b.sc. actuarial and financial mathematics program syllabi. (afm)_1_2_9_2015.pdf · b.sc. actuarial...

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B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Program Syllabi

Course Title : Calculus-1 Semester-1

Course Code : MTH-101

Credit hrs. : 5

Unit-I:

The tangent and velocity problems, limit of a function, - definition of a limit, calculating limits using

limit laws, continuity, limits at infinity, horizontal asymptote, derivatives and rates of change, derivative

as a function.

Unit-II: Derivatives of polynomial and exponential functions, product and quotient rule, derivatives of

trigonometric functions, chain rule, implicit differentiation, derivatives of logarithmic functions, rates of

change, exponential growth and decay, linear approximations and differentials

Unit-III:

Maximum and minimum values, the Mean Value Theorem, how derivatives affect the shape of a graph,

indeterminate forms and L’Hospital’s Rule, curve sketching, optimization problems

Unit -IV: Antiderivatives, areas and distances, the definite integral, the Fundamental Theorem of Calculus,

indefinite integral.

Textbook:

Calculus – Early Transcendentals by James Stewart

Supplementary books:

Calculus by Thomas and Finney. Morgan Kaufmann Pub.

A First Course in Calculus - by Serge Lang,

Calculus – by Howard Anton

Integral Calculus - by Hari Krishan

Calculus I & II by Tom Apostol

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Course Title : Computer Fundamentals Semester-1

Course Code : CS101

Credit hrs. : 3+1

Unit-I:

Introduction to Computers and Information Technology, Computers. Structures of a Computer System. Basic

Components and Block Diagram. I/O devices and Storage devices. H/W and S/W Concepts, Transforming data

into information, Binary Number System and Logic Gates. System S/W vs. Application S/W. Computer

Configuration, Advantages and Disadvantage of Computers.

Unit-II:

Operating System: Overview, functions and types, Basics of Data Communications and Networking: Overview,

features and types. Topologies and Media. Internet and WWW: Overview, importance and applications. File

Systems: Concepts and types. Databases: Overview, features and types.

.

Unit-III:

Introduction to office Tools: Fundamental of MS-Word, MS-Excel, MS-Power Point. Introduction to Computer

Security: Types of threats: Data, hardware, privacy and identity. Types of infections: Viruses and Bombs, Spam,

Trojans, Virus Detection, Prevention and Cure Utilities (Firewalls, Antivirus).

Unit-IV:

Fundamentals of problem solving techniques, Concepts of Flowcharts and Algorithms. Developing Algorithms

for basic mathematical and Logical problems. Introduction to Programming language ‘C’.

Reference books:

1. P.K. Sinha, “Computer Fundamentals, 2005”, BPB, New Delhi.

2. Perter Dyson, “Understanding Norton Utilities”, AET Publications.

3. Peter Dyson, “Understanding PC Tools”, AET Publications.

4. Peter Norton, “Inside the PC, 2001”, SAMS Tech. Media.

5. Peter Norton, “Introduction to computers”, TMH

6. Sanjay Saxena, “MS Office for Everyone, 2005”, Vikas Publications.

7. Suresh K. Basandra, “Computers Today 2005”, Galgotia Publications.

8. Taxali, “PC Software, 2005”, Tata McGraw Hills, New Delhi 9. V. Raja Raman, “Introduction to computers”, TMH 10. E.Balaguruswamy, “Programming in ANSI C”

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Course Title : Professional Communication Semester-1

Course Code : ENG-101

Credit hrs. : 4

Unit-I: Essentials of communication : Communication, its significance & Role

The process of communication, Barriers to communication. Methods of communication, verbal & non-

verbal communication, Interpersonal communication, decoding body language.

Unit-II: Written communication: Introduction to phonetic sounds, enriching vocabulary, using

vocabulary in different contexts, essentials of strong writing skills, language and style. , Paragraph

writing, developing perspective.

Technical written communication: Nature, origin and development of technical written communication,

salient features, difference between technical writing and general writing.

Unit-III : Technical written communication: Report writing, importance, structure, style and drafting of

reports.

Speaking: Public speaking, fear management, elocution, extempore speeches, Group discussions, Multi-

perspective debates, how to write and present papers, resume writing.

Unit-IV: Reading comprehension, Précis writing, Note-taking, comprehension, discussion on the basis

of reading from prescribed text.

Business correspondence, ramification of business letters, analyzing audience, purpose, layout & form

and types.

Unit-V: Business correspondence: Proposal writing, presentation skills,

Tips for good communication , Interview etiquette, e-mail etiquette, telephone etiquette,

Suggested Readings

1. Seely, John. Writing and Speaking Delhi: OUP

2. Wallace, Michael J. Study Skills in English. New Delhi: CUP, 1998.

3. Mohan, Krishna and Meera Banerji. Developing Communication Skill, Delhi: Macmillian,

1990.

4. Sasikumar V., P. Kiranmai Dutt and Geetha Rajeevan. A Course in Listening and Speaking (I

& II) Bangalore: Foundation Books, 2006.

5. Sood, S C et al. Developing Language Skills, Delhi: Manohar, 1998.

6. Day, Richard R, ed. New Ways in Teaching Reading. Illinois: TESO 1993.

7. Chaturvedi, P.D and Mukesh Chaturvedi. Business Communication, Delhi: Pearson Education,

2006.

8. Trimble, Louis. English for Science and Technology, Cambridge: CUP, 1985.

9. Prasad, LM. Organisational Behaviour New Delhi: Sultan Chand & Sons, 1984.

10. Taylor, Shirley. Communication for Business New Delhi: Pearson Education, 1988.

11. Wilfred Gruein et al. MLA Handbook for Writers of Research Papers.

12. Battacharaya, Indrajit. An Approach to Communication Skills.

13. O’Conner, J.D. Better English Pronunciation.

14. Roach, Peter. English Phonetics and Phonology with Cassette

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Course Title : Management Process Semester-1

Course Code : MTH111

Credit hrs. : 4

Unit-1:

Various approaches to management, process and functions of management, managerial role, managerial

skill, Management environment scanning, approaches to counter environment. Management philosophy,

values and value system.

