What's a good book or resource to learn math from scratch (for adult)?
August 3, 2022 10:03 AM
As a young child I was never taught real math... that is I was never taught how to solve a problem. It was all memorization.
As in memorizing times tables, problems and answers. Needless to say I was truly horrible in the subject. Though I probably never had an aptitude for math anyway, I'm sure the way I was taught made things significantly worse.
Anyway, I'm an adult now and have long since graduated from college (did not have to take a single math course in college back in the day due to being in a specialized honors program that focused on other subjects. So I dodged a bullet on that one). I feel I've missed out on a way of thinking that I don't understand at all. I don't understand how the thinking process works for problem solving numbers. When I pick up a first grade level math book all I see are memorization techniques so they don't seem very helpful. I'd like to explore the foundations of math- real math- in my spare time. Any suggestions on resources and such?
As in memorizing times tables, problems and answers. Needless to say I was truly horrible in the subject. Though I probably never had an aptitude for math anyway, I'm sure the way I was taught made things significantly worse.
Anyway, I'm an adult now and have long since graduated from college (did not have to take a single math course in college back in the day due to being in a specialized honors program that focused on other subjects. So I dodged a bullet on that one). I feel I've missed out on a way of thinking that I don't understand at all. I don't understand how the thinking process works for problem solving numbers. When I pick up a first grade level math book all I see are memorization techniques so they don't seem very helpful. I'd like to explore the foundations of math- real math- in my spare time. Any suggestions on resources and such?
Look up the “Lockdown Math” videos from the YouTube channel “3 Blue 1 Brown.” They’re targeted at a high school audience, but I encourage you to give them a try. The guy behind that channel is great at building mathematical intuition with a combination of logic and visuals.
posted by Alterscape at 10:13 AM on August 3, 2022
posted by Alterscape at 10:13 AM on August 3, 2022
Well, a lot of first grade math *is* memorization. It would be annoying to have to use a calculator every time you needed to know what 3 * 7 is. And memorization is a helpful technique for solving a lot of everyday problems. Like, if you have a box for books that's 24 inches wide, and each book is 3 inches wide, how many books can you fit? I could probably write a proof to explain why it's eight, but it's a lot quicker for me just to remember that 24 / 3 = 8. Or for that matter, that multiplication is just a lot of addition, 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3. And there are all sorts of mnemonics to help remember, like if the digits of a number add up to a multiple of three, that number is divisible by three. (E.g., 174 is divisible by three because 1 + 7 + 4 = 12, and 12 is divisible by three. Although if you didn't know 12 was divisible by 3, you could add 1 + 2.)
Memorization is helpful in a lot of post-first grade math, too. In geometry, it would be really annoying to measure every complementary angle, when you could just remember that complementary angles add up to 180 degrees.
Two things that I remember finding helpful in terms of learning basic arithmetic were sports and money (making change). In American football, a touchdown and a point-after are together worth seven points, so I learned multiples of seven pretty quickly. (Which is helpful, because there isn't an easy mnemonic for that. And field goals are worth three points, so I learned a lot of permutations of sevens and threes. Two touchdowns and a field goal is 17 points. Three field goals and a touchdown is 16. Seven touchdowns and three field goals is 58. Likewise, a quarter and a two dimes is 45 cents. Three dimes and four nickels is fifty cents. Do these enough, and you really start to remember the relationships between the numbers.
Personally, I don't think I ever really "got" math until I started messing with computer stuff. When I learned HTML, I was exposed to hex codes, and that made me understand the decimal system better than any explanation of the decimal system ever did. Likewise, learning PHP taught me more about variables than any algebra class.
One thing that bothered me about math pedagogy was how abstract it was. The common complaint was always "when am I going to use this in real life?", and it turns out the answer is, kind of often. Accounting, statistics, programming. It's useful. And like anything else, once you know it, you find ways to use it. Like, So-and-So Baseball Guy is hitting .394 after 500 at bats. Assuming he'll get 100 more at bats the rest of the season, how many hits would he need to hit over .400? These kinds of questions just start occurring to you, and that strengthens your skills.
posted by kevinbelt at 10:59 AM on August 3, 2022
Memorization is helpful in a lot of post-first grade math, too. In geometry, it would be really annoying to measure every complementary angle, when you could just remember that complementary angles add up to 180 degrees.
Two things that I remember finding helpful in terms of learning basic arithmetic were sports and money (making change). In American football, a touchdown and a point-after are together worth seven points, so I learned multiples of seven pretty quickly. (Which is helpful, because there isn't an easy mnemonic for that. And field goals are worth three points, so I learned a lot of permutations of sevens and threes. Two touchdowns and a field goal is 17 points. Three field goals and a touchdown is 16. Seven touchdowns and three field goals is 58. Likewise, a quarter and a two dimes is 45 cents. Three dimes and four nickels is fifty cents. Do these enough, and you really start to remember the relationships between the numbers.
