Self-Teaching in Mathematics, Assistance Sought

[Nate Barna]

Hi,

 

I'm considering beginning studying mathematics as an autodidact. For those of you who are knowledgeable in mathematics, i'm hoping you can help me with some of my questions.

 

To give you some background information, i'm thinking of working through this curriculum to the best of my ability. Also, i have studied at a public high school level of calculus, but it is my understanding that, because of this fact, regressing a little might not be a bad idea.

 

1. Is it unwise or too difficult to pursue mathematics alone (besides having you gals and guys, i mean), given that i'll still be seeking the best textbooks available?

 

2. Is Philosophy of Mathematics okay to study early on? The curriculum has students waiting until the third and fourth year. (I'm under the unevaluated impression that philosophy is good to know so all that is learned are put in their proper perspectives upon being learned.)

 

3. Are there better recommendations for studying mathematics in a self-teaching manner?

 

If this kind of situation has already been discussed thoroughly in this forum, just let me know. Sometimes i get overwhelmed with the volume and overlook things.

 

Thanks!

[Dave]

1. Is it unwise or too difficult to pursue mathematics alone (besides having you gals and guys, i mean), given that i'll still be seeking the best textbooks available?

 

In my honest opinion, yes, it is. The problem with teaching yourself this kind of curriculum is the fact that it's extremely complex to start out with. You have to start at a very basic level (in some cases, axioms) and then work your way up. Analysis is a key part of any mathematics course, which means you're going to have to deal with delta-epsilon arguments (very confusing at first) and various other bits. It always helps to have someone to bounce your ideas off of.

 

2. Is Philosophy of Mathematics okay to study early on? The curriculum has students waiting until the third and fourth year. (I'm under the unevaluated impression that philosophy is good to know so all that is learned are put in their proper perspectives upon being learned.)

 

I've never been big into philosophy, but I should think studying this in the second year would help because your mindset will be a lot more adapted to logical thought.

 

3. Are there better recommendations for studying mathematics in a self-teaching manner?

 

Go to uni

 

Seriously, I would considering going to some kind of college course or something like that. You'll probably find that the volume of stuff you have to do is best learned by a rigorous set of lecture courses and assignments. It makes the whole thing a lot more managable.

[Nate Barna]

Great, this really helps me out. Regressing slightly from that particular curriculum, i just received my first book yesterday An Introduction to Mathematical Reasoning by Peter J. Eccles. I bought it because the author suggests that it is a good gateway to uni mathematics. Already in the first chapter, although i found the reading manageable, i couldn’t complete most of the first chapter exercises without referring to the answers in the back. This was quite frustrating because i’d figure i’d at least be able to get through two or three books without getting stuck to the point where no amount of deliberation would get me through the problems on my own.

 

Now that you’ve confirmed that this enterprise would likely be much harder than what it looks i don’t feel so bad. I will take your advice and possibly look into taking some mathematics courses. I basically want to get into business later on, like in about five years, for i can’t help but think that it is vital to have more than a generally-deemed-adequate knowledge base in the physical sciences before i'm excessively pressured into caring about real-world trivialities. Preceding the physical sciences, of course, even at an intermediate level would be strong skills in mathematics. I might ultimately just have to bite the bullet, however, and accept that i might not be made for academia to the extent i think important.

 

Spirits are high though! It looks like you’re very knowledgeable in mathematics. I’ll be careful not to bother you too much, but if i do decide to give it a shot on my own (at least so i can say to myself that i didn’t give up too quickly), then i know there’s always a place to bounce ideas around, even if you wouldn't consider your much appreciated assistance “optimal.”

[Dave]

If you have any questions at all, just ask them. There's a plethora of people around who can answer them now.

[MandrakeRoot]

Yeah i think the beginning would be the most hard with maths. Once you get the hang of it, it is easy to self study and continue improving your skills. But if you have never seen a definition, theorem or lemma of your life and dont know what is the difference then it would be quite a challenge to learn that alone. I would say that it is not impossible but you need some serious perseverence !!

 

=> What is the best text book is also quite ambiguous, what one finds a great book others dont like it at all. I personally hate books with lots of exemples, but not everybody would think the same way.

 

Why not study the philosophy of mathematics early on ?

I dont see any harm in that, though the "reasons why it is like so" might escape you if you never did a lot of math i guess ?

 

Mandrake

[Nate Barna]

If you have any questions at all, just ask them. There's a plethora of people around who can answer them now.

Dave, this is such an awesome forum.

[Nate Barna]

Hi MandrakeRoot,

 

Yeah i think the beginning would be the most hard with maths. Once you get the hang of it, it is easy to self study and continue improving your skills.

Yes, i think you’re right, or at least i want to believe you’re right. Coming to understand the formalities of logic and pure mathematics, which is suggested by the Oxford course to be the starting point, i’ve realized is quite different than doing high school math problems where the answer and some vague indication of how that answer was derived were all that really mattered. I believe if it’s possible to survive and understand formality and underlying mathematical assumptions, it could be possible to grasp most mathematical concepts later on. (Although being original is an entirely different matter.)

 

What is the best text book is also quite ambiguous, what one finds a great book others dont like it at all. I personally hate books with lots of exemples, but not everybody would think the same way.

I agree that the “best” textbook thing is ambiguous. I may not always converge to the optimal text, but my method of converging involves first knowing the topic at hand and then receiving indirect suggestions from various uni sites, textbook publishers, and amazon.com. On an unimportant note, i learn best when there are thorough examples and enough problems for each concept or small set of concepts to run the gamut from easy to mind-provoking synthesis.

[MandrakeRoot]

The best beginning is maybe to simply follow some advanced courses. Once you are into the way of thinking you will easily learn new stuff. IT is surely worth putting lots of effort in in the beginning i think.

 

Mandrake

[Dave]

Why not study the philosophy of mathematics early on ?

I dont see any harm in that' date=' though the "reasons why it is like so" might escape you if you never did a lot of math i guess ?[/quote']

 

I don't think there's a problem with it, but I do think that if you leave it until the second year then your brain will have become more mathematically minded (because of the different style of mathematics). This, in turn, may make it easier to argue a particular viewpoint.

[MandrakeRoot]

Yeah you are probably right on that dave. It was what i was trying to say though not very clearly

 

Mandrake