Unit-II:

Planning concepts, process, and parameters. Types of planning. Strategic planning concept and

significance, planning for change. Management by objective concept and significance. The control

process: concept and significance.

Unit-III:

Importance of organization, formal organization elements: organizational chart. Division of labor,

departementation-methods of departmentation. Source of authority; the scalar chain of command,

decentralization of authority. Responsibility-accountability.

Unit-IV:

Distinctive features of the human resources, manpower planning, recruitment and selection: sources of

recruitment, selection criteria. Motivation, meaning and approaches. Work motivation. Theories of

motivation-Maslow need hierarchy. Herzbrg’s motivation theory. Meaning of leadership, theories of

leadership/ trait and situational theories. Management control and audits: accounting audit. The

management audit: purpose and scope.

Suggested Readings:

1. George R. Terry and Stephan G. Franklin, “Principles of Management”.

2. Knootz, Harold and C.O. Dinell, “Management a system and contingency analysis of managerial

functions”.

3. Banerjee Shyam, “Principles and practices of management”.

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Course Title : Calculus-II Semester-1I


Credit hrs. : 4

Unit I: Applications of integration, areas between curves, volumes, volumes by disks and cylindrical

shells, arc length.

Unit II: Strategy for integration, integration by parts, trigonometric integrals, trigonometric substitution,

integration of rational functions by partial fractions, improper integrals

Unit III: Infinite sequences and series, convergence of a series, divergence test, integral and comparison

tests, alternating series, absolute convergence, ratio and root tests, power series, Taylor and Maclauren

series.

Unit IV: Parametric equations, calculus with parametric curves, polar coordinates

Textbook:

Calculus – Early Transcendentals by James Stewart


Calculus by Thomas and Finney. Morgan Kaufmann Pub.


Calculus – by Howard Anton

Integral Calculus - by Hari Krishan


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Course Title : Introduction to Actuarial Mathematics Semester-1I


Credit hrs. : 5

Unit I: Probabilities and events, conditional probability, random variables, expected values, variance.

Unit II: Simple interest, compound interest, continuously compounded interest, present value of future

payments, rate of return, continuously varying interest rates.

Unit III: Annuities, calculating annuity premiums, amortization of a debt, sinking funds, capital

budgeting.

Unit IV: Risk and insurance, long-term and short-term insurance, life insurance, automobile insurance,

property insurance, indemnity principle, coinsurance principle, stocks, dividends and bonds

Unit V: Deterministic cash flows: net present value, internal rate of interest, modified internal rate of

interest, project choice. Fixed income securities (bonds): bond price and yield, duration, convexity,

immunization against interest rate fluctuations, short and forward rates, term structure of interest rates,

incorporating term structure into price/duration/convexity/immunization.

Textbooks:

An Elementary Introduction to Mathematical Finance – Sheldon Ross

An Undergraduate Introduction to Financial Mathematics – by Robert Buchanan

Business Mathematics - by Lerner and Zima (Schaum’s Outline Series)

Corporate Finance by Brealy and Myers

Fundamentals of Actuarial Mathematics by David Promislow

Investment by Sharpe and Bailey Upper Saddler River, N.J. Prentice Hall, c1999.

Investment Science by Luenberger (Indian Edition), Oxford University Press

Investments by Bodie, Kane and Marcus, McGraw-Hill Irwin, c2005.

Lecture Notes on Actuarial Mathematics – by Jerry Veeh

Actuarial Mathematics by Bowers et al, Society of Actuaries, USA.

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Course Title : Fundamentals of Accounting Semester-1I


Credit hrs. : 5

Unit 1: Accounting - Meaning, Nature, Functions & Usefulness. Generally Accepted Accounting

Principles (GAP). Recording of Transaction Journals, Ledger posting and Trial Balance, Preparation of

Financial Statement.

Unit 2: Accounting for depreciation. Company Accounts Final Statements Valuation of Good will and

shares, Hire Purchase System

Unit 3: Amalgamation, absorption and external reconstruction. Alternation of Share Capital & Internal

Reconstruction. Liquidation Accounts of Holding Companies - Consolidated Balance Sheet

Unit 4: Bank accounts Insurance Company Accounts. Double Account System. Accounts of Non- Profit

Organization.

Suggested readings:

1. Antony R.N. & Recce J.S. "Accounting -Test & Cases", Richard Irwan. Inc. Home Wood

Illionois.

2. Aulandam & Raman "Advanced Accounting" Himalyan Pub. House Mumbai.

3. Gupta R.L. & Radhaswamy. M. "Advanced Accounting" Sultan Chand & Sons.New Delhi.

4. Maheswari. S.N "Financial Accounting" Vikas Publishing House. New Delhi.

5. Mukherjee & Hanif"Modern Accounting" Tata McGraw Hill

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Course Title : Environmental Studies Semester-1I

Course Code : MTQGE01

Credit hrs. : 4

Unit – I

Introduction to Environmental Science: Scope and importance, Environmental Ethics-

Anthropocentricism and Ecocentricism, Environmental issues and Development, Developing v/s

Developed countries, Public Environmental awareness and methods of its propagation, Campaigns as

instruments to achieve better Environmental Outcomes, Green Consumerism.

Unit – II

Introduction to Ecosystem and Ecology, Types of Ecosystems, Structure of an Eco system-biotic and

abiotic components, Trophic Structure, Food chain and Food Web, Ecological Pyramids; Ecological

Succession, Bioenergetics, Energy flow in an ecosystem, Biogeochemical cycles, Major World

Ecosystems and their characteristics.

