Discrete Mathematics and Number Theory
- Acquaint the students with the fundamentals of discrete mathematics and number theory and its applications.
- Make the students aware about graph theory, theorems related to prime numbers, relations and digraph etc.
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
Paper Title |
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MAT 101 |
Discrete Mathematics and Number Theory(Theory)
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The students will be able to –
CO1: Represent a graph using an adjacency list and an adjacency matrix and apply graph theory to application problems such as computer networks. CO2: Determine if a graph has an Euler or a Hamilton path or circuit. CO3: Determine whether a graph is a binary tree, N-ary tree, or not a tree; use the properties of trees to classify trees, identify ancestors, descendants, parents, children, and siblings; determine the level of a node, the height of a tree or subtree and apply counting theorems to the edges and vertices of a tree. CO4: Perform calculation based on Pigeon hole principle. Evaluate Recurrence relation and generating function also analysis ordered relation. CO5: Find quotients and remainders from integer division and apply Euclid’s algorithm and backwards substitution CO6: Determine the proof of chinese remainder theorem and know its application. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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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.
Elementary divisibility properties, Division algorithm, Greatest common divisor, Least common multiplier, Euclid’s lemma.
Bezout’s lemma, Prime number, Eucledian Algorithm, Fundamental theorem of arithmetic, Congruence, Chinese remainder theorem.
- 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.
