BCA MATHS

5th semester

BCA THIRD SEMESTER

DISCRETE METHAMATICS STRUCTURES

Module -I
Sets and Subsets, Operations on Sets, Characteristics functions, Properties of Integers.

Module -II
Propositions and Logical Operations, Conditional Statements, Methods of Proof, Mathematical Induction.

Module -III
Permutations, Combinations, Pigeonhole Principles, Recurrence Relations.

Module -IV
Product Sets and Partitions, Relations and Digraphs, Paths in Relations and Digraphs, Properties of Relations, Equivalence Relations, Operations of Relations.

Module -V
Functions, Growth of Functions, Permutation Functions.

Module -VI
Partially Ordered Sets, External Elements of Partially Ordered Sets, Lattices.

Module -VII
Binary Operations, Semigroups, Groups, Other Mathematical Structures – Rings, Fields.

BCA SECOND SEMESTER

Module -I
Set Theory: Introduction, Venn Diagram, Algebra of sets, Cardinal number of set, Cartesian product.

Module -II
Relations: Relation, Inverse Relation, Composition of relation, Equivalence of relations and Classes.

Module -III
Functions and Binary Operations: Functions as a set, Representation of function, Types of Functions, Functions applicable in Computer Science: Integer function, Factorial function, Absolute, Characteristic, Floor, Ceiling, Remainder, Boolean, Exponential, Logarithmic, Hashing functions and Binary operation on a set.

Module -IV
Abstract Algebra: Group, Subgroup, Order of group, Cyclic group and Simple theorems, Ring, Integral domain, Field and Simple theorem related to Integral domain and field.

Module -V
Linear Algebra: Vector spaces, Subspaces, Span of a set, Linear Dependence, Independence, Dimension and Basis, Linear Transformation: Definition and example, Range and Kernel of a Linear map, Rank and Nullity.

Module -VI
Matrix Algebra: Elementary Transformation, Elementary matrices, Inverse of a matrix by Row operation, Rank of matrix by Echelon form, Solution of a System of Linear Simultaneous equation by matrix method, Eigen valve and Eigen vector, Caley Hamilton theorem (without proof), to find the inverse of a non singular matrix using Caley-Hamilton theorem.

Module -VII
3D Coordinate Geometry: Cylindrical, Spherical Co-ordinate Systems, Distance formula, Direction Cosines, Direction rations, Projections, Plane, Different form of planes with simple treatment, Shortest distance between two skew lines, Equation of sphere, Tangent plane at a point on the sphere.