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Swayam Central

Discrete Mathematics

By Minirani S   |   MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai.
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.

Learners enrolled: 492

SUMMARY

Course Status : Upcoming
Course Type : Not Applicable
Duration : 12 weeks
Start Date : 13 Jan 2020
End Date :
Exam Date :
Category :
  • Mathematics
  • Level : Undergraduate

    COURSE LAYOUT

    WEEK -1

    Module - 01 
    Sets and subsets-Representations-Cardinality-Set operations-Set identities- principle of mathematical induction- principle of inclusion-exclusion
    Assignment - 1
    Deadline – last day of the week 

    Module - 2 
    Ordered sets-languages-phase structure grammars-types of grammars and languages
    Assignment - 2
    Deadline – last day of the week 

    Module - 3
    Interaction/Discussion on Module 1 & 2 and Assignments 

    WEEK - 2 

    Module - 4
    Basics of counting-permutations-combinations. Pigeon hole principle
    Assignment - 3
    Deadline – last day of the week 

    Module - 5
    Elements of probability-sample spaces-asssigning probabilities to events-equally likely outcomes
    Assignment - 4
    Deadline – last day of the week 

    Module - 6
    Interaction\Discussion on Module 4 & 5 and Assignments 

    WEEK - 3

    Module - 7
    Relations and their properties-binary relations and their applications-representing relations-equivalence relations
    Assignment - 5
    Deadline – last day of the week 

    Module - 8 
    Product sets and partitions-partial orderings-lattices-chains and antichains-functions
    Assignment - 6
    Deadline – last day of the week 

    Module - 9
    Interaction/Discussion on Module 7 & 8 and Assignments 

    WEEK - 4

    Module - 10 
    Basic definitions and terminology-multigraphs-weghted graphs-paths and circuits
    Assignment - 7
    Deadline – last day of the week  

    Module -11
    Shortest paths- Eulerian paths and circuits-Travelling Salesman problem-planar graphs
    Assignment - 8
    Deadline – last day of the week  

    Module - 12
    Interaction/Discussion on Module 10 & 11 and Assignments 

    WEEK - 5

    Module -13
    Definitions-properties-applications of trees
    Assignment - 9
    Deadline – last day of the week 

    Module - 14 
    Spanning trees-minimum spanning trees-applications-Prims and Kruskals algorithm
    Assignment - 10
    Deadline – last day of the week  

    Module -15
    Interaction/Discussion on Module 13 & 14 and Assignments 

    WEEK-6

    Module - 16
    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

    Module - 17
    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

    Module - 18
    Interaction/Discussion on Module 16 & 17 and Assignments 

    WEEK - 7 

    Module - 19 
    Linear recurrence relations- homogeneous and non-homogeneous and solutions
    Assignment  - 13
    Deadline – last day of the  week

    Module - 20 
    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   

    Module - 21
    Interaction/Discussion on Module 19 & 20 and Assignments 

    WEEK - 8 

    Module - 22 
    Binary operations-semigroups-products and quotient of semigroups
    Assignment  - 15 
    Deadline – last day of the  week

    Module - 23 
    Groups- products and quotient groups-other mathematical structures
    Assignment  - 16 
    Deadline – last day of the  week

    Module - 24
    Interaction/Discussion on Module 22 & 23 and Assignments 

    WEEK -  9 

    Module - 25 
    Lattices and algebraic structures-sub lattices-isomorphic lattices-Principle of duality-special types of lattices-
    Assignment  - 17
    Deadline – last day of the  week

    Module - 26 
    Boolean Algebra-Boolean expressions and Boolean functions-identities of Boolean algebra-
    Assignment  - 18 
    Deadline – last day of the  week

    Module - 27
    Interaction/Discussion on Module 25 & 26 and Assignments 

    WEEK - 10 

    Module - 28 
    Functional completeness-logic gates-exmples of circuits-minimisation of circuits-Karnaugh maps-Quine Mc Clusckey method
    Assignment  - 19
    Deadline – last day of the  week
     
    Module- 29
    Interaction/Discussion on Module 28 & other modules and Assignments 

    Module- 30
    Term end assessment:
    Will provide the video answers to the frequently asked questions by the students. 
    Interactions and Online evaluation process 



    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 % for in course Assessment & 70 % of end term Proctored Exam

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