Discrete Definition and 897 Threads

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.
Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.
Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well.
In university curricula, "Discrete Mathematics" appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first-year students; therefore, it is nowadays a prerequisite for mathematics majors in some universities as well. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics is sometimes seen as a preparatory course, not unlike precalculus in this respect.The Fulkerson Prize is awarded for outstanding papers in discrete mathematics.

View More On Wikipedia.org
Recent contents Top users
  1. pizzicato

    A discrete equivalent of the Poisson coefficient

    Hello, I'm about elaborating a discrete mass-spring model to describe the vibration of a thin isotropic plate. For the flexion i choose a kind of spiral spring in the two directions X and Y: so the momentums will be Mx= Cbx.(Delta Thêta) ; My = Cby.(Dela Psi). and the energies: Eb =...
  2. C

    Discrete Lagrangian Homework: Minimize S, Find EoM's & Discrete Trajectory

    Homework Statement In this exercise, we are given a discrete Lagrangian which looks like this: http://imgur.com/TL0P61r. We have to minimize the discrete S with fixed point r_i and r_f and find the the discrete equations of motions. In the second part we should derive a discrete trajectory for...
  3. P

    I Could Planck have used different energy-frequency relation?

    Hello, as a non-physicist enthusiast, but with decent math background, I tried to learn a bit about origins of quantum theory and very soon raised some questions, which I hope this community will answer. So, Planck tried to model the blackbody radiation on where Raighley and Jeans have failed...
  4. B

    MHB Probability of identifying both defective fuses in four or less tests

    This question is driving me crazy. According to the textbook, the answer is 7/15, but I get 2/5. If anyone can tell me where I am going wrong I would be much obliged Here is the question Six fuses, of which two are defective and four are good, are to be tested one after another in random...
  5. Z

    I Discrete Random Vectors vs. Continuous Random Vectors

    Given a continuous random vector (X,Y) with a joint density function In order to check whether it is indeed a joint density ƒ(x,y) the method is to check if ∫∫ƒ(x,y)dxdy=1 where the integrals limits follow the bounds of x and y. However, is it the case that if given an arbitrary discrete random...
  6. C

    Maxima of discrete functions involving nPr, nCr, etc?

    Homework Statement So I want to prove that the expression 20Cr×0.1r 0.9(20-r) reaches maximum value for r=(0.1)×20=2 Homework EquationsThe Attempt at a Solution I can prove it by trial and error but can't differentiate the expression because nCr isn't continuous.
  7. P

    B Is the Universe discrete or continuous?

    Apologies if this question has been asked already. I've been given resources to help me understand, but it's been hard for me to wrap my head around the answer and, for that matter, it is difficult to understand a text when you have to look up every other word (an exaggeration, but you know ...
  8. M

    MHB Combinatorics problem. Discrete Mathematics II

    There is a table tennis tournament consisted of 8 participants that is guided by the following rules: 1. Each player plays with every other player for exactly one party 2. If in the i-round there was a party between A and B and a party between C and D, and A and C play In i+1, then in i+1...
  9. S

    A Discrete Multivariate Probability Distribution

    Homework Statement A fair coin has a ##1## painted upon one side and a ##2## painted upon the other side. The coin is tossed ##3## times. Write down a sample space for this experiment. Let ##X_1## be the sum of the numbers obtained on the first ##2## tosses and ##X_2## be the sum of the numbers...
  10. N

    Discrete Math Computer Science Question

    Homework Statement Find the probability that a randomly generated bit string of length 10 begins with a 1 or ends with a 00 if a)a 0 bit and a 1 bit are equally likely. b)The probability that a bit is a 1 is .7 c)The probability that the ith bit is a 1 is 1/2i for i=1,2,3,...,10 Homework...
  11. E

    MHB Discrete Probability Distribution

    Okay, my online class has posed another word problem and I cannot seem to understand this week's material or how to formulate a solution. Here it is: Imagine you are in a game show, a money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000...
  12. I

    I What's The Discrete Math Derivative Equivalent?

    $$ƒ = b^n$$ $$ b,n,I ∈ ℤ $$ Condition: Upon choosing a base value b.. $$ n | b^n ≤ I $$ (n is determined based off the value of b to yield the highest ƒ without going over I) $$1<b<L , L<<I$$ where I is some large number, and L is also sufficiently large such that we want to avoid going...
  13. J

    B Continuous or discrete acceleration?

    Good day to you all, First, I want to let you all know that I'm new at this and that my question could be a bit vague so I'll try and do my best to explain what I want to know. I read on a forum about the Hubble's value decreasing over time despite the fact that the expansion of the Universe...
  14. S

    Non-Zero Discrete Distributions

    Homework Statement Suppose we have a discrete random variable whose values $X = x$ can include the value $0$. Some examples are: ##X\sim \text{Binomial}(n,p)## with ##x = 0,1,2,\ldots,n## and ##X\sim \text{Poisson}(\lambda)## with ##x = 0,1,2,3,\ldots## Sometimes we can only observe these...
  15. B

    I F'(n) = f(n) in discrete calculus

    We know that in the continuous math, e is special number because if f(x) = e^x, so f'(x) = f(x). But in discrete math, what's the constante base that satisfies this condition? Is not the 2? I. e. f(n) = 2^n ? Thanks,
  16. F

    A Can Discrete Parameters Be Used in Limit Calculations?

