Reddit reviews Mathematics: Its Content, Methods and Meaning (3 Volumes in One)

Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev.

Personally read only the first chapter, but the book is praised by lots of people. I bet Mr. Nikolaevich has read it.

You can find it on Amazon https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

No matter what his interests may be, this wonderful survey will cover it, Mathematics: Its Contents, Methods, and Meaning. It was written by a team of prominent Russian mathemations, and became a classic. It's now a single Dover edition, but if possible, find it used in the original MIT 3-volume hardcover edition -- it demands that kind of respect!

I am also refreshing my calculus skills. I would like to suggest Mathematics: Its Content, Methods and Meaning .

It is classical "survey" written by 18 outstanding mathematicians. First published in 1956(?) in USSR. I have the 1999 Dover edition, all volumes in one. It covers lot more than just calculus. There is linear and non-Euclidean geometry, topology, functional analysis.

Using this book as companion to any book you currently use is highly recommended. It is total classic.

Mathematics, its Content, Methods, and Meaning - an amazing survey of analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, theories of probability and functions, linear and non-Euclidean geometry, topology, functional analysis, and more.

• The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
  
• Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov et al.
  
• Visual Complex Analysis by Tristan Needham
  
• Geometry and the Imagination by David Hilbert and Stephan Cohn-Vossen
  

Take my recommendation as a grain of salt as i didn't take my formal math education further than where you're currently at, but I felt the same way after similar classes learning the mechanics but not the motivations. Mathematics: Its Content, Methods and Meaning was recommended to me by a friend and I think it help fills the gaps in motivation and historical context/connecting different fields not covered in classes.

http://www.amazon.com/Mathematics-Its-Content-Methods-Meaning/dp/0486409163

Hi there,

For all intents and purposes, for someone your level the following will be enough material to stick your teeth into for a while.

Mathematics: Its Content, Methods and Meaning https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

This is a monster book written by Kolmogorov, a famous probabilist and educator in maths. It will take you from very basic maths all the way to Topology, Analysis and Group Theory. It is however intended as an overview rather than an exhaustive textbook on all of the theorems, proofs and definitions you need to get to higher math.

For relearning foundations so that they're super strong I can only recommend:

Engineering Mathematics
https://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1403942463

Engineering Mathematics is full of problems and each one is explained in detail. For getting your foundational, mechanical tools perfect, I'd recommend doing every problem in this book.

For low level problem solving I'd recommend going through the ENTIRE Art of Problem Solving curriculum (starting from Prealgebra).
https://www.artofproblemsolving.com/store/list/aops-curriculum

You might learn a thing or two about thinking about mathematical objects in new ways (as an example. When Prealgebra teaches you to think about inverses it forces you to consider 1/x as an object in its own right rather than 1 divided by x and to prove things. Same thing with -x. This was eye opening for me when I was making the transition from mechanical to more proof based maths.)


If you just want to know about what's going on in higher math then you can make do with:
The Princeton Companion to Mathematics
https://www.amazon.co.uk/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809

I've never read it but as far as I understand it's a wonderful book that cherry picks the coolest ideas from higher maths and presents them in a readable form. May require some base level of math to understand

EDIT: Further down the Napkin Project by Evan Chen was recommended by /u/banksyb00mb00m (http://www.mit.edu/~evanchen/napkin.html) which I think is awesome (it is an introduction to lots of areas of advanced maths for International Mathematics Olympiad competitors or just High School kids that are really interested in maths) but should really be approached post getting a strong foundation.

https://www.amazon.com/gp/product/0486409163/ref=ya_st_dp_summary

This does not specifically target game programmers. However, it's not just specific categories of math that is important to game programmers. It's EVERYTHING math related. And knowing the meaning of it and understanding is more important than just a formula.

The book I just linked is an amazing book. It is well written, and avoids academia where possible. It's balance between math and explination is just right where it can effectively get the point across, and even help you understand more complex explinations.

