Top products from r/mathematics

We found 33 product mentions on r/mathematics. We ranked the 91 resulting products by number of redditors who mentioned them. Here are the top 20.

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Top comments that mention products on r/mathematics:

u/lurking_quietly · 5 pointsr/mathematics

As with Michael Spivak's Calculus, Apostol's two-volume Calculus is much, much more proof-centric than your introduction to calculus has been until now. That will make the material challenging but really rewarding, too.

Since you've had three semesters of calculus, I'm confident you likely have the relevant calculus background. I'd be more interested, though, in your background in reading, understanding, and writing proofs. Have you taken any such proof-based courses? In many American university curricula, for example, this is often introduced in a class like discrete mathematics. You'll likely have to be comfortable with the following, for example:

  • set and function notation

  • basic results in set theory, including unions, intersections, collections of subsets, and possibly countably and uncountably infinite sets

  • basic results and concepts with functions, including the image and preimage/inverse image of a function

  • basic ideas about sequences and subsequences

  • mathematical induction

  • familiarity with logical quantifiers

    This is just off the top of my head, but don't worry if the above list seems intimidating. What you don't already know, but will need, should be included in the text itself.

    Self-study is great, and I applaud your ambition in choosing this text. From my experience, you'll likely be even more successful if you can find someone to join you in self-study, especially if you don't have a teacher or professor to guide you through what will inevitably include very new material. If you can't find someone local with whom you can study together in person, then the internet may be a good way to find a fellow study partner. If you know (or are learning) LaTeX, then Overleaf or similar tools can be really useful for sharing math that's actually legible.

    I'd add one other remark: if memory serves, Apostol introduces integration before differentiation, something that I believe is uncommon. Since you're already familiar with both integration and differentiation, that will likely matter less for you.

    Good luck with your project!
u/ProctorBoamah · 1 pointr/mathematics

RPCV checking in. This is a good idea... you're going to have a lot of downtime and it's a great opportunity to read all the things you've wanted to but haven't yet found the time for. That could mean math, or languages, or just old novels.

When I was learning functional analysis, if found this book by Bollobas to be incredibly helpful. Of course, the only real analysis reference you need is Baby Rudin, but if you want to learn measure theory you may want his Real & Complex Analysis instead.

For texts on the other subjects, take a look at this list. You should be able to find anything you need there.

If you have any questions about Peace Corps, feel free to PM me. Good luck!

u/xanaxmonk · 1 pointr/mathematics

hey there the bridges conference is about your research topic. Here is a really cute video displaying some of the pieces, which there are descriptions of on the site.

This youtube channel also has a lot of other maths inspired art such as this sculpture and a cute little video on symmetry in music.

Good luck with your project!

e: also thirding the mc escher suggestion :)

e2: also if you're interested here is an accessible book (pdf)on symmetry in mathematics, which as you can imagine, ends up being a relevant topic for thinking about art.

u/DataCruncher · 7 pointsr/mathematics

I think the most important part of being able to see beauty in mathematics is transitioning to texts which are based on proofs rather than application. A side effect of gaining the ability to read and write proofs is that you're forced to deeply understand the theory of the math you're learning, as well as actively using your intuition to solve problems, rather than dry route calculations found in most application based textbooks. Based on what you've written, I feel you may enjoy taking this path.

Along these lines, you could start of with Book of Proof (free) or How to Prove It. From there, I would recommend starting off with a lighter proof based text, like Calculus by Spivak, Linear Algebra Done Right by Axler, or Pinter's book as you mentioned. Doing any intro proofs book plus another book at the level I mentioned here would have you well prepared to read any standard book at the undergraduate level (Analysis, Algebra, Topology, etc).

u/NSAFedora · 1 pointr/mathematics

AH HA, one of the few times I will link a dover book in good heart!

http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178

Pinter offers a fine introduction to abstract algebra.

