# Math is great! discussion

Welcome!

Hey thanks for the above link. I just checked it out and it looks pretty funny.

Don't worry about discussions being difficult. I'm a middle school math teacher and that's where most of my math reading falls, level wise.

Feel free to share anything else you've read or discovered online. =)

Don't worry about discussions being difficult. I'm a middle school math teacher and that's where most of my math reading falls, level wise.

Feel free to share anything else you've read or discovered online. =)

Hello everyone. My name is Ashley and I'm pretty good at math. Don't really read math related books but I do plan to be a teacher and I think it would be useful to be in this group to get good math books that I could use in my teaching when I become a teacher. :). Not only that I can always use some help understanding some math problems for I am taking a math course at my college right now. I think it is fun to get math books at local book sales and do the problems out of them to keep your mind fresh on the different math concepts.

Hi, everyone, I'm Matt. I have a phd in mathematics, and I am a mathematics lecturer at the University of Washington. I'm not an active researcher, but I do dabble (primarily number theory and probability), and am always up for a good math (or math book) discussion.

cheers,

Matt

cheers,

Matt

In K-12 school sure, math was my best subject. However, college was another story. Some math classes were wonderful and I did awesome. Some, not so much and I needed repeating.

Are you going into elementary ed, Ashley? I taught 5th grade for 3 years before I switched this year to middle school math.

Are you going into elementary ed, Ashley? I taught 5th grade for 3 years before I switched this year to middle school math.

yes i plan to teach elementary education and then i will eventually move my way up...unless i like elementary education so much i'll do it till i retire.

Chad - I haven't thought about P and NP for a long time, and I never knew too much about it. But, I think I can help explain what P is, at least. A problem is in P if it can be solved in "polynomial time". What does that mean? For a lot of problems, the time it takes to solve it depends on the size of the input. For instance, when multiplying two numbers together, it takes more time if the numbers have more digits. As that rsa site mentions, the length of time to multiply two numbers together is no worse than proportional to the square of the numbers digits. Since k^2 is a polynomial, multiplication can be done in "polynomial time".

A lot of problems are not as easy as multiplication. The Traveling Salesman Problem (TSP) is a classic example of a problem that does not seem to be polynomial. Suppose you have to visit n cities, in any order, but you want to take the shortest trip that will pass through all n. How do you decide what route to take? There are (essentially) n! routes, and n! grows faster than any fixed power of n, so, unless we can be clever and figure out a way to not have to check all n! possible routes, this is not a "polynomial time" problem. (I've read that one can actually solve this in "n^2 2^n" time, which is much better than n!, but still far from polynomial.)

As for that NP business, consider if someone told you they had the best route connecting n cities. Could you verify that this was indeed the best route without simply solving the problem for yourself? Compared to the factoring problem: while coming up with factors for a given large number n, if someone claims that n factors as n=ab, it can be checked easily simply by multiplying a times b. So, it seems factoring and the TSP are problems of different sorts.

I've never investigated these types of problems myself, except for a computer science course or two many years ago. And while number theory is my thing, I've never found cryptography to be very appealing. But these are very interesting questions, nonetheless.

cheers,

Matt

A lot of problems are not as easy as multiplication. The Traveling Salesman Problem (TSP) is a classic example of a problem that does not seem to be polynomial. Suppose you have to visit n cities, in any order, but you want to take the shortest trip that will pass through all n. How do you decide what route to take? There are (essentially) n! routes, and n! grows faster than any fixed power of n, so, unless we can be clever and figure out a way to not have to check all n! possible routes, this is not a "polynomial time" problem. (I've read that one can actually solve this in "n^2 2^n" time, which is much better than n!, but still far from polynomial.)

As for that NP business, consider if someone told you they had the best route connecting n cities. Could you verify that this was indeed the best route without simply solving the problem for yourself? Compared to the factoring problem: while coming up with factors for a given large number n, if someone claims that n factors as n=ab, it can be checked easily simply by multiplying a times b. So, it seems factoring and the TSP are problems of different sorts.

I've never investigated these types of problems myself, except for a computer science course or two many years ago. And while number theory is my thing, I've never found cryptography to be very appealing. But these are very interesting questions, nonetheless.

cheers,

Matt

Wow doctormatt! You're smart!

