Mathematical Foundation for Computer Applications

Paper Code: 
MCA 124
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 

  The course will enable the students to

  1. Define the concepts and operations of matrix algebra.
  2. Understand the concepts of probability, Bayes’ theorem and independence problems.
  3. Illustrate the basic concepts of statistics and graphs.
  4. Differentiate between Propositional Calculus and Predicate Calculus
  5. Evaluate the understanding of the concepts by applying them in different domains.
  6. Develop the skills to solve the problem using mathematical ability.

  Course Learning Outcomes (CLOs):

 

Learning Outcome (at course level)

Students will be able to:

Learning and teaching strategies

Assessment Strategies

  1. Define the concepts and operations of matrix algebra.
  2. Understand the basic concepts of probability, statistics and graphs.
  3. Demonstrate their understanding of concepts and apply methods in algorithmic design and analysis.
  4. Examine the use of logical operators, propositions in different fields of computer science.
  5. Evaluate and analyze the problem statistically.
  6. Formulate the problem mathematically and design the solution.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Demonstration

 

Learning activities for the students:

Self-learning assignments, Effective questions, Quizzes, Presentations, Discussions

 

  • Assignments
  • Written test in classroom
  • Classroom activity
  • Written test in classroom
  • Semester End Examination

 

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.
  • JurajHromkovic, “Theoretical Computer Science”, Springer Indian Reprint, 2010.
  • David Makinson, “Sets, Logic and Maths for Computing”, Springer Indian Reprint, 2011.
Academic Year: 
2019-20
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