__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)