Page 10 of 10

Re: Math Books

Posted: Thu Dec 03, 2015 1:38 pm UTC
by doogly
Dan Rockmore's Stalking the Riemann Hypothesis could be good too. The reviews indicate that it can be pretty frustratingly non-mathy - only one equation! I think these reviewers do not actually know what "popular level" means.

Also worth noting that he is a sweet dude who taught my calc 3 class.

Re: Math Books

Posted: Wed Dec 09, 2015 6:55 pm UTC
by sciencenerd
Everyday Calculus: Discovering the Hidden Math All Around Us by Oscar E. Fernandez
Seems like a good book

Re: Math Books

Posted: Wed Jan 27, 2016 8:15 pm UTC
by AngelAttractor
Can someone please recommend me a book on the subject of nonlinear systems?

Re: Math Books

Posted: Sat Aug 27, 2016 6:44 am UTC
by chi-squared
I've really enjoyed Infinite Dimensional Analysis by Aliprantis and Border.

It has a reasonably comprehensive coverage (at least, as comprehensive as you can get given the breadth of the subject matter) of topology, measure theory and functional analysis.

If anyone has suggestions of texts with a similar bend, I'd love to hear them.

Re: Math Books-Banach Lattices

Posted: Wed Oct 12, 2016 12:05 am UTC
by Farabor
I'm trying to learn about Banach Lattices (Riesz spaces which are Banach Spaces). The textbook my professor gave me to work from is Peter Meyer-Nieberg's "Banach Lattices", 1st edition, 1991. I'm finding it extremely dense/hard to follow. (I didn't have any problem with Kreyszig's Introductory Functional Analysis, which is my background). Does anyone have other books to recommend that I might find more accessible?

Re: Math Books-Banach Lattices

Posted: Wed Nov 09, 2016 1:06 am UTC
by chi-squared
Farabor wrote:I'm trying to learn about Banach Lattices (Riesz spaces which are Banach Spaces). The textbook my professor gave me to work from is Peter Meyer-Nieberg's "Banach Lattices", 1st edition, 1991. I'm finding it extremely dense/hard to follow. (I didn't have any problem with Kreyszig's Introductory Functional Analysis, which is my background). Does anyone have other books to recommend that I might find more accessible?


The book I mention one post above (Aliprantis & Border) covers Banach Lattices. I think that was also one of Aliprantis' main research areas, so it might be worth a look.

Re: Math Books

Posted: Tue Apr 25, 2017 7:44 am UTC
by monkey3
can anyone recommend a good calculus book ? :)

Re: Math Books

Posted: Tue Apr 25, 2017 9:02 am UTC
by Bane Harper
If you are new to calculus begin with YouTube videos and Pre‑Calculus For Dummies by Yang Kuang

Re: Math Books

Posted: Tue Apr 25, 2017 1:34 pm UTC
by monkey3
I like that book already , i mean i was sort of stuck at trigonometry for sometime now
Not sure where it begins or where it ends .

I somehow need to understand trigonometry a bit more deeply , i mean everything in it , the beginning and the end . i hope there is such a thing in trigonometry :x

Anyway that book looks nice especially this part

Image

Do you know any other good trigonometry books or trigonometry teaching websites ?

Re: Math Books

Posted: Tue Apr 25, 2017 3:26 pm UTC
by monkey3
Image

Image

What do you learn after this if your aim is learning calculus ?

Re: Math Books

Posted: Tue Apr 25, 2017 5:22 pm UTC
by doogly
What is motivating your study for this? Any particular application or field, or just a pure math curiosity?

Re: Math Books

Posted: Tue Apr 25, 2017 5:31 pm UTC
by monkey3
Do you want to see a list of things i have gathered ? i don't know if i should use this thread to post that list of things ...

Are you interested in that list of things ?

Anyway i am trying to learn calculus

Re: Math Books

Posted: Tue Apr 25, 2017 5:59 pm UTC
by ucim
monkey3 wrote:What do you learn after this if your aim is learning calculus ?
I'm not sure what you mean by "learn". You posted a great list of trigonometric identities, which are useful tools in actually doing trigonometry. But it almost seems as if you equate memorizing these tables with "learning trig". For example, missing on this page is the unit circle, which visually conveys what "sin" and "cos" etc. mean.

In any case, trig is not a precursor to calculus. It's just that a lot of the useful applications of calculus require trig anyway, and trig gives you a whole bunch of new functions to play calculus with, so it's good to have those tools under your belt first.

Calculus is first and foremost about rates of change. Things change over time (or distance, or whatever), and at any given (one) point there is a certain rate of change, but you can only "see" the change by comparing two points. So, you consider two points "very" close together and get an approximation (because it's changing!)... the closer together your two points the better the approximation. Calculus is about taking this to eleven.

For that, you need the idea of a limit. As "delta x" (the difference between the two points) goes to zero, the value of the expression you are looking for will get closer and closer to some value; that value is the limit.

Trivial case: y=2x. As x approaches 4, y will approach 8.
Problematic case: y=1/x. As x approaches 0, y increases without bound ("approaches infinity").
Useful illustration: y=x2/x.

