- Fri Feb 27, 2015 4:04 pm
- Forum: Discrete Math
- Topic: Find two proofs for the identity
- Replies:
**4** - Views:
**96**

Using a combinatorial argument, prove the following identity: \binom{2n}{2}\,=\,2\,\binom{n}{2}\,+\,n^2 To use a "combinatorial argument", one must consider sets of elements. On the left-hand side: Consider a set with 2n elements, and pick two elements at a time. This may be done in C(2n,...

- Sun Feb 15, 2015 3:05 am
- Forum: Calculus
- Topic: Finding the derivative of arctan
- Replies:
**1** - Views:
**97**

y=arctan sqrt[(1+x)/(1-x)] what i did: let u= sqrt[(1+x)/(1-x)] du=1/2 [(1-x)/(1+x)]^1/2 [{(1+x)(-1)-(1-x)}/(1+x)^2]dx I solved this problem many times, but I don't get the right answer.... Where did you take the derivative of the inverse tangent? What did you get for your answer? What is "the...

- Fri Jan 30, 2015 7:37 pm
- Forum: Matrix (Linear) Algebra
- Topic: is A C B^T = B C^T A^T ?
- Replies:
**1** - Views:
**275**

I don't understand how A C B^T + B C^T A^T = 2 A C B^T This may be rearranged as: A C B T + B C T A T = A C B T + A B C T This results in: B C T A T = A B C T Two properties of transpositions are that the transpose of a transpose is the original matrix, and that the transposition of a product resul...

- Fri Jan 30, 2015 7:26 pm
- Forum: Advanced Algebra ("pre-calculus")
- Topic: Eigen Vaues and Eigen Vectors
- Replies:
**1** - Views:
**223**

The information at the link appears to be as follows: \left[ \begin{array} {rr} 50&-40\\-40&45 \end{array} \right] \,\left[ \begin{array} {cc} X_1\\X_2 \end{array} \right]\, =\, \lambda\,\left[\begin{array}{rr}2&0\\0&5 \end{array} \right] \,\left[ \begin{array} {cc} X_1\\X_2 \end{arr...

- Fri Jan 30, 2015 7:10 pm
- Forum: Geometry
- Topic: Line Geometry and Euclid proposition 4 and 8 in book I
- Replies:
**1** - Views:
**187**

Is there a book which has axioms for geometry on a line? Possibly ("probably"?) not. However, some information is available, such as ( this ) online article. Most other resources appear to be quite advanced, usually treating one-dimensional "cases" of other topics, such as "...

- Wed Jan 28, 2015 1:03 pm
- Forum: Calculus
- Topic: Inverse Function for y = x^(m+1) + x
- Replies:
**2** - Views:
**251**

wan nini wrote:I...need to find the inverse function.

y=x^{m+1}+x

I can't think of any way to invert this. How did you arrive that this function? What was the original exercise? Thank you.

- Mon Dec 22, 2014 5:38 pm
- Forum: Advanced Algebra ("pre-calculus")
- Topic: Multi Variable Partial Fraction Problem
- Replies:
**2** - Views:
**374**

The problem is to develop . . . . . \dfrac{(x\, -\, \alpha)(x\, -\, \beta)(x\, -\, \gamma)}{(x\, -\, a)(x\, -\, b)} into partial fractions. Someone challenged me to solve this and said that the answer is . . . . . x\, -\, (\alpha\, +\, \beta\, +\, \gamma\...

- Sun Dec 07, 2014 5:47 pm
- Forum: Uncategorized
- Topic: Calculation of point of no hope
- Replies:
**1** - Views:
**327**

Is there a mathematical way to calculate a student's grade standing in real time so that they can know when they have reached the point of "no hope" in passing the course? I would like to provide a simple method for my students to know when they need to take action regarding my course bas...

- Sat Oct 04, 2014 3:25 am
- Forum: Discrete Math
- Topic: Counting
- Replies:
**1** - Views:
**418**

Let A be a set with n elements and B with m elements. How many functions are there from A to P(B)? A has n elements so A = n, B has m elements so B = m. P(B) = 2 m . Are there (2 m ) n functions from A to P(B)? What is the definition of "P(B)"? Mathematically, a set is not equal to its ca...

- Thu Oct 02, 2014 1:12 pm
- Forum: Discrete Math
- Topic: Functions And Encylopedia of Integer Sequences
- Replies:
**2** - Views:
**435**

1. Where did the concept of a function first arise, and describe how this concept was first used. This is a question related to the history of mathematics. Resources (such as books ) may be consulted for this information, should it be available. (It is noted that many questions, such as "why u...