Syllabus - AS1 Mathematical Foundations I

AS1 Mathematical Foundations I

(4 Hours – 5 Credits)

UNIT I

           Set Theory – Relations,  equivalence relations – partial order - Function – binary operations – groups: definitions and examples – elementary properties

UNIT II 

            Logic: introduction – connectives – truth table – Tautology implication and equivalence of formulae. 

UNIT III

Matrices: Elementary transformation – Inverse of a matrix - Rank of a matrix – Simultaneous linear equations – Cayley Hamilton theorem. 

UNIT IV

           Graph theory: Introduction – definition and examples – degrees and subgraphs –  matrices - connectedness: walks,  trials and paths,  connectedness and components. 

UNIT V

          Eulerian graphs – Hamiltonian graph – trees: characterisation of trees,  centre of a tree. 

Text Books:

1. Modern Algebra,   S.   Arumugam & A.   Thangapandi Issac,  Scitech publications,  2005 ( for Units I and III)

2. Discrete Mathematics,  Dr.  M.  K.  Venkaatraman,  Dr.  N.  Sridharan and Dr.  N.  Chandrasekaran,  National Publishing Company,  2000.   (for Unit II )

3. Invitation to Graph Theory,  S.  Arumugam and S.  Ramachandran ,  Scitech

Publications,  2005,  Chennai.   ( for Units IV and V )

UNIT I     : Chapters1,  2,  3.  1,  3.  2  

UNIT II    : Chapter 9                      

UNIT III   : Chapters 7.  3 – 7.  7

UNIT IV  : Chapters  2.  1,  2.  2,  2.  3,  2.  8,  4.  0,  4.  1,  4.  2     

UNIT V   :  Chapters 5 and 6