This book features three volumes, and each volume goes over a wide array of topics in depth.

There's a lot of ground to cover in math, but completely doable. I'm going to recommend a dense book, but I truly think it's worth the read.

Let me leave you with this. You understand how number work correct? 1 + 1 = 2. It's a matter of fact. It's not up for debate and to question it would see you insane.

This is all of math. You need to truly understand

1 + 1 = 2

a + a = b everything is a function. There are laws to everything, even if people wish to deny it. If we don't understand it, it's easier to state that there are no laws that govern it, but there are. You just don't know them yet. Math isn't overwhelming when you think of it that way, at least to me. It's whole.

Ask yourself, 'why does 1 + 1 = 2 ?' If you were given 1 + x = 2, how would you solve it? Why exactly would you solve it that way? What governing set of rules are you using to solve the equation? You don't need to memorize the names of the rules, but how to use them. Understand the terminology in math, or any language, and it's easier to grasp that language.

The book Mathematics

Not quite encyclopaedic, but this gives a good overview of most topics you might encounter in an undergraduate course. The first section also gives a very good defense of the need for basic research into mathematics.

I recommend this:

https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

Unlike most professional mathematical literature, it is aimed at novices and attempts to communicate ideas, not details. Unlike most popular treatments of mathematics, and in particular unlike the YouTubers you mention, it is written by expert mathematicians and is about advanced mathematical topics. I got a hardcover set from a used bookstore when I was young and enjoyed it very much. It's well worth your time.

Another book that you wouldn't use in a class: "Mathematics: Its Content, Meaning, and Methods"

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163

For your situation I would highly recommend Mathematics: Its Content, Methods and Meaning, which is ~1000 page survey of mathematics topics.

I would also highly suggest the 3 volume set, Mathematical Thought from Ancient to Modern Times by Morris Kline. I'm not finding the words for why I think anyone, but particularly teachers, to have a historical context for mathematics, but I strongly believe it.

It also helps to read about what sort of problems people were interested in when they came up with things such as groups, or sqrt(-1), etc.

Mathematics for the Nonmathematician (very cheap atm - $3.99 )

https://www.amazon.com/Mathematics-Nonmathematician-Morris-Kline/dp/0486248232/ref=sr_1_1?ie=UTF8&qid=1522215994&sr=8-1&keywords=Mathematics+for+the+Nonmathematician


If you get hooked on math later, consider "Mathematics: Its Content, Methods and Meaning (3 Volumes in One)".

https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163/ref=sr_1_1?ie=UTF8&qid=1522216524&sr=8-1&keywords=kolmogorov+mathematics

or the Princeton companion to mathematics - https://press.princeton.edu/titles/8350.html


Cool youtube channels:

3blue1brown

PBS Infinite Series

patrickJMT

Welch Labs

Are you thinking of this one?

Mathematics: its Content, Methods, and Meaning by Alexandrov, Kolomogrov, and Lavrent'ev.

Κατ' αρχάς συγχαρητήρια και καλή αρχή. Έχεις επιλέξει φοβερά ενδιαφέρον πεδίο κατά τη γνώμη μου και ζηλεύω λίγο :P

Ήθελα κι εγώ να μάθω σωστά μαθηματικά κάποια περίοδο και είχα ψάξει σε φόρουμ για κάποιο προτεινόμενο βιβλίο που να είναι ολοκληρωμένο και εύκολα κατανοητό. Ήταν πολλοί που πρότειναν αυτό το βιβλίο: https://www.amazon.com/dp/0486409163/?coliid=IFD6IMMG22STW&colid=3J1YAUNLTYQCX&psc=0&ref_=lv_ov_lig_dp_it

Δυστυχώς τελικά δε το αγόρασα επειδή δεν είχα χρόνο να αφιερώσω αλλά τα σχόλια που διάβασα με είχαν πείσει. Ίσως σε βοηθήσει.

