MA2265 DISCRETE MATHEMATICS syllabus

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
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).