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Abstract_Logic
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07 Dec 2008, 10:43 am

Does anyone here currently have an obsession with any branch or topic in Mathematics?

My current obsession is with Set Theory of Discrete Mathematics. I am also reading a delightful book called "How Mathematicians Think" by William Byers. I have already read about 1/6th of the book and I'm enjoying every word of it. I strongly recommend this book to anyone who is interested in numbers or Mathematics.

Take care and have a great day/evening/night!

Jeff 8)



Aleph0
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07 Dec 2008, 11:09 am

Yes. but I am a mathematician...
And Set Theory is GREAT!! ! ENLOY!! !
:lol:



mystyc
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07 Dec 2008, 3:16 pm

I don't like real math much, even though I am a physics major, and even though my research involves integral equations, hah.


Real math is about abstract logic that need not have any basis in reality. While mathematicians may dislike when the need to make a physical assumption gets in the way of their logical proof, that is the part I find most interesting.



ValMikeSmith
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07 Dec 2008, 4:34 pm

Quote:
Set Theory of Discrete Mathematics

I think that this might be the kind of math that I am particularly obsessed with.

I am always trying to find new fast ways of enumerating the lexicographical order of members of sets of permutations. To me these functions are the most interesting and useful, and I've built a special computer to do them. I am currently most interested in large SNOOBs, numbers that have the Same_Number_Of_One_Bits (as Zeroes) in Binary such as:
0-0011
1-0101
2-0110
3-1001
4-1010
5-1100
Except with Thousands or Millions of bits instead of only 4 bits.



Shiggily
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07 Dec 2008, 6:45 pm

Abstract_Logic wrote:
Does anyone here currently have an obsession with any branch or topic in Mathematics?

My current obsession is with Set Theory of Discrete Mathematics. I am also reading a delightful book called "How Mathematicians Think" by William Byers. I have already read about 1/6th of the book and I'm enjoying every word of it. I strongly recommend this book to anyone who is interested in numbers or Mathematics.

Take care and have a great day/evening/night!

Jeff 8)


your avatar made me happy for today.



Alien8ed
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12 Dec 2008, 12:13 pm

I'm not sure if this counts as an obsession, but constants in equations have had my mind unsettled since I was middle school. They have always appeared to be suspect logic to me. Why force an unchanging value into a formula when often no one knows what is, or its exact function?



mystyc
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13 Dec 2008, 12:10 am

Alien8ed wrote:
I'm not sure if this counts as an obsession, but constants in equations have had my mind unsettled since I was middle school. They have always appeared to be suspect logic to me. Why force an unchanging value into a formula when often no one knows what is, or its exact function?



Give an example of an equation that describes what you mean.



Shiggily
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13 Dec 2008, 1:12 am

Alien8ed wrote:
I'm not sure if this counts as an obsession, but constants in equations have had my mind unsettled since I was middle school. They have always appeared to be suspect logic to me. Why force an unchanging value into a formula when often no one knows what is, or its exact function?


I do not get this



Xelebes
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13 Dec 2008, 1:14 am

mystyc wrote:
Alien8ed wrote:
I'm not sure if this counts as an obsession, but constants in equations have had my mind unsettled since I was middle school. They have always appeared to be suspect logic to me. Why force an unchanging value into a formula when often no one knows what is, or its exact function?



Give an example of an equation that describes what you mean.


I think he's refering to e, pi and phi.

Or, to round them all up:

0 = e^(pi*i) - 1



Shiggily
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13 Dec 2008, 2:11 am

Xelebes wrote:
mystyc wrote:
Alien8ed wrote:
I'm not sure if this counts as an obsession, but constants in equations have had my mind unsettled since I was middle school. They have always appeared to be suspect logic to me. Why force an unchanging value into a formula when often no one knows what is, or its exact function?



Give an example of an equation that describes what you mean.


I think he's refering to e, pi and phi.

Or, to round them all up:

0 = e^(pi*i) - 1


e and pi both have exact functions. I forget it phi does since I haven't used it much



Xelebes
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13 Dec 2008, 2:44 am

Phi is the golden ratio. You use it for natural growth models in biology and games.



