Is there nuber theorists here?
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
I am not a number theorist, just an engineer, but, what is your purpose? If algebraic symbols are intimadating, you should probably slow down a bit before advancing rapidly into full-fledged theories. Symbols, after all, stand for concepts and then theories are even further integrated concepts. All the same, you could probably read articles on the topic from Encyclopaedia Brittanica. Another good start might be Prof. Morris Kline's books on the nature of Mathematics. Dr. Harry Binswanger might have written a separate article or so on the basic nature of mathematical concepts; pl. check at http://www.secondrenaissance.com. (He certainly has audio cassettes on the topic.) As to your career goal: once you advance, I hope, you will come to the conclusion that "pure" mathematics is a misnomer. Your project today is your great-grandchildrens' "ancestor clock."
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
Almost...:) The "Code" Project is about programming, i.e. source code, not cryptographic code, although I can see how you were confused because the article of the week is the (superb) article about cryptography. Who knows, someone about might be able to help you anyway, though... > Andrew.
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
In a way, were all number theorists, since computer science has taken so much from the work in this area. If you've ever generated a Fibonacci sequence, you're having 'fun with number theory'. There's a classic work by Douglas R Hofstader called Godel,Esher,Bach that pulls number theory, complexity, and computer science together in wondrous ways, and is entertaining enough to keep a neophyte involved. Read it. Hofstader also used to write the Computer Recreations column in Scientific American, (hmmm... during the 80s) and these were vastly entertaining to me when I first discovered 'puters. Number theory all over 'em. Also, for bits and bytes and possible links try: http://forum.swarthmore.edu/library/topics/number\_theory/ Looks like it could be scary, since there's so many links. Hmmm... now I understand your quest. Maybe its like asking for a basic guitar course. I'd think its better to find a song you like, learn it well, and go from there. There should be lots to choose from. Anyway, that's 2 cents worth from a lowly code mechanic who occasionally likes playing with the pretty numbers. :) later... Oops - I spelled Hofstadter wrong... :-o
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
What aspect of Number Theory? It's kind of a broad topic :) Check out http://www.math.niu.edu/~rusin/known-math/index/11-XX.html for some starters. cheers, Chris Maunder
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
Number theory at 14, I think we have the next Einstein. The subject also interests me. I doubt you'll find many books on number theory in your local library (I do not know though). A good place to start with number theory is to visit UWA's mathematics site. Should be able to find it from www.uwa.edu.au. Look for the mathematics department. They have an introductory course on Group Theory. (all the notes on the web.) which I am fairly sure is another name for number theory. this is called '2GA2'. It covers Non Euclidean geometry which is a complicated name for the mathematics to create 3D graphics. Quake3 uses this stuff! The second half of the course is introductory group theory - looking at the patterns in numbers, and using them to prove a lot of theories you have not had the chance to see yet. The great think about number theory is that is an alternative way to learn mathematics. number theory proves the base principles that you and your teachers take for granted which is why I like the subject and hope to do more of it in the future. It is possible to learn number theory from scratch without other mathematical prerequisites, but very hard to because people design the courses with the student already have achiving 1 and half years of university level maths. This is not to say that it is impossible and I sincerly hope you give it a good try because there is a lot of wonderful things to learn. As for the symbols, the only advice on that I can give is start slowly and concentrate on trying to learn what the symbols mean. Each symbol encompasses a lot of ideas which when the person understands that symbol he actually understands that concept. Its only when all these symbols (concepts) are put together that it enables one to being able to describe the complicated mathemathical concepts. Best wishes Ivan
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Number theory at 14, I think we have the next Einstein. The subject also interests me. I doubt you'll find many books on number theory in your local library (I do not know though). A good place to start with number theory is to visit UWA's mathematics site. Should be able to find it from www.uwa.edu.au. Look for the mathematics department. They have an introductory course on Group Theory. (all the notes on the web.) which I am fairly sure is another name for number theory. this is called '2GA2'. It covers Non Euclidean geometry which is a complicated name for the mathematics to create 3D graphics. Quake3 uses this stuff! The second half of the course is introductory group theory - looking at the patterns in numbers, and using them to prove a lot of theories you have not had the chance to see yet. The great think about number theory is that is an alternative way to learn mathematics. number theory proves the base principles that you and your teachers take for granted which is why I like the subject and hope to do more of it in the future. It is possible to learn number theory from scratch without other mathematical prerequisites, but very hard to because people design the courses with the student already have achiving 1 and half years of university level maths. This is not to say that it is impossible and I sincerly hope you give it a good try because there is a lot of wonderful things to learn. As for the symbols, the only advice on that I can give is start slowly and concentrate on trying to learn what the symbols mean. Each symbol encompasses a lot of ideas which when the person understands that symbol he actually understands that concept. Its only when all these symbols (concepts) are put together that it enables one to being able to describe the complicated mathemathical concepts. Best wishes Ivan
