Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A Gentle Introduction to the Art of Mathematics

giam.southernct.edu

Post reply on HN
Print view View original

51–60 of 72 posts

Re: A Gentle Introduction to the Art of Mathematics

#51

Post by __rito__ »

nicf wrote: post #28
xk_id wrote: post #8

Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.

I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the one…

I have read many parts of Cummings'es book, and I can vouch for its quality.

It's the ideal book for learning proofs if you are self-learning.

Re: A Gentle Introduction to the Art of Mathematics

#52

Post by nicf »

nyrikki wrote: post #46
nicf wrote: post #28

Earlier quoted context omitted.

I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the one…

As someone who tutors adults, can you suggest a more digestible book for abstract algebra? While I was motivated, I used one of the typical college books. For me Abstract Algebra is what opened a lot of doors for me... but I am simply using applied math. That moving away from proofs being magical across sub-topics is what I would like to share with some co-workers who are unwilling to buy a textbook and answer key. A…

I assume you're talking about an algebra book for self-study? Gallian's "Contemporary Abstract Algebra" is a common suggestion for a more accessible algebra book, and people also sometimes suggest Fraleigh's "A First Course in Abstract Algebra", but I can really only speak to what it's like to work on this stuff with a teacher --- since my students are by definition not self-studying the things I'm working on with them, my suggestions might be of limited use!

In general, I think self-studying proof-based math can certainly be done if someone's motivated enough, but it's pretty hard and takes a lot of work, especially if you're still getting used to the skill of reading and writing proofs. It's very valuable to be able to have a person available to evaluate the proofs you're writing, and I've definitely seen a few people who came to me thinking they'd mastered proof-writing on their own and were kind of mistaken about that. (I've definitely also seen people who really did learn this skill pretty well without help! It varies a lot.)

Re: A Gentle Introduction to the Art of Mathematics

#54

Post by ChainOfFools »

wyager wrote: post #47
ChainOfFools wrote: post #40

Earlier quoted context omitted.

> I've found that mathematicians generally suck at introducing or explaining things. and then there's Grant Sanderson

I don't think it's much of an exaggeration to describe Sanderson as a contemporary Feynman, at least from the pedagogy side of things.

And Feynman himself was characterized by his advisor in a recommendation letter as "another Dirac, but this time human."[0]

[0] paraphrasing from memory, might have been a different supervisory figure.

Re: A Gentle Introduction to the Art of Mathematics

#55

Post by sn9 »

nicf wrote: post #28
xk_id wrote: post #8

Would be nice if we could see experienced mathematicians endorse this, please. It would help to decide whether to put time into it. At first glance it looks really nice.

I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the one…

The 3rd edition of Velleman's book has an online supplement that uses Lean to work through the book so you can get feedback about your proofs.

Re: A Gentle Introduction to the Art of Mathematics

#56

Post by sn9 »

nyrikki wrote: post #46
nicf wrote: post #28

Earlier quoted context omitted.

I'm a mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the one…

As someone who tutors adults, can you suggest a more digestible book for abstract algebra? While I was motivated, I used one of the typical college books. For me Abstract Algebra is what opened a lot of doors for me... but I am simply using applied math. That moving away from proofs being magical across sub-topics is what I would like to share with some co-workers who are unwilling to buy a textbook and answer key. A…

Abstract Algebra: A Student Friendly Approach by Dos Reis and Dos Reis [0] is like The Little Schemer but if it was a first course in abstract algebra.

[0] https://www.amazon.com/gp/product/1539436071?psc=1

Re: A Gentle Introduction to the Art of Mathematics

#57

Post by tarkin2 »

__rito__ wrote: post #49

This looks good. And I have already covered these things. What are some other resources for learning more Math that are very approachable when studying alone?

Khan academy will teach you all of pre-k, high-school, pre-calc, calculus and infinite series pretty well. mathsisfun.com is a great resource if that's ever lacking. High school physics on khan is good to give you a practical application of the concepts if they seem too abstract.

I found Strang's youtube lectures the best for linear algebra along with 'vector maths for 3d graphic'. Khan's linear algebra course seems like more a collection of practical things you can do with linear algebra rather than a coherent cource but it's still a great resource.

Khan academy's multi-variable calculus is good enough to give you a reasonable grasp, but I'd call it a good complement rather than sole resource.

I've tended to go through the cycle of watching the lectures, then doing the exercises, going forward, going back after a few months to ensure I understand the whys and not just the hows, and then writing my own notes. Machine Learning et al is a great practical application of all this maths.

Re: A Gentle Introduction to the Art of Mathematics

#58

Post by nyrikki »

nicf wrote: post #52
nyrikki wrote: post #46

Earlier quoted context omitted.

As someone who tutors adults, can you suggest a more digestible book for abstract algebra? While I was motivated, I used one of the typical college books. For me Abstract Algebra is what opened a lot of doors for me... but I am simply using applied math. That moving away from proofs being magical across sub-topics is what I would like to share with some co-workers who are unwilling to buy a textbook and answer key. A…

I assume you're talking about an algebra book for self-study? Gallian's "Contemporary Abstract Algebra" is a common suggestion for a more accessible algebra book, and people also sometimes suggest Fraleigh's "A First Course in Abstract Algebra", but I can really only speak to what it's like to work on this stuff with a teacher --- since my students are by definition not self-studying the things I'm working on with th…

Thanks for the suggestion. I personally used Dummit and Foote's book and found it useful, but like early Calculus with Spivak, it seems most people prefer clear and concise over slightly more comprehensive and rigorous while still being introductions.

With self study I prefer a bit more breadth to make up for the realities of needing to self study which often ends up with deep but not wide understanding of topics.

Having a brother who had a PHD in complex analysis to bother probably helped with self-learning. That is the only option when you are on-call for decades at a time as higher math courses are/were always in person.

But hopefully someone will figure out a business model to help people who need to grow and adapt.

Thanks again for the suggestions, I have ordered both books to add to my lending library.

Re: A Gentle Introduction to the Art of Mathematics

#59

Post by Nifty3929 »

wyager wrote: post #47
ChainOfFools wrote: post #40

Earlier quoted context omitted.

> I've found that mathematicians generally suck at introducing or explaining things. and then there's Grant Sanderson

I don't think it's much of an exaggeration to describe Sanderson as a contemporary Feynman, at least from the pedagogy side of things.

Perhaps on pedagogy, or at least nice, intuitive, layperson (but technically accurate) explanations of things. And plenty of fully-rigorous explanations of some things too.

I'm a big fan of Sanderson.

But I don't think we can compare Sanderson to Feynman on raw intelligence or contributions to the state of the art in math/science.

Post reply on HN