Course Title : Calculus-1 Course Code : MTH-101 Credit hrs. : 5

Semester-1

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

1

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Computer Fundamentals Course Code : CS101 Credit hrs. : 3+1

Semester-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"

2

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Professional Communication Course Code : ENG-101 Credit hrs. : 4

Semester-1

Unit-I: Essentials of communication : Communication, its significance & Role The process of communication, Barriers to communication. Methods of communication, verbal & nonverbal 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, Multiperspective debates, how to write and present papers, resume writing. Unit-IV: Reading comprehension, Prйcis 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

3

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Management Process Course Code : MTH111 Credit hrs. : 4

Semester-1

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".

4

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Calculus-II Course Code : MTH-201 Credit hrs. : 4

Semester-1I

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 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

5

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Introduction to Actuarial Mathematics Course Code : MTH-202 Credit hrs. : 5

Semester-1I

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.

6

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Fundamentals of Accounting Course Code : MTH211 Credit hrs. : 5

Semester-1I

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

7

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Environmental Studies Course Code : MTQGE01 Credit hrs. : 4

Semester-1I

Unit I Introduction to Environmental Science: Scope and importance, environmental ethicsAnthropocentricism 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.

8

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Excel for Business Course Code : MTH-210 Credit hrs. : 2

Semester-1I

Course Contents

Learning Objectives 1 Excel Basics 2 Developing charts in Excel 3 Some useful functions 4 Interest and Amortization 5 Data Handling Wizards 6 Data Handling Functions 7 Cash Flow Analysis 8 Sensitivity Analysis 9 Optimization 10 Linear Regression 11 Exploring Data 12 Visual Basic for Applications (VBA)

Excel Topics Naming Cells and Ranges, Descriptive statistics functions, Display options (Custom views, Freeze panes) Bar chart, Stacked bar chart, line chart, dynamic charting (this uses the OFFSET function) IF, SUMIF, SUMIFS, COUNTIF, COUNTIFS, COUNT, COUNTA FV, PV, PMT, PPMT, IPMT, RATE, NPER Sort, Filter, Text-to-Columns, Remove Duplicates, Consolidate, Data Validation. VLOOKUP, HLOOKUP, text functions, MATCH, INDEX NPV, XNPV, IRR, XIRR, GOAL SEEK Data Tables and Scenario Manager Using the SOLVER add-in to solve some important problems in Finance and the industry. LINEST, STEYX, INTERCEPT,SLOPE, FORECAST, TREND, ANALYSIS TOOLPAK Add-in Pivot table and Pivot Chart VBA can tackle situations that an analyst faces in his routine work for which Excel does not have a `readymade' answer.

Textbooks: Excel 2007 for Starters by M. McDonald. Analyzing Business Data with Excel by G. Knight Mathematical Modeling with Excel by B. Albright.

9

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Vector Calculus Course Code : MTH-301 Credit hrs. : 4

Semester-III

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: A First Course in Calculus - by Serge Lang, Calculus by Howard Anton, Textbook of Calculus - by Larson and Edwards, Schaum's Outline of Vector Analysis, Calculus I & II by Tom Apostol

10

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Linear Algebra Course Code : MTH-302 Credit hrs. : 4

Semester-1II

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

11

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Mathematics and Art Course Code : MTH-303 Credit hrs. : 4

Semester-1II

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

12

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Introduction to Concepts of Peace and Conflict Course Code : PSGE01 Credit hrs. : 4

Semester-1II

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 intrapersonal, 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

13

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 14

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Principles of Economics Course Code : MTH311 Credit hrs. : 4

Semester-1II

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

15

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Probability Theory Course Code : MTH-401 Credit hrs. : 5

Semester-1V

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.

16

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : differential equations Course Code : MTH-402 Credit hrs. : 4

Semester-1V

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 Supplementary books: 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

17

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Real Analysis Course Code : MTH-403 Credit hrs. : 4

Semester-1V

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)

18

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Financial Management Course Code : MTH411 Credit hrs. : 4

Semester-1V

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

19

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Programming Concepts Course Code : CS401 Credit hrs. : 2+2

Semester-1V

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. 20

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. 21

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Statistics Course Code : MTH-501 Credit hrs. : 5

Semester-V

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 tdistribution. 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)

22

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Optimization

Semester-V

Course Code : MTH-505

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.

23

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Introduction to Numerical Methods Course Code : MTH-503 Credit hrs. : 4

Semester-V

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

Supplementary texts: 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

24

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Abstract Algebra Course Code : MTH-504 Credit hrs. : 4

Semester-V

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 Supplementary texts: 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)

25

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Models Course Code : MTH-601 Credit hrs. : 5

Semester-VI

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

26

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Insurance Course Code : MTH-602 Credit hrs. : 4 Insurance and risk management (MTH602)

Semester-VI

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.

27

B.Sc. ACTUARIAL AND FINANCIAL MATHEMATICS

Course Title : Financial Derivatives Course Code : MTH-604 Credit hrs. : 4

Semester-VI

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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