Discrete Mathematics & Linear Algebra [BCA -504] Syllabus BCA 5th-V Sem Syllabus for DAVV Indore Affiliated Institutions

 DEVI AHILYA VISHWAVIDYALAYA (DAVV), INDORE

Bachelor Of Computer Applications (BCA) (Full-Time) 
Fifth-5th-v Semester Curriculum/ Syllabus 2011-12 Academic Year Onwards

Discrete Mathematics & Linear Algebra – Syllabus

   

Discrete Mathematics & Linear Algebra [BCA – 504] Syllabus /Course contents

Max.Marks:50

Min.Marks:17

UNIT –I

ALGEBRA OF LOGIC:

Recall of Statements & Logical Connectives, Tautologies & Contradictions, Tautologies & Contradictions, Logical Equivalence, Algebra of Propositions, Quantifiers, Universal & Existential Quantifiers.

BOOLEAN ALGEBRA :

Boolean Algebra and its Properties, Algebra of Propositions, De- Morgan’s Laws, Algebra of Electric Circuits & Its Application, Design of Simple Automatic Control System.

UNIT – II

BOOLEAN FUNCTION OF FUNDAMENTAL FORMS :

Boolean Function – Disjunction and Conjunction Normal Forms, Bools Expansion Theorem Fundamental Forms, Many Terminal Networks, Trees and Binominal Networks.

UNIT – III

BASIC CONCEPTS :

SETS : Union, Intersection, Difference, Complement, De- Morgan’s Laws & Cartesian Product.

MAPPINGS : Types of mappings, Identify & Inverse mapping, Product of Mappings

GROUPS : Definition, Order of an Element,

SUBGROUP: Definition Necessary and sufficient condition.

COSET DECOMPOSITION : Right & Left Cosets, Lagrange’s Theorem

DEFINITIONS AND BASICS OF : Normal subgroup, Quotient Group, Homomorphism & Isomorphism of groups, Kernel of Homomorphism, Ring and Field.

UNIT – IV

VECTOR SPACES: Vector Space, Subspace and Quotient Spaces, Linearly Dependent and Independent Vector.

LINEAR MAPS : Definition & Properties, Homomorphism & Isomorphism of Vector Spaces, Kernel of A linear Map.

UNIT –V

Matrix Representation of a Linear Map, rank and Nullity of Linear Map. Fundamental Theorem of Vector Space Homomorphism. Eigen values and Eigen Vector of Matrix, Cayley Hamilton Theorem : Proof & Applications.

Text Book:

1. A text book of Discrete Mathematics by H. K. Pathak and D.C.Agrawal, Shiksha Sahitya Prakashan, Meerut. (Text)
2. A text book of Linear Algebra by H. K. Pathak and D.C.Agrawal, Shiksha Sahitya Prakashan, Meerut

Reference Books:

1. A text book of Algebra by H. K. Pathak and D.C.Agrawal, Shiksha Sahitya Prakashan, Meerut.(TEXT)
2. Linear Algebra by S.N.Goel, Kedarnath Ramnath Publication, Meerut.
3. Linear Algebra by Kenneth Hoffman and Ray Kunze, Prentice Hall of India Pvt. Ltd. New Dehli.

Objective : Introduce Concepts of discrete mathematics and algebra.

Examination: The internal examination will carry 20% marks i.e. 10 marks. The external examination will be of 80% marks i.e. 40 marks. The question paper will contain questions equally distributed in all units. The balance of the paper will be maintained by including appropriate (numerical/objective/conceptual/analytical/theoretical) combination of subsection in each question.