**JNTUK R20 2-1 MFCS Study Material** : JNTUK R20 CSE Branch students can access the Unit-wise R20 2-1 Mathematical Foundations of Computer Science (MFCS) Material/Notes/Test Books PDFs provided below. The course aims to provide a comprehensive understanding of the following:

- Introducing the students to the topics and techniques of discrete methods and combinatorial reasoning
- Presenting a wide range of applications that reinforce the close ties between discrete mathematics and computer science

**By the end of the course, students will be able to:**

- Solve mathematical problems with ease
- Comprehend mathematical principles and logic
- Demonstrate knowledge of mathematical modelling and proficiency in using mathematical software
- Analyze and manipulate data using appropriate software
- Communicate mathematical ideas and results effectively through verbal or written means

**The course is divided into five units:**

- Unit 1: Mathematical Logic
- Unit 2: Set Theory
- Unit 3: Combinatorics and Number Theory
- Unit 4: Recurrence Relations
- Unit 5: Graph Theory

Each unit covers specific topics and techniques, and students can download the PDFs for each team from the provided links. The course also provides recommended textbooks and reference books for further reading and clarification.

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**UNIT-1**

Mathematical Logic: Propositional Calculus: Statements and Notations, Connectives, Well Formed Formulas, Truth Tables, Tautologies, Equivalence of Formulas, Duality Law, Tautological Implications, Normal Forms, Theory of Inference for Statement Calculus, Consistency of Premises, Indirect Method of Proof, Predicate Calculus: Predicates, Predicative Logic, Statement Functions, Variables and Quantifiers, Free and Bound Variables, Inference Theory for Predicate Calculus.

**Download UNIT-1 Material PDF** | **Reference-2**

**UNIT-2**

Set Theory: Sets: Operations on Sets, Principle of Inclusion-Exclusion, Relations: Properties, Operations, Partition and Covering, Transitive Closure, Equivalence, Compatibility and Partial Ordering, Hasse Diagrams,

Functions: Bijective, Composition, Inverse, Permutation, and Recursive Functions, Lattice and its Properties, Algebraic Structures: Algebraic Systems, Properties, Semi Groups and Monoids, Group, Subgroup and Abelian Group, Homomorphism, Isomorphism.

**UNIT-3**

Combinatorics: Basis of Counting, Permutations, Permutations with Repetitions, Circular and Restricted Permutations, Combinations, Restricted Combinations, Binomial and Multinomial Coefficients and Theorems,

Number Theory: Properties of Integers, Division Theorem, Greatest Common Divisor, Euclidean Algorithm, Least Common Multiple, Testing for Prime Numbers, The Fundamental Theorem of Arithmetic, Modular Arithmetic, Fermatâ€™s and Eulerâ€™s Theorems

**UNIT-4**

Recurrence Relations: Generating Functions, Function of Sequences, Partial Fractions, Calculating Coefficient of Generating Functions, Recurrence Relations, Formulation as Recurrence Relations, Solving Recurrence Relations by Substitution and Generating Functions, Method of Characteristic Roots, Solving Inhomogeneous Recurrence Relations

**UNIT-5**

Graph Theory: Basic Concepts, Graph Theory and its Applications, Sub graphs, Graph Representations: Adjacency and Incidence Matrices, Isomorphic Graphs, Paths and Circuits, Eulerian and Hamiltonian Graphs, Multigraphs, Bipartite and Planar Graphs, Eulerâ€™s Theorem, Graph Colouring and Covering, Chromatic Number, Spanning Trees, Primâ€™s and Kruskalâ€™s Algorithms, BFS and DFS Spanning Trees.

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### e-Resources:

### Text Books:

1) Discrete Mathematical Structures with Applications to Computer Science, J. P. Tremblay and P. Manohar, Tata McGraw Hill.

2) Elements of Discrete Mathematics-A Computer Oriented Approach, C. L. Liu and D. P. Mohapatra, 3rd Edition, Tata McGraw Hill.

### Reference Books:

1) Discrete Mathematics for Computer Scientists and Mathematicians, J. L. Mott, A. Kandel and T. P. Baker, 2nd Edition, Prentice Hall of India.

2) Discrete Mathematical Structures, Bernand Kolman, Robert C. Busby and Sharon Cutler Ross, PHI.

3) Discrete Mathematics and its Applications with Combinatorics and Graph Theory, K. H. Rosen, 7th Edition, Tata McGraw Hill.