Personally, I don't think I ever really "got" math until I started messing with computer stuff. When I learned HTML, I was exposed to hex codes, and that made me understand the decimal system better than any explanation of the decimal system ever did. Likewise, learning PHP taught me more about variables than any algebra class.
One thing that bothered me about math pedagogy was how abstract it was. The common complaint was always "when am I going to use this in real life?", and it turns out the answer is, kind of often. Accounting, statistics, programming. It's useful. And like anything else, once you know it, you find ways to use it. Like, So-and-So Baseball Guy is hitting .394 after 500 at bats. Assuming he'll get 100 more at bats the rest of the season, how many hits would he need to hit over .400? These kinds of questions just start occurring to you, and that strengthens your skills.
posted by kevinbelt at 10:59 AM on August 3, 2022
khan academy is a good resource. if you want something more narrative driven, with little bits of history thrown in, i recommend Mathematics for the Million, by Lancelot Hogben. You can check it out on archive.
posted by Foie G Biv at 11:00 AM on August 3, 2022
posted by Foie G Biv at 11:00 AM on August 3, 2022
If you want to embrace your "inner child" MEP maths or Beast Academy.
If you want a more electronic approach there's DragonBox or STMath (might need to register as a homeschooler).
If you want an approach tailored to adults, GRE Prep books probably do what you want. (I liked these Manhattan Prep workbooks, but I don't know what's going on with the later, more affordable versions ).
Alternatively go to your local library and borrow all the math books, and see what sticks.
posted by oceano at 11:12 AM on August 3, 2022
If you want a more electronic approach there's DragonBox or STMath (might need to register as a homeschooler).
If you want an approach tailored to adults, GRE Prep books probably do what you want. (I liked these Manhattan Prep workbooks, but I don't know what's going on with the later, more affordable versions ).
Alternatively go to your local library and borrow all the math books, and see what sticks.
posted by oceano at 11:12 AM on August 3, 2022
I am nth-ing Khan Academy. I have a friend in my small town who feels as though she didn't get what she should have out of her early math education and wants to correct that. She's in her early 70s and it's not vital that she does so, except to her, but she feels strongly about it and has been progressing through their curriculum for several years, during the spare time she devotes to it.
Anyway - with my occasional help to clarify a point on which she is having difficulty, she has been using Khan Academy to teach herself the math she never mastered as a child. She's a self-guided learner for many things but the structured lessons provided by Khan Academy have been really helping her with this particular subject. For her it has been a really good resource and I've seen enough of it while helping her to appreciate how much work they've made available for free.
posted by Nerd of the North at 11:52 AM on August 3, 2022
Anyway - with my occasional help to clarify a point on which she is having difficulty, she has been using Khan Academy to teach herself the math she never mastered as a child. She's a self-guided learner for many things but the structured lessons provided by Khan Academy have been really helping her with this particular subject. For her it has been a really good resource and I've seen enough of it while helping her to appreciate how much work they've made available for free.
posted by Nerd of the North at 11:52 AM on August 3, 2022
Brilliant.org has interactive demonstrations of principles, that can be more engaging than memorization.
And look into Explorable Explanations in general. I like Curves and Surfaces and 2d Visibility.
posted by Phssthpok at 1:59 PM on August 3, 2022
And look into Explorable Explanations in general. I like Curves and Surfaces and 2d Visibility.
posted by Phssthpok at 1:59 PM on August 3, 2022
I'm going to take a different route and encourage you to pick up some popular science books about mathematics. I've read and recommend many of the books in this list. They will help you witness the "way of thinking" without jumping into the hard work right away.
posted by redlines at 4:47 PM on August 3, 2022
posted by redlines at 4:47 PM on August 3, 2022
I'm not well-endowed with natural ability in math - though I did muddle through up to calculus, but damned if the first few chapters of Calculus Made Easy aren't the best summary I have ever read.
posted by Jessica Savitch's Coke Spoon at 5:14 PM on August 3, 2022
posted by Jessica Savitch's Coke Spoon at 5:14 PM on August 3, 2022
I enjoyed Mathematics for the Non-Mathematician(1967) by Morris Kline -- it's published by Dover, and you can probably find free PDFs online. He traces the history of mathematics and places developments in their historical contexts, explains the different mathematical fields and their relations to each other, and provides practical exercises. Some of the historical research may have been superseded in the intervening years, but it is a really useful, well-written book.
posted by Saxon Kane at 5:40 PM on August 3, 2022
posted by Saxon Kane at 5:40 PM on August 3, 2022
Back when I was taught math in the 1950s and '60s, all was memorization and practice until they started giving you word problems like: how many minutes does it take to drive from NYC to Albany averaging 50 mph? The distance is 150 miles.
Most of these problems give you a couple of numbers and it comes down to deciding whether to add, subtract, multiply or divide. This particular one also requires the outside knowledge that there are 60 minutes in an hour.
There are a couple of helpful rules. One is "per means divide". Usually. So miles per hour is the number of miles divided by the number of hours.