u/imd · 4 pointsr/mathematics

We used the Dover textbook by Pinter. It's my favorite math textbook ever, the writing was just so clear, and even entertaining and funny. We had a good professor too.

u/minitheorem · 1 pointr/mathematics

The books Engineering Mathematics and Advanced Engineering Mathematics are fantastic self-teaching texts which will take you from basic arithmetic to complex analysis in a series of frame-by-frame "programmes". They will reinforce what prior knowledge you do have (allowing you to brush up on important algebra, for example), while gently and swiftly bringing you through trig, pre-calc, and then calculus. All of that is in the first volume (which also has matrix algebra, probability, and statistics). You may not need the second volume, but it's just as good for the same reasons. I've found that it's basically impossible to be confused by these books. They make sure you learn.

u/semiring · 1 pointr/mathematics

I highly recommend Cornerstones of Decidability. It is presented in an accessible way but does not sacrifice rigour in the process. Rozenberg and Salomaa are not only very accomplished theoretical computer scientists, they are outstanding teachers as well.

u/cjak · 1 pointr/mathematics

I love Russell's Principles of Mathematics for its exposition of the history of mathematical development, and found it really useful for putting some of the hairier concepts into context. Have you read it?

u/sstadnicki · 2 pointsr/mathematics

One of my favorite recent mathematics books - and one that offers a nice continuum between 'pure' mathematics and a specific application of it, as well as a nice spread of mathematical sophistication from pop math to some research-level depth, is The Symmetries Of Things by John Conway, Heidi Burgiel and Chaim Goodman-Strauss. It's an exploration of 'discrete' symmetries of the plane and of space - and of the tilings, polyhedra, etc. that they give rise to - as well as an introduction to some aspects of Coxeter groups and a (slightly out-of-place) chapter on the number of finite groups of various orders. I can highly recommend all of Conway's writing, but this is perhaps the finest instance available right now.

u/dangerlopez · 9 pointsr/mathematics

Try Naive Set Theory by Paul Halmos. I think it's aimed at undergraduates, so the content is a bit dense, but the style and tone is very conversational and engaging. I thoroughly recommend it.

u/koherence · 1 pointr/mathematics

My go to book for anything graph theory related is the intro book by West.

Great book for undergrad / first year grad students. Goes into detail on numerous topics and if I can recall, you can find a bit of good application there. I know computer science replies on applications of graph theory quite a bit, so you may be able to delve further into that.

u/thenumber0 · 5 pointsr/mathematics

Polya's How to Solve it is a classic.

You might prefer Housten's How to Think Like a Mathematician which is much more modern.

I found that they both had useful insights, though there was a fair bit of information which I didn't find helpful.

u/woh3 · 1 pointr/mathematics

Don't give her books just on pure math, as an undergrad in math, one of the most fascinating books I ever read was a biography of the master mathematician Leonard Euler (pronounced Oiler) http://www.amazon.com/Euler-Master-Dolciani-Mathematical-Expositions/dp/0883853280/ref=sr_1_2?s=books&ie=UTF8&qid=1450373882&sr=1-2&keywords=leonard+euler he was one of the giants in the field, overcoming the loss of multiple families members, disease, his sight and hearing, and yet was still a level of brilliant that is marveled even by today's standards.

u/[deleted] · 2 pointsr/mathematics

There is a resource list on math stack for undergraduate and graduate level books inmathematics. There are similar pages like this but this has a few good ones.