You must have went to one of those fancy colleges!

:P

Speaking of cryptography, guess what book I'm currently reviewing: http://www.goodreads.com/book/show/15...

You must have went to one of those fancy colleges!

:P

Speaking of cryptography, guess what book I'm currently reviewing: http://www.goodreads.com/book/show/15...

Fancy? Yes, it was all tea and crumpets, but they let all kinds of riff-raff in...

Reviewing, eh? That's cool. Personally, I think cryptography is "a pretty flower, that smells bad." That is, nice math, but applied to problems that seem quite un-fun, and at least a little ugly.

But, as long as you like it...

cheers,

Matt

Reviewing, eh? That's cool. Personally, I think cryptography is "a pretty flower, that smells bad." That is, nice math, but applied to problems that seem quite un-fun, and at least a little ugly.

But, as long as you like it...

cheers,

Matt

Hi everyone.

Like doctormatt, I have a PhD in mathematics. (We attended the same fancy university, where we specialized in number theory and volleyball.)

I have a mathematics shelf here:

http://www.goodreads.com/review/list/...

which I will try to add to.

Like doctormatt, I have a PhD in mathematics. (We attended the same fancy university, where we specialized in number theory and volleyball.)

I have a mathematics shelf here:

http://www.goodreads.com/review/list/...

which I will try to add to.

Chad,

If you're mainly interested in the RSA encryption scheme, you should be able to get whatever you want from the RSA website. If you're also interested in the "information theory" behind encryption schemes in general, then you'd probably like Katz and Lindell's book. It's a fairly complete presentation of the ideas behind public-key cryptography.

If you're mainly interested in the RSA encryption scheme, you should be able to get whatever you want from the RSA website. If you're also interested in the "information theory" behind encryption schemes in general, then you'd probably like Katz and Lindell's book. It's a fairly complete presentation of the ideas behind public-key cryptography.

Hi everyone! I'm Veronica, and I love math! I am currently taking algebra and next year I will move on to honors geometry, or something similar.

I don't usually read math related books, but there is one, I havn't really made it all the way through, but what I have read so far has been useful. It is called Rapid Math Tricks and Tips. You spend 30 days learning 2 tricks a day and then you will have a ton of useful tricks at hand(or at head I should say, because you would remember the tricks.)

I don't usually read math related books, but there is one, I havn't really made it all the way through, but what I have read so far has been useful. It is called Rapid Math Tricks and Tips. You spend 30 days learning 2 tricks a day and then you will have a ton of useful tricks at hand(or at head I should say, because you would remember the tricks.)

Welcome, Veronica.

Feel free to keep sharing stuff with us and jump into any conversations. We're small, but we have a good time.

Feel free to keep sharing stuff with us and jump into any conversations. We're small, but we have a good time.

k. my REAL name is Heather, but here, i am Snowfoot. dont ask, its from a roleplay i participate in elsewhere on this site. i'm currently in 10th grade, taking Honors Algebra 2, and its fun! most of the time... anywhoo, math is my FAVORITE subject, along with computer related classes, and i would never have the patience to teach kids. programming computers is more my thing. btw, what

*level*math is the p=np thing? cuz i sorta get it! ... or at least, the basic idea.
oh, well, thanks! i was just curious what class i might find it in... probly not a High Skool class... but it makes sense!

Hi everybody. My name is Pat, I am a math teacher in senior high school in Australia. I studied maths at university before I became a teacher. This year I have got back into doing some of my own study so I am halfway through my Masters at the moment. Hopefully I will join a few of the others on this site and do a PhD in a few years! Anyway, hopefully I can contribute to a few discussions.

am i the youngest here? im still IN high school.... 16... i feel young... most othr groups i feel old, lol!

Hi Everyone! I'm Elaine and I really like math (duh!)! =D Numbers are SO fun! I'm currently in Algebra 2 (which includes algebra, geometry, and trigonometry). As far as "fun" mathematical books, I'm currently reading The Numbers Behind NUMB3RS Solving Crime with Mathematics which is fun and interesting, although I don't always understand it very well. Anyone else here a fan of the show? That book you mentioned, Veronica, sounded cool! I'll have to look at that.

