Study Math Effectively: Tips & Book Recommendations for High Schoolers

[Kevin Licer]

Recently my curiosity and general interest in math and physics has grown considerably, even though I feel it's a bit too late for me to achieve success in these fields (second year high school) I am still willing to give a go at it because there's nothing else that interests me as much. So, with the summer coming and all, I would want to study math on my own, but the problem is I don't know from which books or even in what order to study things and I want to get involved in things connected to math and take part in contests etc. in the following years that I have left in high school. I've found some books like The art of problem solving, Schaum's Outlines and others, but they are too expensive for me as I'm not in such a good financial situation (particularly The art of problem solving books - they seem very good judging from the reviews, but oh so expensive, well at least for me) and thus I have searched the web for torrents and stuff like that (illegal, and I know that it's also unfair to the publisher, but I promise that as soon as I have the money I'll buy them right away it's just that I need them now, because they aren't going to be of great use to me in 2 years) and so far I haven't gotten lucky. So, I would like to ask for book recommendations and advice in general on how to succeed in maths (and where to get the books from - again I apologize for being such a cheapskate). Also take in account that I would like to begin at an early level like pre-algebra as I feel that I'm lacking sufficient skills there as well. I apologize in advance for the rather long sentences, English is not my native language. Thanks!

 

[gazz haggis]

If you're not comfortable with algebra then I'd recommend starting with a book on GCSE maths which would provide a good basic foundation. CGP books generally have excellent reviews and I've used them myself:
https://www.amazon.com/dp/B00HEE3P2A/?tag=pfamazon01-20

I think it would definitely be worth at least buying this one as it provides the essential foundation in algebra that is at the core of virtually all more advanced maths and don't think you can get an online version.

Having a firm grasp of algebra is crucial so you should make sure you understand all the concepts and do all the problems as this is probably the most important bit of maths you'll be learning. If you don't understand some of the stuff that's normal, just keep thinking about it and going through examples. If you get really stuck watching a video on it can help. It helps me to go through the steps involved and to figure out the exact bit that doesn't make sense before getting help on it.After you've mastered algebra you can progress to more advanced topics. As an engineering student I'm particularly fond of Strouds Engineering Mathematics which provides a good foundation in maths that you should be able to understand by this stage. You can then progress to the more advanced stroud books or delve into any introductory book you're interested in.

I taught myself pretty much all maths I know and I'm definitely not a genius, so it is definitely posssible if you just stick it out and work hard.

Good luck!

 

[verty]

Have a look at these lectures. They look pretty good to me.

 

[Kevin Licer]

@gazz haggis I'll take a look at the book and thank you. Also, do you know in what order I should Math cause I went through the Maths textbooks for self-study on this forum and it starts with Calculus and everything is mixed up, I thought it would go from basic to advanced math starting from pre-algebra and then algebra an so on. Nonetheless, thanks for the advice.
@verty I'm not into the method of learning by videos, but I guess beggars can't be choosy. Nevertheless, I'll take a look at them.

 

[gazz haggis]

@gazz haggis I'll take a look at the book and thank you. Also, do you know in what order I should Math cause I went through the Maths textbooks for self-study on this forum and it starts with Calculus and everything is mixed up, I thought it would go from basic to advanced math starting from pre-algebra and then algebra an so on. Nonetheless, thanks for the advice.
@verty I'm not into the method of learning by videos, but I guess beggars can't be choosy. Nevertheless, I'll take a look at them.

The book starts with the basics so don't worry too much about the order, just follow it from beginning to end and you should be fine. For getting more adbanced books you should check ebay and amazon for second hand copies as they are usually available for quite cheap and it's good to have a copy for reference.

I'm not sure about online resources as I generally prefer to have a book in front of me so I can flick through it and take notes/bookmark sections. i think these websites do similar content but the quality might be off:
http://www.mathsrevision.net/gcse-maths-revision
http://studymaths.co.uk/

Once you've finished the book you can do some more advanced problems by practicing past papers available here:
http://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-4360/past-papers-and-mark-schemes

Maths is a sruggle at first, but the more you practice and understand the easier it gets and you can move on to more complex (and interesting) areas like calculus, linear algebra, differential equations, analysis etc.

 

[Kevin Licer]

@gazz haggis I know it's going to be a struggle, but my goal is to succeed. Also, what is your opinion on the free textbooks offered on this site, do you think that their quality is significantly lower than say a textbook which you would have to pay for?