Unit – III

Introduction to global climate change; Causes of climate change; Major ways in which climate change is

manifested – temperature and extreme events- El-nino, Future projections about climate change,

Melting of glaciers and polar ice caps, Sea level rise.

Unit – IV

Natural resources and their conservation; Biodervisty-Definition, values and threats; Habitat and Species

Loss; Classification of species as per conservation status; Conservation approaches – In-Situ and Ex-Situ

conservation; Alternatives to conventional developmental approaches – Sustainable Development; Non

– Conventional Sources of Energy

Unit – V

Relevance of Mathematics in Environmental Sciences; Introduction to Mathematical Models; Types of

Mathematical Models; Role of Models in Environmental Sciences/ Ecology; Gaussain plume Model,

Lotka-Volterra Model-Nature and their relevance. Some Statistical Problems based on Environmental

Data.

Reading List:

1. Ecology and Environment by P.D. Sharma. (Rastogi Publications)

2. Environmental Science Towards a Sustainable Future by Nebel and Wright (PHI) LPE

3. Environmental Studies by Erach Barucha (Oxford Publications)

4. Environmental Studies From Crises to Cure authored by R. Rajagopalan; Published by Oxford

University Press. Price INR 160.

5. Environmental Management by Oberoi

6. Principles Of Environmental Science: Inquiry & Applications (Special Indian Edition) authored

by William Cunningham & Mary Cunningham; Published by Tata McGraw Hill. Price INR 375.

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Course Title : Excel for Business Semester-1I


Credit hrs. : 2

Course Contents

Textbooks:

Excel 2007 for Starters by M. McDonald.

Analyzing Business Data with Excel by G. Knight

Mathematical Modeling with Excel by B. Albright.

Learning Objectives Excel Topics

1 Excel Basics Naming Cells and Ranges, Descriptive statistics functions, Display

options (Custom views, Freeze panes)

2 Developing charts in

Excel

Bar chart, Stacked bar chart, line chart, dynamic charting (this uses the

OFFSET function)

3 Some useful functions IF, SUMIF, SUMIFS, COUNTIF, COUNTIFS, COUNT, COUNTA

4 Interest and

Amortization

FV, PV, PMT, PPMT, IPMT, RATE, NPER

5 Data Handling Wizards Sort, Filter, Text-to-Columns, Remove Duplicates, Consolidate, Data

Validation.

6 Data Handling

Functions

VLOOKUP, HLOOKUP, text functions, MATCH, INDEX

7 Cash Flow Analysis NPV, XNPV, IRR, XIRR, GOAL SEEK

8 Sensitivity Analysis Data Tables and Scenario Manager

9 Optimization Using the SOLVER add-in to solve some important problems in

Finance and the industry.

10 Linear Regression LINEST, STEYX, INTERCEPT,SLOPE, FORECAST, TREND,

ANALYSIS TOOLPAK Add-in

11 Exploring Data Pivot table and Pivot Chart

12 Visual Basic for

Applications (VBA)

VBA can tackle situations that an analyst faces in his routine work for

which Excel does not have a ‘readymade’ answer.

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Course Title : Vector Calculus Semester-III


Credit hrs. : 4

Unit I: Three dimensional coordinate system, vectors, dot product, cross product, equations of lines and

planes, cylinders and quadric surfaces, cylindrical and spherical coordinates

Unit II: Vector functions and space curves, derivatives and integrals of vector functions, arc length and

curvature, motion in space- velocity and acceleration.

Unit III: Double integrals over rectangles, iterated integrals, double integrals over general regions,

change of order of integration; double integrals in polar coordinates, applications, surface area, triple

integrals, triple integrals in cylindrical and spherical coordinates, change of variables.

Unit IV: Vector fields, line integrals, fundamental theorem for line integrals, Green’s theorem, curl and

divergence, parametric surfaces and their areas, surface integrals, Stoke’s theorem, Divergence theorem

Textbooks: Calculus – Early Transcendentals by James Stewart (2006 Edition)

Supplementary texts:


Calculus – by Howard Anton,

Textbook of Calculus - by Larson and Edwards,

Schaum’s Outline of Vector Analysis,


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Course Title : Linear Algebra Semester-1II


Credit hrs. : 4

Unit I: Introduction to systems of linear equations, Gauss-Jordan elimination, matrices and matrix

operations, matrix arithmetic, transpose and adjoint of a matrix, inverses, diagonal, triangular and

symmetric matrices, determinants, cofactor expansion, row reduction.

Unit II: Euclidean n-space, linear transformations on n-spaces, vector spaces, subspaces, linear

independence, basis and dimension, row space, column space, null space, rank and nullity. Inner

products, orthogonality, orthonormal bases, Gram-Schmidt process, change of basis

Unit III: Complex numbers, arithmetic of complex numbers, polar form, brief introduction to complex

functions, complex vector spaces.

Unit IV: Eigenvalues and eigenvectors, diagonalization, orthogonal diagonalization, general linear

transformations, kernel and range, inverses, similarity and isomorphism

Textbooks: Elementary Linear Algebra by Howard Anton and Chris Rorres

Linear Functions and Matrix Theory by Bill Jacob

A Textbook on Matrices by Hari Krishen

Linear Algebra – Schaum’s Outline Series

Linear Algebra and its Applications by David C. Lay, Springer

Linear Algebra and its Applications by Gilbert Strang Thomson Learning

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Course Title : Mathematics and Art Semester-1II


Credit hrs. : 4

Unit I: Perspective, its origins and examples from art, Brunelleschi’s peepshow, the Perspective

Theorem, one-point and two-point perspective, vanishing point and its location, use of vanishing point in

viewing art, Durer and da Vinci’s work, optical illusions.

