Math
"Why bother learning math? I hate math"
This difficult discipline is the foundation of success in everything else you learn that has any element of accuracy in it. *5/24/22 It unlocks the rest of the skill tree in the sciences. You have basically no chance of properly understanding Science and its related disciplines if you don't get darned good at this, sorry* If you want things to work according to plan, if you like having your constructions and inventions not break down, if you like having control over your environment, and if you like to know the truth, you need math. It helps you call bullshit when someone's lying with statistics. It defines the correct infusion rate of an IV drip to ensure patients don't die. It prevents screwups in the workplace when inventorying, making change, or writing checks. It is also a crucial part of physics, chemistry, biology, astronomy, engineering, finance, economics, medicine, and everything else worth learning. It lurks at or near the heart of all these, and the better you know how it works, the easier it is for you to understand them as well. These disciplines, if you 'get' them, are notorious for making your life both easy and good. Therefore, this difficult subject, math, might make life easy, and the better you understand it, the better you understand the other stuff, and the easier your life is could get. I would even say that good math is the backbone of every successful career, if for no other reason than calculating lifetime finances from that career, but it often plays a part in the job itself. Pretty big claims, but hey, that's what power does - it gives you a greater likelihood to succeed.
2/27/23 Here's a new term that has recently shown up in my studies: numeracy. After mulling over a statement by Theodore Grey in one of his books about how math is related to the language of the universe, well, that is quite correct. A lot of folks think in English, possibly in visuals and other imaginative stuff, but if you think in numbers, you can think in the language of science, and the language of truth. Numbers lie to you less than everything else. After a long time of hating math due to the rote memorization and abuse carrot-and-stick approach in my shitty schools, I finally like it again, and I suggest you slog at it also. It's worth every effort.
Books
HELPFUL FOR HOMESCHOOLING: Math for Every Kid by Janice VanCleave - gets the basics learned with no muss, no fuss, no filler. Great for toddlers on up. Also great for people who (like me) despite understanding advanced math still don't feel fully comfortable with the basics. Okay so I re-read this thing and found something out. One of the exercises claims that you can find the exact center of a circle by drawing a chord (a line) across the circle from point A to point B and then criss-crossing that line with another chord from point C to point D, and these points can be anywhere on the circle. Provably false; the only way this works is if each chord has a length that is exactly the width of the circle's diameter. Any kid being told that this would work would lose a lot of trust in this book and in math in general. Come to think of it, that's a major reason why math is so hated by a lot of people - they're told "this is how math works" and "your own brain is deceiving you" when their own eyes and ears are telling them it's b.s.
- HELPFUL FOR HOMESCHOOLING: Sir Cumference and the First Round Table by Cindy Neuschwander - not only is this book great for learning about circles, it's hilarious and kid-friendly. There is a whole math series with Sir Cumference too and I bet it's good.
- 7/10/22 HELPFUL FOR HOMESCHOOLING: Math With Bad Drawings by Ben Orlin - this author draws a direct comparison between a bad romance novel of great popularity and his book and his book is indeed a better love story. This could be a love story of you and mathematics, so give the book a try so you have a chance to really fall head over heels. If you want to know "hey there, why should I give a crap about math after all" this is the book for you. The author also has a blog, and other books he has written, here is his blog, Math With Bad Drawings, it does have a seeming yen for getting angry at capitalism which is in my opinion kind of sus. But eh, professors, you get left wing ones, you get right wing ones, the bottom line is you hope they know what they're doing. This professor seems to. Happily, unlike the evil gits that taught me in high school and thought they were "so clever" by shoving thinly disguised Communism down my throat, he never goes too far with personal opinion and scathing judgment and it's a pleasant reading experience.
- HELPFUL FOR HOMESCHOOLING: Must Know High School Algebra by Christopher Monahan - NOTE: I have not had the chance to thoroughly explore this book, so I skimmed it. It looks pretty good, but be careful and if it turns out that it sucks, blame me.
- HELPFUL FOR HOMESCHOOLING: Mastering Numbers by Andrew Jeffrey - for mental math and getting a good bag of tricks to ensure you're the boss of math, and it is not the boss of you
- Math for Real Life for Dummies by Barry Shoenborn - if you, like me, are always wondering "what the heck do I use this for?" when learning math, this helps, a lot.
- The Art of Problem Solving series by Richard Rusczyk et al. - I have not had a chance to read this but according to a friend it takes you from basic principles to highly advanced math step by step, building on solid foundations at each. This friend currently works at Nvidia and is wicked good at what they do so take my word for it, try this series out.
