What is Discrete math: Definition and 213 Discussions
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West (University of Illinois, Urbana).
I have a doubt about the notation and alternative ways to represent the terms involved in sums.
Suppose that we have the following multivariable function,
$$f(x,y)=\sum^{m}_{j=0}y^{j}\sum^{j-m}_{i=0}x^{i+j}$$.
Now, let ##\psi_{j}(x)=\sum^{j-m}_{i=0}x^{i+j}##. In the light of the foregoing, is...
I submitted this solution, and it was marked incorrect. Could I get some feedback on where I went wrong?
Let S represent the event that Party A wins the senate and H represent the event that Party A wins the house.
There are 4 cases: winning the senate and house (##S \cap H##), winning just...
I need to show the following thing: Given a collection of 5 rays (half-lines) in the plane, show that it can be partitioned into two disjoint sets such that the intersection of the convex hulls of these two sets is nonempty.
Attempt - I am stuck at this problem for hours, couldn't make any progress. Still, here's what I've done :
Let ## e_1 \in E_1 \setminus E_2 ## be arbitrary. Suppose for the sake of contradiction that ## \forall ## ## e_2 \in E_2 \setminus E_1 ##, ## T_1' = \langle V,(E_1\setminus \{ e_1 \})...
There are 4 people that they going to split 50 gold between them. They got one extra gold that they can pay for punishment. All person makes a proposal that how can share the gold. Of the remaining players in the game, including the bidder
If more than half (half is not enough) accepts the bid...
Homework Statement
p→(q→r)
¬q →¬p
p
-----------------------
∴r
Homework Equations
The Attempt at a Solution
My book gives the following solution:
(1) p - premise
(2) ¬q→¬p premise
(3) q, (1) and (2) and rule of detachment,
(4) p and q, law of conjuctive addition
.
.
.
Can anyone explain to...
Here's a math question I've been thinking about lately.
We have a stick of length one which is broken in one spot (with that spot chosen randomly and uniformly). Of the two broken pieces we take the one on the right and break it into two pieces in the same manner as before.
With our three...
Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance...
Homework Statement
Prove by Strong Mathematical Induction[/B]
Homework Equations
N/A
The Attempt at a Solution
The steps to solving this problem are shown below. I understand all steps of the problem until the part where it says 44/49 becomes 49/49 since 44 < 49. Can someone please explain...
Hey everyone,
Pardon the novel of a post.
Short story:
Got an 'A' in Discrete 1 (proof methods) using Epp's book at community college with an easier professor (the only offering for that course), and I'm understanding nothing to very little amount of information in Discrete 2 (computational...
Homework Statement
We have JUST started writing proofs recently, and I am a little bit doubtful in my abilities in doing this, so I just want to verify that my proof actually works. I was expecting this one to be a lot longer since the previous 2 were. I don't see any glaring flaws in it, but...
The title more accurately should have been "How do you cancel floors and ceilings in discrete functions"
For instance,
##\frac{log{\frac{3x}{-6(z)}}}{8t} < 1##
If I wanted to get rid of the log, I'd just raise the expression by base 10.
##\frac{(\frac{3x}{-6(z)})}{10^{8t}} < 10^1##
But what...
Sorry in advance if I've posted in the wrong section.
given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}##
where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##
How would you go about finding the bounds of something like this, or determining if it even has any?
##( \...
Hi,
My classes don't start until next week and I am trying to get a head start in my linear algebra, discrete math and calc 3 class!
I am using Discrete Math by Epp 4th edition.
1) I know 4 =/ {4} but why? 4 is a symbol representing the number 4, and {4} is a set with only one element which...
I have been studying discrete mathematics for fun and I am kind of stuck on this bijection problem.
1. Homework Statement
I wanted to apologize in advance if i put this homework question in the wrong part of the forums. Discrete Math and much logic math is a computer science type math of...
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...
$$ƒ = b^n$$
$$ b,n,I ∈ ℤ $$
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...
To prove that n log n is big oh of log(n!), I did:
n log n <= C log(n!)
n log n/ log(n!) <= C
Let k = 1
n > k, so for n = 2
2 log 2 / log 2 <= C
2 <= C
C is an element of [2, infinity)
Taking C = 2 and k = 1
can we say, n log n <= 2 log(n!)
and hence n log n is big oh of log(n!) ?
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...
Hi guys,
I have functioning MATLAB code for my solution of the 3D Diffusion equation (using a 3D Fourier transform and Crank-Nicolsen) that runs just from the command window and automatically plots the results. However, it seems like my solution just decays to zero regardless of what initial...
my attempt.
