Maths as a hobby

[Eddi]

I've decided to take up mathematics as a new hobby

I want to teach myself into becoming a mathematician!

How might I go about this?

Is there any book anyone might recommend?

I'm going to start at the very beginning and work my way up

And where can I find questions/problems to work out, to practice my skills?

Perhaps @Polymath257 might know how I could go about teaching myself?

 

[ecco]

https://play.google.com/store/books...hs_For_Dummies?id=gjap55J-gygC&hl=en-US&gl=us

 

[Eddi]

https://play.google.com/store/books...hs_For_Dummies?id=gjap55J-gygC&hl=en-US&gl=us

Thanks! I have this coming today:

I need to get back to the level I was at when I left high-school

 

[Polymath257]

First, practice a LOT.

The first level of basic arithmetic is just learning how to add, subtract, multiply, and divide. Be able to do these reliably and with whole numbers, decimals, and fractions.

Next, is basic algebra. Here, we use symbols to denote numbers in various ways. We learn how to solve for unknowns, to manipulate simple algebraic expressions, do proportions, direct and inverse relations, rules of exponents, and some simple factoring.

Next, some basic geometry: learn about measurement of angles, computation of simple areas, perimeters, similar and congruent figures,

Next, more advanced algebra. here you study the quadratic equation, inequalities, factorization of more complicated expressions, polynomials, square roots, and other roots, basic graphing.

Then comes trigonometry. Here you should learn about the six basic trig functions, their properties, get practice writing the same expression in several different ways, verify identities, learn how to solve for unknowns in a triangle.

Then, I would recommend some analytic geometry. This should involve conic sections, how to translate the formula of a graph, how to use trig to rotate a curve. Do a LOT of practice here to get the basic algebra and trigonometry skills to the place they are automatic.

That will get you started. After that, I would recommend some logic, and then go into the calculus.

 

[Eddi]

First, practice a LOT.

The first level of basic arithmetic is just learning how to add, subtract, multiply, and divide. Be able to do these reliably and with whole numbers, decimals, and fractions.

Next, is basic algebra. Here, we use symbols to denote numbers in various ways. We learn how to solve for unknowns, to manipulate simple algebraic expressions, do proportions, direct and inverse relations, rules of exponents, and some simple factoring.

Next, some basic geometry: learn about measurement of angles, computation of simple areas, perimeters, similar and congruent figures,

Next, more advanced algebra. here you study the quadratic equation, inequalities, factorization of more complicated expressions, polynomials, square roots, and other roots, basic graphing.

Then comes trigonometry. Here you should learn about the six basic trig functions, their properties, get practice writing the same expression in several different ways, verify identities, learn how to solve for unknowns in a triangle.

Then, I would recommend some analytic geometry. This should involve conic sections, how to translate the formula of a graph, how to use trig to rotate a curve. Do a LOT of practice here to get the basic algebra and trigonometry skills to the place they are automatic.

That will get you started. After that, I would recommend some logic, and then go into the calculus.

Thank you for your advice

Much of what you have mentioned makes no sense to me so I must have a lot to learn!

It all sounds very interesting though

 

[Polymath257]

Thank you for your advice

Much of what you have mentioned makes no sense to me so I must have a lot to learn!

It all sounds very interesting though

I would point out that this is a list of *basic* topics. Calculus, which is mentioned at the bottom, is still considered 'elementary mathematics'. But what I listed will get you ready to do calculus, which is often a stumbling block for people who don't have the basics absolutely solid.

Practice a LOT.

At each stage, find a book where you understand the topics in the first part of the book, but not the last. Then do *every* problem in the book. Then do the same at the next level.

 

[Onoma]

Having only gotten serious about math at age 40, I've struggled against years of not using my mind for it, and regardless of how many books on math I've picked up at the bookstore, it has remained an uphill battle

but,..that said, I have slowly started to understand

My biggest hurdle, growing up, was in understanding the real world applications - No teacher ever challenged me to the point where I felt it necessary to learn, no job I ever had required using it, etc, so my first real introduction was figuring out how to use simple math for everyday things around the house

The next hurdle was understanding notations - it all " looked like Greek ", as they say, and wading through the various conventions of math leaves one's head swimming in symbols

I'd crack open a college textbook and just shake my head in dismay - " I won't ever be able to learn this ", so I started re-writing things in a format that allowed me to understand more clearly what was being said

An example would be the eclipse year equation : EY ( eclipse year ) = SM ( synodic month ) x DM ( draconic month ) / SM ( synodic month ) - DM ( draconic month )

I'd rewrite it to say:

" The average period of the Moon's orbit with respect to the line joining the Sun and Earth, multiplied by the period of time between two consecutive passages of the Moon through the same orbital node, divided by the average period of the Moon's orbit with respect to the line joining the Sun and Earth, minus the period of time between two consecutive passages of the Moon through the same orbital node, equals the length of the eclipse year "

Then, I would make pictures to accompany the written form, so I had a good visual example of what was actually being stated

When I put them all side by side, then I had the textual description, the pictorial representation, then finally the basic equation EY = SM x DM / SM - DM

Then came the realization " Oh, I'm just looking at a simple ratio ....dur ....simple averages....dur ...."

This may be a very convoluted way to learn math, but for me personally, I don't feel like I can start to really wrap my mind around something until I have taken it apart

Also, learning math history....this has perhaps been the biggest help, looking at how mathematical techniques developed, how one math works with another type of math, etc

Good luck, OP !

