.
9. Double Integrals: User defined function for calculating double integrals - area properties with double integrals.
10. Line integrals – Curl and Green’s theorem, divergence theorem.

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

Course Description: This course provide the students an opportunity to gain work experience in the relevant institution / industry, connected to their subject of study. The experience gained in the workplace will give the students a competitive edge in their career.

Course Objective: This course help the learner to

COBJ1. get exposed the work ethics of the field of their professional interest

COBJ2. gain practical experience on the field of their interest

COBJ3. choose their career through practical experience

B.Sc. students of EMS (Economics, Mathematics and Statistics) have to undertake a mandatory internship in Mathematics or Economics or Statistics for a period of not less than 30 working days at any of the following: reputed research centers, banking sectors, recognized educational institutions, summer research fellowships, programmes like M.T.T.S, or any other industry internship approved by the Head of the Department.

The internship is to be undertaken at the end of fourth semester (during second year vacation). The report submission and the presentation on the report will be held during the fifth semester and the credits will appear in the mark sheet of fifth semester.

The students will have to give an internship proposal with the following details: Organization where the student proposes to do the internship, reasons for the choice, nature of internship, period on internship, relevant permission letters, if available, name of the mentor in the organization, email, telephone and mobile numbers of the person in the organization with whom Christ University could communicate matters related to internship. Typed proposals will have to be given at least one month before the end of the fourth semester.

The HOD will assign faculty members from the department as mentors at least two weeks before the end of fourth semester. The students will have to be in touch with the mentors during the internship period either through personal meetings, over the phone or through email. At the place of internship, students are advised to be in constant touch with their mentors in the organization.

At the end of the required period of internship, the candidates will submit a report in a specified format adhering to department guidelines. The report should be submitted within first 20 days of the reopening of the University for the fifth semester. 

Within a month from the day of reopening, the department holds a presentation by the students. During the presentation the guide or a nominee of the guide should be present and be one of the evaluators.

Students will get 2 credits on successful completion of internship. If a student fails to comply with the aforementioned guidelines, the student has to repeat the internship.

The components of evaluation include the preliminary report, weekly reports, the comprehensive report, and the viva voce examination.

Evaluation Rubrics

Criteria                                  Marks     

Preliminary Report                     5

Weekly Reports                         15

Draft Report                             10

Final Report                              20

Viva-voce Exam                        50