Syllabus of Madhya Pradesh Bhoj Open University BCA - BCA03 Computer Mathematics

Syllabus effective from 2004-05 session

Unit-I

Set Theory: The Concept of a Set, Notations, Representation of a Set, Types of Sets, Theorem on Subsets, Number of Subsets of a Set, Venn Diagram, Set Operations, Laws of Union of sets, Laws of Intersection of Sets, Law of Complement of a Set, Theorem (on Symmetric Difference) De-Morgan’s Laws, Applications of Venn Diagrams

Relations & Functions: Ordered Pairs, Equality of Ordered Pairs, Cartesian Product of Sets, Theorems on Cartesian Products’ Relation, Domain and Range of a Relation, Inverse Relation, The Inverse of an Inverse Relation, Binary (or Dyadic) relations ­, Type of Relations, Equivalence Relations, Equivalence Class, Properties of Equivalence Classes Composition of Two Relations, Partition of a Set, Partial Order, Theorem, Functions (Mapping), Types of Mapping, Other Specific Mappings, Types of Binary Operations, Algebraic Structure, Graph of a Function, Real Valued Map., Product of Functions, Method of Construction of Operation Table Countable and-Uncountable Sets

Unit - II

Group Theory: Introduction-Algebraic Structures, Groups: Definition, Abelian Group, Order of a Group, Semi-group, Some General Properties of Groups, Some Important Theorems on Groups, Theorem on Subgroups, Homomorphism (Definition), Isomorphism (Definition), Theorems on Homomorphism, Definition (Kernel of f), Theorems on Homomorphism, Definition (Cyclic Groups), Fundamental Theorem of Homomorphism
Rings and Fields: Quotient Spaces, Rings in General, Some Special Classes of Rings, Field and its Axioms, Sub-ring and Sub-fields

Unit-III

Vector Space: Definition, Linear Combination, Linear Independence and linear Dependence, Basis of Vector Space, Vector Space of linear Transformation, Linear Algebra, Algebra of Quaternions

Arithmetic Progression: Sequence, Series, Arithmetic Progression, The General Term or Nth Term of an AP., The Sum of n terms of an AP., Arithmetic Mean, AM. Of two Given Numbers, Insertion of N AM. Between Two Given Numbers Properties of A P.

Geometric Progression: Definition, The Nth Term of G.P., The Sum of N Terms of a G.P., The Sum of an Infinite G.P., Recurring Decimal an Infinite G.P., Geometric Means, Geometric Mean of Two Given Numbers A And B Insertion of N Geometric Means Between Two Quantities Properties of G.P., To Find the Sum of N Terms of the Series

Unit-IV

System of Measuring Angles: Trigonometric Functions: Rectangular Coordinate System, Trigonometric Ratios (of an angle), Trigonometric Functions of Actual Angles, Co-Functions and Trigonometric Functions of Complementary Angles, Fundamental Relations Involving One Angle, Limits to the Values of Trigonometric Functions

Trigonometric Functions of Some Special Angle: Trigonometric Functions of 45. , Trigonometric Functions of Quadrantal Angles

Unit-V

Limit and Continuity: Differentiability, Elementary, Differentiation: Standard Forms, Successive Differentiation, Maxima & Minima.

Coordinate Geometry: Coordinate Lengths of Straight Lines and Areas of Triangles , Differentiation of Vector Functions, Gradient, Divergence and Curl