Semester 3 Computers DIS
Semester 3 Computers DIS

Chapter: Set Theory

(Note: A very easy and high scoring chapter. A must for all students who want to pass DIS)

 

Topics to be prepared

I want to Just Pass: Problems based on

  • Definitions and Statements of Laws.
  • Sets, Venn diagrams.
  • Operations on Sets – Union, Intersection, Complement, Difference, Symmetric Difference, etc.
  • Laws of Set Theory.
  • Power set and Cartesian Products.
  • Partitions of sets.
  • Principle of Inclusion and Exclusion

 

I want to get good Marks: (As above and plus)

  • Proving Laws and statements involving operations on Sets.

 

Chapter: Logic

(Note: A very easy and high scoring chapter. A must for all students who want to pass DIS)

Topics to be prepared

I want to Just Pass: Problems based on

  • Definitions and Statements of Laws.
  • Propositions and logical operations.
  • Negation, Conjunction, Disjunction, Conditional, Bi-Conditional.
  • Truth values and Truth tables;
  • Equivalence
  • Implications – Converse, Inverse and Contrapositive.
  • Laws of logic.
  • Normal Forms
  • Predicates and Quantifiers.
  • Mathematical Induction: (Very Important. One problem will surely be asked)

 

I want to get good Marks: (As above and plus)

  • Proving statements using Laws of logic.

Chapter: Relations

(Note: A very easy chapter. Only a fool will leave this chapter for Option) 

Topics to be prepared

I want to Just Pass: Problems based on

  • Relations – Reflexive, Symmetric and Transitive.
  • Paths, Relation Matrix and Digraphs.
  • Properties and types of binary relations.
  • Operations on Relations.
  • Closures, Warshall’s algorithm.
  • Equivalence relations

 

I want to get good Marks: (As above and plus)

 


Chapter: Lattice and Posets 

Topics to be prepared

I want to Just Pass: Problems based on

  • Partial Ordered Relations,
  • Hasse diagram and Lattice,
  • Distributive Lattice
  • Extremal Elements

 

I want to get good Marks: (As above and plus)

 


Chapter: Functions

(Note: A very easy chapter. Only a fool will leave this chapter for Option) 

Topics to be prepared

I want to Just Pass: Problems based on

  • Types of functions – Injective, Surjective and Bijective.
  • Composition of functions.
  • Identity and Inverse function.
  • Pigeon-hole principle. (Very Important. One problem will surely be asked)

 

I want to get good Marks: (As above and plus)

 


Chapter: Counting

(Note: A new chapter) 

Topics to be prepared

I want to Just Pass: Problems based on

  • Permutations & Combinations.
  • Elements of Probability,
  • Discrete Probability;
  • Conditional Probability
  • Introduction to Functional Programming

I want to get good Marks: (As above and plus)

 


Chapter: Generating Functions (G.F.) Recurrence Relations (RR)

(Note: Small and easy chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • Ordinary and Exponential Generating Functions.
  • Solution of Linear Homogenous RR with Constant Coefficients.
  • Solution of Linear Non-Homogenous RR with Constant Coefficients.
  • Recursive Functions

 

I want to get good Marks: (As above and plus)

 


Chapter: Graphs

(Note: Important and Major chapter) 

Topics to be prepared

I want to Just Pass: Problems based on

  • Paths and circuits: Eulerian and Hamiltonian
  • Types of graphs, Sub Graphs
  • Isomorphism of Graphs
  • Handshaking Lemma

I want to get good Marks: (As above and plus)

 


Chapter: Algebraic Structures

(Note: Difficult but a major chapter. A must for all students who want to pass DIS)

Topics to be prepared

I want to Just Pass: Problems based on

  • Definitions
  • Algebraic structures with one binary operation: – Semigroup, Monoid, Group, Abelian Group. (Very Important. One problem will surely be asked)
  • Identity and Inverse

I want to get good Marks: (As above and plus)

  • Isomorphism, Homomorphism and Automorphism, Cyclic groups, Normal subgroups.

 


Chapter: Coding Theory

(Note: Small and easy chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • Codes and Group codes.
  • Hamming distance, Minimum Distance.
  • Number of Errors detected and Corrected

 

I want to get good Marks: (As above and plus)

 

 

 

 

 

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