As x approaches 0, what happens? The bottom makes the expression want to blow up ("approach infinity"), but the top looks well behaved. You can't just divide both sides by x to simplify, because at x=0 you're dividing by 0. However, you can do that as long as x doesn't equal zero. What happens? We simply get y=x in those cases. As x approaches zero, y also approaches zero. The limit of the expression x2/x as x approaches 0 is zero.
More interesting expressions where the limit isn't obvious are available in a zillion textbooks. But that's the idea of a limit.

We then apply that idea to rates of change, to find (say) the slope of a curve. That curve needs to be expressed first in math, for example,
y=3x2
Slope is rise over run; that's easy if you have a straight line. Just pick two points and do arithmetic; the slope is constant. But with this curve, the slope keeps changing. We want an expression for the slope of this curve at any point. To do this, we still pick two points. One of them will be x (the point at which we want the value of the slope), and the other will be nearby: (x+a), where a is small.

Slope is rise over run. The run is easy... it's the horizontal distance between the two points It's just a.
Algebraically, it's (x+a)-x (the x coordinate of the second point, minus the x coordinate of the first point)
The rise is a little harder; we need to use the formula for our original curve and take the difference of the two resulting values. For the first point it's just
3(x)2
For the second point it's
3(x+a)2
Subtract the two, and the rise is:

rise = 3(x+a)2 - 3(x)2
rise = (3x2 + 6xa + 3a2) - 3(x)2
rise = 6xa + 3a2

so the slope = rise/run = (6xa + 3a2)/a = 6xa/a + 3a2/a

Now, take the limit as a=>0 (as the distance between the two points we used to calculate the slope approximation vanishes)

We get slope = 6x

The a in the denominator can never be zero, but we can see from the expression that the closer we get to a=0, the closer the equation comes to y=6x.

The slope actually increases (linearly in x). As x moves to the right, the slope gets steeper. (and as it moves to the left of zero, it gets steeper in the other direction). When x is zero, the slope is zero, and the curve is at a minimum (or maximum).

That is calculus in action.

No trig involved. But of course trig functions have slopes, and there's lots of fun to be had with calculus on trig functions.

Jose

Re: Math Books

Posted: Tue Apr 25, 2017 6:25 pm UTC
by monkey3
Thanks ucim ,

To be honest , i started this account to improve my math from the very beginning ...

Arithmetic
Algebra
Trigonometry
Differentiation
Integration
Differential equation

Spoiler:
Image

whole numbers , natural numbers , integers , rational numbers , irrational numbers .

factors ( reducible), prime factors (irreducible), greatest common factor (same as greatest common divisor ), least common multiple

Monomial , binomial , trinomial , polynomial

simplify , factoring (factorization )

Factoring polynomials

’To factor’ means to break up into multiples.

Methods of Factoring

Factor by Distributive law method

Image

Factor by grouping

Image

Factor by Splitting

Image

Factor by Very Famous Polynomials

Image

Image
Image

After that trigonometry

Image

Image

Calculus derivatives and limits

Image

Calculus integrals

Image


The sad part is i haven't got a list like that for differential equations , i don't even know what i should be looking for ...

Re: Math Books

Posted: Tue Apr 25, 2017 8:26 pm UTC
by gmalivuk
I put the middle of that post in [spoiler] tags to make the page a bit easier to read. Please do that whenever a post is going to be more than a couple of screen-heights to scroll through.

Re: Math Books

Posted: Wed Apr 26, 2017 1:44 am UTC
by doogly
Kline's Calculus: An Intuitive and Physical Approach is pretty tight, combo it up with Spivak if you want a little more high falutin delightfulness.

Re: Math Books

Posted: Wed Apr 26, 2017 8:24 am UTC
by monkey3
Thanks for putting it in the spoiler tag , and thanks for the books suggestions :D

Re: Math Books

Posted: Fri May 12, 2017 1:34 am UTC
by CTepp
Can anyone recommend a book on advanced numerical analysis of differential equations? I am particularly interested in one with reasonably fast techniques for stiff non-periodic PDEs with both a finite and infinite [0,Inf) horizon.

Math Non-Textbook

Posted: Fri Nov 10, 2017 4:09 pm UTC
by rwrdb
I'd like some recommendations on a book I could read to my kids to get them to get them excited/inspired about the value of Math, and that may interest them to pursue Math studies on a serious level.

They're all pretty good at math, doing work 2-3 grade levels above where they're at. But I think the right interest may allow them to really enjoy and pursue math, rather than just learning it as a necessary evil.

I'd prefer a book not written towards kids. Something that will be a challenge for them, but not require technical understanding of more than just elementary math. Learning math isn't the focus, becoming interested in math is the objective.

This may be a biography of a mathematician, or history of the development of mathematics, or something along those lines.

Any recommendations? What peaked your interest and motivated you to pursue this field?

Personally, I found my interest at age 8 that I obsessed about and still love to this day and has turned into a very successful career and personal satisfaction for me. I want to provide the opportunity for my kids to find their interest/obsession at a young age as well...

Re: Math Books

Posted: Fri Mar 29, 2019 11:34 am UTC
by Orangong
Looking for a book with lots of mathematical and logical problems to solve. Difficultly would be around Junior to Intermediate Maths Olympiad, therefore it would be challenging and would make you think.

It is supposed to help with Cambridge interviews or Maths interviews of any sort. I am trying to improve my logical thinking skills and the way I approach contextual mathematical problems.