- Professor Stewart's Cabinet of Mathematical Curiosities - tricky. Tough. It's interesting also. Unless you're a faster thinker than I am you might need to break it up into day-by-day bits of tackling this thing. Ian Stewart also wrote a whole lot of other books about the interesting frontiers of math, with the actual math in them, meaning give yourself plenty of time to read these if your brain, like mine, does the thing when math is involved and jams up. I'm serious though, this guy makes math interesting. Here is his website
- 3/7/23 Ooh look! Ian Stewart Website Resources Literally listed on the site under the subheading "goodies," contains math resources links. Gonna be looking through this soon. Also links to math websites from same source.
- The Pleasures of Pi,e and Other Interesting Numbers by Y E O Adrian - take it a little at a time, and pause to go "what the heck?" often. It's worth chewing on. Interesting!!!
- Calculus: Early Transcendentals by Jon Rogawski - I stan this calculus book. It's fantastic stuff. You'll need this in order to 'get' physics, too. THIS ALSO CONTAINS THE PRECALCULUS YOU WILL NEED IN ORDER TO USE CALCULUS. I always hated precalc because it doesn't really stand alone and is lawfully wedded to Calculus but pretends to be single so you can have a messy and unprofitable one-sided affair; this solves that problem without wasting time. In other words yes this calculus textbook can probably help you with your precalc homework.
- Must Know High School Pre-calculus by Christopher Monahan - not my first choice for previously stated reasons, but contains the necessary b.s. to get through precalc, and if for some reason the Rogawski text doesn't help enough this should do the trick.
- Euclid’s Elements by Euclid, translated by Sir Thomas L. Heath - For learning geometry and adding to your mathematical bag of tricks
- Differential Equations by Boyce and Diprima - I have not had a chance to read this but it is highly recommended to me by a bunch of nerds. Likely very useful.
- Mathematics in 10 Lessons by Jerry King - believe it or not, if you can manage to force yourself page by page through this stodgy text you might actually start to have fun. Why? Because unlike every other math book out there, pretty much, it explains exactly why and how the rules of math were created. It also provides proof. No rote memorization here.
- HELPFUL FOR HOMESCHOOLING: the Math chapter of The Handy Science Answer Book, second edition copyright 1997
Websites
- HELPFUL FOR HOMESCHOOLING: One of the original Math Blaster titles Math Blaster Plus
- HELPFUL FOR HOMESCHOOLING: Math Waffles by MeglyMoo86 10/26/23 This is an Instructable that teaches fractions, multiplication, and more arithmetic. It's great for basic math skills. Here's a recipe for a "glue" for these that doesn't set like royal icing: 1/2 cup brown sugar, packed, 1/4 c. sunflower oil, mix well. Add 2 tbsp hot water and mix well. Let it sit there for a good 5 minutes, or stir it around in a saucepan on medium heat to melt the sugar completely. Add 1 cup of peanut butter. Mix well. This should work fine with sunflower butter too.
- HELPFUL FOR HOMESCHOOLING: Mathigon Added 9/12/23. Fun to play around with. Very helpful with geometry and with visual explanations of various mathematical principles.
- HELPFUL FOR HOMESCHOOLING: Math Is Fun I kid you not, the entire K-12 math curriculum is in here. And better explained than all the math textbooks I remember. That being said, more advanced math is generally better for understanding life, the universe, and everything, so don't just stop there. Index Common Core Standards
- HELPFUL FOR HOMESCHOOLING: Better Explained This is good for some more advanced topics in math.
- 4/27/23 Georgia Tech Online Math Textbooks This could likely help some people in college.
- 3/16/23 r/learnmath Has a surprisingly large amount of resources. Since this will take uh, a long time, for me to get through the recommended links myself, I'll just beam this resource hub over to you for now.
- 5/28/23 Online Math Degrees Leading Sites for Teachers List Contains an intriguing list of internet resources for learning math for free. Hmmm. Putting this here for future reference for myself, and for you in case I don't get to it anytime soon.