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Number theory at 14, I think we have the next Einstein. The subject also interests me. I doubt you'll find many books on number theory in your local library (I do not know though). A good place to start with number theory is to visit UWA's mathematics site. Should be able to find it from www.uwa.edu.au. Look for the mathematics department. They have an introductory course on Group Theory. (all the notes on the web.) which I am fairly sure is another name for number theory. this is called '2GA2'. It covers Non Euclidean geometry which is a complicated name for the mathematics to create 3D graphics. Quake3 uses this stuff! The second half of the course is introductory group theory - looking at the patterns in numbers, and using them to prove a lot of theories you have not had the chance to see yet. The great think about number theory is that is an alternative way to learn mathematics. number theory proves the base principles that you and your teachers take for granted which is why I like the subject and hope to do more of it in the future. It is possible to learn number theory from scratch without other mathematical prerequisites, but very hard to because people design the courses with the student already have achiving 1 and half years of university level maths. This is not to say that it is impossible and I sincerly hope you give it a good try because there is a lot of wonderful things to learn. As for the symbols, the only advice on that I can give is start slowly and concentrate on trying to learn what the symbols mean. Each symbol encompasses a lot of ideas which when the person understands that symbol he actually understands that concept. Its only when all these symbols (concepts) are put together that it enables one to being able to describe the complicated mathemathical concepts. Best wishes Ivan
Number theory is an umbrella term for a whole bunch of fields. Group theory is just one tiny, specialised area - but a good place to start. For starters check out Group and Ring theory, factorization (primes, perfect numbers, and congruences (you'll use these in computing even if you don't realize). Then go onto Set Theory and Class theory and be prepared to have your brain turned inside out. It's too much fun! cheers, Chris Maunder
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
Number theory can be quite daunting. I would suggest developing a good grounding in Boolean and first order logic, along with basic set theory and combinatorics, before wading into number theory. A good backdoor into all this is the book “Introduction to Algorithms” by Cormen, Leiserson, and Rivest. Their primary goal is to teach algorithms, however they also teach the background math as they go along. A second book is “Applied Cryptoanalysis” (don’t know the author offhand) Chapter 11 gives a quick introduction into number theory. P.S. - Trust me, you really don't want to go into pure math. I know more than one PhD in math that ended up switching to computer science just to find a job. If you want to get rich, go into math/finance and work on wall street developing economic models. You will be doing the same work, and being paid 20X as much. P.P.S. - There are serveral series of math and engineering "problem solver" books that teach the fundimentals and provide sets of worked problems. A university bookstore should carry them. P.P.P.S. - If you really are that good consider trying to graduate early or taking college courses part time during high school. Lots of places will bend the rules for outstanding students.
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
For what you want, you may want to look at Manfred R. Schroeder's book, Number Theory in Science and Communication, with Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity, (Springer-Verlag, 1997). This book does not provide "complete basics" in the sense of a complete rigorous axiomatic derivation of number theory, but it does provide an excellent balance between a scholarly treatment and something that is accessible to the beginner. I would think that a completely rigorous axiomatic treatment might be more than you are looking for and would only discourage you anyway. Schroeder provides copious bibliographic references, so you can easily find resources that provide deeper and more rigorous treatment than he does. He explains what he's writing about clearly in English, so you don't need to understand lots of obscure mathematical notation to follow him. He also includes at the end a glossary of symbols, so if you forget what he means by a particular notation, you can look it up. You should be quite familiar with basic algebra (symbolic variables, polynomials, roots of equations, etc.), but if you're motivated and have two years or so of algebra, you can probably follow almost all of this book. Even if you can't follow all the mathematical parts, the descriptions in plain english should help you get a sense of what number theory is all about. The book is expensive for a 14-year-old, so you probably want to borrow it from a library for a test-drive before paying hard-earned cash for it (if your local library doesn't have it, your librarian should be able to borrow it from another library as an inter-library loan). You may also be able to pick up a used copy of an older edition for not so much money. Schroeder is a very accomplished physicist and mathematician, whose credentials include being Director of Research at Bell Laboratories and a professor of physics at the University of Göttingen, so the treatment is quite authoritative and I find it eminently readable. Schroeder's primary interest in number theory is in its application to acoustics (he works on the design of concert halls), but his book includes a fair bit about cryptographic applications as well. This book is one of my primary resources for number theory when I want context and understanding more than axiomatic derivations. If you're specifically interested in Cryptography, you might enjoy Dor
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Hello, I am a 14 year old pupil that has been serching for a way to get the complete basics of the theory of numbers, and I mean the COMPLETE BASICS; something that I can progress from. When I first encountered number theory I immediately needed more but when I proceeded to the local library I was confounded by a series unknown algebriac symbols even in a book entitled 'The Basics of Number Theory'. I came here presuming that a site devoted to the latest cryptography (a topic that is now extremly dependant upon mathmatics instead of linguistics) would contain some number theorists or at least someone with a backround in number theory. Please, if there is tell me - is there a backdoor way into simple number theory or am I doomed to wait another four years untill I go to university. Any in formation would be much appreciated. From a budding pure mathmatician in need of help
I asked a friend about books in this field, and he came up with this: Well, the book I learned much of what what little I know is _The_Theory_ _of_Numbers_, Niven, Suckermand and Montgomery. Looks like the 5th edition is the current one, despite being 10 years old. Here's link: http://catalog2.wiley.com/catalog/frameset/1,8279,,00.html However, the cost is prohibitive. Thought I'd pass it along. He also mentions the same website chris did.
