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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

Hello I'm looking to pursue mathematics as a hobby but might consider taking it up professionally depending on my progress and how much I like it. I was always good at math and seem to pick it up pretty quickly. I am here to discuss mathematics with people that like it because I there''s something special about hearing a person speak about a topic they're passionate about.

Since then I covered: prime numbers, fractions/ratio/proportion/percentages, probability, statistics/graphs, indices, surds, linear equations & graph, Quadratic equations/factoring/solving,completing square, pythagorus theorom, circle theoroms, vectors, matrices, truth tables, basic set theory, basic sequences and algebraic proof.

I think my knowledge is somewhere around GCSE or the beginning of A level or early high school in the USA. I want to understand all the fundamentals first so I can move on to calculus then the college/university level mathematics.

So if you please would help, I want to know what topics I need to cover and in how much depth? I would also like to know the best books around for teaching myself mathematics. I also want to know the best way you learn mathematics.

*Last edited by PatternMan (2014-07-30 03:27:09)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

Welcome PatternMan!

It's sad that you couldn't complete your education, but better late then never. I think you have covered much more then early high school. Vectors and matrices are only scarcely covered in the 12th grade in high school in USA. However, you are missing a few topics. I suggest you fill your gaps in Algebra 2 and Elementary functions (precalculus) by going through a standard book, rather then learning topic by topic. As for books, try "Basic Mathematics" by Serge Lang, "Algebra" by IM Gelfand. A great set of books are NCERT books (www.ncert.nic.in/ncerts/textbook/textbook.htm). They are the primary set of books used by students in India, and covers man topics. You might want to start at grade 9 and move forward quickly. Another set of books, though expensive, is Art of Problem Solving. They are a bit expensive, but they give you great understanding. You can supplement all this with khanacademy.org or examsolutions.

Good luck!

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

ShivamS wrote:

Welcome PatternMan!

It's sad that you couldn't complete your education, but better late then never. I think you have covered much more then early high school. Vectors and matrices are only scarcely covered in the 12th grade in high school in USA. However, you are missing a few topics. I suggest you fill your gaps in Algebra 2 and Elementary functions (precalculus) by going through a standard book, rather then learning topic by topic. As for books, try "Basic Mathematics" by Serge Lang, "Algebra" by IM Gelfand. A great set of books are NCERT books (www.ncert.nic.in/ncerts/textbook/textbook.htm). They are the primary set of books used by students in India, and covers man topics. You might want to start at grade 9 and move forward quickly. Another set of books, though expensive, is Art of Problem Solving. They are a bit expensive, but they give you great understanding. You can supplement all this with khanacademy.org or examsolutions.Good luck!

I forgot to put basic functions down too. I breifly covered that when they started replacing standard quadratics with functions. Thank you for the help. What do you find is the best method to learn mathemtics? I usually just follow the method, then try to understand it, then look at the proof or justification, then practice some problems.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

Apart from quadratics, you should be familiar with other functions like exponential, trigonometric, logarithmic, reciprocal, square root and cube etc. Elementary functions, or precalculus is a lot more then just knowing those functions. Go through all the resources I told you, and you'll have a very solid and rigorous foundation in high school maths.

Everyone has a different method of learning and it usually depends on how the teacher/book teaches it. I think the best one is which gives a student the most understanding, through intuitiveness, proof, justification etc. Practice as many hard problems as you can. Get them from Artofproblemsolving.com, their books, contests and olympiads. Ask your teacher (if you have one) for some, or try to make some up your selves. Another strategy is to take notes from the book and while walking, reteach yourself the material.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

Thank you wise Yoda. These resources seem to go into a lot more depth than what I'm usually given. Those ncert books look good and cover more than the books we get here. Those problem solving books look great and are what I have been looking for. I am ready for that rigour but the price puts me off lol. I think I'll leave those till later. Thanks again ShivamS.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,512

Hi PatternMan;

Welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,308

hi PatternMan

**Welcome to the forum.**

If you're not having to follow a syllabus then you are in a good position, because you can follow what interests you instead.

A good place to start would be here:

You can fill in any gaps in the basics and you'll also find many more advanced topics too. Great teaching resource and it's all free!!!

Then when you want to learn about something not listed there, you can come back here to ask us. There's a good chance someone will know.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,499

Hi PatternMan,

**Welcome to the forum!**

Character is who you are when no one is looking.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

PatternMan wrote:

Thank you wise Yoda. These resources seem to go into a lot more depth than what I'm usually given. Those ncert books look good and cover more than the books we get here. Those problem solving books look great and are what I have been looking for. I am ready for that rigour but the price puts me off lol. I think I'll leave those till later. Thanks again ShivamS.