​

Typical math undergrad curriculum goes: Calc 1-3, Diff eq, proofs, real analysis, linear algebra, abstract algebra, complex analysis and topology along with some electives.


i see high school students try to take on too much frequently. I'd look at real analysis andlinear algebra.

u/WhackAMoleE · 2 pointsr/mathematics

> I would like to be among the many mathematicians researching Riemann Hypothesis or Prime Number Theory

Get ahold of a copy of Hardy and Wright, https://www.amazon.com/Introduction-Theory-Numbers-G-Hardy/dp/0199219869, start reading, don't stop.

u/BOBauthor · 1 pointr/mathematics

There is a fine book by Willian Dunham called "Euler: The Master of Us All." Take a look at amazon's preview to see if you will be comfortable with the level of the mathematics.

u/justanotherconsumer · 9 pointsr/mathematics

How to Study as a Mathematics Major by Lara Alcock
https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/ref=nodl_

This book was given to me my senior year of high school and it secured me as a mathematics major. I think it gives an excellent introduction to university mathematics and advice on how to think when approaching problems. Really I think this is exactly what you’re looking for.

u/magnomagna · 2 pointsr/mathematics

This webpage has a solid list of recommended textbooks: https://mathblog.com/mathematics-books/

For Linear Algebra, Linear Algebra Done Right (3rd Ed.).

u/Ozymandius383 · 2 pointsr/mathematics

I've got a few recommendations:
A First Course in Abstract Algebra. The importance of this subject in mathematics cannot be overstated, even if it seems very counterintuitive. Most number theory problems are solved through advanced algebra. This book examines most aspects of groups, rings, and fields, and many major applications of them. Anyone can read the first chapter, but you're going to have a very bad time if you don't get each chapter DOWN before the next one. This subject matter took me two of the hardest classes ever to get through, so don't be discouraged.

Like I said elsewhere, Rudin's Principles of Mathematical Analysis. Starting from basic set theory, it provides a thorough construction of the concept of real numbers, followed by sequences, series, single-variable calculus, multi-variable calculus, touches on standard and partial differential eqs, and VERY basic functional analysis. Again, a short but extremely dense book, anyone can do it, but not easily. Don't take shortcuts, and it will massively expand your mathematical literacy.

Neither of these requires much set theory, but if you're having problems there is this book. It is what it looks like, but the first few chapters are logic so you can probably skip them. It's an easy read and it seems to me that set theory is very similar in operation to logic.

u/cthechartreuse · 5 pointsr/mathematics

This book is full of proofs you can work through. It could keep you busy for quite a while and it's considered a standard for analysis.

https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X

u/Manakin · 1 pointr/mathematics

You should also check out the comment about Kurt Gödel's incompleteness theorem. If you're interested in the history of Russel's struggle with the same problem as you, somebody actually made a comic book about it! Link

u/Illumagus · 1 pointr/mathematics

3.3

>The universe is certainly mathematics-like

The universe is mathematics - numbers - sinusoidal waves, within an infinite plenum of dimensionless Leibnizian monads. How can mathematics explain perfectly a non-mathematical universe? Cartesian substance dualism again. The universe is a monism. Otherwise you have to explain how two disparate substances can possibly interact with each other in any coherent, rational way.

The universe is in fact a dual-aspect monism (aka neutral monism). 'Matter' is dimensional, spacetime mathematics. 'Mind' is dimensionless, frequency mathematics. They interact with each other via mathematics (Fourier transforms in both directions). The universe is mathematics and nothing besides.

>reality seems to be something deeper

Ah yes, the vague and unknown, inexplicable "something" rears its head once again! There is nothing deeper than ontological mathematics. What the hell would that be exactly, and how would it interact with mathematics?

>I'm both.

Sorry kid, you can't be an empiricist and a rationalist (unless you're deluding yourself). To be an empiricist is to be irrational, and to reject objective Truth and a priori reason (the PSR) as you attempt to do later on.

>Pure reason

...is the objective, rational, a priori PSR (and the God Equation -- Euler's Fomula, it's mathematical equivalent).

The universe is made from pure reason. It is irrational and absurd to claim otherwise. Simply read the God Series if you want to know more. I can't go into that degree of detail here, it would take too long - already my response needs several parts as it is breaking the character limit.

>we don't really know

Your credo, perhaps? I know. Simply approach ontological mathematics with a rational mind. Dare to know!

