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Mathematical Foundation for Computer Applications [1]

Paper Code: 
MCA 124
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 
  • To understand the concepts and operations of matrix algebra needed for computing graphics modeling.
  • To understand and apply the class of functions which transform a finite set into another finite set which relates to input output functions in computer science.
  • To impart discrete knowledge in computer engineering through finite automata and Context free grammars.
12.00
Unit I: 

Matrices, Rank of Matrix, Solving System of Equations, Eigen Values and Eigen Vectors, Inverse of a Matrix, Cayley Hamilton Theorem

12.00
Unit II: 

Set theory, Principle of inclusion and exclusion, partitions, Permutation and Combination, Relations,  Properties of relations,  Matrices of relations,  Closure operations on relations, Functions- injective,  subjective and objective functions.

12.00
Unit III: 

Propositions and logical operators, Truth table, Propositions generated by a set, Equivalence and implication, Basic laws, Functionally complete set of connectives, Normal forms, Proofs in Propositional calculus, Predicate calculus.

12.00
Unit IV: 

Languages and Grammars-Phrase Structure Grammar-Classification of Grammars, Pumping Lemma For Regular Languages, Context Free Languages.

12.00
Unit V: 

Finite State Automata-Deterministic Finite State Automata(DFA), Non Deterministic Finite State Automata (NFA), Equivalence of DFA and NFA, Equivalence of NFA and Regular Languages

ESSENTIAL READINGS: 
  • Kenneth H.Rosen, “Discrete Mathematics and Its Applications”, Tata McGraw Hill, Seventh Edition, 2011.
  • Hopcroft John E. ET. AL., “Introduction to Automata Theory, Languages and Computation”, Pearson Education; 3rd edition, 2008.
REFERENCES: 
  • A.Tamilarasi & A.M.Natarajan, “Theory of Automata and Formal Languages”, New Age International Pvt Ltd Publishers, 2008.
  • Juraj Hromkovic, “Theoretical Computer Science”, Springer Indian Reprint, 2010.
  • David Makinson, “Sets, Logic and Maths for Computing”, Springer Indian Reprint, 2011.
Academic Year: 
2015-16 [2]

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Source URL: https://www.csit.iisuniv.ac.in/courses/subjects/mathematical-foundation-computer-applications-2

Links:
[1] https://www.csit.iisuniv.ac.in/courses/subjects/mathematical-foundation-computer-applications-2
[2] https://www.csit.iisuniv.ac.in/academic-year/2015-16