- 11/18/23 For Dummies Graphing Calculators Section Official website of the For Dummies brand graphing calculator how-to books. Some of these also have multiple free online articles on them which is pretty cool. Here's one for using the calculator on an iphone Iphone calculator article
Math Miscellany - the fun stuff, seriously this is really cool
- A lot of the time in school you're taught formulas and numbers and equations with no real reason why. Guess what? A lot of the time the reason "why" the reason why is not taught to you is that no one knows. It is a mystery. Take for instance e, the Golden Ratio, and pi. Why do thse numbers exist in nature? Why does pi HAVE to be 3.14159 (etc., etc.) and not say, 7? Trust me there are a whole bunch of these just lurking in your textbooks and in nature. Questions without answers readily available.
- Casting out nines Check your arithmetic with this.
- Where can you find Platonic solids? Look no further than your local geek store for D&D dice. I shit you not.
- Math toys: mobius strips, slide rules, Chinese abacus, Cuisenaire rods, fish ponds/garden ponds of assorted shapes and sizes, fancy rice krispy treat construction, fancy cake construction, vPython
- If you decide to work through Euclid's Elements, or other geometry, you can use a compass, a straightedge, a pencil tied to another pencil with some string (for drawing circles), a ruler, and a whole lot of cardboard and scrap paper to help you visualize things. This helps with art projects later on too
- If you also suck at visualization like I do, then draw what you're trying to understand, if you can do that. Or even make a 3d small version of it (what is this, a school for ants?!)
- Sewing, weaving, crochet, knot-tying, carpentry, cooking, gardening, and knitting can also illustrate some mathematical principles. Which is really nice considering it's tough to apply math if you don't have some basic IRL example of its uses.
- The universe does have a language. It speaks to itself and to mathematicians in the language of math. In fact, it's been theorized that the best way to talk to aliens is also through math because it seems to apply everywhere in the universe. E remains e. Pi remains pi. The Fibonacci series and the Golden Ratio exist at macrocosms and microcosms. It's pretty weird and trippy stuff.
Practical Applications: Try out what you learn in math as you go by actually using it in real life. That way you can see that it's not just philosophy and actually is useful instead of boring. Generally speaking math is a good subject to learn if you've ever asked yourself "How can I gain power in order to fend for myself as a capable adult in this world?" It is extremely helpful in understanding all the other sciences and in many other things.
- Algebra: Long-term financial planning, figuring out compound interest, ensuring you're rich in retirement, making a lifetime financial plan so you aren't a broke millenial (quietly sobs)
- Geometry, arithmetic, and basic algebra: Carpentry, designing a garden, and construction. Also metalworking, machining, sewing, budgeting, farming, taking inventory of household or business goods, most DIYing. You can do these things without math, badly, but math adds an element of power and control, not to mention scientific rigor. And if you know, you know - that shit's dope.
- Algorithms: Computer programming
- Calculus and basically all advanced math: Applied physics and engineering
- Statistics and logarithms: Medical research, medicine, and chemistry. Also good for analyzing the results of experiments or studies to determine if the conclusions are garbage or not.
- All math is helpful for making things work correctly. I mean, you could say Heck with it, let's just estimate
R/osha probably didn't use math at all
Impractical Applications
A note on teaching math or on learning it: one of the things I noticed from a very young age is that math is commonly taught through rote memorization and the expectation that there are a bunch of seemingly arbitrary rules which you just have to accept without questioning. However, I also learned at a very young age that if you use anything powerful without understanding exactly how and why it works, it is usually a recipe for disaster or at the very least not being able to use the powerful thing properly. Therefore although it's far easier (and frankly a cop-out) to teach yourself or others math in the usual way of simple cram, purge, and regurgitate, I think it's far more worthwhile to explain exactly why and how every step of the way. Yes, that means using proofs. Yes, that means something like a hundred times the time investment. It is worth it.
Some tips for studying math if you, like me, have a brain that refuses to cooperate and understand anything in math, pretty much:
- 12/9/22 Had a bit of an epiphany today. It seems that if you are ever in my shoes for any length of time, i.e. have serious mobility issues, it can get pretty rough staring at a wall or a TV screen. It's not the "vacation" people think it is, it gets old fast. Studying math helps. Yes, math. And here's why. With extra time on your hands, you don't have to cram to rote memorize anything, and taking math at your own pace helps you comprehend nifty stuff in it that's really cool, from great authors and teachers and books. Ian Stewart's books are a great example, as are the stuff I recommended up top. The first step in convincing yourself math doesn't suck? Dabble in it now and then til you get hooked. Once hooked, seriously study one book. Then another... ;)
- Remember your "why." Specifically, your "why am I learning this?"
