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Discrete Mathematics and Number Theory [1]

Paper Code: 
25CMAT113
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Acquaint the students with the fundamentals of discrete mathematics and number theory and its applications.
  2. Make the students aware about graph theory, theorems related to prime numbers, relations and digraph etc.

 

Course Outcomes: 

 Course

Learning outcomes

 

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

25CMAT

113

Discrete Mathematics and Number Theory

   (Theory)

 

CO12: Identify types of graphs, analyze paths and cycles, Graph isomorphism.

CO13: Explore product sets and partitions, analyzing paths in relations, Digraphs and trees.

CO14: Apply the Pigeonhole principle, recurrence relations, generating function and POSET.

CO15: Apply the division algorithm, Greatest common divisor (GCD) and Least common multiplier (LCM).

CO16: Explore prime numbers, Euclidean algorithm, Congruence and the Chinese remainder theorem.

CO17: Contribute effectively in course specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self-learning assignments, Effective questions, presentations.

 

 

Quiz,

Individual and group projects,

Open Book Test, Semester End Examination

 

Unit I: 
Graphs Theory
12.00

Basic terminology, Types of graph, Paths and cycles, Euler graph and cycle, Hamiltonian graph and cycle, Shortest path algorithm (Djikstras algorithm), Graph isomorphism, Planar graph, Graph colorings and chromatic number.

Unit II: 
Relation, Digraphs and Tree
12.00

Product sets and partitions, Paths in relation and digraphs, Properties of relations, Equivalence relations. Tree Introduction, m-array trees, Properties of trees, Spanning trees, Minimal spanning trees, Binary search trees.

 

Unit III: 
Recurrence relation, Generating functions and Posets
12.00

Pigeonhole principle, Recurrence relation, Generating functions, Partially ordered sets, Extremal elements of partially ordered sets.

                                                                                                                      

Unit IV: 
Divisibility
12.00

Elementary divisibility properties, Division algorithm, Greatest common divisor, Least common multiplier, Euclid’s lemma.

Unit V: 
Congruence
12.00

Bezout’s lemma, Prime number, Euclidean Algorithm, Fundamental theorem of arithmetic, Congruence, Chinese remainder theorem.

 

Essential Readings: 
  • Bernard Kolmann, Robert C. Busby and Sharon Ross, Discrete Mathematical Structures, PHI Delhi, 2008.
  • R.C. Choudhary, M.C. Goyal and D.C. Sharma, Discrete Mathematics, Ramesh Book Depot, 2018.
  • C. L. Liu, Elements of Discrete Mathematics, McGraw Hill, 2009.
  • Thomas Koshy, Elementary Number Theory with applications, Elsevier Academic Press, 2014.
  • S.K. Pundir and R. Pundir, Theory of Numbers, Pragati Prakashan, Meerut, 2012.

 

References: 
  •   Norman Biggs, Discrete Mathematics, Oxford University Press UK, 2003.
  • V. K. Bala krishnan, Introductory Discrete Mathematics, Prentice Hall, 2010.
  • Richard Johnson Baugh, Discrete Mathematics, Pearson Education Asia, New Delhi, 2008.
  • David M. Burton, Elementary Number Theory, McGraw Hill, 2007 J.P.Trembly and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw Hill Pub. Co. Ltd, New Delhi, 2010.
  • Ralph. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, Pearson Education Asia, Delhi, 2019.

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Academic Year: 
2025-2026 [7]

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[7] https://maths.iisuniv.ac.in/academic-year/2025-2026