For those interested in the "abstractness" of non-natural numbers, there's a phenomenal brief introduction in one of my favorite math texts, Mathematics: Its content, methods and meaning. A cold war Russian standard that covers a helluva lot of ground in applied math.

They make the point that the number "1" seems pretty intuitive to humans... you can have "1" of something, or "2" of something. But having "0" of something doesn't really make any sense, and for a long time it was argued whether or not "0" was even a "number". You certainly can't have "1/2" of a thing. If you cut an object in half, you just have 2 things now. And to have negative something is just absurd. There's a blurb about some primitive isolated tribes that have words for the number "1", "2", and "many". The number 1,237,298 is still pretty abstract to a human, because it's not like you can count that or really visualize that many things, but we acknowledge such a quantity can be useful.

If you only want one math book, SO said this is it: Mathematics

Check out:

• Concepts of Modern Mathematics by Stewart
  
• Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov & Lavrent’ev
  
  

Recentemente estive procurando algo interessante pra ler e me deparei com várias recomendações do livro How to solve it: A New Aspect of Mathematical Method.


Um livro extremamente denso mas com muito conteúdo é o Mathematics: Its Content, Methods and Meaning. Comecei a ler esse livro, mas outras atividades me fizeram dar uma pausa. Vou tentar voltar a ele e colocar como meta terminar antes de 2020 rs.


Já li alguns livros explicando a origem dos números. Mas, de todos que li, Os números é imbatível.

Mathematics - Its Content, Methods and Meaning gives you an overview of the major topics covered in university Math curriculum.

Before the Princeton Companion to Mathematics, there were:

What Is Mathematics? by Courant and Robbins

Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrent'ev

Concepts of Modern Mathematics by Ian Stewart

Aleksandrov, Kolmogorov, Lavrent'ev. http://amzn.com/0486409163. Foundations to applicationsl.

Courant, Robbins, Stewart. http://amzn.com/0195105192. Tour of mathematics.

Aside from The Princeton Companion to Mathematics, you might like to check out What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant and Robbins, and Mathematics: Its Content, Methods and Meaning by three Russian authors including Kolmogorov.

Mathematics Content Methods Meaning

I think this may be what you look for. I have read some chapters of it. It talks about meanings, where theories come from..

I also remembered it when I saw it in my bookshelve. Written by Roger Penrose. Penrose talks about math from numbers to modern physics application of math. Especially Einstein's math of space time can be understood in this book;
The Road to Reality

Thanks! what do you think about Mathematics: Its Content, Methods and Meaning ? from what I searched it can teach a lot a novice like me and quite the wonderful book.

By Kolmogorov himself: http://www.amazon.ca/Mathematics-Its-Content-Methods-Meaning/dp/0486409163

Thanks for your reply. I read positive reviews about this , what do you think?

The closest thing I can find to a self-contained series of math courses is this:

https://www.myopenmath.com/info/selfstudy.php

Prealgebra, Algebra, Precalculus, and Trigonometry.
However, I have no guarantee of the quality of this self-contained self-study resource. And it doesn't contain calculus. So, it's not really self-contained, but it's close.
_
Yet another source. Unfortunately the bibliographies may not be comprehensive.

https://www.reddit.com/r/bibliographies/wiki/directory

What is /r/bibliographies?, answered here: https://www.reddit.com/r/bibliographies/wiki/faq

>A bibliography is a text post in this subreddit that has a specific scope and provides a list of sources that, taken together, constitute an introduction to the knowledge within this scope. This subreddit seeks to collect as many high-quality bibliographies as possible that collectively cover anything readers might wish to learn. Within each bibliography is an explanation of the bibliography's scope, suggestions for learning the topic, and a list of resources that cover the scope and give readers a way to get started in their learning. Bibliographies are created and maintained by redditors called "librarians". Anyone is welcome to create a bibliography and become a /r/bibliographies librarian (see "How do I create a bibliography?" below).

