Pure mathematics

[tridianprime]

Are there any other math enthusiasts here? If so, please post what your favourite topics are, and if relevant, any books you would recommend as i am always looking to expand my mathematics textbook library.

Ill go first. My favourite area is topology and some good books i recommend for people ho want to start learning maths, in order of use, are:

Note: This assumes high school level.

General idea-

"Naive Set Theory"
"What i mathematics?" by Courant

Single Variable Calculus-

"Calculus made easy" by Thompson
"Calculus" by Michael Spivak

Multi Variable Calculus-

"Vector calculus, linear algebra, Nd differential forms" by Hubbard

Linear Algebra-

"Introduction to linear algebra" by Lang
"Linear algebra" by Lang

Differential Equations-

"Ordinary differential equations" by Arnold
"Partial Differential Equations" by Strauss

Real analysis:

"Elementary analysis" by Ross
"Introduction to mathematics analysis" by Rudin

Other:

This is what you want to learn to start and then you can delve into topology by starting with munkres or basic number theory with hardy and then apostol's analytical number theory.

I would note this is for pure mathematics not applied, for which you want to do complex analysis as well.

I id do complex analysis by Ahlfors hut its jot vital

Anyway, i would like to hear from other maths enthusiasts about their ideas and books.

 

[total-recoil]

I was doing some maths last night. The maths I do is quite basic but very practically applied. I often have to find specific resistances to place in a circuit so I can drop voltage so I have to do calculations with series resistors or resistors in parallel. I'm now beginning to suspect that a lot of the mathematics I'm taught may not be as reliable as assumed in practice due to so many other variables like internal resistances or derated capacitors and so on.
In other words, yes, I do like maths but it has to be applied to something concrete. I do a lot of calculations with milliamps or even picofarads and sometimes I like to mess with division of thousandths and millionths just to give my brain a workout.
I also have my own system of thinking. If some diagram talks of half an amp, I see it in my mind as 500 milliamps and the digit 0.5. (and also 50 per cent). Basic stuff really but I try to know it as well as I can.

 

[apt-get]

I've read a few chapters of this:
Tensors, Differential Forms, and Variational Principles (Dover Books on Mathematics): David Lovelock, Hanno Rund, Mathematics: 9780486658407: Amazon.com: Books

Hopefully it will be useful for an upcoming general relativity course.

 

[scott]

I have an interest in math, but the same as total recoil, it has to have a practical application for me to be interested.

also i have a different way to calculating stuff in my head then most people seem to, and i find it very difficult to calculate stuff on paper or show working out (hence why i failed maths at school)

like if i'm asked what's 784 plus 256, i'll work it out like this.

700+200=900
80+50=130
4+6=10

900+130+10=1040

at school i never finished my exams, because it took so long for me to write out my working out, and usually failed my classes as a result.

these day's i use maths to figure out things like ignition timing for engines and voltage in engine ignition systems, energy densities of materials (steel aluminium ect), i work as a boilermaker (metal fabricator) so when i'm welding or heating things, i find it interesting to work out in my head how many joules of heat energy i'm using to heat a certain piece of steel, even though it doesn't really make a difference knowing for my job, but i cant be bothered working it out if i'm not working if that makes sense.

 

[Levinus]

I absolutely love math! I get lost in numbers and number systems so easily. I love finding numerical relations in everything I do. I love the idea that I can take a snapshot of the world around me and calculate anything I want! Roads are lines on a graph with slopes and angles. Clouds and trees are crazy fractals. People have mass, velocity, trajectory. Computers have ones and zeros that spell out letters as easy as 01000001, 01000010, 01000011. Letters can be converted to 11 21 13 2 8 18 19. I have a special love for encryption and modal arithmetic. I love to develop algorithms for encryption.

Math to me is a solid irrefutable truth. It can't ever be taken away. It can't be wrong. I've had to teach myself how to do math, because my brain doesn't work like it should. But I've been working on new ways to find the area under a curve exactly, instead of approximations. My latest obsession.

I mentioned in a post that I can't seem to pass algebra in college. I love algebra, and I understand it intimately. But when they start scribbling away and making noise at me, I get utterly confused about what they are telling me to do. I remember trying in vain to explain a geeky attempt at humor to my professor. I told him that, regardless of what I put down, using non-euclidean geometry, I could make any value the answer. He didn't get the joke. I also failed that class.

 

[StephF]

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

G. H. Hardy

 

[Ronald Zeeman]

I like mathematics. Exposed to all the major branches in my last year of high school what I like is my mind can relate.
different types of mathematics together without actually doing any type of proof can just visualize that they are connected. really like this when it comes to physics. When others make the connection later it really gives me a warm and fuzzy feeling, like why did it take you so long. Currently monster moonshine is deeply related to how the universe functions I can just see it. A few years ago, someone did connect it to string theory, waiting for more head way. years ago, I read a book called Fermat's Enigma by Simon Singh, connections. Just popped into my mind.

 

[BoltzmannBrain17]

I took AP Calculus BC in highschool and got a 4 on the AP test. I have Mathematical Reasoning, Writing and Proof by Ted Sundstrom downloaded. I'd eventually like to work through it and then maybe an abstract algebra textbook but I haven't had the motivation. Plus I'm probably too stupid for math beyond watered down highschool calculus anyways.

 

[Ronald Zeeman]

I watched lectures in multi variable calculus. On DVD from the great courses, not hard to follow, the lectures the visual method took a bit more, must admit it would be challenging to the most gifted math majors.

 

[Ronald Zeeman]

The best book on mathematics I have ever found is mathematics 101, by Dr. Richard Elves basically covered what I learned in high school taking a 5-year program specializing in math and science.

 

[Cryptid]

Most of the maths I've used in the last 40+ years has been oriented toward radio-based communications. Not just the basic stuff cited by Total-Recoil, but some of the more in-depth applications in spread-spectrum, antenna impedance matching, and converting between Azimuth/Elevation and Altitude/Latitude/Longitude for tracking Amsats.

Wrote 2 programs still used by the U.S. Navy today, one for satellite tracking (Milsats) and another for Great Circle navigation. Good times!

 

[Ronald Zeeman]

Most of the maths I've used in the last 40+ years has been oriented toward radio-based communications. Not just the basic stuff cited by Total-Recoil, but some of the more in-depth applications in spread-spectrum, antenna impedance matching, and converting between Azimuth/Elevation and Altitude/Latitude/Longitude for tracking Amsats.

Wrote 2 programs still used by the U.S. Navy today, one for satellite tracking (Milsats) and another for Great Circle navigation. Good times!

You would have got along great with my older brother similar work experience similar education.