Draft syllabus for b. A/B. Sc. (Honours) in mathematics under Choice Based Credit System (cbcs) Effective from the academic session 2017-2018 sidho-kanho-birsha university purulia-723104 West Bengal

Reference Books

10. 
    Titu Andreescu and Dorin Andrica, Complex Numbers from A to Z, Birkhauser, 2006.
    
11. 
    Edgar G. Goodaire and Michael M. Parmenter, Discrete Mathematics with Graph Theory, 3rd Ed., Pearson Education (Singapore) P. Ltd., Indian Reprint, 2005.
    
12. 
    David C. Lay, Linear Algebra and its Applications, 3rd Ed., Pearson Education Asia, Indian Reprint, 2007.
    
13. 
    K.B. Dutta, Matrix and linear algebra.
    
14. 
    K. Hoffman, R. Kunze, Linear algebra.
    
15. 
    W.S. Burnstine and A.W. Panton, Theory of equations.
    
16. 
    S.K,Mapa, Higher Algebra (Classical).
    
17. 
    S.K,Mapa, Higher Algebra (Linear and Abstract).
    
18. 
    Friedberg, Insel and Spence, Linear Algebra.
    

GE3– Differential Equations and Vector Calculus [Credit: 1+5]
Unit 1 [Credit: 3]

Lipschitz condition and Picard’s Theorem (Statement only). General solution of homogeneous equation of second order, principle of super position for homogeneous equation, Wronskian: its properties and applications, Linear homogeneous and non-homogeneous equations of higher order with constant coefficients, Euler’s equation, method of undetermined coefficients, method of variation of parameters.

Systems of linear differential equations, types of linear systems, differential operators, an operator method for linear systems with constant coefficients, Basic Theory of linear systems in normal form, homogeneous linear systems with constant coefficients: Two Equations in two unknown functions.
Equilibrium points, Interpretation of the phase plane

Power series solution of a differential equation about an ordinary point, solution about a regular singular point.

Unit 2 [Credit: 2]

Triple product, introduction to vector functions, operations with vector-valued functions, limits and continuity of vector functions, differentiation and line integration of vector functions, Surface and volume integration [Gauss’s theorem, Green’s theorem, Stoke’s theorem (proof not required)].

Graphical Demonstration (Teaching Aid)

1. Plotting of family of curves which are solutions of second order differential equation.

2. Plotting of family of curves which are solutions of third order differential equation.
Reference Books

12. 
    Belinda Barnes and Glenn R. Fulford, Mathematical Modeling with Case Studies, A Differential Equation Approach using Maple and Matlab, 2nd Ed., Taylor and Francis group, London and New York, 2009.
    
13. 
    C.H. Edwards and D.E. Penny, Differential Equations and Boundary Value problems Computing and Modeling, Pearson Education India, 2005.
    
14. 
    S.L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, India, 2004.
    
15. 
    Martha L Abell, James P Braselton, Differential Equations with MATHEMATICA, 3rd Ed., Elsevier Academic Press, 2004.
    
16. 
    Murray, D., Introductory Course in Differential Equations, Longmans Green and Co.
    
17. 
    Boyce and Diprima, Elementary Differential Equations and Boundary Value Problems, Wiley.
    
18. 
    G.F.Simmons, Differential Equations, Tata Mc Graw Hill
    
19. 
    Marsden, J., and Tromba, Vector Calculus, McGraw Hill.
    
20. 
    Maity, K.C. and Ghosh, R.K. Vector Analysis, New Central Book Agency (P) Ltd. Kolkata (India).
    
21. 
    M.R. Speigel, Schaum’s outline of Vector Analysis
    
22. 
    P.R.Ghosh and J.G.Chakraborty, Vector Calculus.
    

GE4 – Numerical Methods & Computer Programming [Credit: 1+5]

Unit 1 [Credit: 3]

Algorithms. Convergence. Errors: Relative, Absolute. Round off. Truncation.

