Relearning Mathematics

Question

First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these subjects. I've begun to search the web in all sorts of science topics and any deep learning will require a solid understanding of math.

This leads me to problem, I don't know where to begin. How does one begin to learn about a subject without knowing a pre-requisite or requirement... I've had this problem my entire life. I work in IT and a couple of years ago enrolled in cs. I completed 2 years worth and quit because I started to get interested in ee. After some self studying in ee, I found I was interested in physics. Soon though I got discouraged because I found I was in this loop of being interested in the whys and the foundation. How does one begin to get a better understanding of a topic without knowing the underlying why?

Which brings me to this forum. Im always finding that the whys Im trying to figure out always have a basis in math. Although I have no advanced studies, I have always been interested in the topic. I just worry that my main interests are in computing and sciences, Ive come to this realization too late in life and to develop any real knowledge in the topic, I will need real knowledge with math. So now I need to start learning the core of math and building upon that, I just worry I will get discouraged and lose sight. I worry about topics that are used as building blocks but I do not see the applications for. I worry about not understanding math but wanting to understand space or electronics or anything else

I worry about where to begin I guess. Anyway, its 3 am and I have been spending the past few weeks wanting to be a true academic and not knowing how I should go about doing so. Im in my 30s with a full time job and would love to start.

Thanks for reading my ramblings and sorry for the writing, Ive been using me phone.

Answer 1

Sounds like you are in for quite an adventure.

Mathematics is a huge, vast forest of knowledge. The choice of foundations to master and the path towards advanced topics depends to a great deal on precisely what it is that interests you. It sounds like you are not sure yourself what precisely it is that interests you so here goes some general advise to self-learning mathematics, assuming that you are interesting in understanding it all and not just memorize some techniques.

Disclaimer: These are only my humble opinions.

The language: Mathematics is written (mostly) in English augmented by set theory and/or category theory. The former is indispensable while the latter is only highly recommended. There are plenty of books on naive set theory (since you certainly don't want to start with formal set theory until you become seriously interested in logic and set theory). Halmos' "Naive Set Theory" is old but very very good. There are also various texts on category theory (including notes on category theory for CS which you might prefer). Category theory might be hard to digest so you might want to take it slow with categories and read on it while you are reading other things.

It is safe to assume that for the topics that seem to interest you you will certainly need a good dose of analysis. To save time and if you are up to a bit of abstractness look for textbooks that talk also about general metric spaces (e.g., Larussens' "Lectures on Analysis").

Linear algebra is also certainly going to be required. The book "Linear Algebra Done Wrong", despite its name, is a good text.

You should probably set this for yourself as a first goal. As you won't have plenty of time to put into it it might take you a good year to reach that milestone, if not longer. Once that is done you can think about how to proceed.

One thing to remember is that even if it will take you a very long time to get where you want to get to, the things you will learn on the way are very likely to assist you not so much on their own right but rather due to the analytic skills you will develop when working on challenging mathematics problems. Good luck!

Answer 2

I found myself in a similar position to you several years back: after a serious illness and a change in life circumstances I found myself with a yearning to learn mathematics. I was about 28 at the time, and had forgotten just about all the "school mathematics" I had studied in high school, aside from the ability to do basic computations and maybe a fuzzy bit of trigonometry.

I disagree with the answer that suggests you spend 2-3 years on algebra (assuming they mean algebra algebra, not linear algebra). Maybe this was realistic in secondary school, but I think it's absurd for an adult learner to spend that long; you'll be bored to tears. The way I did it, and what I suggest, is to dive right in with a copy of a calculus textbook - I used a dog-eared old edition of Stewart, and start reading and working on the exercises. Many calculus textbooks have an algebra and trigonometry "boot camp" section before the main material, which will help refresh your memory on stuff you may have forgotten (how do I divide polynomials? What's $\sqrt{-4}?$), and you'll find all the trig identities that you need on the inside front cover. I think once you become adept with single variable calculus the world is your oyster - it will make an excellent branch point for other areas of mathematics, as well as enhancing your understanding of the science and EE topics that you mention.

Why, Coursera has a single variable calculus course starting this January. If you're able, why not enroll?

Answer 3

I have a somewhat similar set of circumstances.(tongue twister) I was a smart-kid in high school, good at math, but also a skate-punk juvenile delinquent. I got off track and got in trouble, then ended up doing construction work for over 10 years. I started my own restoration co. but was bored to tears, decided to go back to school for engineering. I'm 37 right now and 1/2 way through, and I've been reminded how much I love math. I took calculus in high school, but it had been so long and I wanted to learn the stuff, not just cruise through it. So I went and started over again at trig and int. algebra. I did refresh myself on geometry and basic algebra first. Anyways, the point is I'm so glad I did it, and not just for career potential. I really do believe that school has value far beyond prep for a career. I'm much happier than I was, too. Even considering that: I make a lot less money working nights at a restaurant, am constantly busy with schoolwork, etc. But I love the idea of sharing an understanding of the secret workings of the universe with other people who get math, or are learning to get math. Also, at the level of calculus it becomes very interesting, challenging, and useful. You start to see the amazing things that can be done, it reminds me of cracking open a motorcycle engine for the first time, looking at the guts and thinking "I have to know how this works", but you're looking at the guts of the world itself. ok, so now I'm just babbling. but you should definitely follow your math bug wherever it leads you. even if it's just to gain more understanding, and I definitely believe school/a teacher is the best way to learn math. community college classes are cheap!

Answer 4

For me learning math to the level you described took 12 years focused on math in school while being young and having no job to take away time from me.

I think you should do 2 things:

• Be realistic of what you can learn now. Take one bite at a time. For instance, start with algebra and don't hurry or berate yourself. Some things you'll get, some you won't. There's no problem as long as you keep trying. Reserve 2-3 years for algebra if you do 4-5 hard exercises per day.

• Find someone that can go with you on this journey. In school we had colleagues and the importance of doing something hard together is not to be underestimated.

Good luck!

Answer 5

Before you pick up a modern text book on Mathematics, Algebra, Geometry or Calculus, Read Euclid's Elements: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

If you really want to learn the foundations of Mathematics, there is no better source for understanding. The elements are the basis for everything that has come since, Algebra, Geometry, Calculus, Science, Physics, Computers... I find it very therapeutic to read through the propositions and figure out the logic used 1000s of years ago to understand basic mathematical analysis. With a compass and straight edge, you may discover more working Euclids problems than you every thought you could understand. Understanding the connection between Euclicean Geometry and Algebraic analysis is something they don't teach in school well.

Sometimes we forget that the best text books were written in Greek a long time ago.