 
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Several free/cheap textbooks from Algebra to Calculus approved by the American Institute of Mathematics. I suppose you could possibly use the lists as a self-contained study resource. Lots of exercises for you to do, or "hands on practice".

Here is what AIM uses for its evaluation criteria: https://aimath.org/textbooks/evaluation-criteria/
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Beginning Algebra from West Texas A&M University:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/

Intermediate Algebra from West Texas A&M University:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm

Clark University, Dave's short Trig course:
https://www2.clarku.edu/faculty/djoyce/trig/

Source of all these 3 links: Originally made for physicists, but it works for people who want to relearn the basic maths(mostly algebra and trig)

http://www.staff.science.uu.nl/~gadda001/goodtheorist/primarymathematics.html



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I'm not sure why I put this here, but here you go.

 

Warning: This book is not for people who are learning the basics of math and it's not even about learning math. It's more like discovering the several fields of math and what each field has to offer.

See why here: https://www.quora.com/Is-Mathematics-Its-Content-Methods-and-Meaning-appropriate-for-someone-with-no-mathematical-knowledge

> No, it is not. This is not a book for learning mathematics. Of course it is appropriate for anyone wanting to know more about mathematics, but the question details say you want to “begin learning math”, and this book is not at all suitable for that purpose.

> It's a survey of mathematics for the generally interested reader. It talks a bit about history, a bit about some of the major results and a bit about the methods used in modern math, but you won't learn how to actually do mathematics by reading this book. You won't be able to pass any test or exam in any undergrad course or even most high-school exams.

> If your goal is to educate yourself about some of the main fields of mathematics and what they are about, this is a great book. If, however, you wish to actually learn mathematics, this is not the right book, and in fact no single book will let you do that.

> You'll need to study linear algebra using a good linear algebra textbook with plenty of exercises and have someone help check your proofs. You'll need to study real analysis with a good real analysis textbook, probably a couple of them, and do lots and lots of exercises. The same for complex analysis, field theory, group theory, number theory, probability theory, differential equations and so on.

> Before you do any of that, if you really have “no prior knowledge”, you'll need to absolutely master the basics: school-level algebra, calculus and geometry.

> Of course, if your purpose is to study a narrow part of math for some specific purpose, you can get by with just a subset of the things I've mentioned. But the book in the question won't help you master any of those domains. It's not meant for that.
https://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163

Mathematics: Its Content, Methods and Meaning (3 Volumes in One) Paperback – July 7, 1999

Here is a review from Michael Berg about the book itself on the Mathematical Association of America website:
https://www.maa.org/press/maa-reviews/mathematics-its-content-methods-and-meaning

If there is something close to an Encyclopaedia Mathematica, but you can read it like a novel, it is these three volumes from Aleksandrov/Kolmogorov/Laurentiev. Amazon

Edit: Ahem, but after reading carefully post0, I would recommend you simply to begin with the textbooks of secondary school or so.

I'll throw out some of my favorite books from my book shelf when it comes to Computer Science, User Experience, and Mathematics - all will be essential as you begin your journey into app development:

Universal Principles of Design

Dieter Rams: As Little Design as Possible

Rework by 37signals

Clean Code

The Art of Programming

The Mythical Man-Month

The Pragmatic Programmer

Design Patterns - "Gang of Four"

Programming Language Pragmatics

Compilers - "The Dragon Book"

The Language of Mathematics

A Mathematician's Lament

The Joy of x

Mathematics: Its Content, Methods, and Meaning

Introduction to Algorithms (MIT)

If time isn't a factor, and you're not needing to steamroll into this to make money, then I'd highly encourage you to start by using a lower-level programming language like C first - or, start from the database side of things and begin learning SQL and playing around with database development.

I feel like truly understanding data structures from the lowest level is one of the most important things you can do as a budding developer.