Transcendental and Polynomial equations: Bisection method, Newton’s method, Secant method, Regula-falsi method, fixed point iteration, Newton-Raphson method. Rate of convergence of these methods.

System of linear algebraic equations: Gaussian Elimination and Gauss Jordan methods. Gauss Jacobi method, Gauss Seidel method and their convergence analysis. LU Decomposition

Interpolation: Lagrange and Newton’s methods. Error bounds. Finite difference operators. Gregory forward and backward difference interpolation.

Numerical differentiation: Methods based on interpolations, methods based on finite differences.

Numerical Integration: Newton Cotes formula, Trapezoidal rule, Simpson’s 1/3rd rule, Simpsons 3/8th rule, Weddle’s rule, Boole’s Rule. Midpoint rule, Composite Trapezoidal rule, Composite Simpson’s 1/3rd rule, Gauss quadrature formula.

The algebraic eigenvalue problem: Power method.

Approximation: Least square polynomial approximation.

Ordinary Differential Equations: The method of successive approximations, Euler’s method, the modified Euler method, Runge-Kutta methods of orders two and four.

Unit 2 [Credit: 2]

Introduction: Basic structures, Character set, Keywords, Identifiers, Constants, Variable-type declaration

Operators: Arithmetic, Relational, Logical, assignment, Increment, decrement, Conditional. Operator precedence and associativity, Arithmetic expression,

Statement: Input and Output, Define, Assignment, User define, Decision making (branching and looping) – Simple and nested IF, IF – ELSE, LADDER, SWITCH, GOTO, DO, WHILE – DO, FOR, BREAK AND CONTINUE Statements. Arrays- one and two dimensions, user defined functions,

References

7. 
   Xavier, C., C Language and Numerical Methods, (New Age Intl (P) Ltd. Pub.)
   
8. 
   Gottfried, B. S., Programming with C (TMH).
   
9. 
   Balaguruswamy, E., Programming in ANSI C (TMH).
   
10. 
    Scheid, F., Computers and Programming (Schaum’s series)
    
11. 
    Jeyapoovan, T., A first course in Programming with C.
    
12. 
    Litvin and Litvin, Programming in C++.
    

7. 
   Brian Bradie, A Friendly Introduction to Numerical Analysis, Pearson Education, India, 2007.
   
8. 
   M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientific and Engineering
   
9. 
   Computation, 6th Ed., New age International Publisher, India, 2007.
   
10. 
    C.F. Gerald and P.O. Wheatley, Applied Numerical Analysis, Pearson Education, India, 2008.
    
11. 
    Uri M. Ascher and Chen Greif, A First Course in Numerical Methods, 7th Ed., PHI Learning Private Limited, 2013.
    
12. 
    John H. Mathews and Kurtis D. Fink, Numerical Methods using Matlab, 4th Ed., PHI Learning Private Limited, 2012.
    
13. 
    Scarborough, James B., Numerical Mathematical Analysis, Oxford and IBH publishing co.
    
14. 
    Atkinson, K. E., An Introduction to Numerical Analysis, John Wiley and Sons, 1978.
    
15. 
    YashavantKanetkar, Let Us C , BPB Publications.
    

Skill Enhancement Subjects Syllabus

SE1- Logic and Sets

Introduction, propositions, truth table, negation, conjunction and disjunction. Implications, biconditional propositions, converse, contra positive and inverse propositions and precedence of logical operators. Propositional equivalence: Logical equivalences. Predicates and quantifiers: Introduction, Quantifiers, Binding variables and Negations.

Sets, subsets, Set operations and the laws of set theory and Venn diagrams. Examples of finite and infinite sets. Finite sets and counting principle. Empty set, properties of empty set. Standard set operations. Classes of sets. Power set of a set.

Difference and Symmetric difference of two sets. Set identities, Generalized union and intersections. Relation: Product set. Composition of relations, Types of relations, Partitions, Equivalence Relations with example of congruence modulo relation. Partial ordering relations, n- ary relations.

