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Relearning math as an adult

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Re: Relearning math as an adult

#201

Post by ramblenode »

Math-Ninja wrote: post #113
ramblenode wrote: post #71

Earlier quoted context omitted.

Thanks for responding. What are some examples of topics that you cut out from the high school math curricula? I have seen modern Algebra II courses remove conic sections in order to make more room for probability and statistics.

Hi, I'm Alex, curriculum director at Math Academy. As Justin mentioned, there are several criteria that we must meet in our high-school pathway that aren't needed for studying higher-level (e.g., undergraduate) math, or they can be postponed. We decided to remove some of these in the Foundations series. The idea behind the foundations series is to provide adult learners with the most efficient path possible to get on…

Thanks for the detailed reply.

This largely makes sense to me. Stuff like jump discontinuities I've only seen as an exercise for calculus classes.

Sad to see Taylor series go but that is kind of a dangling topic in an intro class and could be picked up later when there is a need for it.

Re: Relearning math as an adult

#202

Post by hyperthesis »

gmadsen wrote: post #174
tux3 wrote: post #139

Earlier quoted context omitted.

It does a little more than zilch. Exercise is important. Reading is also important. If you want to learn fast, you need a balance of both that works for you. Some people will spend months grinding hard problems on their own in a single chapter to make sure they really understand. Some people will read too fast and have to go back because they don't have solid foundations, and only thought they understood. Reading is…

This is just not true. Reading is necessary but hardly about as important. If you are lucky and get a good text, the exercises guide you to "invent" the important parts of the theory. Otherwise its just definitions and theorems, and its up to you to make your own examples to gain an intuition, which to be fair is closer to life outside of a classroom.

Could you elaborate on this please: "the exercises guide you to "invent" the important parts of the theory."

BTW: I think time not doing exercises is just as important; it's when your mind tries to piece together the data. Coincidentally(?) time resting, after physically exercising, is when your muscles strengthen.

Re: Relearning math as an adult

#203

Post by woolion »

bsdpufferfish wrote: post #24
fiforpg wrote: post #15

> but I needed a good reason that would justify the time investment It should be understood though that there are cases when math(-like) language is abused, leading to overcomplication and obscurantism [1]. In mathematics, there is always the temptation of formalizing for formalization's sake. Indeed, 99% of pure math is non-constructive ("there exists a group such that", "the algorithm converges in O(N) steps"), as…

> leading to overcomplication and obscurantism Mathematicians attempt to express ideas in the most readable and clear way possible. It's actually code that must be obfuscated by the constraints of the language and computer. Mathematicians have no constraints preventing them from presenting something in the way that makes the most sense. The part that can be called "Obscurantism" is when they use a high-level abstract…

No, "there exists a group" is not constructive, in general. You just need to prove that non-existence leads to a contradiction. The whole deal about "constructive mathematics" is to have that if you can prove something exists, you can also construct it.

I think the success of the constructive mathematics program is really debatable, but in any case I don't think it leads to more 'natural' mathematics.

(The terms used by GP are very confused and I agree with most of your reply)

Re: Relearning math as an adult

#204

Post by tuukkah »

apwell23 wrote: post #195
baq wrote: post #128

Earlier quoted context omitted.

> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.

OP described a specific type of practice to get good test grades using 'Anki cards' . Standardized tests test for grinding and dedication not expertise or 'getting good'.

There is no (multiple choice) standardized testing in the Finnish school system and I cannot imagine passing the math tests based on rote learning. I have to assume she took the test somewhere else.

EDIT: The exams at the end of high school can be considered standardized tests, but they are taken at your own school, graded by your own teacher and only verified by the national test organisation. They are not multiple-choice tests.

Re: Relearning math as an adult

#205

Post by Math-Ninja »

ramblenode wrote: post #201
Math-Ninja wrote: post #113

Earlier quoted context omitted.

Hi, I'm Alex, curriculum director at Math Academy. As Justin mentioned, there are several criteria that we must meet in our high-school pathway that aren't needed for studying higher-level (e.g., undergraduate) math, or they can be postponed. We decided to remove some of these in the Foundations series. The idea behind the foundations series is to provide adult learners with the most efficient path possible to get on…

Thanks for the detailed reply. This largely makes sense to me. Stuff like jump discontinuities I've only seen as an exercise for calculus classes. Sad to see Taylor series go but that is kind of a dangling topic in an intro class and could be picked up later when there is a need for it.

Removing Taylor series was a tough call. It's one of my favorite calculus topics topics. Something had to give. However, those topics will still serve as prerequisite material for courses that explicitly need them.

Re: Relearning math as an adult

#206

Post by econner »

For anyone coming back to math I can't recommend enough the book "Journey through Genius: The Great Theorems of Mathematics". It's interesting how much of algebra came originally from geometry and the path to developing these fields makes it so much more intriguing / understandable vs just learning math to learn math.

Re: Relearning math as an adult

#207

Post by galaxyLogic »

chasd00 wrote: post #181
viraptor wrote: post #129

Earlier quoted context omitted.

> it must be a tree, not just a directed graph It may be a tree. But it must be a DAG (directed acyclic graph).

Heh knowledge graphs sometimes don’t feel acyclic, at least not to me anyway. Sometimes I’m stuck bouncing back and forth :)

it may be because the the "graph" is not accurate

Re: Relearning math as an adult

#208

Post by galaxyLogic »

ginnungagap wrote: post #105
galaxyLogic wrote: post #93

Earlier quoted context omitted.

I find the concept of "underlying knowledge graph" interesting. What does it mean? I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc. But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to…

If to understand D you need to know both B and C, each of which requires familiarity with A, the graph is not a tree

Right, but if it is not acyclic, in which order should I try to understand them all?

Re: Relearning math as an adult

#209

Post by galaxyLogic »

viraptor wrote: post #129
galaxyLogic wrote: post #93

Earlier quoted context omitted.

I find the concept of "underlying knowledge graph" interesting. What does it mean? I assume it means such a graph connects the topics together as "pre-requisites". To understand A you need to already understand B and C, and to understand B you need to understand D and ... etc. But the thing about such a graph is that really it must be a tree, not just a directed graph. Why? Because there cannot be cycles in it. If to…

> it must be a tree, not just a directed graph It may be a tree. But it must be a DAG (directed acyclic graph).

Right, it must be acyclic. Which means it can be presented as a tree with some duplicate nodes. The important thing is the student must understand in which order they can try to understand the topics.

Re: Relearning math as an adult

#210

Post by dheavy »

juunpp wrote: post #27
UncleOxidant wrote: post #22

So... basically an ad for Math Academy? How about some free resources like Khan Academy?

That's basically what it is. There is nothing to learn from this post other than "smash that beta sign-up button". Has anyone tried that course? Is it any good?

It's very good. I've tried it after hesitating a bit because of the price tag compared to Khan Academy — no regrets.

K.A. is great and I still use with my kid, but M.A. is more condensed and to the point for my needs. I was properly guided through the first program choices according to my profile, and the diagnostic exam you start with was perfect to highlight what I actually need to work on given my limited time.

Explanations and courses are super condensed, with the right amount of example and pedagogy that clicks for me.

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