MATHEMATICAL FOUNDATIONS IN COMPUTER SCIENCE

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

Course Objectives

The Course enables 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 Outcomes(COs):

 

Learning Outcome (at course level)

 

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, 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.

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: 

Essential Readings:

  • Kenneth H.Rosen, “Discrete Mathematics and Its Applications”, Tata McGraw Hill, 8th Edition, 2021.
  • Seymour Lipschutz, Marc Laras Lipson,  “ Discrete Mathematics (Schaum's Outlines) (SIE)”, McGraw Hill, 4th Edition, 2021
  • John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman, “Introduction to Automata Theory, Languages and Computation”, Pearson Education; 2nd Edition, 2018.
  • Murray Spiegel  John Schiller, R. Alu Srinivasan, Debasree Goswami, “ Probability and Statistics”, 3rd Edition, 2017

 

Suggested Readings:

  • Peter Linz, “An Introduction to Formal Languages and Automata, 6/e”, Jones & Bartlett, 2016
  • Juraj Hromkovic, “Theoretical Computer Science”, Springer Indian Reprint, 2010.
  • David Makinson, “Sets, Logic and Maths for Computing”, Springer Indian Reprint, 2011.
  • A.Tamilarasi & A.M.Natarajan, “Theory of Automata and Formal Languages”, New Age International Pvt Ltd Publishers, 2008.

 

REFERENCES: 

E-Resources

  • Discrete Mathematics by NPTEL (https://onlinecourses.nptel.ac.in/noc22_cs33)
  • Mathematical Foundation Introduction (https://www.tutorialspoint.com/mathematical-foundation-introduction)
  • Discrete mathematics for Computer Science(https://www.javatpoint.com/discrete-mathematics-for-computer-science)
  • Mathematical Foundations of Computing (http://web.stanford.edu/class/archive/cs/cs103/cs103.1184/)

 

 

 

Academic Year: 
2023-24
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