Discrete Mathematics detailed syllabus scheme for Information Technology (IT), 2019-20 onwards has been taken from the DBATU official website and presented for the Bachelor of Technology students. For Subject Code, Course Title, Lecutres, Tutorials, Practice, Credits, and other information, do visit full semester subjects post given below.
For 6th Sem Scheme of Information Technology (IT), 2019-20 Onwards, do visit IT 6th Sem Scheme, 2019-20 Onwards. For the Elective-V scheme of 6th Sem 2019-20 onwards, refer to IT 6th Sem Elective-V Scheme 2019-20 Onwards. The detail syllabus for discrete mathematics is as follows.
Discrete Mathematics Syllabus for Information Technology (IT) 3rd Year 6th Sem 2019-20 DBATU
Course Objectives:
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Course Outcomes:
After learning the course the students should be able:
- To perform operations on various discrete structures such as sets functions, relations, and sequences.
- To solve problems using counting techniques, permutation and combination, recursion and generating functions
- To construct and verify correctness of a boolean expression using K-Maps and truth tables
- To use graphs as tools to visualize and simplify Problems.
- To solve problems using algebraic structures (Rings, Monoids and Groups)
Unit I
The Foundations: Sets theory and its applications sets, Set operations, Laws of set theory, Power sets, Partitions, Multi-sets, Cardinality, Principle of inclusion and exclusion, Algebra of sets and duality, Applications of sets: Problems on set operations and principle of inclusion-exclusion, Logics and proofs, Propositional logic, Propositional equivalences, Propositional algebra, Basic logical operations, De Morgans laws, Predicates and quantifiers, Nested quantifiers, Rules of inference, Proof methods and strategy, Applications of logic: Translating English statements into propositions, Boolean searches in web pages, Bit operations.
Unit II
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Unit III
Basic Counting Principles: Permutations, Combinations, Binomial coefficients, Generalized permutations and combinations, combinations and permutations with repetition, Generating permutations and combinations, Recurrence relation, Solving linear recurrence relations with constant coefficients, Applications of counting principles, Pigeonhole principle and its applications.
Unit IV
Relations: Properties of binary relations, Closure of relations, Warshalls algorithm, Equivalence relations and partitions, Partial ordering relations and lattice application of relations: n-ary relations and their applications, Databases and relations.
Unit V
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Unit VI
Algebraic Structures: Algebraic systems, Groups, Semi groups, Monoid, Subgroups, Permutation groups, Codes and group codes, Isomorphism and automorphisms, Homomorphism, Fermats little theorem, Polynomial rings, Applications of groups.
Text Books:
- K. H. Rosen, Discrete Mathematics and Its Applications, Tata McGraw Hill Publication, 7th edition, 2012.
- J. P. Tremblay, R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, 1st edition, McGraw Hill Publication, 2001.
Reference Book:
- B. Kolman, R. Busby, S. Ross, Discrete Mathematical Structures, Pearson Education, 6th edition, 2009.
- R. K. Bisht, H. S. Dhami, Discrete Mathematics, Oxford University Press, 2015.
For detail syllabus of all subjects of Information Technology (IT) 6th Sem 2019-20 onwards, visit IT 6th Sem Subjects of 2019-20 Onwards.