Continuing math education questions - Page 3

nibble4bits · 2006-01-22, 23:40

The manuals that come with some calculators are very good at teaching you how to get the answer so you be sure that you're using the right method when you go to a calculator-less test. Even better is that you have another method to use depending on what's the best way to solve a problem, using your experience with both ways.

Some (if not most) of the math books offered with online extensions allow you to get a list of chapters and sometimes even examples and practice tests. Use the practice tests to determine which areas to study first!

The examples in the books should point you in the right direction as far as solving a class of problems is concerned. Good luck!

jasong · 2006-08-16, 22:02

Can you guys point me in the right direction as to how I can learn about the following symbol?

Σ

Also there is another symbol(used at oddperfect.org) which I think is the lowercase version of the above symbol. I'd like to learn about that symbol too.

Any help is appreciated.

fetofs · 2006-08-16, 22:20

To enlighten you, an example:

$\sum_{k=2}^6 {k^2} = 2^2+3^2+4^2+5^2+6^2 = 90$

The value on below is the initial setting, k=2. k is incremented up to the upper bound, the upper value, 6. On the right is the expression to be summed, $k^2$ . It means, for k initially equal to 2 and up to 6, sum the value of k^2.

Did I make myself any clear?

OTOH, the σ symbol (the lower case one) is the divisor function. Take an example on the oddperfect.org page: $\sigma(3^4) = 11^2=121$

Let's factor 3^4. It factors as 3*3*3*3, which means it has 1, 3, 9, 27 and 81 as divisors. 1+3+9+27+81=121.

jasong · 2006-08-17, 23:02

I would like to purchase books that deal with these symbols and give lots of problems to practice on.

(1) Can anyone recommend something to me?

(2) If I only asked questions if I got stuck, is anyone willing to accept email from me with pictures of my math scanned and emailed to them? I may also be willing to buy them their own copies of the books I get to expedite things.

akruppa · 2006-08-18, 07:13

Knuth, Graham, Patashnik: Concrete Mathematics. I love this book.

It starts with sums, goes into solving recurrences; special numbers such as binomial, Sterling, Fibonacci etc; basics of number theory; generating functions; discrete probabilities; and the notation of asymptotics, i.e. O(f(n)) etc.

The difficulty varies from very basic to pretty advanced, so you won't be able to digest the whole thing in one reading. But you can start with a few things you find interesting and later come back and discover new things. There are heaps of exercises (with answers or at least hints in an appendix), too.

Alex

jasong · 2006-08-18, 19:32

Quote:

Originally Posted by akruppa

Knuth, Graham, Patashnik: Concrete Mathematics. I love this book.

It starts with sums, goes into solving recurrences; special numbers such as binomial, Sterling, Fibonacci etc; basics of number theory; generating functions; discrete probabilities; and the notation of asymptotics, i.e. O(f(n)) etc.

The difficulty varies from very basic to pretty advanced, so you won't be able to digest the whole thing in one reading. But you can start with a few things you find interesting and later come back and discover new things. There are heaps of exercises (with answers or at least hints in an appendix), too.

Alex

/me goes to look it up

The cheapest price is $35, which is more than two days pay for my handicapped butt.

I'll have to think about it.

akruppa · 2006-08-18, 19:45

Being an imported book, it costs a whooping €67 at amazon.de. IIrc, I paid a bit more than €50 when I got it, and I consider it some of the best money I ever spent.

This book will keep you good company for years and if you work through the whole thing, you'll probably learn more math than during a full semester at college. Makes $35 sound like a pretty good offer, imho.

Alex

em99010pepe · 2006-08-18, 20:25

Jasong,

I'm downloading the ebook. If you want I can send you a copy.

Carlos

jasong · 2006-08-18, 22:39

Quote:

Originally Posted by em99010pepe

Jasong,

I'm downloading the ebook. If you want I can send you a copy.

Carlos

That'd be great.

jasong at conwaycorp dot net

em99010pepe · 2006-08-18, 22:49

Quote:

Originally Posted by jasong

That'd be great.

jasong at conwaycorp dot net

Sending the ebook in several parts.

Carlos

EDIT: Done, please check you email.

2006-08-16, 22:20	#25
fetofs Aug 2005 Brazil 2·181 Posts	To enlighten you, an example: $\sum_{k=2}^6 {k^2} = 2^2+3^2+4^2+5^2+6^2 = 90$ The value on below is the initial setting, k=2. k is incremented up to the upper bound, the upper value, 6. On the right is the expression to be summed, $k^2$ . It means, for k initially equal to 2 and up to 6, sum the value of k^2. Did I make myself any clear? OTOH, the σ symbol (the lower case one) is the divisor function. Take an example on the oddperfect.org page: $\sigma(3^4) = 11^2=121$ Let's factor 3^4. It factors as 3333, which means it has 1, 3, 9, 27 and 81 as divisors. 1+3+9+27+81=121. Last fiddled with by fetofs on 2006-08-16 at 22:27 Reason: adding lower-case explanation*

2006-08-18, 07:13	#27
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Knuth, Graham, Patashnik: Concrete Mathematics. I love this book. It starts with sums, goes into solving recurrences; special numbers such as binomial, Sterling, Fibonacci etc; basics of number theory; generating functions; discrete probabilities; and the notation of asymptotics, i.e. O(f(n)) etc. The difficulty varies from very basic to pretty advanced, so you won't be able to digest the whole thing in one reading. But you can start with a few things you find interesting and later come back and discover new things. There are heaps of exercises (with answers or at least hints in an appendix), too. Alex Last fiddled with by akruppa on 2006-08-18 at 07:15

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2006-01-22, 23:40	#23
nibble4bits Nov 2005 2×7×13 Posts	The manuals that come with some calculators are very good at teaching you how to get the answer so you be sure that you're using the right method when you go to a calculator-less test. Even better is that you have another method to use depending on what's the best way to solve a problem, using your experience with both ways. Some (if not most) of the math books offered with online extensions allow you to get a list of chapters and sometimes even examples and practice tests. Use the practice tests to determine which areas to study first! The examples in the books should point you in the right direction as far as solving a class of problems is concerned. Good luck!

2006-08-16, 22:02	#24
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Can you guys point me in the right direction as to how I can learn about the following symbol? Σ Also there is another symbol(used at oddperfect.org) which I think is the lowercase version of the above symbol. I'd like to learn about that symbol too. Any help is appreciated.

2006-08-17, 23:02	#26
jasong "Jason Goatcher" Mar 2005 3×7×167 Posts	I would like to purchase books that deal with these symbols and give lots of problems to practice on. (1) Can anyone recommend something to me? (2) If I only asked questions if I got stuck, is anyone willing to accept email from me with pictures of my math scanned and emailed to them? I may also be willing to buy them their own copies of the books I get to expedite things.

2006-08-18, 19:45	#29
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Being an imported book, it costs a whooping €67 at amazon.de. IIrc, I paid a bit more than €50 when I got it, and I consider it some of the best money I ever spent. This book will keep you good company for years and if you work through the whole thing, you'll probably learn more math than during a full semester at college. Makes $35 sound like a pretty good offer, imho. Alex

2006-08-18, 20:25	#30
em99010pepe Sep 2004 2·5·283 Posts	Jasong, I'm downloading the ebook. If you want I can send you a copy. Carlos