You're welcome.

These resources are quite in-depth, but exactly what you need to pursue mathematics. Going through those "For Dummies" books hardly teaches anything. You don't have to go through the problem solving books, especially not now. If you go with the rest of the material, you will be fine and it's very inexpensive.

I forgot to mention geometry. The art of problem solving and NCERT books cover all the geometry you need. If you want, you can go through Lang's "Geometry" book for more information or Harold Jacobs's Geometry (1st of 2nd edition - the 3rd and henceforth are dumbed down). If you use Khanacademy to help you (which I highly recommend), it covers geometry as well.

You can find **all** of these books online for free or you can purchase them for $5 from abebooks.com.

To sum it all up, all you really need is the NCERT books supplemented with khanacademy.org. You can supplement all that to get much better understanding with "Basic Mathematics" and "Geometry" by Lang, "Geometry" by Harold Jacobs, the art of problem solving books etc. I highly recommend you go through at least all of that (excluding the art of problem solving books), but you will be fine with just NCERT books and khanacademy.org. Note that going through all of this won't take you too long, as you will learn a lot but some material may overlap.

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Hi PatternMan,

What is your favorite color?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

Thank you for the greetings everyone. I really appreciate the help. I just ordered the NCERT books 9 and 10. Also oes anyone know anywhere I can find practice questions and answers online anywhere?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,375

Hi PatternMan

Welcome to the forum!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Also oes anyone know anywhere I can find practice questions and answers online anywhere?

Yes, go to mathopolis...

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

If you want answers to the NCERT books, they are available at meritnation.com (the solutions are free). For problems, go to aops.com and try the contest problems, FTW and Alcumus (all free).

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Or Brilliant?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,512

Those two places seem to me to be a little stiff, suppressing creativity. I would suggest the OP start posting like mad right here.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

I don't mean going to the AoPS forums. I apologize if it sounded like I was advertising it. I recommended it because it has a large collection of difficult problems.

After some maturity, Patternman can try "Problem Solving Strategies" by Engel (not now).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,512

Hi ShivamS;

No problem no need to apologize. I was being whimsical.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

mathepolis is nice but I would prefer to be able to print worksheets out and work on them m away from the computer. I get tired of staring at a screen. Brilliants questions can be a bit challenging for me and I don't wish to tackle them now until I get better. I will not even consider questions from aops right now.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

Why not AoPS questions? They are from contests like AMC. Anyways, NCERT has good problems. Print off problems from "Algebra" by Gelfand.

*Last edited by ShivamS (2014-04-06 09:50:03)*

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

ShivamS wrote:

Why not AoPS questions? They are from contests like AMC. Anyways, NCERT has good problems. Print of problems from "Algebra" by Gelfand.

I was intimidated but I checked them out and can answer the lowest level ones. They have good videos on there too. I struggled on some of the problems and am ashamed because they're for kids.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

Being "ashamed" is common but very stupid. You made a few mistakes in the past but what matters is that now you're ready and determined to learn. Do the Mathcounts and AMC 8 problems if you can. After going through my books and the problems, you'll be able to solve most of the problems. Also, there is great merit in just thinking about the problem but not solving it. Don't give up or look at the solution on AoPS without thinking for at least a couple of days.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,512

Hi PatternMan;

ShivamS wrote:

Also, there is great merit in just thinking about the problem but not solving it.

Yep! Of what use is working on and solving a problem quickly because it was too easy? You learn a lot more from ones you can not solve. Those force you to hit the books and to learn and try new things.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,518

When I went through the horror they call Spivak's exercises, it took me weeks on each problem. But then, finding the solution was so much more rewarding. After going through the whole book, solving all the exercises made me gain so much more insight.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 171

Do you guys actually spend that long thinking about the math problems? The problems you're solving must be a lot harder than these then. These took longer than the average problems in textbooks that only take 5-30 seconds to do but none of the questions I answered from aops took more than a couple of minutes to solve. I had an idea of how to solve the ones I didn't answer but I wouldn't be able to answer them under exam considitions. It would be cheating to google some information then answer these questions right?

Also I like that they have multiple solutions to their problems. A few times my solution wasn't even there when I checked them. I can print of the questions from there and practice them anywhere. The NCERT books haven't arrived yet but I should be getting them on the weekend.

*Last edited by PatternMan (2014-03-12 13:31:01)*

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