Ask HN: How to learn mathematical proofs from scratch? • Hacker News Board

Re: Ask HN: How to learn mathematical proofs from scratch?

#121

Post by vkazanov » Tue, Jun 21, 2022, 7:01 AM UTC

greymalik wrote: post #118

vkazanov wrote: post #82

Earlier quoted context omitted.

I love, love, love Velleman's book. I worked through it after uni years, and after working for a few years. It changed my perspective on proofs and math completely! It showed how the language of logic combined set theory form a very small and comprehensible foundation for most of math. After reading it and a few introductory-level books on number theory, calculus and combinatorics, most of CS proofs started feeling..…

> a few introductory-level books on number theory, calculus and combinatorics Any particular recommendations?

Of recent gems: Elementary Number Theory by Underwood Dudley is easy to like. You can really see how it was written with an active reader in mind, with a good and doable set of inline excercises, key problems and additional problems. The material covers all the basics and doesn't try to be original, which is good for self-study.

Instead of listing other books I would suggest the following learning scheme of a programmer trying to deepen their math:

1. No need to go beyond basics. Any uni-level introductory math course is already more advanced than 99.99% uses you might have.

2. Know your basics well. Get 2-3 classic books. Work through the one you like most, but still read through the rest.

3. Practical book size limit - 200-250 pages. Math material is hard, 200 pages of good math is months and months and months and mo...

4. Setup a learning/reading routine.

Re: Ask HN: How to learn mathematical proofs from scratch?

#122

Post by vkazanov » Tue, Jun 21, 2022, 8:23 AM UTC

vkazanov wrote: post #121

greymalik wrote: post #118

Earlier quoted context omitted.

> a few introductory-level books on number theory, calculus and combinatorics Any particular recommendations?

Of recent gems: Elementary Number Theory by Underwood Dudley is easy to like. You can really see how it was written with an active reader in mind, with a good and doable set of inline excercises, key problems and additional problems. The material covers all the basics and doesn't try to be original, which is good for self-study. Instead of listing other books I would suggest the following learning scheme of a program…

One last important bit: don't forget to enjoy the adventure, take it slow, think and feel how your reasoning toolbox expands :-)

Re: Ask HN: How to learn mathematical proofs from scratch?

#123

Post by ipnon » Sat, Jun 25, 2022, 9:38 PM UTC

FPGAhacker wrote: post #76

k__ wrote: post #67

Earlier quoted context omitted.

I studied CS and it never clicked for me. For me, a proof is essentially transforming one formular into another one until someone who understands math says "yes, now you have proven it!" For me, any step is as good as the others. I wish, I could understand what's happening.

That's what algebra was like for me. I never was able to develop any intuition for algebra. Calculus on the other hand was very intuitive for me. Algebra was like solving a puzzle where you randomly move pieces around to try to get them in order. There didn't seem to be any real principles involved. Just a set of rules to memorize.

It seems like this is because abstract algebra is the study of invented number games. These new games can seem a little too, well, abstract at times. The power comes from being able to play the same game with different rules when necessary.

Re: Ask HN: How to learn mathematical proofs from scratch?

#124

Post by CrisPerdue » Thu, Jun 30, 2022, 12:30 AM UTC

rramadass wrote: post #116

CrisPerdue wrote: post #106

You might find my own effort in this area appropriate to you: https://prooftoys.org/ . Whether it is _exceedingly gentle_ is a legitimate question, but the site works hard to present logic and an embedded deductive system for learners whose background may be just ordinary high school mathematics. You might think of the website in these parts: 1) An introduction to logic through pictures, basically Venn diagrams with…

Great Work! Just browsed through it and it looks quite promising. I highly encourage you to submit it to HN as a "Show HN: ..." (instead of being buried in a comment) and solicit feedback. Projects like this deserve more and better recognition.

Thanks again for the encouragement!

I have submitted to "Show HN" at https://news.ycombinator.com/item?id=31927224.

Your input (and potential upvote) would be much appreciated.

Re: Ask HN: How to learn mathematical proofs from scratch?

#125

Post by rramadass » Thu, Jun 30, 2022, 3:32 AM UTC

CrisPerdue wrote: post #124

rramadass wrote: post #116

Earlier quoted context omitted.

Great Work! Just browsed through it and it looks quite promising. I highly encourage you to submit it to HN as a "Show HN: ..." (instead of being buried in a comment) and solicit feedback. Projects like this deserve more and better recognition.

Thanks again for the encouragement! I have submitted to "Show HN" at https://news.ycombinator.com/item?id=31927224 . Your input (and potential upvote) would be much appreciated.

Just looked at your submission. Your "Prooftoys" link is not clickable! It also doesn't have the "Show HN" phrase at the beginning.

Maybe resubmit as a link with a title something like "Show HN: Simple Proof System for Beginners" (look at previous "Show HN" posts) and add the text which will show up as a comment.