Unit II: Golden ratio. derivation of the Golden Ratio, geometric construction of the Golden Ratio,

irrationality of the Golden Ratio, Golden rectangle, use of Golden ratio in art, Fibonacci sequence and its

relation to Golden ratio, polygons, pentagon and pentagram.

Unit III: Regular, semi-regular and irregular tessellations; vertex configurations for possible tilings;

dual tilings; use of parallel translation, glide reflection, mid-point rotation and side rotation in

constructing irregular tilings; Conway’s Criterion; the patterns of M.C. Escher; construction of different

tessellations; symmetry of scale; Penrose tiling; pinwheel pattern

Unit IV: Introduction to groups, four rigid symmetries, Rosette groups and point symmetry, Leonardo’s

Theorem, Frieze pattern groups, wallpaper patterns and plane symmetry, description of the 17 symmetry

groups and their identification. Islamic lattice patterns. Girih patterns and tiles.

Textbooks: Since textbooks on this subject are not available locally, supplementary materials will be

provided in class.

Supplementary Texts:

Symmetry, Shape and Space by Kinsey and Moore

Squaring the Circle -Geometry in Art and Architecture by Paul Calter

The Heart of Mathematics by Burger and Starbird

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Course Title : Introduction to Concepts of Peace and Conflict Semester-1II

Course Code : PSGE01

Credit hrs. : 4

Unit-I

An overview of the concepts of “peace” and “conflict”; Definitions of peace and conflict; Positive and

negative peace; positive and negative conflict; Importance of perceptions in conflict; Introduction to and

definitions of terms used in conflict studies (peace making, peace keeping and peace building; conflict

management, conflict resolution and conflict transformation); Levels of conflict (inter- and intra-

personal, local, regional and global); Inter-disciplinary approach of peace and conflict studies.

Unit-II

The Seville Statement on Violence; Theories of conflict (Basic Human Needs, Relative Deprivation and

Social Contract Theory); Intervention and its types (negotiation, mediation and arbitration); Conflict

situations, attitudes and behavior; Contemporary conflict resolution – the prevention, management and

transformation of deadly conflicts; Conflict Resolution and Inner Peace – Conflict response modes,

stress mapping.

Unit-III

Conflict analysis – importance and limitations, Models of conflict analysis, Conflict mapping, Case

studies of conflict mapping .

Unit-IV

Escalation and de-escalation of conflict; Contentious tactics ; Building positive peace – through

education, sustainable development; Corporate Social Responsibility (CSR) and peace - the different

faces of CSR); The gender dimensions of peace and conflict

Unit-V

Environmental security and peace

Media, peace and conflict (role of the media-propaganda vs. conflict coverage), peace journalism.

Creating zones of peace

Requirements:

Regular attendance

Participation in class discussions and the quality of participation

Preparation of readings assigned each day and additional knowledge acquired about the subject

Submission of class assignments on time

Course Structure

Activities:

Interactive session about the students’ own experience of peace and conflict; simulation of a

situation of interpersonal conflict and the ways/suggestions of resolving it

Activity of perceptions to prepare students to accept different points of view for the same stimuli

Theatre of the Oppressed

Role plays

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REFERENCES

Abdalla, A., et al. (2002). Understanding C.R. SIPABIO: A Conflict Analysis Model. In Say

Peace: Conflict Resolution Training Manual for Muslim Communities (pp. 44-51). Virginia,

USA: The Graduate School of Islamic and Social Sciences.

Burton, John W. (1993). Conflict Resolution as a Political Philosophy. In Conflict Resolution

Theory and Practice: Integration and Application. (pp. 55-64). Ed. Dennis J. D. Sandole and

Hugo van der Merwe. Manchester and New York: Manchester University Press,. pp. 55-64.

Summary by Mariya Yevyukova. Retrieved June 1, 2009, from

http://www.colorado.edu/conflict/transform/burton.htm,

Fisher et al., (2000). Working with Conflict: Skills and Strategies for Action. London and New

York: Zed Books Ltd.

Mitchell, C. R. (1981). The Structure of International Conflict. London and New York:

Macmillan Press Limited.

Richard E Rubenstein, (n.d.). Basic Human Needs: the Next Steps in Theory Development.

Retrieved June 19, 2009, from http://www.gmu.edu/academic/ijps/vol6_1/Rubenstein.htm

Rubin, J. Z., Pruitt, D. G., & Kim, S. H. (1994). Social Conflict: Escalation, Stalemate and

Settlement (4th ed.). USA: McGraw Hill, Inc.

Wilmot, W., & Hocker, J., (1998). Interpersonal Conflict. New York: McGraw Hills.

Young, J. (n.d.), Relative Deprivation. Retrieved June 15, 2009, from

http://www.malcolmread.co.uk/JockYoung/relative.htm

http://www.colorado.edu/conflict/transform/burton.htm

http://www.gmu.edu/academic/ijps/vol6_1/Rubenstein.htm

http://www.malcolmread.co.uk/JockYoung/relative.htm

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Course Title : Principles of Economics Semester-1II


Credit hrs. : 4

Unit I:

Nature and scope of economics. Positive and Normative economics. Micro and Macro economics.

Methods of economic analysis; Economic systems, Major economic problems.

Unit II:

Demand and supply concept: Law of demand, elasticity of demand and its measurement. Law of

diminishing marginal utility, law of equi-marginal utility. Law of Supply

Indifference curve analysis; meaning of indifference curve; properties of indifference curve.

Consumer's equilibrium; consumer's surplus; effects of price change; income effect and substitution

effect; breaking up of price effect into income and substitution effect.