But the real key is units. Units always work out. It was a big part of my college physics class that units work out. In the example you start with distance (miles) and have to get to time (hours and minutes). You need time per distance, they give you distance per time, so you have to turn it over. So 150 miles divided by 50 mph gives three hours. Then 3 hours times 60 minutes per hour gives you 180 minutes.
So, when you go to Kahn, or any of the other good places suggested above, look for the advice about word problems. They are the link between arithmetic and real world problem solving.
posted by SemiSalt at 5:21 AM on August 4, 2022
Most of these problems give you a couple of numbers and it comes down to deciding whether to add, subtract, multiply or divide. This particular one also requires the outside knowledge that there are 60 minutes in an hour.
There are a couple of helpful rules. One is "per means divide". Usually. So miles per hour is the number of miles divided by the number of hours.
But the real key is units. Units always work out. It was a big part of my college physics class that units work out. In the example you start with distance (miles) and have to get to time (hours and minutes). You need time per distance, they give you distance per time, so you have to turn it over. So 150 miles divided by 50 mph gives three hours. Then 3 hours times 60 minutes per hour gives you 180 minutes.
So, when you go to Kahn, or any of the other good places suggested above, look for the advice about word problems. They are the link between arithmetic and real world problem solving.
posted by SemiSalt at 5:21 AM on August 4, 2022
These Art of Problem Solving math books are all explicitly structured around the idea that the best way to learn math is to try to solve problems. They're available both as physical books and as online texts that let you enter your answers to problems to check your work (plus some explanatory videos linked in among the text), and I think you might find them right up your alley.
The most introductory level available in these texts is pre-algebra, but you might find it basic enough, because it digs into the foundations at every stage. Their more elementary books are the "Beast Academy" series, which is presented in a kid-friendly comic book style, but does absolutely share the same problem-solving orientation of the later books.
posted by redfoxtail at 11:39 AM on August 4, 2022
The most introductory level available in these texts is pre-algebra, but you might find it basic enough, because it digs into the foundations at every stage. Their more elementary books are the "Beast Academy" series, which is presented in a kid-friendly comic book style, but does absolutely share the same problem-solving orientation of the later books.
posted by redfoxtail at 11:39 AM on August 4, 2022
I am a big fan of The Nature of Mathematics. A quote from the Preface (I have the 6th edition): "... most students ... have postponed taking this course as long as possible, are dreading the experience, and are coming with a great deal of anxiety. To you I say, relax and enjoy. I wrote this book with one overriding goal: to create a positive attitude toward mathematics. ... I want you to come away ... with the feeling that mathematics can be pleasant, useful, and practical - and enjoyed for its own sake."
And from the website: "The author introduces you to Polya’s problem-solving techniques and then shows you how to use these techniques to solve unfamiliar problems. You’ll also find coverage of historical topics, and exercise sets that feature problems applied to real world settings."
You might also enjoy The Number Devil : "In a series of twelve dreams, Robert, a young boy persuaded that math can only be a tedious and taxing endeavour, is confronted by a witty, hot-headed number devil who is determined to show him otherwise. ... The Number Devil masterfully leads us through a path of math discovery, starting with the very basics and building up to much more complex observations."
Finally, that site (Mathical Books) has a whole bunch of books about math that are much more "how do math lovers think?" and much less "here, memorize the multiplication tables." I bet you could check an armload of kids' math books out from your library every week and flip through them at home and just see which ones lead you to greater understanding.
Good luck - and enjoy!
posted by kristi at 1:31 PM on August 5, 2022
And from the website: "The author introduces you to Polya’s problem-solving techniques and then shows you how to use these techniques to solve unfamiliar problems. You’ll also find coverage of historical topics, and exercise sets that feature problems applied to real world settings."
You might also enjoy The Number Devil : "In a series of twelve dreams, Robert, a young boy persuaded that math can only be a tedious and taxing endeavour, is confronted by a witty, hot-headed number devil who is determined to show him otherwise. ... The Number Devil masterfully leads us through a path of math discovery, starting with the very basics and building up to much more complex observations."
Finally, that site (Mathical Books) has a whole bunch of books about math that are much more "how do math lovers think?" and much less "here, memorize the multiplication tables." I bet you could check an armload of kids' math books out from your library every week and flip through them at home and just see which ones lead you to greater understanding.
Good luck - and enjoy!
posted by kristi at 1:31 PM on August 5, 2022
Mortensen Math is great if you are the least bit visual. They're manipulatives and math made sense for the first time in my life.
posted by intrepid_simpleton at 9:19 AM on August 6, 2022
posted by intrepid_simpleton at 9:19 AM on August 6, 2022
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Click on “courses” for an overview — it will walk you through the basic curriculum from the very foundation on up.
I would also recommend getting some workbooks (maybe someone here has some great recommendations for those). Working math by hand is the only way to really absorb it, in my experience.
And best of luck to you — math is so cool!
posted by Silvery Fish at 10:10 AM on August 3, 2022