MA2265 Discrete Mathematics Notes, Problem material


MA2265 Discrete Mathematics Notes, PROBLEM MATERIALS
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MA2265 DISCRETE MATHEMATICS L T P C
3 1 0 4
AIM
To extend student’s Logical and Mathematical maturity and ability to deal with
abstraction and to introduce most of the basic terminologies used in computer science
courses and application of ideas to solve practical problems.
OBJECTIVES
At the end of the course, students would
 Have knowledge of the concepts needed to test the logic of a
program..
 Have an understanding in identifying structures on many levels.
 Be aware of a class of functions which transform a finite set into another
finite set which relates to input output functions in computer science.
 Be aware of the counting principles
 Be exposed to concepts and properties of algebraic structures such as
semi groups, monoids and groups.
UNIT I LOGIC AND PROOFS 9 + 3
44
Propositional Logic – Propositional equivalences-Predicates and quantifiers-Nested
Quantifiers-Rules of inference-introduction to Proofs-Proof Methods and strategy
UNIT II COMBINATORICS 9 + 3
Mathematical inductions-Strong induction and well ordering-.The basics of counting-The
pigeonhole principle –Permutations and combinations-Recurrence relations-Solving
Linear recurrence relations-generating functions-inclusion and exclusion and
applications.
UNIT III GRAPHS 9 + 3
Graphs and graph models-Graph terminology and special types of graphs-Representing
graphs and graph isomorphism -connectivity-Euler and Hamilton paths
UNIT IV ALGEBRAIC STRUCTURES 9 + 3
Algebraic systems-Semi groups and monoids-Groups-Subgroups and homomorphisms-
Cosets and Lagrange’s theorem- Ring & Fields (Definitions and examples)
UNIT V LATTICES AND BOOLEAN ALGEBRA 9 + 3
Partial ordering-Posets-Lattices as Posets- Properties of lattices-Lattices as Algebraic
systems –Sub lattices –direct product and Homomorphism-Some Special lattices-
Boolean Algebra
L: 45, T: 15, TOTAL: 60 PERIODS
TEXT BOOKS:
1. Kenneth H.Rosen, “Discrete Mathematics and its Applications”, Special Indian
edition, Tata McGraw-Hill Pub. Co. Ltd., New Delhi, (2007). (For the units 1 to 3,
Sections 1.1 to 1.7 , 4.1 & 4.2, 5.1 to 5.3, 6.1, 6.2, 6.4 to 6.6, 8.1 to 8.5)
2. Trembly J.P and Manohar R, “Discrete Mathematical Structures with Applications to
Computer Science”, Tata McGraw–Hill Pub. Co. Ltd, New Delhi, 30th Re-print
(2007).(For units 4 & 5 , Sections 2-3.8 & 2-3.9,3-1,3-2 & 3-5, 4-1 & 4-2)
REFERENCES:
1. Ralph. P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied
Introduction”, Fourth Edition, Pearson Education Asia, Delhi, (2002).
2. Thomas Koshy, ”Discrete Mathematics with Applications”, Elsevier Publications,
(2006).
3. Seymour Lipschutz and Mark Lipson, ”Discrete Mathematics”, Schaum’s Outlines,
Tata McGraw-Hill Pub. Co. Ltd., New Delhi, Second edition, (2007).
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