DISCRETE MATHEMATICS AND NUMBER THEORY

Paper Code: 
MAT 101
Credits: 
3
Contact Hours: 
45.00
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 (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

MAT 101

Discrete Mathematics and Number Theory

   (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO1: Learn about partially ordered sets, lattices and their types.

CO2: Understand Boolean algebra and Boolean functions.

CO3: Familiarise with modular arithmetic and find primitive roots of prime and composite numbers.

CO4: Assimilate various graph theoretic concepts and familiarize with their applications.

CO5: Learn about some important results in the theory of numbers

including the prime number theorem, Chinese remainder theorem,

and their consequences.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
9.00
Graphs Theory: 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: 
II
9.00
Relation and Diagraphs: Product sets and partitions, Paths in relation and diagraphs, Properties of relations, Equivalence relations. Trees: Introduction, m-ary trees, Properties of trees, Spanning trees, Minimal spanning trees, Binary search trees.
 
Unit III: 
III
9.00

Pigeonhole principle, Recurrence relation, Generating functions. Ordered relations and Structures: Partially ordered sets, Extremal elements of partially ordered sets.

Unit IV: 
IV
9.00

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

Unit V: 
V
9.00
Bezout’s lemma, Prime number, Eucledian Algorithm, Fundamental theorem of arithmetic, Congruence, Chinese remainder theorem.
Essential Readings: 
 
  • Bernard Kolmann, Robert C. Busby and Sharon Ross, Discrete Mathematical Structures, PHI Delhi, 1997.
  • 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.
  • Norman Biggs, Discrete Mathematics, Oxford University Press UK, 2003.
  • V. K. Bala krishnan, Introductory Discrete Mathematics, Prentice Hall, 1996.
  • Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw Hill Pub. Co. Ltd., New Delhi, 2003.
  • 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, 2003.
  • Ralph. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, Pearson Education Asia, Delhi, 2002.

 

Academic Year: 
2020-2021
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