 

[Onoma]

Also, to add, one thing that has has helped immensely is practicing doing math in my head....no calculators allowed ( When I was growing up, if you got caught with a calculator in school, you got it taken away at the least, sometimes even a suspension )

Sometimes I will drift off to sleep attempting to calculate some sum or otherwise, and it's this gradual training of my mind that has gradually began to build the architecture I was missing due to dyscalculia

Also, learning about unorthodox methods like the Trachtenberg system

 

[LightofTruth]

There are some good learning sites out there. Kahn Academy is one. Another I used and found really helpful but can't remember the name off hand. They are free too.

 

[Onoma]

I can also suggest several excellent channels on youtube

3Blue1Brown
Mathologer
Eddie Woo
N J Wildberger
Numberphile

 

[Polymath257]

Also, to add, one thing that has has helped immensely is practicing doing math in my head....no calculators allowed ( When I was growing up, if you got caught with a calculator in school, you got it taken away at the least, sometimes even a suspension )

Sometimes I will drift off to sleep attempting to calculate some sum or otherwise, and it's this gradual training of my mind that has gradually began to build the architecture I was missing due to dyscalculia

I would second this. Do as much practice in your head as you can. Avoid calculators and computers as much as possible (at least, don't let them do the calculations---do them yourself).

At one point, I had a clock with an LED display and I would factor the number shown into primes before the next number came up.

 

[The Hammer]

I would point out that this is a list of *basic* topics. Calculus, which is mentioned at the bottom, is still considered 'elementary mathematics'. But what I listed will get you ready to do calculus, which is often a stumbling block for people who don't have the basics absolutely solid.

Practice a LOT.

At each stage, find a book where you understand the topics in the first part of the book, but not the last. Then do *every* problem in the book. Then do the same at the next level.

Yeah, I don't think my basics were solid enough when I got to Calculus (and I am pretty decent at math), as I failed out of the class several times, before dropping for a less math intensive degree. ****'s no joke.

 

[Polymath257]

Yeah, I don't think my basics were solid enough when I got to Calculus (and I am pretty decent at math), as I failed out of the class several times, before dropping for a less math intensive degree. ****'s no joke.

I tell my students that the biggest problem in Calc I is algebra, the biggest problem in Calc II is trigonometry, and the biggest problem in Calc III is Calc I and Calc II.

 

[The Hammer]

I tell my students that the biggest problem in Calc I is algebra, the biggest problem in Calc II is trigonometry, and the biggest problem in Calc III is Calc I and Calc II.

Apparently my algebra sucked then

 

[robocop (actually)]

You can order books from your High School, College, etc... and go through them in order.

 

[Yerda]

How might I go about this?

A great place to start is Khan Academy. You can start from the most basic arithmetic and work your way all the way to single and multivariable calculus, linear algebra and differential equations.

There are videos explaining each idea as they come up, problem sets to solve and badges to be earned as you progress. It isn't as good as taking courses at college but for getting yourself going it's an amazing resource.

Then you could think about signing up for distance learning and I've heard that community colleges in the US offer great courses at a fraction of the price of the universities.

Good luck, ask questions, and enjoy.

I can also suggest several excellent channels on youtube

3Blue1Brown
Mathologer
Eddie Woo
N J Wildberger
Numberphile

These are all great channels. YT is also jam packed with free lectures from all the fancy universities.

 

[Jayhawker Soule]

I tell my students that the biggest problem in Calc I is algebra, the biggest problem in Calc II is trigonometry, and the biggest problem in Calc III is Calc I and Calc II.

At some point some thought must be given to how one learns, and that 'how' differs from person to person. Geometry was all about puzzles for me and I loved it. Trig was simply a continuation of geometry and algebra. But I can remember hitting a wall somewhere around Calc II.

It was only when I found myself using a calculus textbook geared for engineering students that the subject started to become interesting and to make sense. I needed it to be 'real' in order for it to be accessible.

And this suddenly brings to mind a brilliant example from years ago:

Elementary Pascal, Learning to Program Your Computer in Pascal with Sherlock Holmes​

 

[robocop (actually)]

I've decided to take up mathematics as a new hobby

I want to teach myself into becoming a mathematician!

How might I go about this?

Is there any book anyone might recommend?

I'm going to start at the very beginning and work my way up

And where can I find questions/problems to work out, to practice my skills?

Perhaps @Polymath257 might know how I could go about teaching myself?

Beware of the John Wiley & Sons books at your college. Those books cover everything, but they're difficult.

 

[Onoma]

To add, doing " recreational " mathematics really started to open things up for me

Just doing random things with numbers, asking random questions " What happens if I take this and do this or that ? ", but most importantly, coming up with ways to represent what is happening with visual aids other than sheer numbers ( Like how we learn to associate fractions with pizzas in grade school )

I firmly believe one of the biggest hurdles math presents for people is the way in which it's taught, which is not the responsibility of the math itself, but the teacher

The semiosis of a wall of numbers and symbols is lost on those without the insight to the notations and expressions, which are themselves the result of the simplification of years of mathematics ( Where math is made as elegant and simple as possible )

It's been shown that babies are able to understand numbers as abstract concepts, yet by the time most of us are 7-10, mathematics starts to become a monster under the bed for many of us

Even simple slime molds solve fairly complex mathematical problems....

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A Gedanken for the forum:

Let's say we take a random federal prison, where the inmates these days have X boxes and Playstations, bags of chips and sodas, but no educational programs, and most of the inmates are poorly educated, if at all

We take these things away from them, then, like the proverbial " banana on a string in a room full of monkeys with a few boxes ", we set up the opportunity to get access to the chips and soda and video games

The opportunity consists of them solving something like partial differential equations

They are given a small library of math textbooks / books covering as wide a variety of mathematics topics as possible

Do you think they could teach themselves ?

 

[Eddi]

Do you think they could teach themselves ?

I don't know but it would be fun to watch!