Syllabus:
BASICS:
i) Elementary complexity motivation, concrete complexity, big O notation.
ii) Integer representation, swtisions, values and variables, types, lvalue, rvalue, unary, binary, ternary operations.
iii) Numerical errors due to data representations and machine precision. Approximation and error analysis. Illustration through examples.
iv) Linux tools. Introduction to shell programming.
COMPUTING:
i) Fundamentals of Computing, Historical perspective, Early computers. Computing machine. Problems, Pseudo-code and flowcharts. Memory, Variables, Values, Instructions, Programs.
INTRODUCTION TO C:
i) The language of C: Phases of developing a running computer program in C
ii) Data concepts in C: Constants, Variables, Expressions, Operators, and operator precedence in C
iii) Statements: Declarations, Input-Output Statements, Compound statements, Selection Statements. Conditions, Logical operators, Precedences. Repetitive statements, While construct, Do-while Construct, For construct.
iv) Conditionals, if-then, if-then-else, nested conditionals, switch-case. Loops, for, while, repeat, loop invariants, precondition, postcondition.
v) Data types, size and values. Char, Unsigned and Signed data types. Number systems and representations. Constants, Overflow.
vi) Arrays. Strings. Multidimensional arrays and matrices.
FUNCTIONS, RECURSIONS, SORTING AND SEARCH:
i) The prototype declaration, Function definition
ii) Function call: Passing arguments to a function, by value, by reference. Scope of variable names. Recursive function calls, Tail recursion. Analysing recursion, Tree of recursion, linear recursion
iii) Sorting problem: Selection Sort, Insertion Sort, Comparison between sorting algorithms. Sorting in multidimensional arrays. Sorting in strings.
IV) Search problem: Linear search and binary search. Comparison between search procedures. Recursive and Iterative formulations.
DATA TYPES IN C:
i) Pointers: Pointer variables. Declaring and dereferencing pointer variables. Pointer Arithmetic. Examples. Accessing arrays through pointers. Pointer types, Pointers and strings. String operations in C.
ii) Structures in C: Motivation, examples, declaration, and use. Operations on structures. Passing structures as function arguments. type defining structures.
iii) Self-referential structures. Dynamic Data Structures. Linked Lists. Examples
iv) File input-output in C. Streams. Input, output and error streams. Opening, closing and reading from files. Programming for command line arguments
Reference Texts:
(a) O J Dahl, E W Dijkstra, C A R Hoare: Structured Programming
(b) David Gries: The Science of Programming
(c) E W Dijkstra: A Short Introduction to the Art of Programming
(d) Dromey: How to solve it by Computer
(e) Goodrich: Data Structures and Algorithms in Java
(f) Thomas A Standish: Data Structures in Java.
https://www.isibang.ac.in/~adean/infsys/database/Bmath/FCP.html
- Teacher: Veena Gadad
Syllabus:
Homogeneous and non-homogeneous systems of linear equations, condition for consistency, solution set as a translate of a subspace.
Vector spaces, subspaces, linear independence, span, basis and dimension, sum and intersection of subspaces, direct sum, complement and projection.
Linear transformation and its matrix with respect to a pair of bases, properties of matrix operations, use of partitioned matrices.
Column space and row space, rank of a matrix, nullity, rank of AA*.
g-inverse and its elementary properties, left inverse, right inverse and inverse, inverse of a partitioned matrix, lower and upper bounds for rank of a product, rankfactorization of a matrix, rank of a sum. Elementary operations and elementary matrices, Echelon form, Normal form, Hermite canonical form and their use in solving linear equations and in finding inverse or g-inverse. LDU-decomposition.
Note: The field of scalars should be assumed to be subfields of complex numbers, i.e., subsets closed under addition, subtraction, multiplication and division by a nonzero number. The main examples to be considered should be the field of real, complex or rational numbers.
Reference Texts:
(a) C. R. Rao: Linear Statistical Inference and its Applications.
(b) A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
(c) K. Hoffman and R. Kunze: Linear Algebra.
(d) F. E. Hohn: Elementary Matrix Algebra.
(e) P. R. Halmos: Finite Dimensional Vector Spaces.
(f) S. Axler: Linear Algebra Done Right!
(g) H. Helson: Linear Algebra. R Bapat: Linear Algebra and Linear Models.
(i) R. A. Horn and C. R. Johnson: Matrix Analysis.
(j) M. Artin: Algebra.
https://www.isibang.ac.in/~adean/infsys/database/Bmath/LAlg1.html
- Teacher: Pankaj Dey
- Teacher: Suresh Nayak