Concerning the P=NP problem being discussed (also known as P vs. NP), I believe it is one of the Millennium Prize Problems ("The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved. A correct solution to each problem results in a US$1,000,000 prize (sometimes called a Millennium Prize) being awarded by the institute." ~ Wikipedia). So, no Snow, I don't believe you will find it in high school as the most amazing and genius mathematicians haven't even found the answer yet. =)

Hey Elaine! Btw everyone, I've changed my mind. Physics is better than math, partially because I'm learning stuff in physics at the moment and pre-calc is nothing but alg 2 on vitamins, as my teacher put it. Plus, physics is math application! yes, I'm a nerd. But aren't we all?

hey elaine, what grade are you in? im in 11th, and physics is one of the "harder" (but not rlly) science classes for the 11th graders. but my school could just be lame and behind, i dunno

Sorry, my mistake - I guess the course I took was called Physical Science, which I'm guessing is like Physics only for a younger grade. The math equations in it were addicting, though. lol!

Do you like the math in Chemistry? I thought Chemistry was tons of fun!

Do you like the math in Chemistry? I thought Chemistry was tons of fun!

Lol, yeah, I loved math in chemistry. I didn't love it enough to take AP Chemistry, but... I loved it enough in physics to take AP Physics w/ Calculus. I'm hoping it'll be fun.

welcome ^^ oh and michael, if you ask a student, AP unofficially stands for advanced procrastination, but teachers will tell you advanced placement.

Hi everyone, I am new to goodreads. I look forward to looking over some of the books and and suggestions from the posts and making new friends who are interested in research in various areas of science. I am working on my profile and I hope to have more about me in the coming days. Thank you for the welcome.

Hi everyone! I LOVE math! ...but I am just a novice :) I wish I had more time to study it.

Here is an interesting link for all of you other novices out there. It has a great learning plan for theoretical physics (all free and online), which I am sure everyone knows is comprised of a lot of math. http://www.phys.uu.nl/~thooft/theoris...

Enjoy!

Here is an interesting link for all of you other novices out there. It has a great learning plan for theoretical physics (all free and online), which I am sure everyone knows is comprised of a lot of math. http://www.phys.uu.nl/~thooft/theoris...

Enjoy!

Hi, all. I just joined, hoping to find some fiction about mathematicians. I got my BA in math and MA in applied statistics, both from UC Berkeley, many, many years ago. I have worked as a programmer and data analyst.

One of the best series of books about math is The World of Mathematics: A Four-Volume Set, which is a collection of essays about various aspects of math. I think my folks got it for me when I was in high school.

As for fiction, here are ones I like, and I hope others can add to this list.

Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession by Apostolos Doxiadis

The Indian Clerk by David Leavitt

I haven't read these but plan to soon.

The Housekeeper and the Professor by Yoko Ogawa

Logicomix: An Epic Search for Truth by Apostolos Doxiadis

One of the best series of books about math is The World of Mathematics: A Four-Volume Set, which is a collection of essays about various aspects of math. I think my folks got it for me when I was in high school.

As for fiction, here are ones I like, and I hope others can add to this list.

Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession by Apostolos Doxiadis

The Indian Clerk by David Leavitt

I haven't read these but plan to soon.

The Housekeeper and the Professor by Yoko Ogawa

Logicomix: An Epic Search for Truth by Apostolos Doxiadis

HI everyone!

My name is Claire and i'm living in London, UK (originally from Gold Coast, QLD, Australia)

I have recently been priming my math skills for an interview for a certificate I hopefully get in to!

I haven't done maths for quite a while but now I am getting back into it, the challenge is quite good.

^ Vicki, is it good being a programmer? It's a career I am currently considering, all my programmer friends say it is hard, but worth it.

My name is Claire and i'm living in London, UK (originally from Gold Coast, QLD, Australia)

I have recently been priming my math skills for an interview for a certificate I hopefully get in to!

I haven't done maths for quite a while but now I am getting back into it, the challenge is quite good.

^ Vicki, is it good being a programmer? It's a career I am currently considering, all my programmer friends say it is hard, but worth it.

Claire, I loved being a programmer. I retired about 2 years ago and I somewhat miss it, but I'm really busy with other things (like reading). I never got into hard-core programming, like C, nor Web-based languages. I started with Fortran, then PL/1, then SAS, which is a statistical analysis language based on PL/1. What I liked best was debugging, although really no program is ever completely debugged.