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Number theory is an umbrella term for a whole bunch of fields. Group theory is just one tiny, specialised area - but a good place to start. For starters check out Group and Ring theory, factorization (primes, perfect numbers, and congruences (you'll use these in computing even if you don't realize). Then go onto Set Theory and Class theory and be prepared to have your brain turned inside out. It's too much fun! cheers, Chris Maunder
Compiling... PreviousPost.cpp C:\CodeProject\PreviousPost\PreviousPost.cpp(3) : error C2143: syntax error : missing ')' before '.' Error executing cl.exe. PreviousPost.exe - 1 error(s), 0 warning(s) haha I have too much time on my hands..... :P Senior Test Engineer GLI Australia www.gli.com.au
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Compiling... PreviousPost.cpp C:\CodeProject\PreviousPost\PreviousPost.cpp(3) : error C2143: syntax error : missing ')' before '.' Error executing cl.exe. PreviousPost.exe - 1 error(s), 0 warning(s) haha I have too much time on my hands..... :P Senior Test Engineer GLI Australia www.gli.com.au
;P Gomake yourself useful and mix us another pint of Bailey's ;) cheers, Chris Maunder
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Number theory at 14, I think we have the next Einstein. The subject also interests me. I doubt you'll find many books on number theory in your local library (I do not know though). A good place to start with number theory is to visit UWA's mathematics site. Should be able to find it from www.uwa.edu.au. Look for the mathematics department. They have an introductory course on Group Theory. (all the notes on the web.) which I am fairly sure is another name for number theory. this is called '2GA2'. It covers Non Euclidean geometry which is a complicated name for the mathematics to create 3D graphics. Quake3 uses this stuff! The second half of the course is introductory group theory - looking at the patterns in numbers, and using them to prove a lot of theories you have not had the chance to see yet. The great think about number theory is that is an alternative way to learn mathematics. number theory proves the base principles that you and your teachers take for granted which is why I like the subject and hope to do more of it in the future. It is possible to learn number theory from scratch without other mathematical prerequisites, but very hard to because people design the courses with the student already have achiving 1 and half years of university level maths. This is not to say that it is impossible and I sincerly hope you give it a good try because there is a lot of wonderful things to learn. As for the symbols, the only advice on that I can give is start slowly and concentrate on trying to learn what the symbols mean. Each symbol encompasses a lot of ideas which when the person understands that symbol he actually understands that concept. Its only when all these symbols (concepts) are put together that it enables one to being able to describe the complicated mathemathical concepts. Best wishes Ivan
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;P Gomake yourself useful and mix us another pint of Bailey's ;) cheers, Chris Maunder
Try this: 1 Bottle chocolate topping 600 ml Thickened Cream 2 tins Condensed Milk 1 tin Evaporated Milk 3 teaspoons coffee 30ml coconut essence 1/2 cup warm water 700ml bottle of whisky (or whiskey... :) Mix all milk products in large bowl, add chocolate topping and mix again. Dissolve coffee in warm water and add, mix again, stir in coconut essence, add whisky / whiskey while stirring. Done! Makes about 2.5 litres so be sure you have plenty of empty bottles to put it into :) Total cost is about $25 if you use a cheapish bottle of whisky. The better the alcohol, the better the finished product tastes... Enjoy! :-D Senior Test Engineer GLI Australia www.gli.com.au