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

Category: Mathematics
Author: Aleksandr Danilovich Aleksandrov, Andre? Nikolaevich Kolmogorov, M. A. Lavrent'ev
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by japhyr   2020-01-02
I studied physics in undergrad many years ago, and it's been a long time since I used higher level math on a regular basis. I just picked up Mathematics: Its Content, Methods, and Meaning, on the recommendation of someone here. It's over 1000 pages, so it's going to be a lifetime reading project for me, but it's been wonderful to start reading. The first part of the book traces the earliest origins of math, and everything was grounded in real-world physical problems.

I've been a high school math teacher for most of my life, and I have deep frustrations with how removed from meaning math is presented to most students. Just because the teacher knows and states the possible relevance doesn't mean students should be expected to take the relevance at face value.

I was mostly focused on teaching algebra 1 classes, which is why I didn't use higher math all that often. But my understanding of higher math grounded my teaching of lower level concepts all the time, and I often spoke of higher level concepts with my students to help demystify math. My 8yo son loves math for now, and the moment school makes math meaningless to him I am planning to find some way to intervene.

https://www.amazon.com/gp/product/0486409163/

by whitepoplar   2019-01-21
This book is fantastic and pretty much takes you through an entire undergrad mathematics course: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
by synthmeat   2018-03-14
I’m going to go with a few assumptions here:

a) You don’t do this full time.

b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach.

c) You are skilled with programming/software in general.

In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Even charting simple tables goes a long way.

Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff.

I’d recommend getting great and cheap russian recap of mathematics up to 60s [1] and a modern coverage of the field in relatively light essay form [2].

Just skimming these will broaden your mathematical horizons to the point where you’re going to start recognizing more and more real-life math problems in your daily life which will, in return, incite you to dig further into aspects and resources of what is absolutely huge and beautiful landscape of mathematics.

[1] https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

[2] https://www.amazon.com/Princeton-Companion-Mathematics-Timot...

by ivan_ah   2017-08-19
I've looked at a bunch of these math compendiums while researching what to include in my book, and this one seemed the best so far: http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... The writing isn't very hand-holdy, but it covers a lot of important topics, and without too much fluff.

For a more "math for general culture" I'd recommend this one: http://www.amazon.ca/Mathematics-1001-Absolutely-Everything-... which covers a lot of fundamental topics in an intuitive manner.

I have both books on the shelf, but not finished reading through all of them so I can't give my full endorsement, but from what I've seen so far, they're good stuff.

by oskarth   2017-08-19
Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning, by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics.

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...