    I'm trying to calculate this limit to answer a question in Quantum Mechanics: \mathop {\lim }\limits_{{t_1} \to 0} \,\,{\left( {\frac{m}{{2\pi \hbar i{t_1}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{im{{(x' - x)}^2}/2\hbar...
  17. M

    Math: discrete probability distribution

    Homework Statement We ask a person to taste 18 biscuits , 8 made to butter ( the other 10 are made to margarine ) , and to identify 8 butter cookies . He does not know the exact number of butter cookies . As he sees no difference , he randomly selects those he claims to be butter . Y = the...
  18. X

    How Do You Solve a Discrete Convolution Sum with Step Functions?

    Homework Statement Find ##x[n] \ast h[n]## when ##x[n] = 3 u[2-n]## and ##h[n] = 4\left( \frac{1}{2} \right)^{n+2}u[n+4]## where ##u[n-k]## is the unit step function. Homework Equations None really The Attempt at a Solution So I know this is probably simple but I am confused. So the...
  19. G

    Discrete Which Discrete Math Textbook Should I Choose?

    Hi everyone, I'm helping my professor pick out a new Discrete math book. He has been using Discrete Mathematical Structures 6th Kolman for at least 4+ years. He's on the search of finding one, but hasn't been successful with it. I was wondering what kind of textbook you would recommend. I will...
  20. Y

    MHB Joint distribution of a discrete random variable

    Hello all I have this question I am trying to solve. In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement. X - the minimal number we see Y - the maximal number we see I need to joint distribution. I understand that X is getting the values 1,2,3 while...
  21. barbara

    MHB Discrete Math: Solve Problem & Describe Equivalence Classes

    Can someone help me solve this problem I need to Define the following relation on the set of real numbers xRy if |x - y| is an even integer and Show that R is an equivalence relation and describe the equivalence classes.
  22. K

    Discrete Math - quick probability questions.

    For the life of me I am having a hard time understanding how to do problems of this nature. As I understand it, were using the multiplication rule here with a twist.a. How many integers from 1 through 100,000 contain the digit 6 exactly once? 5 * 9 * 9 * 9 * 9 = 38805 is what I have. Because...
  23. K

    Discrete Fourier series derivation

    Hello,*please refer to the table above. I started from x(n)=x(n*Ts)=x(t)*delta(t-nTs), how can we have finite terms for discrete time F.S can anyone provide me a derivation or proof for Discrete F.S.?
  24. F

    MHB Finding Least Value m with Property P in Discrete Math

    Consider a set X with |X|=n≥1 elements. A family F of distinct subsets of X is sad to have property P if there exist A and B in F, such that A is a proper subset of B and |B\A|=1. Determine the least value m, so that any F with |F|>m has property P. This is a problem asked by our Discrete...
  25. T

    Discrete Math: Poset Characteristics and Minimum Element Count

    Homework Statement My task is to find out what is the lowest # of elements a poset can have with the following characteristics. If such a set exists I should show it and if it doesn't I must prove it. 1) has infimum of all its subsets, but there is a subset with no supremum 2) has two maximal...
  26. little neutrino

    Calculating Probability of 3 Pennies in 30 Boxes Using Poisson Distribution

    One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1? I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5...
  27. L

    Advice request good study stats along discrete math

    I study a textbook in Discrete Math 7e Rosen , I am in ch.4 Number Theory Mainly for computer science improvement (cs) Is it ok study same time a Probability & Statistics textbook again for cs...? I have background in Calculus I II and Linear Algebra & web development.
  28. D

    How to design discrete circuits for transistor beta changes?

    In my circuits/active devices course we had to make amplifier designs with various type of transistors (BJT, JFET, MOSFET). In each design the transistor beta parameter played an important role in deciding which resistors to use in the final amplifier circuit. This beta parameter changes widely...
  29. Dewgale

    Discrete Independent Study of Discrete Mathematics

    Hi all, Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject? Thanks!
  30. L

    Discrete M: Show that if A ⊆ B and C ⊆ D, then A X C ⊆ B X D

    Homework Statement [/B] Sorry that I wasn't able to fit everything in the title. I got 2/3 on this on my quiz, and am wondering what I did wrong, or could have done better. Thanks in advance. Show that if A ⊆ B and C ⊆ D, then A X C ⊆ B X D Homework Equations The Attempt at a Solution For a...
  31. T

    Discrete probability distribution

    Homework Statement 1. Consider selecting at random a student who is among the 15,000 registered for the current semester at a school Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution x: 1 2 3 4 5 6...
  32. K

    Power of discrete sinusoidal signal?