Unit III:

Production: Factors of production. Determination of factors pricing; modem approach. Production

function and producers equilibrium. Laws of returns and returns to scale. Consumption function:

psychological law of consumption function. Investment function; multiplier and accelerator.

Unit IV:

Theory of employment: classical theory of employment. Say's law - basic assumption of say's law of

market and its implications; Keynesian theory of employment; determination of equilibrium level of

employment. National income; measurement of national income. Balance of payment; concept and

causes of disequilibrium; methods of correction of disequilibrium. Trade Cycles: meaning and types of

economic fluctuation.

Suggested Readings:

1. H, L, Ahuja, Modem Economics.

2. J.K.Mitra, Economics Micro and Macro.

3. M.C.Vaish, Macro Economic Theory.

4. Edward Shapiro, Macro Economic Analysis

5. John Solomon, Economics.

6. Stenier and Hague, Economics Theory.

7. A.Nag, Macro Economic for management Students

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Course Title : Probability Theory Semester-1V


Credit hrs. : 5

Unit I: Sample spaces and events; axioms of probability; counting principle; permutations and

combinations; conditional probability; independent events; Bayes’ Theorem; discrete and continuous

random variables; distribution and density functions; expected value, variance, standard deviation.

Expectation of a function of a.r.v.

Unit II: Bernoulli, Binomial, multinomial, negative binomial, geometric, hypergeometric distributions

and Poisson distributions; uniform, exponential, normal, log normal, Gamma, Beta, Chi Square, t and F

distributions, expected values and variances of these distributions, expectation of a function of a

random variable; MGF, Probability generating function and characteristic function of these

distributions

Unit III: Two-dimensional random variables, Joint distributions (continuous and discrete case);

covariance and correlation, conditional distributions; independent random variables, conditional

expectation, covariance and variance of sums of random variables; joint probability distribution of

functions of random variables.

Unit IV: Markov and Chebyshev’s inequalities, normal approximation to binomial; strong and weak

law of large numbers; central limit theorem with proof (using Levy’s Continuity Theorem). Moment

generating functions, probability generating functions and characteristics functions; Cumulant

generating functions, derivation for various distributions; sums of independent random variables.

Text Book: John E. Freund’s Mathematical Statistics by Miler and Miler

Supplementary books

A first Course in Probability by Sheldon Ross

An Introduction to Probability Models by Sheldon Ross

An Introduction to Probability Theory and Mathematical Statistics by V.K. Rohtagi and Saleh

Elementary Probability Theory by K.L. Chung

Fundamentals of Mathematical Statistics by S.C. Gupta

Linear Statistical Inference and its Applications by C.R. Rao

Modern Probability Theory by B.R. Bhat

Schaum’s Outlines in Probability by Seymour Lipschutz, Marc L. Lipson and Kanchan Jain (second edition 2010), Tata McGraw Hill Education Pvt. Ltd.

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Course Title : Differential Equations Semester-1V


Credit hrs. : 4

Unit I: Some basic differential equations; classification of differential equations; first order differential

equations; linear equations and method of integrating factors; separable equations; modeling with first

order equations; exact equations; numerical approximation and Euler’s method

Unit II: Second order differential equations, homogeneous and non-homogeneous equations;

fundamental solutions; linear independence and Wronskian; complex roots of the characteristics

equation; higher order equations

Unit III: Series solutions of differential equations, Bessel and Legendre equations; series solutions near

an ordinary point; regular singular points, Euler equations

Unit IV: Laplace transform; Laplace transforms of common functions, inverse transform and transforms

of derivatives; Dirac-Delta function

Text Book:

Elementary Differential Equations and Boundary Value Problems by William E. Boyce and

Richard C. DiPrima


Differential Equations with Application and Historical Notes by G Simmons

Differential Equations by Dennis Zill

Differential Equations – Schaum Series

Introduction to Differential Equations by E.G. Phillips

Differential Equations by Jane Cronin

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Course Title : Real Analysis Semester-1V


Credit hrs. : 4

Unit I: Real numbers; ordered sets; bounded and unbounded sets; supremum and infimum of a set,

ordered fields; completeness of the set of real numbers.

Unit II: Limits of functions, continuity, uniform continuity; sequences; limits of sequences and limit

theorems; bounded and monotone sequences; Cauchy sequences; Bolzano-Weistrass Theorem;

Unit III: Riemann integrals, upper and lower sums; integrability of continuous and monotone

functions; fundamental theorem of integral calculus, mean value theorems of integral calculus;

improper integrals and their convergence

Unit IV: Limit, continuity and differentiability of real-values functions of two variables; partial

derivatives; changing the order of derivation; change of variables, Jacobians

Text Books:

An Introduction to Real Analysis by Bartle and Sherbert (Wiley & Sons). Supplementary books:

Mathematical Analysis by Tom Apostol

Principles of Mathematical Analysis by Walter Rudin

An Introduction to Analysis by William Wade

A Course in Real Analysis by Shanti Narayan

Real Analysis by R.R. Goldberg

Undergraduate Analysis by Serge Lang

Real Analysis by Terence Tao, Hindustan Book Agency (TRIM Series)

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Course Title : Financial Management Semester-1V


Credit hrs. : 4

Unit I:

Concept, scope and functions of financial management, relationship with other areas of management.

Objectives of financial management, profit and wealth maximization. Organization of finance function.

Role of financial Manager. Mathematics of finance. Short and long-term sources of funds, internal

financing.

Unit II:

Capital structure concepts and theories, net income approach, MM approach, traditional approach.

