**Mathematical Foundation of Computer Science Notes: **Candidates pursuing B.Tech can make use of the Mathematical Foundation of Computer Science Notes & Study Material. Get the complete information needed during your preparation for the Mathematical Foundation of Computer Science Exam. You can download the MFCS Notes PDF through the links available on this page and prepare whenever you feel like.

B. Tech Students can even get additional info such as Important Questions List, Best Books on Mathematical Foundation of Computer Science, Syllabus by diving deep into the article.

- Mathematical Foundation of Computer Science Notes PDF Download
- Mathematical Foundation of Computer Science Syllabus – B.Tech 2nd Year 1st Sem
- List of Mathematical Foundation of Computer Science Reference Books
- Mathematical Foundation of Computer Science Important Questions
- How can I Download the B.Tech Mathematical Foundation of Computer Science Books & Notes in PDF?
- Which is the Best Book for Mathematical Foundation of Computer Science?
- How can I Learn the Mathematical Foundation of Computer Science?

## Download Mathematical Foundation of Computer Science Study Material

Aspirants can get guidance regarding the Mathematical Foundation of Computer Science Study Material from here. You can even have additional information such as MFCS Reference Books, Syllabus, and Important Questions List in the further modules. B. Tech Students can use direct links to download the **MFCS Study Material & Notes** without paying a single penny. Make your preparation effective with the ultimate preparation tools and score well.

### Mathematical Foundation of Computer Science Notes PDF Download

Candidates can utilize the quick links over here to access the Mathematical Foundation of Computer Science Notes & Study Material. Make your preparation effective by referring to the study resources and crack the exam with better grades. For the sake of your convenience, we even listed MFCS Question Papers, Lecture Notes all in one place. You can get them free by simply downloading using the direct links and can use it during your exam preparation.

MFCS lecture notes | Download |

MFCS Notes ppt | Download |

Mathematical Foundation of Computer Science Question Paper | Download |

Mathematical Foundation of Computer Science Study Material | Download |

**Do refer: Engineering Mechanics Books**

### Mathematical Foundation of Computer Science Syllabus – B.Tech 2nd Year 1st Sem

Detailed Mathematical Foundation of Computer Science Syllabus is provided here. Be familiar with the course structure, units, and the topics in it. Here we have listed the MFCS Syllabus for students to better understand the concepts. Syllabus prevailing is based on the latest guidelines and you can begin your preparation without wasting time. Go through the **Mathematical Foundation of Computer Science Exam Syllabus** in advance, i.e., before appearing for the exam. Thus, you will not have any difficulty during the time of the exam. Have an overview of the concepts and make a preparation strategy as per it.

#### Unit I – Mathematical Logic

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

#### Unit II – Set Theory

Introduction, Principle of Inclusion and Exclusion, Operations on Binary Sets, Relations: Properties of Binary Relations, Relation Matrix and Digraph, Partition and Covering, Operations on Relations, Transitive Closure, Compatibility, and Partial Ordering Relations, Hasse Diagrams, Equivalence, Functions: Bijective Functions, Inverse Functions, Composition of Functions, Recursive Functions, Permutation Functions, Lattice, and its Properties.

#### Unit III – Algebraic Structures and Number Theory

Algebraic Structures: Algebraic Systems, Examples, Semi Groups and Monoids, General Properties, Group, Homomorphism of Semi Groups and Monoids, Subgroup, Homomorphism, Abelian Group, Isomorphism, Number Theory: Properties of Integers, Division Theorem, The Greatest Common Divisor, Euclidean Algorithm, Least Common Multiple, Testing for Prime Numbers, The Fundamental Theorem of Arithmetic, Modular Arithmetic (Fermat‘s Theorem and Euler‘s Theorem).

#### Unit IV – Combinatorics

Basic of Counting, Permutations, Permutations with Repetitions, Restricted Permutations, Circular Permutations, Combinations, Restricted Combinations, Generating Functions of Permutations and Combinations, Binomial and Multinomial Theorems, The Principles of Inclusion-Exclusion, Binomial and Multinomial Coefficients, Pigeonhole Principle and its Application.

