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Syllabus BCA203
Mathemactical Foundation of Computer Science
hr> Gujarat University SY BCA Syllabus (Revised) Effective from June, 2006| 1. | Connectives | 10% |
| Introduction | ||
| Objectives | ||
| Statements | ||
| Connectives | ||
| Negation | ||
| Conjunction | ||
| Disjunction | ||
| Conditional and Bi-conditional | ||
| Equivalence of Formulae and Well Formed Formulae | ||
| Two State Devices | ||
| Gate and Module | ||
| Tow Level Networks | ||
| NOR and NAND gates | ||
| 2. | Normal Forms And The Thory Of Inferences | 10% |
| Introduction Disjunctive normal forms | ||
| Conjunctive normal forms Principal Disjunctive forms | ||
| Principal Conjunctive forms | ||
| Valid inferences using truth table and direct method of proof | ||
| Rules of inference ( rule P, T and CP) | ||
| implications | ||
| Equivalence | ||
| Consistency of Premises and indirect method of proof. | ||
| 3. | Relations And Orderding | 15% |
| Introduction | ||
| Relations | ||
| Relation in a set | ||
| Domain and range of a relation | ||
| Total no. of distinct relation from a set A to B | ||
| graph of relations | ||
| Relation and sets of Ordered pairs | ||
| Types of relations in a set | ||
| Properties of relation in a set | ||
| Equivalence Relation | ||
| More example on relations | ||
| Equivalence classes or Equivalence sets | ||
| Partition | ||
| Partial Order Relations | ||
| Hasse diagram | ||
| Upper and Lower Bounds | ||
| Minimal, Maximal element | ||
| Binary Operations | ||
| Closure Operation. | ||
| 4. | Posets And Lattices | 10% |
| Introduction | ||
| Posets | ||
| Lattices as Posets | ||
| Lattices as algebraic systems | ||
| Sub lattices | ||
| Complete Lattices | ||
| Complemented lattices | ||
| Chains | ||
| 5. | Boolean Algebra | 10% |
| Introduction | ||
| Definition and important properties | ||
| Sub Boolean Algebra | ||
| Atoms | ||
| Anti toms Irreducible | ||
| Stone’s reprEsentation Theorem ( Without Proof ) | ||
| Boolaen Expression and their equivalence | ||
| Min terms and max terms | ||
| Values of Boolean expression and Boolean Functions | ||
| 6. | Matrices | 20% |
| Algebraic operations ( Multiplication ) computation of inverse | ||
| Rank of Matrix | ||
| Solution of Simultaneous linear equations | ||
| Cramer’s Rule | ||
| Gauss elimination Method, Matrix Inversion Method. | ||
| Matrix Inversion Method | ||
| 7. | Graph Theory | 25% |
| Introduction to graph | ||
| abstract definition of Graph | ||
| Isomorphism | ||
| Matrix representation of Graphs | ||
| Path | ||
| Reachability | ||
| Connectedness | ||
| Node base | ||
| trees | ||
| Definitions of basic terms related trees an Binary trees | ||
| TEXT BOOK: | ||
| Discrete Mathematic , Schaum’s Series. | ||
| REFERNCE BOOKS | ||
| Discrect Mathematical Structure ( Third Edition ), Bernard Kolman, Robert C. Busby , Sharon Roass ; , prentice Hall Of India Pvt. Ltd. | ||
| Discrect Mathematics And Its Applications , Tata Mcgraw Hill ( 5th Edition ), Kenneth . H . Rosen | ||
| Business Mathematics , Dr . D.C.Sancheti And V.K.Kapoor | ||
| Discrect Mathematical Structures With Applications To Computer Science , J.P.Tremblay And R. Manohor , McGraw Hill, New Delhi. |
| Total Marks of this Subject | 100 Marks |
| External (University ) Examination | 70 Marks |
| Internal Sessional Examination | 20 Marks |
| Term Work | 10 Marks |
| Teaching Hours per week | 3 Hrs |
| Practicals | There is no practical in this subject. |
Last Updated on 10th Jun 2009