Reference Books

1. 
   R.P. Grimaldi, Discrete Mathematics and Combinatorial Mathematics, Pearson Education, 1998.
   
2. 
   P.R. Halmos, Naive Set Theory, Springer, 1974.
   
3. 
   E. Kamke, Theory of Sets, Dover Publishers, 1950.
   

SE2- Object Oriented Programming in C++

Programming paradigms, characteristics of object oriented programming languages, brief history of C++, structure of C++ program, differences between C and C++, basic C++ operators, Comments, working with variables, enumeration, arrays and pointer.

Objects, classes, constructor and destructors, friend function, inline function, encapsulation, data abstraction, inheritance, polymorphism, dynamic binding, operator overloading, method overloading, overloading arithmetic operator and comparison operators.

Template class in C++, copy constructor, subscript and function call operator, concept of namespace and exception handling.

Reference Books

1. 
   A. R. Venugopal, Rajkumar, and T. Ravishanker, Mastering C++, TMH, 1997.
   
2. 
   S. B. Lippman and J. Lajoie, C++ Primer, 3rd Ed., Addison Wesley, 2000.
   
3. 
   Bruce Eckel, Thinking in C++, 2nd Ed., President, Mindview Inc., Prentice Hall.
   
4. 
   D. Parasons, Object Oriented Programming with C++, BPB Publication.
   
5. 
   Bjarne Stroustrup, The C++ Programming Language, 3rd Ed., Addison Welsley.
   
6. 
   E. Balaguruswami, Object Oriented Programming In C++, Tata McGrawHill
   
7. 
   Herbert Scildt, C++, The Complete Reference, Tata McGrawHill.
   

SE3-Graph Theory

Definition, examples and basic properties of graphs, pseudo graphs, complete graphs, bi‐partite graphs isomorphism of graphs.

Eulerian circuits, Eulerian graph, semi-Eulerian graph, theorems, Hamiltonian cycles,theorems

Representation of a graph by matrix, the adjacency matrix, incidence matrix, weighted graph,

Travelling salesman’s problem, shortest path, Tree and their properties, spanning tree, Dijkstra’s algorithm, Warshall algorithm.

Reference Books

1. 
   B.A. Davey and H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
   
2. 
   Edgar G. Goodaire and Michael M. Parmenter, Discrete Mathematics with Graph Theory, 2nd Edition, Pearson Education (Singapore) P. Ltd., Indian Reprint 2003.
   
3. 
   Rudolf Lidl and Gunter Pilz, Applied Abstract Algebra, 2nd Ed., Undergraduate Texts in Mathematics, Springer (SIE), Indian reprint, 2004.
   

SE4-Operating System: Linux

Linux – The Operating System: Linux history, Linux features, Linux distributions, Linux’s relationship to Unix, Overview of Linux architecture, Installation, Start up scripts, system processes (an overview), Linux Security.

The Ext2 and Ext3 File systems: General Characteristics of The Ext3 File system, file permissions. User Management: Types of users, the powers of Root, managing users (adding and deleting): using the command line and GUI tools.

Resource Management in Linux: file and directory management, system calls for files Process

Management, Signals, IPC: Pipes, FIFOs, System V IPC, Message Queues, system calls for processes, Memory Management, library and system calls for memory.

Reference Books

1. 
   Arnold Robbins, Linux Programming by Examples The Fundamentals, 2nd Ed., Pearson Education, 2008. Cox K, Red Hat Linux Administrator’s Guide, PHI, 2009.
   
2. 
   R. Stevens, UNIX Network Programming, 3rd Ed., PHI, 2008.
   
3. 
   Sumitabha Das, UNIX Concepts and Applications, 4th Ed., TMH, 2009.
   
4. 
   Ellen Siever, Stephen Figgins, Robert Love, Arnold Robbins, Linux in a Nutshell, 6th Ed., O'Reilly Media, 2009.
   
5. 
   Neil Matthew, Richard Stones, Alan Cox, Beginning Linux Programming, 3rd Ed., 2004.
   

Syllabus for AEL1-to be done

Syllabus for AEL1 -to be done