>dumb people think they're saying something clear as day

Tell me about it. That's what happens when you reject the PSR and rely on empiricism (the subjective senses).

>network of cause and effect in your brain actually reflects reality or your reasoning will not reflect reality

Preaching to the choir. My thinking is firmly rooted in reality, yours is not. As soon as you reject the PSR and ontological mathematics, it's game over. At that point you have lost your connection to noumenal reality.

>before Galileo was able to overturn it. Through empiricism, lol.

Fucking hell. How about: through mathematics, lol. All empiricists like to believe that they are "straddling the fence" i.e. deploying both empiricism and reason -- but as it turns out, they always end up rejecting reason.

>reason and reflection of reality

Reason alone. -- in accordance with the ontological mathematics and the PSR. Since reality is 'made up of' Leibnizian monads (mathematical, dimensionless points with infinite capacity and reason built in to them, reality is 100% rational and 100% mathematical. It would be literally impossible for it to be otherwise.

>locked to reality is what I call a coherence lock

The PSR is the ultimate 'coherence lock'. It is in fact the only thing that can function as one. It is the 'coherence lock' for all sufficiently intelligent minds in the universe.

>all have different ideas of what mathematics is

That's what operating without the PSR does to you. Mathematicians in general are dull, dreary functionaries -- slaves to the irrational meta-paradigm of empiricism and materialism, spending their time on irrelevant details and their career prospects. They have no grand vision of reality. They are Mandarins.

https://www.amazon.com/Mandarin-Effect-Crisis-Meaning-ebook/dp/B07VHTRDTJ

I am no "abstract mathematician" or Mandarin functionary, I am a Sage/Gadfly and an ontological mathematician.

Do you know what ontological mathematics is? Read the God Series by Mike Hockney to find out. And if you refuse to, then we all know you're just subscribing to the same 'divergence theory' you suggested. :P

>highly abstract math that doesn't reflect reality

Then it's no longer valid (ontological) mathematics, it's an abstract Sudoku puzzle for autistic functionaries.

>observe it in the real world

Empiricists are always obsessed with "observations". (Read the extract in 3.1 to see why this is so, so wrong.)

The "real world" is dimensionless and mental. Or at the very least, you must assign matter and mind ontological parity. But in truth, matter always originates from dimensionless mind. (And both are fully mathematical.)

>observe it in the real world to "know" it.

No, I could be a disembodied mind and not observe anything within collective spacetime at all, and yet still know that 1+1 = 2: it isn't based on observations (extreme sensory empiricist again...) but on reason.

>Why is 1+1 not equal to 1 ?

Because that violates the PSR. One sinusoidal wave plus another makes both of them (two sinusoidal waves.) Energy loss, i.e. information loss (of mathematical information, there's no such thing as non-mathematical information) also violates the PSR. The PSR has the only claim of being "God" - there's no other candidate. You can reject the PSR all you want, but then you have declared yourself ipso facto irrational - and there's no point having a rational debate, or trying to say anything about Truth or absolute (noumenal) reality -- base reality.

>brain processes patterns it observes ... observes ... observes ... observes ... observes ... observes ...

Your focus on observation indicates you're an extreme sensory type. Re-read the extract from 3.1 if you still haven't 'got it'. Truth, reality, reason, mathematics et al are not dependent on observation. They are not even accessible to sensory observation!

The brain is an interface for a dimensionless, monadic mind to 'dock' with, via Fourier mathematics. I'm not a 'body with a brain', I'm controlling a body with a brain -- in order to type this, for instance. (Like a drone piloted by a person from thousands of miles away, the mind 'pilots' a body from another dimension.) I am in fact a dimensionless, mathematical mind (Leibnizian monad, 0D point, or Riemann sphere with infinite capacity).

As are you, except you don't realize it yet. You are too busy relying on "observations" rather than mathematics, reason and logic.