 # JNTUK B.TECH R20 2-1 Syllabus For Mathematical foundations of computer science PDF 2022

### Get Complete Lecture Notes for Mathematical foundations of computer science on Cynohub APP  You will be able to find information about Mathematical foundations of computer science along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Mathematical foundations of computer science after reading this blog. Mathematical foundations of computer science has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Mathematical foundations of computer science can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

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### Mathematical foundations of computer science Unit One

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.

### Mathematical foundations of computer science Unit Two

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.

### Get Complete Lecture Notes for Mathematical foundations of computer science on Cynohub APP  ### Mathematical foundations of computer science Unit Three

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, Fermat’s and Euler’s Theorems

### Mathematical foundations of computer science Unit Four

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

### Mathematical foundations of computer science Unit Five

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, Euler’s Theorem, Graph Colouring and Covering, Chromatic Number, Spanning Trees, Prim’s and Kruskal’s Algorithms, BFS and DFS Spanning Trees.

### Mathematical foundations of computer science Course Objectives

This course is designed to:

To introduce the students to the topics and techniques of discrete methods and combinatorial reasoning

To introduce a wide variety of applications. The algorithmic approach to the solution of problems is fundamental in discrete mathematics, and this approach reinforces the close ties between this discipline and the area of computer science

### Mathematical foundations of computer science Course Outcomes

At the end of the course student will be able to

Demonstrate skills in solving mathematical problems

Comprehend mathematical principles and logic

Demonstrate knowledge of mathematical modeling and proficiency in using mathematical software

Manipulate and analyze data numerically and/or graphically using appropriate Software

Communicate effectively mathematical ideas/results verbally or in writing

### Mathematical foundations of computer science Text Books

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

Elements of Discrete Mathematics-A Computer Oriented Approach, C. L. Liu and D.

P. Mohapatra, 3rd Edition, Tata McGraw Hill.

### Mathematical foundations of computer science Reference Books

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

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

Discrete Mathematics and its Applications with Combinatorics and Graph Theory, K.

H. Rosen, 7th Edition, Tata McGraw Hill.

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