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Discrete Mathematics

Discrete mathematics is defined as a branch of mathematics which deals with discrete mathematical structures. It does not support continuous mathematical structures and deals with various topics like discrete calculus, discrete analysis, operations research, combinatorics, probability, and many others. Few applications of the Discrete Mathematics are as follows:

• Computability
• Data Structures
• Algorithm design
• Complexity theory
• Compiler design
• Relational database theory
• Mathematical logic

Discrete mathematics tells about the proof techniques and mathematical reasoning. It is extended through algorithms of computer programming to analyze the difficult infrastructure such as utility distribution, highway and traffic pattern, and many more. It interrelates with the other major disciplines such as physics, science, computer science, topology, algebra, etc. It is real world mathematics and essential to the college–level mathematics. Theory of computation and graph theory are considered as the parts of the discrete mathematics.

Discrete mathematics becomes popular in the today’s world due to its applications in CS. It is also known as the mathematics of computing as its concepts plays an important role in determining the problems in the section of computer science, such as cryptography, programming languages, computer algorithm, etc. Some of the core topics that involved in the Discrete Mathematics are listed below:

• Sets: it refers to the disordered collection of various elements. There are various types of set, including Subset, Proper subset, Finite set, Universal set, Overlapping set, Disjoint set, and many others.
• Functions: functions are allotted to the each element of the set.
• Predicate logic: it deals with predicates which contain variables.
• Counting theory: it involves the combination rule, counting rule and permutation rule.
• Probability: it refers to the sub-disciplines of mathematics that mainly concerned with the events that occur in the countable sample spaces.
• Rules of Inference: Rules of inference is used in acquiring the new statements from the given statement whose truth we already know.
• Propositional logic: it refers to a statement which is either true or false.
• Relation: it occurs between the objects of sets.

Extremal graph theory in discrete computing refers to the branch of graph theory that tells about the intrinsic structures of graphs which satisfy a definite property under the suitable conditions.

However, Extremal finite set theory is known as the quickly developing areas in Combinatorics. It has the several applications in the branches of CS and Mathematics such as Probability theory, Functional Analysis, Discrete Geometry, etc. It also involves the applications of probabilistic arguments in itself.

Here is an exposure to core Advanced topics in Discrete Mathematics:

• Upper-level set theory: set theory mainly concerned with the sets which are the collections of objects. Countable sets play an important role in the Discrete Mathematics.Major topics that involved in the Upper level set theory are Zermelo-Frankel Axioms, Topoi and Axiomatic set theory.
• Upper-level number theory: it concerned with the properties of numbers, mainly with the positive integers. It has applications in various areas such as Diophanyine equations, cryptanalysis, cryptography and many more. Major concepts that involved in this are Analytic Number theory, polynomials, number representations, arithmetic functions, finite fields and modular arithmetic.
• Upper-level logic: major concepts that involved in the Upper-level logic are second order logic and Godel’s incompleteness theorem.

Asymptotic Notation is known as the algorithm’s growth rate which enables user to analyze the algorithm’s running time by recognizing its behavior as the input size for algorithm increases.

Furthermore, Automata theory is a theory in discrete mathematics which concerned with the automata and abstract machines for solving the computational problems. Four major families of automata theory are Pushdown automata, Turing machine, Linear-bounded automata and Finite-state machine.

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• Bijective principle
• Extremal set theory
• Hardy-Ramanujan theorem
• Random graphs and Subgraph count
• Regularity method
• Girth and Chromatic number
• Local Lemma
• Chebysev inequality

Beside these complex topics, our experts provides the assignment on several more topics of Discrete Mathematics such as boolean algebra, graphs, trees, modeling computation, mathematical inductions, integers, matrices, and many other. Our experts are capable to write assignment on any topic of Discrete Mathematics. There is nothing is impossible for them. Choose us for getting the best Discrete Mathematics Assignment help. Advantages you get by going for our Discrete Mathematics assignment help are listed below:

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Discrete mathematics which is another name for mathematics that mainly deals with discrete objects. Discrete objects are those which are separated from each other. Integers , rational numbers , people houses ,automobiles, etc. are the example of discrete objects. But real numbers which include irrational as well as rational numbers are not discrete. The main reason behind it is: between any two different real numbers there is another real number which is different from either of them. So they are packed such that there are no gaps and they can't be separated from their immediate neighbors.So,according to this they are not discrete.

