MA20013: Discrete Mathematics
| MA20013 | |||||||||||||||||||||||||||||
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| Course name | Discrete Mathematics | ||||||||||||||||||||||||||||
| Offered by | Mathematics | ||||||||||||||||||||||||||||
| Credits | 4 | ||||||||||||||||||||||||||||
| L-T-P | 3-1-0 | ||||||||||||||||||||||||||||
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| Semester | Spring | ||||||||||||||||||||||||||||
Syllabus
Syllabus mentioned in ERP
Prerequisite: void Cartesian product, relations, domain and range, composition of relations, equivalence relations, partial ordering relation. Lattices. Functions Function as a relation, injection, surjection and bijection, composition of functions, identity and inverse function. Cardinality, characteristic function. Peano postulates and finite induction, example of proof by induction. Recursive definitions. Binary operation on a set, groupoid, commutative and associative binary operations, binary operation with identity. Semigroup, monoid. Boolean algebra - Axioms and properties, atomic structure of a finite Boolean algebra. Homomorphism and isomorphism. Disjunctive and conjunctive normal forms. Algebra of position. First order predicate calculus. Theory of groups - Axioms, properties, subgroup, cyclic group, cosets, Lagrange’s theorem. Rings, subrings, ideals, ring homomorphism. Finite field - Field of order p. (p is prime).
Concepts taught in class
Basic Number Theory(Recurrence relations) - Combinatorics(Pigeonhole Principle), Sets, Relations and Functions, Groups - Axioms, Theories, Graphs - Eulerian, Hamiltonian, Trees and Tree Algorithms
Student Opinion
| A very theoretical but interesting course. Professors do not provide lecture notes, hence one needs to be pretty regular to classes. |
How to Crack the Paper
| Question Papers usually involve a lot of proofs and less numeric problems to solve, hence one should be aware of the exact topics covered in class. Assignments are a good source of knowing the type of problems which may occur in the examinations. |
Classroom resources
Kenneth H Rosen, Discrete Mathematics and its applications with combinatorics and graph theory and Gary Chartrand, Introductory graph theory