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55 points

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23rd May 2017

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

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

1 point

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19th Nov 2021

I always suggest this as an overview of the most important math fields up to the 70s, written by famous Soviet mathematicians.

I consider it pretty accessible to anyone with an interest in higher math, with a strong background of high school math and physics and a deep desire to learn more.

1 point

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2nd Nov 2021

Well you can understand/get-the-frelong-of some stuff/concepts by reading high level books such as this:

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

But imho, if you want to understand a mathematical concept deeply, you'll have to go through the hard road of solving actual problems.

1 point

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25th Dec 2016

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.

1 point

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18th Jul 2011

"Mathematics: Its Content, Methods and Meaning" http://www.amazon.com/Mathematics-Its-Content-Methods-Meaning/dp/0486409163 I thought this was a pretty good read. Its not programming oriented, but it does help for showing a brief dip into different maths fields and some of the concepts therein.

1 point

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22nd Feb 2010

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.

6 points

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20th May 2021

2 points

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21st Apr 2021

For an amazing bird's eye view of most mathematical fields:

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

2 points

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4th Jun 2015

2 points

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25th Feb 2015

Available on Amazon

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

1 point

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15th Jun 2022

Get this book. It's cheap, given it's over 1200 pages.

https://www.amazon.es/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/

1 point

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13th May 2022

https://www.amazon.es/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/

It's like a 1200 paged encyclopedia of math.

1 point

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9th Apr 2022

> felt inspired to deepen and recap my math skills.

https://www.amazon.es/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/

> Hence, I was wondering if anyone has a recommendation for a math book that focuses on applied mathematical questions (but also provides solutions).

Uhmmm...maybe G. Strang's Linear Algebra book. It's pretty applied.

> My goal is to improve my math skills to improve my coding skills, hardware building capabilities, and in general, understand the world around us better (mathematically speaking).

You'll need many books and a lot of time to invest for such a goal. I can offer some suggestions:

- The book(s) mentioned earlier & a good Calculus book. Learn Calculus & Linear algebra well, and you'll be ready to attack most engineering problems.

- For hardware: https://www.nand2tetris.org/

- Coding: Project Euler, Leetcode, or/and any good algorithms book such as Skiena's "Algorithm design manual" or J. Erickson's Algorithms book.

1 point

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27th Mar 2022

> I sometimes feel like my degree isnt good as I don't know a lot of the words used in formal mathematics which then makes me feel like I'm not a proper mathematician and not as "good" as I thought I would have been by this point.

As a person that entered math from a physics BSc, I can feel you.

I still have the feeling that I'm not a "proper mathematician" because I still lack foundations in real analysis, topology, abstract algebra and differential geometry, but I've set a long-term plan to cover such fields via self-study.

And I feel this imposter syndrome ever since I've entered in a math dept. for a MSc in computational math. The philosophy of the dept. was radically different from that of physics, so I did long personal readings to fill in any gaps I would have comparing to my math BSc co-students. Did graduate with an "Excellent" grade (~85%, my physics BSc was with a 70%), but I know I still have a lot to learn.

If you'd like to have a high-level view of what is out there, I can recommend 1 book for math, and 2 books for math physics. The good with physics, at least for me, was that it showed me how many important math fields (linear algebra, vector calculus, ODEs, PDEs, Fourier series, orthogonal polynomials, etc) were applied in real life problems. So I had seen the applications, and then I decided I wanted to dive deeper in the "tools" of Physics.

In my MSc I've fallen in love with mathematical logic too and the foundations, and computability, complexity theory etc. So...naturally the next step for me is to do a PhD in theoretical computer science, just for the sake of knowledge.

Anyway. The books:

- https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163
- https://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406498/
- https://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406501

As a final note:

the feeling that "you're not good enough", never really goes away.

You just get used to it, and maybe at some point you'll learn not to mind it that much.

In the end, the best thing we can do in our short lives is to learn what we don't know and do then our best to try to broaden the shore of our knowledge some centimeters inside the ocean of ignorance...

Keep it up. Never give up.

1 point

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4th Feb 2022

I have a physics bg, but become increasingly interested in mathematics as years passed by. So I got into the habit of self-studying, mostly from translated Soviet Dover books.

I found that the following provides a nice overview of the basic math sub-fields, and it should be helpful for you too:

https://www.amazon.es/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/

You might like my goodreads list too.

Keep up the good work, believe in yourself, look out for friendly math communities either online (eg. this one) and offline, and never again let others define what you like and what you don't like :).

1 point

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18th Dec 2021

1 point

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28th Nov 2021

1 point

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29th Oct 2021

1 point

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2nd Oct 2021

1 point

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30th Aug 2021

1 point

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19th May 2019

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

1 point

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16th Jun 2018

I've found this book does a good job of explaining the history and motivations for a variety of foundational topics: https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

1 point

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19th Nov 2016

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

1 point

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1st Feb 2016

1 point

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14th Nov 2015

The classics are always available online and for free. The Internet Archives has the largest list but only the scanned copies are available (mostly). They also has a cool online reading mode with even cooler real page turning effect. Project Gutenberg has better formatted textbooks but not much on math.

I recommend G.H. Hardy's 'A Course of Pure Mathematics'. It is the best bet for calculus. It's not for calculus alone as it also discusses some trigonometry and complex numbers but the writing is crystal clear and the exposition sublime. (https://archive.org/details/coursepuremath00hardrich)

S.L. Loney's classic 'Plane Trigonometry' is a good book for trigonometry. (https://archive.org/details/planetrigonomet00lonegoog)

If you like books titled 'Thumb Twiddling for Dummies' or 'Potty Training simplified 12th ed' then Thompson's 'Calculus made easy' is the book for you. Don't get me wrong it's quite a good book and just perfect if you want to get to the meaning of calculus quickly.

Hall and Knight's 'Higher Algebra' is my favourite math book. It's teaches you everything that your teacher never taught you. Their 'Elementary Algebra' for schools is a prequel to 'Higher Algebra'. I haven't read it so I can't recommend it.(https://archive.org/details/higheralgebraseq00hall) If you're on a quest and need to hike across troll country or wade through a crocodile infested swamp and make your way through an impenetrable jungle then you must take care to securely stow away this book in your backpack. It's that good.

A. D. Aleksandrov, A. N. Kolmogorov and M. A. Lavrentev 's 'Mathematics: Its content, methods and meaning' is an old soviet era book that takes up the task of summarising a sizeable chunk of mathematics for the wayward mathematician. It's not free but a kindle edition that you can read on your android/iphone is available on amazon (http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163). Don't bother about the second volume if you only want calculus. P.S. it's properly formatted. P.P.S. Some reviewers on amazon compared it to the Feynman lectures on physics. That is definitely something.

Luck.

1 point

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4th May 2015

Here's a good choice, 1120 pages and very wide ranging: http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163

1 point

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4th May 2015

1 point

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21st Jan 2015

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

1 point

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11th Jun 2011

1 point

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25th Dec 2010

I'm surprised that nobody has mentioned this one yet: http://www.amazon.com/Mathematics-Its-Content-Methods-Meaning/dp/0486409163

It's a tome, but worth every penny. Of course, it also helps that the authors are revered geniuses in academia.

0 points

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6th Aug 2019

Your post belongs to this sub: https://www.reddit.com/r/badmathematics/

It is good to have interest in mathematics, but you have serious gaps in the foundations. Get good books on logic, abstract algebra and general mathematics.

This one is decent for general mathematics introduction: https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

< $50

< $50