 

[WWGD]

I would think that at your age, non-structured learning would be preferable: look at definitions, play around and then post
here with questions. After you have a better grasp, you can start doing more formal, by-the-book learning/studying.

 

[gazz haggis]

@gazz haggis I know it's going to be a struggle, but my goal is to succeed. Also, what is your opinion on the free textbooks offered on this site, do you think that their quality is significantly lower than say a textbook which you would have to pay for?

I couldn't say, I haven't really looked at them, but I'm sure once you've nailed the basics you should be able to work your way through it.

 

[Kevin Licer]

@WWGD I have no clue on how to start with this, "rehabilitation" let's say, I actually think that I have some clue as to how to solve the average and sub-average problems of my school textbook, it's just that every time I come across a difficult problem like: "Prove this theorem..." or "For ever n number prove that" I just get demotivated thinking that I'll never be able to understand and solve such complex problems, I may be able to solve standard problems but that's because we were taught the "plug and chug" mathematics and our textbooks offer no deep explanation of concepts just formulas and memorizing. And because of this, my math knowledge from prior years just fades away. So this is why I want to find a couple of textbooks from the beginning like pre-algebra and work my way up from there until basic calculus with actually understanding the stuff because that's all I want to do, is understand it at a deeper level.

 

[verty]

[USER=54975]@verty I'm not into the method of learning by videos, but I guess beggars can't be choosy. Nevertheless, I'll take a look at them.[/USER]

My advice to you is to not only look at them but study them and learn everything you can from them, even if it means watching each video three times. But if you're not into the method of doing that then that's fine.

PS. You should do this even if they seem too hard right now because you will pick up some of it and it will help tremendously.

 

[WWGD]

@WWGD I have no clue on how to start with this, "rehabilitation" let's say, I actually think that I have some clue as to how to solve the average and sub-average problems of my school textbook, it's just that every time I come across a difficult problem like: "Prove this theorem..." or "For ever n number prove that" I just get demotivated thinking that I'll never be able to understand and solve such complex problems, I may be able to solve standard problems but that's because we were taught the "plug and chug" mathematics and our textbooks offer no deep explanation of concepts just formulas and memorizing. And because of this, my math knowledge from prior years just fades away. So this is why I want to find a couple of textbooks from the beginning like pre-algebra and work my way up from there until basic calculus with actually understanding the stuff because that's all I want to do, is understand it at a deeper level.

Why don't you ask us any question you have with the harder problems and we will do our best to guide you through?

 

[Kevin Licer]

@WWGD Because there are a lot of problems which I consider hard and it's partly due to the fact that our textbooks offer us no insight to the harder problems, you have to be a gifted student and be liked by the professors so they work with you and give you books, and I'm not a part of those students and I'm basically left on my own. I don't think it would be as effective if I asked questions about all the problems here at the expense of your time whereas if I had textbooks to work from and self study I could just work at my own rate and speed and not rely on waiting for an answer from here.
@verty I'll try and look at them, but I'm not such a fan of that way. However, I'll give it a go.

 

[phion]

The Method of Three Passes

Pass 1. Three or more nights before recitation (or when the homework is due), make a fast pass through all problems. Plan to spend 1-1.5 hours on this pass. With roughly 10-12 problems, this gives you around 6-8 minutes per problem. Spend no more than this much time per problem and if you can solve them in this much time fine, otherwise move on to the next. Try to do this the last thing before bed at night (seriously) and then go to sleep.

Pass 2. After at least one night’s sleep, make a medium speed pass through all problems. Plan to spend 1-1.5 hours on this pass as well. Some of the problems will already be solved from the first pass or nearly so. Quickly review their solution and then move on to concentrate on the still unsolved problems. If you solved 1/4 to 1/3 of the problems in the first pass, you should be able to spend 10 minutes or so per problem in the second pass. Again, do this right before bed if possible and then go immediately to sleep.

Pass 3. After at least one night’s sleep, make a final pass through all the problems. Begin as before by quickly reviewing all the problems you solved in the previous two passes. Then spend fifteen minutes or more (as needed) to solve the remaining unsolved problems. Leave any “impossible” problems for recitation – there should be no more than three from any given assignment, as a general rule. Go immediately to bed.

 

[FL0R1]

A good book to start off is calcus, and geometry introduction, you search on google for them with pdf extensions.Those books have helped me so much :D