#### Unit V – Recurrence Relations

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

#### Unit VI – Graph Theory

Basic Concepts of Graphs, Subgraphs, Matrix Representation of Graphs: Incidence Matrices, Adjacency Matrices, Isomorphic Graphs, Paths and Circuits, Multigraphs, Eulerian and Hamiltonian Graphs, Planar Graphs, Graph Colouring, and Covering, Euler‘s Formula, Chromatic Number, Spanning Trees, Algorithms for Spanning Trees (Problems Only and Theorems without Proofs).

### List of Mathematical Foundation of Computer Science Reference Books

Aspirants preparing for B.Tech 2nd Year 1st Sem can use the following books suggested by experts during preparation. Go through the **Mathematical Foundation of Computer Science Reference Books & Notes** over here to have a strong foundation of concepts. Preparation becomes a way more effective with these handy study materials and notes. Try picking a book that matches your requirement and cover all the topics in it before appearing for the exam itself. You can score good grades in the exam by going through the MFCS Suggested Books as they give you an explanation of all the topics in a detailed manner.

- 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, 3rdEdition, Tata McGraw Hill.
- Discrete Mathematics and its Applications with Combinatorics and Graph Theory, K. H. Rosen, 7th Edition, Tata McGraw Hill.
- Discrete Mathematics for Computer Scientists and Mathematicians, J. L. Mott, A. Kandel, T.P. Baker, 2nd Edition, Prentice Hall of India.
- Discrete Mathematical Structures, BernandKolman, Robert C. Busby, Sharon Cutler Ross, PHI.
- Discrete Mathematics, S. K. Chakraborty and B.K. Sarkar, Oxford, 2011.

**Also, Check: ****Engineering English Lecture Notes**

### Mathematical Foundation of Computer Science Important Questions

Have a glance at the **Mathematical Foundation of Computer Science Review Questions** and give priority to them during your preparation. Students should read them without fail as there are more chances of appearing in the final exam.

- Prove that a group consisting of three elements is an abelian group?
- Prove that G={-1,1,i,-i} is an abelian group under multiplication?
- Let G= {-1,0,1} . Verify that G forms an abelian group under addition?
- Prove that the order of a-1 is the same as the order of a?
- Prove that the Cancellation laws hold good in a group G?
- State Division algorithm and apply it for a dividend of 170 and divisor of 11.
- Explain in brief about Fermat’s theorem?
- Explain in brief about the Division theorem?
- Prove that the sum of two odd integers is an even integer?
- Explain in brief about GCD with example?
- Define the Prime number? Explain in brief about the procedure for testing of prime numbers?
- Explain in brief about the Principle of Mathematical Induction with examples?
- Use Euler’s theorem to find a number between 0 and 9 such that a is congruent to 7 1000 (mod 10)
- Explain in brief about Euler’s theorem with examples?
- If a=1820 and b=231, find GCD (a, b). Express GCD as a linear combination of a and b.
- Using Fermat’s theorem, find 3201 mod 11.
- Determine GCD (1970, 1066) using the Euclidean algorithm.
- Find 117 mod 13 using modular arithmetic.
- Find the integers x such that i) 5x≡4 (mod 3) ii) 7x≡6 (mod 5) iii) 9x≡8 (mod 7)

### FAQs on Mathematical Foundation of Computer Science

**1. How can I Download the B.Tech Mathematical Foundation of Computer Science Books & Notes in PDF?**

You can download the Mathematical Foundation of Computer Science Books & Study Material for free from this page. Aspirants can find the quick links available online.

**2. Which is the Best Book for Mathematical Foundation of Computer Science?**

There are plenty of books out there in the market for the Mathematical Foundation of Computer Science. We have listed some of the Best Books for MFCS and they are in the following fashion

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, 3rdEdition, Tata McGraw Hill.

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

### Final Words

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