61–70 of 72 posts
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?
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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…
The exercises for each chapter are split into several sections each section covering a different aspect of the chapter's material. Sometimes there is a section of exercises applying the material to some interesting area.
For example, the chapter on groups of permutations has 6 pages of text, then 5 pages of exercises divided into 9 sections. Those sections are: computing elements in S6 (5 problems), examples of groups of permutations (4 problems), groups of permutations in R (4 problems), a cyclic group of permutations (4 problems), a subgroup of SR (4 problems), symmetries of geometric figures (4 problems), symmetries of polynomials (4 problems), properties of permutations of a set A (4 problems), and algebra of kinship structures which consists of 9 problems covering how anthropologists have applied groups of permutations to describe kinship systems in primitive societies.
There are answers in the back for a decent number of the exercises.
It's a Dover republication so is not too hard on the wallet. List price is $30 at Dover but its around $20 on Amazon.
The combination of short chapters and lots of exercises make it easier than most textbooks to fit into a busy adult schedule.
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?
* For an introduction (and a reference) to various areas of Modern Mathematics that one didn't even know existed, The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics are a must.
* All the Math You Missed: (But Need to Know for Graduate School) by Thomas Garrity - A survey and a good adjunct to a textbook.
* Mathematics: Its Content, Methods and Meaning by Kolmogorov et al. - Classic text from the great Russian Mathematicians.
* Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming - Unique text from the great Richard Hamming (also checkout his other books).
There is plenty more of course, specifically; checkout "Dover Publications" texts, many of which are classics and affordable.
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?
"Approachability" might vary somewhat but you might find the following useful; * For an introduction (and a reference) to various areas of Modern Mathematics that one didn't even know existed, The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics are a must. * All the Math You Missed: (But Need to Know for Graduate School) by Thomas Garrity - A survey and a good adjunct to a textbo…
I already know the basics, and I want to learn more.
I cam handle hard, but the textbooks need to be written in a manner that doesn't require the help of a teacher or a classroom.
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?
My context is CNC programming, but I've found the Make: Geometry, Make: Trigonometry, and Make: Calculus books excellent.
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…
I am not really looking for the basics. I am looking for advanced material that can be handled without the help of a teacher. The book should be written in that manner.
As I have a good background, I can read AI papers and get the math directly or study some and get that.
But whenever I start to study something, more often than not, the book is written in a dry manner and cannot hold my interests.
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"Approachability" might vary somewhat but you might find the following useful; * For an introduction (and a reference) to various areas of Modern Mathematics that one didn't even know existed, The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics are a must. * All the Math You Missed: (But Need to Know for Graduate School) by Thomas Garrity - A survey and a good adjunct to a textbo…
Yeah, thanks for the recommendation. I already know the basics, and I want to learn more. I cam handle hard, but the textbooks need to be written in a manner that doesn't require the help of a teacher or a classroom.
https://press.princeton.edu/books/hardcover/9780691118802/th...
https://press.princeton.edu/books/hardcover/9780691150390/th...
PS: In an earlier HN thread, somebody had highly recommended the 4-vol Foundations of Applied Mathematics developed for Brigham Young University’s Applied and Computational Mathematics degree program for beginning graduate and advanced undergraduate students. I have not browsed/read them yet but they are on my "future acquisition and study" list. They seem great and well worth looking into - https://foundations-of-applied-mathematics.github.io/
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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…
Pinter, "A Book of Abstract Algebra", is very nice. It's rigorous but not too terse. It divides the material into many small chapters with many exercises. Chapters are mostly around 10+/-3 pages with about 40-60% of that being text and the rest exercises. The exercises for each chapter are split into several sections each section covering a different aspect of the chapter's material. Sometimes there is a section of e…
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Yeah, thanks for the recommendation. I already know the basics, and I want to learn more. I cam handle hard, but the textbooks need to be written in a manner that doesn't require the help of a teacher or a classroom.
None of the above are "basics", they range from undergraduate to research level topics, in particular; the two Princeton Companions are a must have. https://press.princeton.edu/books/hardcover/9780691118802/th... https://press.princeton.edu/books/hardcover/9780691150390/th... PS: In an earlier HN thread, somebody had highly recommended the 4-vol Foundations of Applied Mathematics developed for Brigham Young Universit…
Among your original recommendations, I have heard about "All the Maths you Missed". And I have read several chapters of the one by Kolmogorov et al. It's a fantastic book. It lays the landscape really well, discusses things, and covers the breadth of the field rather than the depth of any particular field. I find the writing style really good. It could be seen as a reference book for people who already know the stuff, or are looking to know about new stuff, but want to have ideas about what those stuff might be.
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> in English whole numbers mean 0, 1, 2, ... According to Wikipedia [1], the term is ambiguous. Its talk page [2] has plenty discussion about it though. [1] https://en.wikipedia.org/wiki/Whole_number [2] https://en.wikipedia.org/wiki/Talk:Whole_number
English is being weird by having three terms then? Inteiros - (...-2, -1, 0, 1, 2...) Naturais - (1, 2, 3...)