Let P = At least one a and at least one b
Let Q = r=a/b
Hence the proposition is simplified to,
For all r where P Then Q
Negation:
Not all r where P Then Q
= Atleast one R When Not(P Then Q)
Not(P Then Q) = P And Not Q
Hence
Atleast one R When Not(P Then Q)
= Atleast one R When...
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.
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...
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...
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...
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.
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!
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...
Homework Statement
Let:
P(x) = "x is a clear explanation"
Q(x) = "x is satisfactory"
R(x) = "x is an excuse"
x be the domain of all English texts
Translate:
1. Some excuses are unsatisfactory
2. All clear explanations are satisfactory
Homework Equations
∃ for "some"
The Attempt at a...
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...
(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...
(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...
<<Mentor note: Missing template due to originally being posted in other forum.>>
So, my professor gave a problem which stated:
Given a 15 x 20 rectangle, prove that if 26 points are chosen, at least one pair will be at most five units away.
What I said was to split the rectangle into 12 5x5...
How do I solve this
1. (a) Solve the recurrence relation
an =6an−2 +8an−3 +3an−4 +64·3^n−4, n>=4
where a0 =0,a1 =1,a2 =4 and a3 =33.
(b) Write down a closed form of the generating function of the sequence an.
Homework Statement
Given a positive integer n written in decimal form, the alternating sum of the digits of n is obtained by starting with the right-most digit, subtracting the digit immediately to its left, adding the next digit to the left, subtracting the next digit and so forth. For...
Homework Statement
Prove that the following four statements are equivalent:
(a) n2 is odd.
(b) 1 − n is even.
(c) n2 is odd.
(d) n2 + 1 is even.
Homework Equations
None really, just the use of different proofs ( indirect, etc...)
The Attempt at a Solution
I'm having trouble with this one...
Homework Statement
How many ways can you select 10 jellybeans from colors Red, Blue, Green so that at most you only have 4 Green jellybeans?
Homework Equations
...
3. The Attempt at a Solution [/B]
# of ways = # of ways to pick 1 Green + # of ways to pick 2 Green + #of ways to pick 3...
< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
(A+B)&(C+D) + (A+B)&(C+D)' + C
(A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans
(A+B)&[(C+D)+(C'&D')] + C by Distributive
I'm just wondering if I did anything wrong in this simplification or if it...
Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major
1. Homework Statement
"If 1+1=3 then 2+2=4"
Homework Equations
We just covered conditional...
Hi everyone,
I haven't been successful in Discrete Math this semester. I have finished all of the calculus I-III series and I did very well. I want to know if anyone can give me some tips on how to study for my final coming up in a few days.
Now, I understand that is a vague question but I am...
Homework Statement
Let A=RxR=the set of all ordered pairs (x,y), where x and y are real numbers. Define relation P on A as follows: For all (x,y) and (z,w) in A, (x,y)P(z,w) iff x-y=z-w
Homework Equations
R is reflexive if, and only if, for all x ∈ A,x R x.
R is symmetric if, and only if, for...
Prove the following theorem:
Theorem For a prime number p and integer i,
if 0 < i < p then p!/[(p− i)! * i] * 1/p
Not sure how to go about this. I wanted to do a direct proof and this is what I've got so far.
let i = p-n
then p!/[(p-n)!*(p-n)] but that doesn't exactly prove much.
Show that A - (B intersection C) = (A - B) union (A - C)
I went about this completely around on a test but here is what I have
Right Hand Side = ( A - B) union ( A - C)
= (A intersection B) union (A intersection C)
= A - (B intersection C) ?
Easy problem but confused..thanks
I am a math major currently in a community college reputed for having an outstanding math department, lucky me :D. I am taking Calculus 2 this semester. Next semester I'll be taking Calculus 3 with linear algebra or discrete math. Can I take all three at the same time or would it be an overkill...
I am currently enrolled in Calculus 1. Will be taking Calculus 2 in summer and Calculus 3 in Fall. I have already registered for these courses. One of the Math electives I have a choice in Fall Semester is either Discrete Math or Linear Algebra. Any suggestions would be greatly appreciated...
Hi all I need some assistance
1. Homework Statement with the attempt
How many 5-digit briefcase combinations contain
1. Two pairs of distinct digits and 1 other distinct digit. (e.g 12215)
I wasn't sure on which approach was correct.
10 * 9 * 8 (because there are three distinct...
How to have better discrete math "insight"
Greetings:
I came a cross a textbook example in a discrete math book that I have been reading on my own, and I thought this example in the book was a good example of what I want to be good at:
Given integers from 0-9 arranged in a circle, is...