- If you just can't make yourself care, then here's a good "why" - mental fitness level. Even the most boring math problem is pretty much guaranteed to stave off "the stupid" if you tackle it with gusto, making brain do hurty hurty noises and making the hamster wheel turn til it burns out. At least in my experience.
- If you ever feel stupid and "argh, I don't understand this at all!" remember this magic quote: "Advance, and the understanding will follow." (I don't remember who said that, so please comment on the page update if you know.) Keep going despite not understanding it the first time you read it, and then do all the practice problems, and then re-read it. Eventually you WILL wrap your head around it. Persist.
- Note for math teachers and anyone studying math for real: when I was reading Math For Every Kid and re-living the usual K-12 math education nonsense, that's when it hit me. Basically none of the practice problems in most textbooks are useful in real life. At all. The way to get yourself or anyone else interested in this stuff is to directly apply it, and better yet link it up to things like physics, chemistry, biology, medicine, home applications, engineering, construction, electronics, and so on. The world is full of math, it's just that apparently textbook makers never noticed? Of course, math teachers can't share all of the burden here, and each discipline needs a thorough, rigorous grounding in the mathematics of that discipline; every other teacher needs to take note. Self-studying? Working for a living? Trying to find some assistance with everyday tasks? Pretty much all fields of study, human endeavors, and jobs involve math if you look hard enough; see if you can find it. Think of it less as a waste of time but as a treasure hunt for some of the most powerful stuff in your field of interest. You have the poweeeerrr!!!!
- If you've been traumatized by math education, which is surprisingly common, seek therapy, and take a look at Mental Health for other help
- Math is hard. It is. But even if you're not learning anything useful with it, learning how you cope with the challenge and seeing if you can push yourself to overcome it can help you overcome other challenges in your life also.
- Practice problems! When the brain goes "I refuse to understand this," thwack it into shape with enough practice problems for it to go "hey it finally makes sense" and then you can have the satisfaction of saying "yes, thank you brain, finally, it only took me two months" Do a few of these every few days over a long period of time until you understand the underlying concept, and then move on to another one. Or, do a few of these for each concept you need to learn in math, and eventually you'll "get" them all.
- When you're just having to pass tests, learn the teacher's way of solving problems, buckle down and stick the info in your mind any way you can quickly, and cram and purge. Whatever, that's how school does it. But when you're trying to actually understand it, counterintuitively you have to slow down and take it piece by piece over a long period of time. Be patient, persistent, pace yourself, and don't put pressure on yourself.
- If you are getting frustrated when you're learning it for real and aren't under a time crunch, walk away. Come back to it later with a fresh mindset. But discipline yourself to actually come back in a reasonable time frame, and later than a month is probably too long.
- When you don't have pressure being put on you to learn math, that's actually when it's most fruitful to learn. So if you have time say, once a month, to sit down and read a good textbook and do some practice problems, you might want to.
- Seize every chance you have to use math in a practical way. For instance, you want to buy a house? Calculate the mortgage loan with the exact interest you can afford. You want to build a grapevine arbor? Calculate everything you need from the cement to sink the wood beams into to the dimensions of the thing. If you could guesstimate, choose to use math instead, and if that involves learning new math, great, now you actually have a reason to pay attention and give a shit.
- Especially seize every chance you can get to learn and use mental math, which is something you will probably use every day once you get the hang of it. I may never use imaginary numbers or Riemann sums practically, but I will certainly be glad to figure out when the sale is a ripoff, if I can scale up my cake recipe with the pans I've got, and how many cubic feet of potting soil I need to fill the plant pots because damn it, I don't want to go back and buy more
- If you need scratch paper and pen or pencil, get some. Incidentally, this is a good reason why you should have a purse or stuff bag on you at all times with paper and pencil or pen (husband likes mechanical pencils, I think they're trash and prefer pen, you might like gel pen, IDGAF). Besides being helpful for phone numbers, mini-maps sketched by you for better navigation, and so on, this really helps when a lot rides on you getting a calculation right. Actually writing stuff down, in my experience, reduces your chances of making a mistake thanks to increased focus. Seems to be related to how brains work. And... history has shown that a lot of seriously bad blunders were done thanks to simple human error and miscalculation. Therefore whatever you can use to reduce that risk is good.
- Are there areas in math that fascinate you, such as logic, chaos theory, fractals, imaginary numbers? Specifically seek out math books in those areas, because with interest comes focus, with focus comes the chance you'll learn the area of math for real, and given how useful math unexpectedly is in most of life, chances are no matter how weird and out-there it is you will find a use for it
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