**“How can you own numbers? Numbers belong to the world.” – Maestro Knuth**

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Recommended Books ** (click for Amazon link)

**Introduction**

Discrete Math is a branch of mathematics that is mainly concerned with the uses of sets and integers, both of which are ‘discrete’, separate objects from one another. The phrase was coined in the 1980s as a catch-all for math topics that were useful for computer science majors, and has evolved into a study on how to think about problem solving in the real world using mathematical (and therefore computational) models.

Discrete math topics often are more concerned with reasoning than numbers – many classes begin with logical statements, mathematical proofs and induction, the important ability to prove something true for infinite amounts of data using two finite steps. When designing programs that will be run on potentially millions of machines around the world, this will help you feel confident that the algorithms and logic you designed will work correctly, no matter the environment it is run in.

Discrete math certainly has its numerical topics as well. The study of summations and their closed algorithmic forms will help you with algorithmic optimization through use of big-O notation, and working with matrices and vectors will give you an introduction into the logic needed to work with large sets of ordered data in their programs.

When companies such as Google and Yahoo were first developing their internet algorithms, they turned to graph theory, another major component of discrete math. Graphs can be used to model relationships between objects and sets of objects. They are also used to model practically any algorithmic problem, and once you have defined the problem as a graph, you can solve it through graph operations like traversal or by checking for connectivity and circularity.

Because discrete math covers such a wide variety of mathematics, it has become the best way to group the most important topics in math needed for computer science. The more exposure a person has to these topics, the better they will be able to handle the challenges of software engineering.

**Resources**

Discrete Mathematics in the Real World (MathILy) (website) [free]

Discrete Mathematics (TutorialsPoint) (website) [free]

Discrete Mathematics (Udemy) (course) [paid]

Discrete Mathematics for Computer Science (Berkeley) (course content) [free]

What exactly is Discrete Mathematics? (Quora) [free]

Spiral Workbook for Discrete Mathematics (PDF) [free]

Discrete Mathematics Notes (Yale) (PDF) [free]

CS 30: Discrete Mathematics in Computer Science (Dartmouth) (lectures) [free]

**IDE**

I used Visual Studio Community 2017 to do coding and testing.

**Code Examples**

01 – Perform all Basic Arithmetic Operations

02 – Generate the Factorial of a Given Number

03 – Generate the Sum of N Numbers

04 – Check Whether the Entered Number is an Armstrong Number or Not

05 – Check Whether the Entered Number is a Perfect Number or Not

06 – Generate Fibonacci Series

07 – Return Factors of Entered Number

08 – Return the H.C.F. of a Given Number

09 – Check Whether the Entered Number is a Amicable Number or Not

10 – Add 2 Complex Numbers

11 – Return Greatest Common Divisor (GCD)

12 – Calculate the Series sin(x)=x-x^3/3!+x^5/!-x^7/7!+

13 – Trigonometry Angles in Degrees

14 – Trigonometry Angles in Radians

15 – Create Multiplication Table

16 – Standard Deviation of a Set of Given Numbers

17 – Mean of Given Set of Numbers

18 – Calculate Simple Interest

19 – Calculate Compound Interest

20 – Find the Value of Cos(x)

21 – Reverse a Number and Check if it is a Palindrome

22 – Calculate the Distance Traveled by Reading Speed and Time

23 – Check Whether Number is a Prime number, if so, Display Largest Factor

24 – Display a Pascal Triangle

25 – Sum of first 50 Natural Numbers using For Loop

26 – Multiply given Number by 4 using Bitwise Operators

27 – Sum of Two Binary Numbers

28 – Display Floyd’s Triangle with a Numeric Mode

29 – Multiplication of two Binary Numbers

30 – Perform Multiplication of Exponents of Same Base

31 – Check the Edge Values in Power Function

32 – Calculate Fractional Power

33 – Calculate the Power Exponent Value

34 – Calculate Period Duration

35 – Calculate Power of Three

36 – Find Whether the Number is Divisible by 2

37 – Show Bitwise Operations

38 – Find Power of 2 using Bitwise Operator

39 – Find Roots of a Quadratic Equation

40 – Display Absolute Value of a Number

41 – Add Two Dates

42 – Generate Register Number Automatically for Students using Static Constructor

43 – Return Lowest Common Multiple (LCM)

44 – Return all the Multiples of 17 which are Less than 100

45 – Return the Sum of all the Multiples of 3 and 5

46 – Return the Cube Root of a Given Number

47 – Return the Square Root of a Given Number

48 – Calculate Area and Volume of a Cone

49 – Calculate nPr

50 – Volume and Surface Area of a Sphere

51 – Calculate Perimeter of Circle and Rectangle

52 – Calculate the Value of nCr

53 – Return the Maximum Range of Values for Decimal, Float, and Double Datatype

54 – Return the Minimum Range of Values for Decimal, Float, and Double Datatype

55 – Calculate 25% Probability

56 – Calculate the Inner Angles of a Trapezoid

57 – Trigonometric Identities

58 – Implement Sin Method

59 – Implement Cos Method

60 – Calculate Root, Mean, Square

61 – Determine if Given Number is a Multiple of 3

62 – Return Prime Factors of Given Number

63 – Return Factorials of 1 through 10

64 – Using Math.Sign Method

65 – Returns Angle whose Tangent is the Given Number

66 – Return Area and Circumference of Circle

tags: Discrete Mathematics, MrNetTek