I like programming, from an unprofessional point of view. I want to program once I'm out of college, though debugging isn't my favorite part. I like being given a problem and figuring out what I need to code to make the program run. ^^

Right, Rockhound. But your first pass at the problem is seldom without flaws. And perfecting your code can take longer than writing it in the first place.

;-)

;-)

Yeah, I know. I wrote enough programs in high school to know that. :P And it doesn't help that I semi-regularly switch numbers around when I'm looking at them. Hasn't happened with letters yet, so lucky me. ^^

Sounds like fun to me. ^^ Debugging's alright, though it's not my absolute favorite passtime in the whole world.

^ Is it not too difficult for someone like me starting Uni at about 25, wanting to get into programming when I have never done anything like it before?

I don't think age has anything to do with it. You need a logical mind and a desire to solve problems. And not to get frustrated too easily.

Which would you say is one of the easier languages? I've used Basic (we called it QBasic, but I think they're the same...), some Java, some HTML, and worked with Alice, though I'm not sure what language that program uses.

I don't think I can comment on which languages are easier. I haven't programmed in anything but SAS for about 25 years. I believe Basic was meant to be easy to pick up and use but I don't know if it's used much in businesses.

It's probably not. It would make more sense that it's used to teach beginners the basics. Though the first time I had freetime in that class (which was pretty often, actually), I made up something WAY more complicated than anything the teacher had taught us... What can I say, I am easily bored. :P

Hi everyone, I just joined the group.

I've gone back to school in my old age of 28, at least I feel old compared to others. I'm majoring in Applied Mathematics. My interests so far are Electromagnetism and Vector Analysis (especially Vector Calculus and I want to do more work with representing divergence and curl using linear algebra techniques).

Anyway, I've only been studying math for a couple years now, but I've gone through all the Calculus tracks, learned how to program in Mathematica, took Differential Equations, went through Linear Algebra, at least those are all the ones I really liked. I get to take Complex Analysis next semester and I can't wait, because I feel like that's one of the things missing from my world of math!

This semester I'm taking Mathematical Physics, Electromagnetism I, Mathematical Analysis, and Discrete Structures. And I am currently teaching myself how to program in LabVIEW for a new research job I got at my University.

I love reading about anything math related. I read all my text books and read a lot of fun outside reading books. There's so much cool stuff to learn!!

I've gone back to school in my old age of 28, at least I feel old compared to others. I'm majoring in Applied Mathematics. My interests so far are Electromagnetism and Vector Analysis (especially Vector Calculus and I want to do more work with representing divergence and curl using linear algebra techniques).

Anyway, I've only been studying math for a couple years now, but I've gone through all the Calculus tracks, learned how to program in Mathematica, took Differential Equations, went through Linear Algebra, at least those are all the ones I really liked. I get to take Complex Analysis next semester and I can't wait, because I feel like that's one of the things missing from my world of math!

This semester I'm taking Mathematical Physics, Electromagnetism I, Mathematical Analysis, and Discrete Structures. And I am currently teaching myself how to program in LabVIEW for a new research job I got at my University.

I love reading about anything math related. I read all my text books and read a lot of fun outside reading books. There's so much cool stuff to learn!!

Congratulations, and good luck in your studies. There are so many fascinating subjects in the field of math.

Hello Adam and everyone.

I've been 'lurking' on this group for a few months now and your post inpired me to respond (though a bit delayed).

Congratulations on going back to school. I wish you luck.

I've enjoyed reading all the posts. It looks like this group has a very diverse membership. That is great to see.

I apologize for the long post. Guess I should have posted sooner ;)

Personally, I love math. I took it in university but I don't use it for my work. I do tutor high school math on a regular basis. I especially love vector calculus and linear algebra. I'd like to try Mathematica some day. Maybe if I ever go back to school and can get a student copy. For now I mostly use a pen and paper :)

About ten years ago I was afraid that my math skills were dwindling as I'd been out of school for over ten years and was working as a programmer that didn't involve much math. I started reviewing my university books and then started learning tensor calculus. It inspired me. I then tried to get into differential forms, quanterions and finally discovered geometric algebra (GA).

I have tried to understand the different approaches by looking at things like divergence and curl and Electromagnatism.

