School of Computer Engineeringcoretheory
DISCRETE MATHEMATICAL STRUCTURES
MAT 2101
Syllabus
- 01Boolean Algebra: Partial ordering sets, Lattices–simple properties, Boolean algebras, Boolean polynomials: Disjunctive normal form (DNF) and Conjunctive normal form (CNF)
- 02Elementary configuration: Permutations and Combinations (basics), Generating function, Applications of Principle of inclusion and exclusion, Partitions, compositions, Fikes ordering of permutations
- 03Graph theory: Basic definitions, properties, Eulerian graphs, Hamiltonian graphs, Trees and Properties, Matrices associated with graphs, Algorithms for finding shortest path
- 04Group theory: Groups-subgroups, group of symmetries and applications, Cyclic groups, Cosets, Lagrange's Theorem
- 05Propositional and Predicate Calculus: Well-formed formula, Connectives, Quantifications, Inference theory of Propositional and Predicate calculus
- 06Matrix Decompositions: Prerequisites, QR, LU and SVD, and Applications
References
- C. L. Liu: Elements of Discrete Mathematics, 2nd edition, 2007, Mc Graw Hill, New Delhi. https://pdfcoffee.com/elements-of-discrete-mathematics-liu-c-l--pdf-free.html
- J. P. Trembaly and R. Manohar: Discrete Mathematics Structures with application to computer science, 2012,Tata Mc Graw Hill. https://www.academia.edu/37284735/Discrete_Mathematical_Structures_with_Applications_by_Manohar_pdf
- E. S. Page and L. B. Wilson: An introduction to computational combinatorics, edn., 1979, Cambridge Univ. Press.
- Narasingh Deo: Graph theory with Applications to computer science, Dover Publications, 2016. Originally published: Englewood Cliffs, N e w J e r s e y : P r e n t i c e - H a l l , I n c . , 1 9 7 4 . https://www.shahucollegelatur.org.in/Department/Studymaterial/sci / it/BCS/FY/book.pdf
- F. Harary, Graph Theory, Narosa Publishing House, New Delhi, Second edition, 1990, Reprint 2013. https://users.metu.edu.tr/aldoks /341/Book%201%20(Harary).pdf
- David C. Lay, Linear Algebra & Its Applications, Pearson Pub. 2016. https://home.cs.colorado.edu/~alko5368/lecturesCSCI2820/math book.pdf
- Alan Tucker, Applied Combinatorics, Wiley Publishers, 2012. https://www.isinj.com/mtusamo/Applied%20Combinatorics%20(6t h%20Edition)%20by%20Alan%20Tucker%20Wiley%20(2012).pdf https://onlinecourses.nptel.ac.in/noc24_ma26/preview
- Introduction to Group Theory https://nptel.ac.in/courses/111106086
- Discrete Mathematics
Credits Structure
3Lecture
0Tutorial
0Practical
3Total