MATHEMATICAL FOUNDATIONS IN COMPUTER SCIENCE

Paper Code: 
MCA 125
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 

The Course enables the students to

  1. Illustrate the basic concepts of statistics and graphs.
  2. Differentiate between Propositional Calculus and Predicate Calculus
  3. Evaluate the understanding of the concepts by applying them in different domains.
  4. Develop the skills to solve the problem using mathematical ability.

Course Outcomes(COs):

 

Learning Outcome (at course level)

 

Learning and teaching strategies

Assessment Strategies

CO27.Demonstrate and apply the concepts of statistics.

CO28.Examine the use of logical operators, propositions in different fields of computer science.

CO29.Evaluate and analyze the problem using graphs.

CO30.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, Inverse of a Matrix,  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 II: 

Probability Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, Bayes’ Theorem and independence problems.

12.00
Unit III: 

Introduction to Statistics- Population, Sample, Variable, Descriptive Statistics-Mean, Mode, Median, Measures of Spread- Range, Inter Quartile Range,  Variance, Standard Deviation

12.00
Unit IV: 

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 V: 

Basic Concepts of Graphs, Sub graphs, Matrix Representation of Graphs: Adjacency Matrices, Incidence Matrices, Isomorphic Graphs, Paths and Circuits, Eulerian and Hamiltonian Graphs, Multigraphs, Planar Graphs, Euler‘s Formula, Spanning Trees

ESSENTIAL READINGS: 
  • Kenneth H.Rosen, “Discrete Mathematics and Its Applications”, Tata McGraw Hill, Seventh Edition, 2017.
  • Seymour Lipschutz, Marc Laras Lipson, Varsha H. Patil,  “ Discrete Mathematics (Schaum's Outlines) (SIE)”, Revised 3rd Edition, 2017
  • Murray Spiegel  John Schiller, R. Alu Srinivasan, Debasree Goswami, “ Probability and Statistics”, 3rd Edition, 2017
  • Hopcroft John E. ET. AL., “Introduction to Automata Theory, Languages and Computation”, Pearson Education; 3rd edition, 2011.
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: 
2021-22
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