There was an interesting paper I read on using differential forms (DF) as a pedigogical approach to teaching Electromagnetic theory. I think that GA also has the same advantages. However, both appoaches can seem a bit strange. Further, I think there is still an advantage to looking at it the conventional way with vector analysis as well as DF or GA. But it is all really exciting because it all adds insight and helps us understand things better.

My learning seems to go in spurts. I am not good at doing it on a daily basis so I often find myself reviewing and catching up. But it is all for fun.

I'm curious if you or anyone else has had any exposure to Geometric Algebra or Geometric Calculus.

-- warning -- shameless plug alert --

For those unfamiliar with Geometric Algebra this is my understanding (which you should take with a grain of salt as I am self taught and may have led myself astray :). GA is a way to represent higher dimentional object beyond vectors in a consistent and systematic way that allows for standard mathematical operation like addition, multiplication and division and exponents. Something that you cannot do with vectors (there is the cross product and dot product but that is not true multiplication). GA is really just a form of clifford algebra that has a simpler syntax like vector calculus but I think that it is much more powerful than vector calculus. Dr. David Hestenes of Arizona State University has been a huge force behind GA and now it seems to me that the University of Cambridge is really behind it now too. Alas, I have yet to see any courses at my local university.

I've been 'lurking' on this group for a few months now and your post inpired me to respond (though a bit delayed).

Congratulations on going back to school. I wish you luck.

I've enjoyed reading all the posts. It looks like this group has a very diverse membership. That is great to see.

I apologize for the long post. Guess I should have posted sooner ;)

Personally, I love math. I took it in university but I don't use it for my work. I do tutor high school math on a regular basis. I especially love vector calculus and linear algebra. I'd like to try Mathematica some day. Maybe if I ever go back to school and can get a student copy. For now I mostly use a pen and paper :)

About ten years ago I was afraid that my math skills were dwindling as I'd been out of school for over ten years and was working as a programmer that didn't involve much math. I started reviewing my university books and then started learning tensor calculus. It inspired me. I then tried to get into differential forms, quanterions and finally discovered geometric algebra (GA).

I have tried to understand the different approaches by looking at things like divergence and curl and Electromagnatism.

There was an interesting paper I read on using differential forms (DF) as a pedigogical approach to teaching Electromagnetic theory. I think that GA also has the same advantages. However, both appoaches can seem a bit strange. Further, I think there is still an advantage to looking at it the conventional way with vector analysis as well as DF or GA. But it is all really exciting because it all adds insight and helps us understand things better.

My learning seems to go in spurts. I am not good at doing it on a daily basis so I often find myself reviewing and catching up. But it is all for fun.

I'm curious if you or anyone else has had any exposure to Geometric Algebra or Geometric Calculus.

-- warning -- shameless plug alert --

For those unfamiliar with Geometric Algebra this is my understanding (which you should take with a grain of salt as I am self taught and may have led myself astray :). GA is a way to represent higher dimentional object beyond vectors in a consistent and systematic way that allows for standard mathematical operation like addition, multiplication and division and exponents. Something that you cannot do with vectors (there is the cross product and dot product but that is not true multiplication). GA is really just a form of clifford algebra that has a simpler syntax like vector calculus but I think that it is much more powerful than vector calculus. Dr. David Hestenes of Arizona State University has been a huge force behind GA and now it seems to me that the University of Cambridge is really behind it now too. Alas, I have yet to see any courses at my local university.

### Books mentioned in this topic

Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession (other topics)The Indian Clerk (other topics)

Mathemagic: Magic, Puzzles and Games with Numbers (other topics)

Flatland: A Romance of Many Dimensions (other topics)

The World of Mathematics: A Four-Volume Set (other topics)

More...

### Authors mentioned in this topic

David Leavitt (other topics)Apostolos Doxiadis (other topics)

Yōko Ogawa (other topics)

Keith J. Devlin (other topics)

message 1:by Nicole (new)Go ahead and introduce yourself (and add some good books while you're at it)!

----------------

I'm Nicole and I teach 7th grade math in California. I've got a BS in architectural engineering and enjoy reading about math. I find it truly fascinating, and look forward to discussing it. I am not, however, a mathematician, so don't get too technical on me. =)