Discrete mathematics mainly discusses the languages which is used in mathematical reasoning and their properties and relationships among them. But there is no time to cover them in this course, discrete mathematics is also concerned with
techniques which help in solving certain types of problems such as how to count or enumerate quantities.

## Some of the homework help topics include:

• Rigorous treatment of theories of international trade , international factor movements, Examination of the impact of trade, labor migration on domestic, world Logic, propositional logic, logical equivalence, predicates, quantifiers, logical reasoning, Sets, basics, set operations, Functions one to one, onto functions, inverse functions, composition functions, graphs functions, Integers, greatest common divisor, Euclidean algorithm, Sequences, Summations, Mathematical reasoning, Proof strategies, Mathematical Induction, Recursive definitions, Structural Induction, Counting, basic rules, Pigeon hall principle, Permutations, Combinations, Binomial coefficients, Pascal triangle Probability Discrete probability Expected values variance Relations, properties, Combining relations, Closures, Equivalence, partial ordering, Graphs, directed, undirected graphs
• Administrivia Propositional logic, Propositional logic, Predicate logic, Formal informal proofs, Informal proofs, set operations, Sequences summations, Countable and uncountable sets, Matrices, Integers division, Congruency, CS applications, Mathematical induction and recursion, Counting, permutations, combinations, Counting, advanced counting methods. Probability, Probabilities, Bayes theorem, Bernoulli trial, Random variables, Expected value, Probabilities, expected value, Relations, Graphs, graph types, graph properties, Graphs, Connectivity, Trees, Compound Statements, Proofs in Mathematics, Truth Tables, The Algebra of Propositions, Logical Arguments, Sets, Operations on Sets
• Binary Relations, Equivalence Relations, Partial Orders, Domain, Range, One-to-One, Onto, Inverses Composition, Cardinality of a Set, Division Algorithm, Divisibility, Euclidean Algorithm, Prime Numbers, Congruence, Applications of Congruence, Mathematical Induction, Recursively Defined Sequences, Solving Recurrence Relations, Characteristic Polynomial, Solving Recurrence Relations, Generating Functions, Principle of Inclusion Exclusion, Addition Multiplication Rules, Pigeon Hole Principle, Permutations, Combinations, Repetitions, , distribution of income, Theoretical analysis of government policies, trade, factor movements, including quotas, tariffs, free trade areas , immigration restrictions, Discussion of contemporary issues , controversies concerning globalization, multinational firms, labor migration

Some of the homework help topics include:

• Rules of inferences , set theory, relations and functions , graphs, trees and sorting , shortest path and minimal spanning trees algorithms
• Quantifiers, proofs of theorems , Fundamental principles of counting  , fundamentals of logic ,the laws of logic
• Linear equations ,  inequalities , matrix algebra , linear programming ,discrete probability

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• Theory of mathematical proof, specification of deductive proofs in an axiomatic system, types of proofs, generalization , falsification, inductive proof , Theory of sets, algebra of sets, functions, relations, counting, combinatorics , Matrices, inverse matrix, system of linear equations, Gauss elimination method, determinants
• Algebraic structures, binary operations, groups, permutations, Boolean algebra, Boolean functions, Graph theory, representation of graphs, planar graphs, paths, cycles, trees, algorithms, applications, set theory, combinatorics, number theory, probability theory, graph theory, Pigeonhole Principle, Proofs, Induction, Strong Induction, Induction
• Propositional logic, Equivalences , Normal Forms, Logic, computers, Quantificational logic , Sets, Relations , functions, Uncountable sets, Structural induction, States , Invariants, Directed Graphs, Graphs , Relations, Undirected graphs, Connectivity, Trees , Coloring, Growth Rates of Functions, Basic counting, Counting subsets, Basic probability, Conditional probability, Bayes Theorem, Random variables , expectation.
• Finite systems, Logic, Boolean algebra, Induction and recursion, Sets, Functions , Relations, Equivalence, Partially ordered sets, Elementary combinatorics, Modular arithmetic , Euclidean algorithm, Group theory, Permutations , Symmetry groups, Graph theory, Selected applications,
• What is a Proof?, Combinatorics and Probability,Introduction to Graph Theory, Number Theory and Cryptography, Delivery Problem
• Basic Algebraic Graph Theory
• Matroids and Minimum Spanning Trees
• Submodularity and Maximum Flow
• NP-Hardness
• Approximation Algorithms
• Randomized Algorithms
• The Probabilistic Method
• Spectral Sparsification using Effective Resistances