    I am a little confused of the last step. We can set an upper boundary for any arbitrary large number M, so it seems ok. do you agree on the last statement?
  33. T

    Defining a function (Discrete Math)

    I have multiple problems in the current homework set that say something along the lines of "try to define a function f: S -> S by the rule f(n) = n^2 for each n in S. Then it asks a couple questions such as "is the function well defined" or "is it one-to-one/onto" I'm just confused on what its...
  34. Callmejoe

    Discrete Math/Introductory number theory problem

    The instructor to my discrete mathematics course gave this question to us. How do you find the smallest achievable value(V) for which all greater values are achievable using only A and/or B, when A and B are relatively prime(coprime). For example for 5 and 7 the answer is 24 (7+7+5+5). Playing...
  35. K

    Different forms of the discrete Fourier Transform

    Hi I am trying to program excel to take the DFT of a signal, then bring it back to the time domain after a low pass filter. I have a code that can handle simple data for example t = [ 0, 1, 2, 3] y = [2, 3, -1, 4] So I think everything is great and so I plug in my real signal and things go off...
  36. evinda

    MHB Discrete Geometry: Info, Knowledge & More

    Hello! Can you give me information about the subject Discrete Geometry? What is it about? What knowledge is required? (Thinking)
  37. J

    Discrete math: A, but not both B and C

    Homework Statement Translate: A, but not both B and C Homework Equations AB = A and B A+B = A or B ~ = not The Attempt at a Solution I'm not sure if my translation of this is correct: A(B XOR C) The statement is throwing off my translation because usually when I use XOR, it means B or C, but...
  38. D

    Finite field with hard discrete log for both groups

    If there a finite field where both group structures have hard discrete logs? Discrete log in the additive group means multiplicative inverse.
  39. S

    Efficient HMM with Feature Vectors for Improved Sequence Analysis

    Hi all, Not sure if this would be the right place for this question, but I know it bothers me for some time already and would really appreciate any kind of help. I am trying to fit an HMM, but here for every observation in the sequence I have feature vector - probability distribution that given...
  40. RooksAndBooks

    Mastering Discrete Math: A Comprehensive Guide for Beginners in Computer Science

    (I guess you could put this in a computer science section since discrete math is the math of computers.) What learning resources do you recommend for learning discrete math from a person who knows none of it to a person who can do it easily? I have tried to study the topics below but the symbols...
  41. RooksAndBooks

    Where Can I Find Resources to Learn Discrete Math for Computer Science?

    (I guess you could put this in a computer science section since discrete math is the math of computers.) What learning resources do you recommend for learning discrete math from a person who knows none of it to a person who can do it easily? I have tried to study the topics below but the symbols...
  42. L

    How two body decay energy spectrum is discrete?

    it is said that the energy spectrum of two body and three body decay is discrete and continuous respectively.
  43. D

    Discrete Fourier Transform of Sine Function

    (1) For a real function, g(x), the Fourier integral transform is defined by g(x) = \int_{0}^{\infty} A(\omega )cos(2\pi \omega x)d\omega - \int_{0}^{\infty} B(\omega )sin(2\pi \omega x)d\omega where A(\omega ) = 2 \int_{-\infty}^{\infty} g(x)cos(2\pi \omega x)dx and B(\omega ) = 2...
  44. L

    Discrete Signals/Systems Even/Odd Problem

    Homework Statement http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-003-signals-and-systems-fall-2011/assignments/MIT6_003F11_sol01.pdf [/B] Homework Equations None[/B] The Attempt at a Solution To be honest, I don't think you can prove something is impossible...
  45. pvvijaykumar

    Difference between digital and discrete signal

    what is difference discrete and digital signal
  46. haruspex

    Insights FME in Probability - Continuous and Discrete Distributions - Comments

    haruspex submitted a new PF Insights post Frequently Made Errors in Probability - Continuous and Discrete Distributions Continue reading the Original PF Insights Post.
  47. S

    Inverse Discrete Laplace Transform

    Hi, I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar. The first two are the laplace transform. The third line is the Fourier Transform. The...
  48. R

    Zero order hold -- Discrete control systems

    I have some questions related to how a discrete control system is designed. One method is to design the controller in the continuous time domain, arriving at a transfer function (in the s-domain). After that, a transfer function for the ADC system must be taken into consideration. I will suppose...
  49. C

    MATLAB Transforming Complex Exponential to Discrete Vector Form

    Hi, I want to transform a complex exponential with quadratic phase to discrete form, in other words to a vector form. can anyone help me with that? Thanks
  50. P

    Are discrete particles and fields both present in Quantum Mechanics?

    Does QM contain both discrete particles and fields? If so, why aren't these two mutually exclusive? It seems like one is chunky and the other continuous.
Back
Top