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Discrete Mathematics

By Minirani S   |   MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai.
Learners enrolled: 174
Discrete mathematics involves the study of objects which are separated or spaced apart from each other. For example, finite sets and the set of integers are discrete sets, while the set of real numbers would be considered to be a continuous, or non-discrete, set of objects. The difference between discreteness and continuity can also be seen in distinguishing between digital signals (discrete) and analog signals (continuous). As these examples suggest, discrete mathematics forms a conceptual complement to the continuous processes which underlie the study of calculus. Discrete sets often carry additional structures such as an operation (addition, multiplication, concatenation, union or intersection, for example) or an inequality relationship, and, when present, these structures are instrumental in developing deeper theories. With both the subject itself, as well as the experience of working with mathematical arguments, the course will provide a foundation for moving into higher level mathematics courses such as real analysis, abstract algebra, math modelling, geometry and topology.
Summary
Course Status : Upcoming
Course Type : Not Applicable
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate
Start Date : 08 Jul 2024
End Date : 20 Aug 2024
Enrollment Ends : 31 Aug 2024
Exam Date : 08 Dec 2024 IST
Exam Shift :

Shift 1

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Week – 1
Module – 1 Introduction to Discrete mathematics , Sets and subsets etc 
Assignment  - 1 Deadline – last day of the  week 
Module – 2 Sets and subsets-Representations-Cardinality-Set operations-Set identities- principle of mathematical induction- principle of inclusion-exclusion
Assignment  - 2 Deadline – last day of the  week 
Computability and formal languages
Module - 3 Ordered sets-languages-phase structure grammars-types of grammars and languages
Assignment  - 3 Deadline – last day of the  week 
Interaction\Discussion

Week – 2
Module -4 Basics of counting-permutations-combinations. Pigeon hole principle
Assignment  - 4 Deadline – last day of the Permutations,combinations and discrete probability - Part 2
Module –5 Elements of probability-sample spaces-asssigning probabilities to events-equally likely outcomes
Assignment  - 5 Deadline – last day of the  week 
Relations and functions – Part 1
Module - 6 Relations and their properties-binary relations and their applications-representing relations-equivalence relations
Assignment  - 6 Deadline – last day of the  week 
Interaction\Discussion

Week – 3
Module – 7 Product sets and partitions-partial orderings-lattices-chains and antichains-functions
Assignment  - 6 Deadline – last day of the  week Graphs and Planar graphs - Part 1 
Module – 8 Basic definitions and terminology-multigraphs-weghted graphs-paths and circuits
Assignment  - 7 Deadline – last day of the  week  
Graphs and Planar graphs - Part 2
Module - 9 Shortest paths- Eulerian paths and circuits-Travelling Salesman problem-planar graphs  
Assignment  - 8 Deadline – last day of the  week  
Interaction\Discussion

Week – 4
Module – 10 Definitions-properties-applications of trees
Assignment  - 9 Deadline – last day of the  week  Trees - Part 2 
Module – 11 Spanning trees-minimum spanning trees-applications-Prims and Kruskals algorithm
Assignment  - 10 Deadline – last day of the  week  Finite state machines 
Module – 12 Finite state machines with output- finite state machines with no output-finite state automata- language recognition by finite state machines-designing finite state automata
Assignment  - 11 Deadline – last day of the  week  
  Interaction\Discussion

Week – 5
Module – 13 Complexity of algorithms-comparing algorithms-Discrete numeric functions-manipulation of numeric functions-generating functions-operations on generating functions-
Assignment  - 12 Deadline – last day of the  week  Recurrence relations and recursive algorithms - Part 1
Module – 14 Linear recurrence relations- homogeneous and non-homogeneous and solutions
Assignment  - 13 Deadline – last day of the  week
Module – 15 Solutions of non-homogeneous type-particular solution and total solution-solution by the method of generating functions
Assignment  - 14 Deadline – last day of the  week Interaction\Discussion Groups and rings -  Part 1
Interaction\Discussion

Week – 6
Module – 16 Binary operations-semigroups-products and quotient of semigroups
Assignment  - 15 Deadline – last day of the  week
Module – 17 Groups- products and quotient groups-other mathematical structures
Assignment  - 16 Deadline – last day of the  week Boolean Algebra -  Part 1
Module – 18 Lattices and algebraic structures-sub lattices-isomorphic lattices-Principle of duality-special types of lattices-
Assignment  - 17 Deadline – last day of the  week
Interaction\Discussion

Week – 7
Module – 19 Boolean Algebra-Boolean expressions and Boolean functions-identities of Boolean algebra-
Assignment  - 18 Deadline – last day of the  week Boolean Algebra -  Part 3
Module – 20 Functional completeness-logic gates-exmples of circuits-minimisation of circuits-Karnaugh maps-Quine Mc Clusckey method
Assignment  - 19 Deadline – last day of the  week
Live Interaction\Discussion

Week – 8
Term end assessment:
Interaction & Online  Evaluation

Books and references

1. Elements of Discrete Mathematics, C.L. Liu., Tata McGraw-Hill Publishing Company Ltds. 2nd edition
2. Discrete Mathematics and its Applications (SixthEdition), Kenneth.H. Rosen, TMH Education Pvt. Ltd.
3. Set Theory and Related Topics, Seymour Lipschutz Schaum’s Outline Series, Second Edition, TMH Education Pvt. Ltd.
4. Applied Discrete Structures for Computer Science, Alan Doerr & Kenneth Lefvasseur.
5. Introduction to Automata Theory, Languages and Computation, John Hopcroft & Jeffrey D. Ullman, Narosa Publishing Company, 1999.

Instructor bio







Minirani S

MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai.
Dr. Minirani S is currently working as an Associate Professor in the Department of Basic Sciences and Humanities in the Mukesh Patel School of technology, Management and Engineering, NMIMS Deemed University, Vile Parle West, Mumbai. Dr. Minirani S has completed her Ph. D. in Mathematics from National Institute of Technology, Calicut. Her areas of interest include Fractal Geometry, Discrete Mathematics and Fluid Dynamics. 

Course certificate

30 Marks will be allocated for Internal Assessment and 70 Marks will be allocated for end term proctored examination Securing 40% in both separately is mandatory to pass the course and get Credit Certificate.


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