I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this.
How can I inspire them to love essential kind of mathematics? They love doing mathematical techniques...
First, I don't know if this is the right place so if not, please direct me. Thank you.
As for the question, I am in a discrete mathematics class online. The instructor is practically non-existent when asking for help simply saying to "refer to the book for clarification". I have scoured google...
1. Homework Statement
a) I have to find and expression for sequence of $b_n$ in terms of generating functions of the sequence of $a_n$
$$b_n = (-1)^{n}(n+1)a_0 +(-1)^{n-1}n a_1+...+(-1)2a_{n-1}+a_n$$ with $$a_n = a_{n-1} +8a_{n-2} -12a_{n-3} +25(-3)^{n-2} + 32n^2 -64$$
b) I have to use the...
1. Homework Statement
The question is counting how many sequence length 10 with 1,2,3 if
a) increasing from left to right with repetition allowed
b) increase from left to right with each number appear at least once (still with repetition allowed)
2. Homework Equations
It is the stars and...
1. Homework Statement
Find the probability that a hand of five cards in poker contains four cards of one kind.
2. Homework Equations
3. The Attempt at a Solution
Solution given in the book:
By the product rule, the number of hands of five cards with four cards of one kind is the product of...
1. Suppose P(x) and Q(x) are propositional functions and D is their domain.
Let A = {x ∈ D: P(x) is true}, B = {x ∈ D: Q(x) is true}
(a) Give an example for a domain D and functions P(x) and Q(x) such that A∩B = {}
(b) Give an example for a domain D and functions P(x) and Q(x) such that A ⊆ B...
Theorem: Let ##A_1, A_2, ..., A_k## be finite, disjunct sets. Then ##|A_1 \cup A_2 \cup \dots \cup A_k| = |A_1| + |A_2| + \dots + |A_k|##
I will give the proof my book provides, I don't understand several parts of it.
Proof:
We have bijections ##f_i: [n_i] \rightarrow A_i## for ##i \in [k]##...
1. Homework Statement
Determine whether the following is valid:
p \rightarrow \neg q , r \rightarrow q , r, \vdash \neg p
2. Homework Equations
Modus Ponens, disjunctive syllogism, double negation.
3. The Attempt at a Solution
I've boiled it down to
p \rightarrow \neg q , q, \vdash...
Hi
All applications of discrete mathematics I know of seem to be in computer science. I want to know if there is somewhere discrete mathematics are applied outside of software.
What can I work as if I like discrete mathematics but do not want to program? (outside of academia, of course)
Homework Statement , relevant equations, and the attempt at a solution are all in the attached file.
I was reading through Invitation to Discrete Mathematics and attempted to solve an exercise that involved a proof. I've typeset everything in LaTeX and made a PDF out of it so that it does not...
1. Homework Statement
http://puu.sh/nYQqE/2b0eaf2720.png [Broken]
2. Homework Equations
http://puu.sh/nYSjQ/e48cad3a8b.png [Broken]
3. The Attempt at a Solution
http://puu.sh/nYYjW/174ad8267c.png [Broken]
My main issue is with part b) and part d). I think that part b) is mostly right...
The problem statement:
How many five-letter strings of capital letters have a letter repeated twice in a row? For example, include ABCCA and AAABC and ABBCC but not ABCAD.
The attempt at a solution:
First, lets break down how we would perform the selection of a string that meets the...
1. 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...
Are fundamental randomness and fundamental determinism inconsistent? Two such different mechanisms would imply a kind of dualism. (Does even the defeatist retreat into Many Worlds avoid this problem - if it is a problem.)
1. Homework Statement
I need to (computationally) solve the following linear elliptic problem for the function u(x,y):
\Delta u(x,y) = u_{x,x} + u_{y,y} = k u(x,y)
on the domain
\Omega = [0,1]\times[0,1] with u(x,y) = 1 at all points on the boundary.
2. Homework Equations
I know...
1. Homework Statement
The question asks me to prove inductively that 3n ≥ n2n for all n ≥ 0.
2. Homework Equations
3. The Attempt at a Solution
I believe the base case is when n = 0, in which case this is true. However, I cannot for the life of me prove n = k+1 when n=k is true. I start...
Hey guys,
I was reading Kenneth's Discrete Mathematics and I came across this definition in the function chapter:
Let f be a function from A to B and let S be a subset of A.The image of S under the function f is the subset of B that consists of the images of the elements of S.We denote...
Hey I was reading Susanna Discrete book and I came across her definition of One-to-One function:
Let F be a function from a set X to a set Y. F is one-to-one (or injective) if, and only if, for all elements x1 and x2 in X,
if F(x1 ) = F(x2 ),then x1 = x2 ,
or, equivalently, if x1 ≠...
Isn't it amusing ?What could be the probable explanation for this?Also when operated by division operator gives the rest of the number as the quotient
(Note only when the divisor is 10)