Futures of an adequate capital structure, analysis of capital structure in practice. Over and under

capitalization. Capital budgeting, decisions need, importance and processes. Determination of relevant

cash flow. Capital budgeting techniques, traditional methods, payback period and accounting rate of

return net present value and internal rate of return

Unit III: Dividend decisions meaning and significance, factors effecting dividend policy, stability of

dividends, forms of dividends, legal contractual and internal constraints and restrictions of dividend

policy. Irrelevance of dividends, MM hypothesis, relevance of dividend, Walters and Gorden’s models

Unit IV: Concepts and nature of working capital. Determinants of working capital. Estimating working

capital needs and its computation. Deciding and appropriate working capital policy. Working capital

control and banking policy

Suggested Readings:

1. Panday I. M. Financial management

2. Chandra Prasana Financial Management, Theories and Practices

3. Khan and Jain Financial Management , Text and Problems

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Course Title : Programming Concepts Semester-1V

Course Code : CS401

Credit hrs. : 2+2

UNIT 1: C: Evolution, Advantages & Disadvantages, Features & Importance. Compilers and Integrated

Development Environments: Editing, Compiling & Linking Programs. Basic Structure of C programs,

Character Set, Identifiers, Reserved Words, Standard Data Types, Constants, Variables, Symbolic

Constants, Casting, and Standard Libraries.

UNIT 2: Operators & Expressions: Assignment, Arithmetic, Relational, Logical, Compound, Increment,

Decrement, Bitwise Operators & Special Operators.

Logical Control: IF, IF – ELSE, ?:, SWITCH CASE. Looping Statements: FOR, WHILE, DO-WHILE,

EXIT, BREAK, CONTINUE AT EXIT statements.

Functions: Concepts, Elements, Prototypes & Types. Storage classes. Recursion. Preprocessing.

UNIT 3: Arrays: Types of arrays, initialization, passing arrays to functions, dynamic arrays. Character

Arrays & Strings. String-handling functions.

Structures and Unions: Syntax & use, members, structures & pointers, array of structures, structures &

functions, structure within structures.

UNIT 4: Pointers: Concepts, Variables, swapping data, swapping address v/s data, pointers & arrays,

pointers to pointers, pointer to strings, pointer arithmetic, additional operators, pointers to functions,

void pointers.

REFERENCE BOOKS:

1. Yashwant Kanetkar, “Let Us C”, BPB

2. E. Balaguraswamy, “Programming in ANSI C”, Tata McGraw Hill

3. “Programming in C”, Schaum Series

4. Foster and Foster, “C By Discovery”, RRI PENRAM

5. ROBERT A.RADCLIFFE, “Encyclopedia C”, “BPB”

6. Maha Patra“Thinking in C”, BPB

Learning expectations:

After the completion of the paper the students are expected to able to:

Draw flowcharts for simple mathematical problems.

Design algorithms from flowcharts.

To understand why an algorithm behind a programme works, the conditions of termination, the

instruction flow sequence through dry runs.

Write programmes to calculate the sum of familiar series like _______, ________, _______ a

given number of terms.

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Write programmes to generate first n prime numbers.

Write programme to calculate the multiplication of two compatible matrices.

Calculate a given term of Fibonacci sequence using recursion.

Check an integer whether it is a palindrome or not.

Empirically appreciate the convergence and divergence of series using simple programmes.

Implement Euclid’s algorithm for calculating GCD of two given numbers.

Implement Horner’s algorithm for calculating the value of a given polynomial at given point.

Efficiently use functions, arrays and pointers in larger programmes.

Instructions for the teacher: While teaching syntax the instructor is advised to give equal

emphasis to the logic and the underlying algorithm so that the students may get well on their way to

learn the art of ‘algorithmic thinking’.

In other words, more emphasis should be given thinking ‘Programmatically’ then doing particular

programmes so that the students may face little difficulties while shifting to another computing

language.

As far as possible illustrations should be mathematical in nature which will sufficiently arouse the

curiosity of students to explore different mathematical topics computationally or their own.

22


Course Title : Statistics Semester-V


Credit hrs. : 5

Unit I. Statistics a conceptual frame work, Statistical enquiry, collection of data, Classification, Seriation and tabulation of data. Diagrammatic and Graphic presentation of data. Measures of central tendency: mean, median, mode. Measures of dispersion-range, mean deviation, quartile deviation Standard deviation and variance. Measure of skewness- Karl-Pearson’s and Bowley's methods. Measures of Kurtosis. Unit II. Correlation Analysis - conceptual frame work .Methods of studying correlation-Scatter diagram, Karl Pearson’s correlation coefficient, Spearman’s rank correlation coefficient and concurrent deviation methods. Probable error (ungrouped data), coefficient of determination. Regression Analysis - definition and uses, Linear and Non-linear regression. Regression equations and regression coefficient, Properties of regression coefficient, multiple regression Unit I: Population and sample; population parameter and sample statistics; Sampling distributions,

Sampling distribution of mean, Variance and proportions. Principles of sampling; probability and non

probability sampling, Simple random sampling, Stratified sampling, Systematic sampling, Cluster

sampling and Multi stage sampling. Criteria of unbiasedness, consistency, efficiency and sufficiency,

Cramer-Rao Inequality, minimum variance unbiased (MVU) estimation

Unit III: Hypothesis testing, general procedure and errors in hypothesis testing, hypothesis testing for population parameters with large and small samples, Hypothesis testing based on F-distribution and t-distribution. Chi-Square test for goodness of fit, chi-square test for population variances, chi-square test for association. Unit IV: Analysis of variance, assumptions for ANOVA test, ANOVA for one-way and two-way classified data. Non-parametric inference, advantages of non-parametric methods over parametric methods, one-sample problem, Sign Test, Wilcoxon-Signed rank test, Kolmogrove Smirnov test, General Two Sample Problem: Wilcoxon-Mann- Whitney Test, Kolmogrov-Smirnov two sample test (for samples of equal size), median test. Textbook: An Introduction to probability Theory and Mathematical Statistics by V.K. Rohtagi and Saleh Supplementary Texts:

A First Course on Parametric Inference, Narosa Publishing by Kale, B.K. (1999)

Applied non parametric statistical methods, second edition by H.C. Tuckwll.