CaptainMac
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13 Dec 2008, 2:51 am

I'm another one who obsesses over math. I'm specifically interested in numbers and their origins, their meanings, etc. I currently work as a part time math tutor for elementary kids and am asking for two books on number theory for Christmas. Additionally, I have a large box of math manipulatives (which I have an excuse to use since I am a tutor) and a collection of calculators...two graphers, a scientific, a ton of four functions, a "Little Professor", and a good old fashioned slide rule. I also managed to snag a few math textbooks whenever the local schools dumped them or have bought them online (I have four Algebra books, one geometry, a calculus book, a stats book with a CD, a few books on basic math, one on math history, and a ton of elementary-grade books including a really nice hardcover third grade book from the 80s; not to mention a book on descriptive geometry, one on fractals, a complete book on Judy Clocks, a few volumes on teaching math, a few workbooks that go with textbooks, and a physics book, which is close enough to math that I'll include it-----basically a whole shelf in my room is devoted to math books). I also have a ton of math software including multiple copies of Math Blaster (and some old computers to run them on for students).



mystyc
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13 Dec 2008, 5:51 am

CaptainMac wrote:
I'm another one who obsesses over math. I'm specifically interested in numbers and their origins, their meanings, etc. I currently work as a part time math tutor for elementary kids and am asking for two books on number theory for Christmas. Additionally, I have a large box of math manipulatives (which I have an excuse to use since I am a tutor) and a collection of calculators...two graphers, a scientific, a ton of four functions, a "Little Professor", and a good old fashioned slide rule. I also managed to snag a few math textbooks whenever the local schools dumped them or have bought them online (I have four Algebra books, one geometry, a calculus book, a stats book with a CD, a few books on basic math, one on math history, and a ton of elementary-grade books including a really nice hardcover third grade book from the 80s; not to mention a book on descriptive geometry, one on fractals, a complete book on Judy Clocks, a few volumes on teaching math, a few workbooks that go with textbooks, and a physics book, which is close enough to math that I'll include it-----basically a whole shelf in my room is devoted to math books). I also have a ton of math software including multiple copies of Math Blaster (and some old computers to run them on for students).


Hah, nice list, CaptainMac. I probably would have wished for something similar for x-mas, had my family the necessary finances for that. But nowadays, I would not wish for such things if I was your age, due to the internet. Now you have wikipedia, google, MIT Open Courseware (free course materials from MIT), and wolfram's Math world. You can get very far with that.

If you buy any books, just stick to the most popular textbooks used in schools appropriate to your math competency level. You sort of asked for that above, but a few standard textbooks and the internet will have you set for years. I am not sure what your level is, but I will take a guess anyways and give you a list of subjects to search for textbooks on:

  • College Algebra: Assuming you can do basic arithmetic, then you need a solid foundation in algebra to proceed further.
  • Trigonometry/Precalulus: Depending on the algebra book you choose, you might be able to get enough trigonometry in a pre-calculus book. Or you may need to go with a highschool geometry book. This topic will be a prerequisite for complex analysis and calculus.
  • Modern algebra: This covers group theory, set theory, rings, and fields. A field is basically a set of "numbers" which can be added, subtracted, multiplied, or divided. So there is the field of real numbers, rational numbers, integers, complex numbers, quaternions (a non-commutative field with three "imaginary numbers", i,j, and k, such that, i^2=j^2=k^2=ijk=-1), onctonions (non-commutative and non-associative field, where there is a 4th "imaginary number", L, and the product relations involving iL, jL, and kL.).
  • Real analysis: Real analysis actually overlaps everything on this list that deals with real numbers, except it is done in a mathematically rigorous fashion.
  • Complex analysis: Similar to real analysis, except with complex numbers. This is where you will learn the math behind the mandelbrot and julia sets, though there will be no focus on them.
  • Number theory: This goes beyond modern algebra and real analysis and examines stuff like prime numbers and stuff.
  • Calculus: The bread and butter of every physicists. You only need algebra and trigonometry/precalculus for this.



ruveyn
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18 Dec 2008, 10:05 am

Abstract_Logic wrote:
Does anyone here currently have an obsession with any branch or topic in Mathematics?

My current obsession is with Set Theory of Discrete Mathematics. I am also reading a delightful book called "How Mathematicians Think" by William Byers. I have already read about 1/6th of the book and I'm enjoying every word of it. I strongly recommend this book to anyone who is interested in numbers or Mathematics.

Take care and have a great day/evening/night!

Jeff 8)


Mathematics and flying are the most exciting things you can do with your clothes on.

ruveyn



Samarda
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20 Oct 2011, 7:44 am

Mathematics is so old and fat. I can't possibly give the specifics a reach around.
And I'm in to MILFs.
(Mathematics I love to foogle)
So my knowledge is fundamental:

- Algebraic Geometry
- Complex Analysis
- Numerical Analysis
- Dynamical Systems
- Order Theory
- Differential Calculus
- Topology
- Vector Analysis
- Finite Mathematics



ruveyn
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20 Oct 2011, 8:58 am

Samarda wrote:
Mathematics is so old and fat. I can't possibly give the specifics a reach around.
And I'm in to MILFs.
(Mathematics I love to foogle)
So my knowledge is fundamental:

- Algebraic Geometry
- Complex Analysis
- Numerical Analysis
- Dynamical Systems
- Order Theory
- Differential Calculus
- Topology
- Vector Analysis
- Finite Mathematics


You left out mathematical logic and algorithmic analysis. What problems are NP Complete, for example.

ruveyn