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Mathematical Foundations of Computing incorporates various techniques to prove various algorithms mathematically, methods and reasons to model problems and the techniques to be applied to explore properties of problems. The elementary nature of computation is perceived along with the determination of its method.

The various aspects that are considered in the computing foundations are discrete mathematics include set theory ,graphs , proof techniques, relations, functions, mathematical induction; finite automata to analyse the limitations of algorithms; turing machines and undecidability that can demonstrate various problems include the set theory ,graphs , proof techniques, relations, functions, mathematical induction with comparatively large running time x ,complexity theory and NP- completeness that help to bring the efficiency in algorithms.

Mathematical Foundations of Computing includes:

Graphs,the mathematical structures used for modeling problems that are complex. These are the basic structures for the models of computation.

When the results about discrete structures and programs are to be proven, mathematical induction techniques are explored in mathematical foundation of computing.

The different ways of interrelation between the objects and their mathematical structures.

The study of properties of infinity that comes under the set theory.

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**Topics for Mathematical Foundations of Computing Assignment help :**

- Proof techniques and logic; induction; sets, functions, and relations; formal languages; DFA's, NFA's, and Regular Expressions; Context-Free Grammars, Turing Machines, and NP-Completeness, Transition to Formal Mathematics: writing mathematically,sets,relations and functions,Logic: propositional logic,predicate logic,logical equivalence proofs
- Techniques,Sequences,Inductionand Recursion:proof structure and strategies,number theory tools that are used in CS,sigma notation,manipulating sequences,strong induction,recurrence relations,Sets, Functions, and Relations:the language of set theory,set theoretic proofs
- Classes of functions,composition of functions,properties of relations,equivalence relations ,Combinatorics: ,counting,possibility trees,permutations,combinations,pigeonhole principle,probability,expected value,random variables,correctness of algorithms,trees,general graphs,automata,algorithm analysis

**Complex topics covered by Mathematical Foundations of Computing Assignment online experts :**

- Cantor's Theorem,Propositional and First-Order Logic,Functions,Cardinality,Relations,Induction,DFAs,NFAs, Regular Languages,Regular Expressions,Nonregular Languages,CFGs,TMs,Church-Turing Thesis,Decidability,Recursion Theorem,Undecidability,Unrecognizability,Verifiers,P and NP,Reducibility,NP-Completeness,Counting: product rule,Counting: permutations, combinations Counting: combinations, complementing,Counting: Inclusion-exclusion, pigeonhole principle; intro to probability,Equally likely outcomes,Conditional probability, Law of Total Probability, Bayes' Theorem,Independent events,Applications of independence
- Naive Bayes classifier,Random variables, expectation, geometric random variable,Linearity of expectation,Variance,Independent random variables,Uniform, Bernoulli, and binomial distributions,Error-correcting codes, Poisson distribution,Continuous random variables,Uniform, exponential distributions,Normal distribution, Central Limit Theorem,Applications of Central Limit Theorem,Counting: product rule,Counting: permutations, combinations,Counting: combinations, complementing,Counting: Inclusion-exclusion, pigeonhole principle; intro to probability,Equally likely outcomes, Conditional probability
- Law of Total Probability,Bayes' Theorem,Independent events,Applications of independence,Naive Bayes classifier,Random variables, expectation, geometric random variable,Linearity of expectation,Variance,Independent random variables,Uniform, Bernoulli, and binomial distributions,Error-correcting codes, Poisson distribution,Continuous random variables,Uniform, exponential distributions,Normal distribution, Central Limit Theorem,Applications of Central Limit Theorem,Formal language theory,Proof techniques and applications,Propositional predicate logic,Induction,constructive proofs & proofs by induction:Triangle numbers, irrational numbers & prime numbers,Greatest Common Divisors & the Euclidean Algorithm,Binary numbers & conversions from binary to decimal
- Egyptian fast-exponentiation algorithm,Congruences and Fermat’s Little theorem ,Applications to Cryptography,Mathematical induction ,Basic arithmetic and geometric sums & closed forms,Growth rate of functions,Big-O notation,Applications to algorithms,Recursion,Compound Interest, Binary Search, Insertion Sort & Merge Sort,Chinese rings puzzle,The Josephus Problem,Solving recurrence equations,Linear homogeneous equation,linear non-homogeneous equations,Combinations and permutations,Pascal’s triangle & binomial coefficients.,Counting problems using combinations,distributions and permutations,Discrete probability,Inclusion/Exclusion Theorem,Associative, Distributive & De Morgan's Laws.,Bit Operations in Java.,Computability and Undecidability,Propositional Logic & Boolean Algebra,Logic Gates ,Circuits and Applications
- partial fractions ,binomial theorem,analytic geometry,functions and graphs,exponential and logarithmic functions,trigonometry,differentiation,implicit differentiation ,stationary points,curve sketching, simple integration,matrix algebra