Business Mathematics & Statistics’, Asian Books Private Ltd. By Verma A.P.

Fundamentals of Mathematical Statistics by S.C. Gupta

Fundamentals of Statistics by Ellance D N, Veena Elhance & Aggarwal B. M, Kitab Mahal.

Linear Statistical Inference and its Applications by C.R. Rao

New Mathematical Statistics ( A Problem-Oriented First Course) by Sanjay Arora and Bansi Lal

Non-Parametric Statistical Inference. By Marcel Decker and J.D. Gibbons (1985)

Schaum’s Outline Statistics by Murrey, R.I, Larry J, Stephens and Narinder Kumar (2010), Fourth Editions: Tata McGraw Hill Pvt. Ltd.

Theory of Point Estimation (Student Edition) by Lehman, E.L. (1986)

23


Course Title : Optimization Semester-V


Credit hrs. : 5 UNIT-I:

Linear programming; concept and uses of linear programming, formulation of linear programming

problem. Solution of LP problem- graphical method, simplex method. Duality in Linear Programming ,

Properties of the primal-dual pair- Dual simplex Method

UNIT II: Transportation and Assignment problems: Formulation of transportation and assignment

problems as linear programs. Methods of obtaining the initial basic feasible solution to a transportation

problem. Solution of the Transportation problem by MODI Method. Unbalanced transportation

problems and their solutions. Degeneracy in Transportation problem and its resolution. Solution of

Assignment Problem by Hungarian Method. Traveling salesman problem as an assignment problem

(Formulation only).

UNIT III Sequencing problems- problems with n jobs and 2 machines, problems with n jobs and k machines.

Games and Strategies: Two person zero-sum games, Maximin-Minimax Principle, Mixed Strategies, Solution of

2 and m games.

UNIT IV Deterministic Inventory Systems: The components of an inventory system, Demand

and replenishment pattern. The Problem of EOQ with uniform demand and several production runs of

unequal length. The problem of EOQ with finite rate of replenishment. The problem of EOQ with

shortages.

UNIT-V: Concept of PERT/CPM networks, estimating the activity time, determination of earliest

expected and latest allowable times, determination of critical path Drawing network diagram, probability

consideration in PERT networks PERT/CPM- cost analysis, applications of PERT/CPM. Simulation:

meaning & uses; Monte Carlo method, random number generation, waiting line simulation model.

Books Recommended:

1. Gass, S.I.: Linear Programming-Methods & Applications.

2. Hillier & Liberman: Introduction to Operations Research, Mc. Graw Hill Book Co.

3. Taha, H.A.: Operations Research-An introduction, Pentice Hall of India Pvt. Ltd. New

Delhi. (7th Edition-2003)

4. Swaroop K, Gupta, P.K. & Mohan, M.: Operations Research, Sultan Chand & Sons, New

Delhi.

5. Vohra, N D: ‘Quantitative Techniques in Management’ Tata McGraw Hill

6. Sharma S.D.: ‘Operational Research’, Kedar Nath Ram Nath and Co., Meerut

7. Kothari C R: ‘Quantitative Techniques’ Vikas Publishing House.

8. Bicrman, H., C.P. Bonini & W.H. Hausman: ‘Quantitative Analysis for Business Decisions,

Homewood, Illions: Rechard D, Irwin Inc.

9. Gordon, R.L. and I. Pressman: ‘Quantitative Decisions making for Business’, Prentice Hall Inc.

10. Kwas, N.K.: ‘Mathematical Programming with Business Applications’, McGraw Hill, New York.

24


Course Title : Introduction to Numerical Methods Semester-V


Credit hrs. : 4

Unit I: Solutions of equations, Newton’s method, interpolation, Lagrange interpolation; Divided

differences, interpolation formulas using differences, Numerical differentiation and integration

Unit II: Ordinary differential equations: Euler method, single-step methods, Runge-Kutta’s method;

multi-step methods, methods based on numerical integration and differentiation, boundary value

problems.

Unit III: Approximations: Different types of approximations, least squares polynomial approximation;

polynomial approximation, approximation with trigonometric functions, exponential functions, rational

functions.

Unit IV: Monte Carlo Methods: Random number generation; statistical tests of pseudo-random

numbers; random variate generation, inverse transform method, composition method, acceptance

rejection method, generation of exponential, normal, binomial and Poisson variates, examples of

applications.

Textbooks: Numerical Methods, Problems and Solutions by Jain, Iyengar and Jain


Introduction to numerical Analysis by C.E. Froberg

Numerical Analysis – A Practical Approach by M. Maron

Simulation and Monte Carlo Methods by R.Y. Rubenstein

Numerical Methods by Burda and Faires. Thomson Brooks/Cole

25


Course Title : Abstract Algebra Semester-V


Credit hrs. : 4

Unit I: Groups, subgroups, examples, cyclic groups and their subgroups, cosets and Lagrange’s

theorem, product of two subgroups

Unit II: Normal subgroups, quotient groups, homomorphism and isomorphism and related theorems,

permutation groups, even and odd permutations, symmetric groups, alternating groups, Cayley’s

theorem

Unit III: Rings and fields, examples, subrings and subfields, ring homomorphism, ideals and quotient

rings

Unit IV: Polynomial rings, characterization of a ring, prime and maximal ideal and their

characterization in terms of the associated quotient ring.

