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MRWmath
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 About
 
Author(s): Michal Ryszard Wojcik
Other collections by the author:
 
 
No. of items: 1505
Rating: 4.0 (out of 5)
Last updated: Apr 28, 2003
 
 
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Due to SuperMemo Library being moved to a new server, you can currently order this collection only as a subset of one of the mixes from Super Memory Store that are listed in the Order as part of... section you can find in the left pane of this page (if available). We sincerely apologize for any inconvenience this may cause.
Our entire assortment is being republished incrementally in order of priority as determined by the quality and popularity of individual collections. If you would like to increase the priority of this collection, contact us by writing to: publish (at) super-memory (dot) com with in the subject.

 Description
 
This is my personal mathematical collection. It is not a commercial product designed for a generic user. The collection is full of references to my notes in my notebooks. It is incomplete without my notebooks. Very often, the answer is simply the number of a page in my notebooks.
Sometimes, the answer is given in the answer field.

I decided to publish my collection in order to inspire other people to use SuperMemo for mathematics. This collection can be downloaded for free.

If you have any comments about this collection please write to the author:

Michal Ryszard Wojcik
(MEE how RISH uhrd VOY chick)

 
 Sample
 
Q: In the extended real number system, why can't we define: oo+(-oo)=0?
A: Because then we could prove that oo+(-oo)=7 by using associativity.

A: 1) oo+(-oo)=0
A: 2) 7+[ oo+(-oo) ] = 7 + 0
A: 3) [7 + oo] + (-oo) = 7
A: 4) oo + (-oo) = 7

Q: Investigate the uniform convergence of
Q: f[n](x) = sqrt(n) * x * (1-x*x)^n on [0,1].
A: No uniform convergence on [0,1].
A: Use: x[n] = 1 / sqrt(n)

A: If 0<M<1, then uniform convergence on [M,1].

Q: What is a ring of sets?
A: Let X be a set. Let R c P(X).

A: R is a ring of sets
A: iff
A: (1) R is nonempty
A: (2) A,B :- R => A u B :- R
A: (3) A,B :- R => A \ B :- R

Q: Let a[n] be a decreasing sequence of positive numbers.

Q: (1) the series a[n] converges
Q: (2) the series 2^k * a[2^k] converges

Q: Prove that (1) <=> (2).

A: page 58 in the first analysis notebook

Q: Express differently:

Q: max(x,y) = ???

A: max(x,y) = ( x + y + |x - y| ) / 2

 
 
  Compatibility
 
To use this material you need the SuperMemo software Go to another website with more information. In the table below can you find what versions of SuperMemo the MRWmath collection is compatible with

SM6 Go to another website with more information SM7 Go to another website with more information SM8 Go to another website with more information SM98 Go to another website with more information SM99 Go to another website with more information SM2000 Go to another website with more information SM2002 Go to another website with more information Palm SM Go to another website with more information SMCE Go to another website with more information
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MRWmath, (SM2000 format or later, 378 KB)
Download time: 1 min @ 56 Kbps

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