Textbook: Topics in Algebra by I.N. Herstein


Elements of Modern Abstract Algebra by Kenneth Miller

Algebra by Serge Lang

Topics in Algebra by I.N. Herstein

Modern Algebra by Frank Ayres, Schaum’s Outlines Series

A Textbook of Modern Algebra by Shanti Narayan

Modern Algebra by Q. Zameer-u-din & S. Singh

Introduction to Abstract Algebra by Fraleigh , Addison Wesley

Introduction to Abstract Algebra by Gallian , Houghton Mifflin Harcourt (HMH)

26


Course Title : Models Semester-VI


Credit hrs. : 5

Unit I: Concept of a stochastic process, counting process, discrete and continuous time processes, mixed

process, examples and applications of mixed processes. Transition probability matrices, classification of

states, Markov property, Markov chains with stationary transition probabilities, some Markov Chain

Models, Chapman-Kolmogorov equations;

Unit II: Markov process, Kolmogorov equations for Markov process, Poisson process, birth and death

processes,

Unit III: Survival models, sickness and marriage models in terms of Markov processes, force of

mortality, hazard rate. Actuarial symbols and and integral formulas, Gompertz-Makeham laws of

mortality, life tables

Unit IV: Lifetime distributions and estimation, Failure rate, mean residual life and their elementary

properties, types of censoring, Estimation of survival function, Kaplan-Meier estimate, Nelson-Aalen

estimate and their applications, Semi-parametric regression for failure rate, Cox proportional hazard

model

Recommended Textbooks:

Stochastic Processes by Sheldon Ross

A First Course in Stochastic Processes by Karlin and Taylor

An Introduction to Stochastic Modeling by Karlin and Taylor

Stochastic Processes by J. Medhi

Stochastic Models: Analysis and Application by B.R. Bhat

Cox, D.R. and Oakes, D., Analysis of Survival Data, Chapman and Hall, New York.

Gross A.J. and Clark, V. A., Survival Distributions: Reliability, Applications in the Biomedical

Sciences, John Wiley and Sons.

Elandt - Johnson, R.E. Johnson N.L., Survival models and Data Analysis, John Wiley and Sons

Miller, R.G., Survival Analysis (Wiley)

Zacks, S., Reliability

Deshpande, J.V. and Purohit S.G., Life-Time Data: Statistical Models and Methods , World

Scientific Book Publishing

Actuarial Mathematics, Bowers et al, Society of Actuaries, USA

27


Course Title : Insurance Semester-VI


Credit hrs. : 4

Insurance and Risk Management (MTH602)

Unit -1. Concept and nature of insurance , purpose and need of insurance ,specific principles of

insurance ,General principles or essentials of insurance contract, miscellaneous principles of insurance.

Re-insurance ,co-insurance ,assignments. Recent developments in insurance.

Unit-2. Concept of risk ,types of risk, sources and measurement of risk, risk evaluation and prediction.

Risk retention and risk transfer. Pooling in insurance: concept, forms of pooling ,costs and benefits of

pooling. Introduction to mutual funds and pension funds.

Unit-3. General insurance : Motor, marine, fire, miscellaneous .Life insurance: clauses in life policy,

types (whole life ,endowment, annuity, term, joint policy)

Unit-4. Control of mal-practices, negligence, loss assessment and loss control, exclusion of perils,

actuaries, computation of insurance premium.

Role, power, and functions of IRDA, LIC, and GIC.

Suggested Readings:

1. Dinsale, W.A:Elements of Insurance, Pitman.

2. Hubner, S.S and Keneth Black: Life Insurance.

3. Majumdar, P.I and Diwan, M.G:Principles of Insurance, Insurance of India, Mumbai.

4. Sharma,R.s:Insurance: Principles and Practice, Vora Publications, New Delhi.

5. George, E. Rejda, Principles of Risk Management and Insurance, Pearson Education.

6. Gupta. P.K, Insurance and Risk Management, Himalaya Publishing House.

7. Mishra, M. N., Principles and Practices of Insurance, S. Chand and Sons.

8.Principles of Insurance: IC-01 Insurance Institute of India.

28


Course Title : Financial Derivatives Semester-VI


Credit hrs. : 4

Unit I: Forward Contracts-Future Contracts-Settlement –Regulation Standardization-Options-Interest

Rates and Bond Prices-Zero Coupon Bond Prices-Discretely and continuously compounded interest

rates.

Unit II: Asset-Price Dynamics-Lognormal Distribution-The Bi-nominal approximation to the

Lognormal Distribution-Stochastic Differential Equation Representation- Complications-Lognormal

Distribution, Continuous Trading, Continuously Changing Prices.

Unit III: Binomial Pricing Model- Single Period Example- Multi period Example- Constructing

Synthetics Option- Risk Neutral Valuation- Hedge Ratio (Delta), Lattice Parameters- Replicating an

option on spot with Future.

Unit IV: Black-Scholes Model, Continuous Time Representative of Stock Price Changes- Ito’s

Lemma- The Equivalent Martingale Probability Distribution- Hedging-Option Strategies- Partial

Differences Equations.

Unit V: SWAPS-Interest Rate Swaps-Pricing, Warehousing, Valuation, Par Swaps, Variants-Foreign

Currency Swaps- Valuation- Commodity Swaps- Valuation and Variants- Equity Swaps- Valuation and

Variants.

Suggested Reading:

Bhalla, V.K. Investment Management: Security analysis and Portfolio Management, New Delhi,

S. Chand, 2001.

Brennet, M. Option Pricing: Theory and Applications. Toronto, Lexington Books, 1993.

Cox John C and Rubinstein, Mark Options Markets, Englewood Cliffs, New Jerxey, Prentice

Hall Inc., 1985.

Huang, Stanley S.C. and Randall, Maury R. Investment Analysis and Management. London,

Allyn and Bacon, 1987.

Hull, John C. Options, Futures and other Derivative Securities. 2nd

ed. New Delhi, Prentice Hall

of India., 1996.

Sharpe, William F. et al. Investment, New Delhi, Prentice Hall of India, 1997.

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