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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Problems are as hard as the solver sees them. You finding the contest problems hard is common. You decide what cheating is. I would say think for a few hours then see part of the solution.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

To be honest 2 days of watching the art of problem solving videos and doing 1 AMC has made me a significantly better at mathematics already, especially considering the time. I am better at using the rules I already know and understand them better. for example I have started using the commutative, associative, and distributive rules just to make the calculations easier. I now split the numbers into factors, convert them to fractions and cancell etc.

Watching the videos, doing the problems on AoPS + Brilliant & seeing the solutions makes me a lot better than class ever did. You can experiment and pick up little things like when you multiply by 5 you just half the number and put a 0 on the end.

This whole experience has made me unhappy with the education system here, even though I didn't finish it. The maths curriculum here is very watered down except maybe in the grammar schools and private schools. They just tell you a rule and a method then you got to use them on the most trivial problems. You go through the work book in class then eventually move on. The teachers make you think you're smart because you got a B or A, even though you don't fully understand. If kids have just learned indices you could ask them what is 2^3^3, or ask why n^0=1 and nearly all would be bewildered.

If I continued at this pace for 1 year I could probably be doing Spivak's exercises in approximately a years time. I'm unemployed at the moment so I have the free time but I might be working in a month or so. So the learning might not go that fast depending on what responsibilities are at the time. If I can find 3 hours of energy and time a day to the it then I'll be able to reach my goals.

"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: 92,398

Do you guys actually spend that long thinking about the math problems?

I do but just do not do it on the job.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Patternman:

That's fantastic! You seem really enthusiastic about learning mathematics and I think you'll be very successful. I can go on and on about how I think the education system is nonsense. Their method: formula/trick, memorize, ace the exam. Method of the books I recommended: intuition, derivation, prove, remarks which works so much better. Take your time, but work at a steady pace. Spivak in one year is a reasonable and definitely doable goal.

Note that you will need more than NCERT to move to Spivak (in my opinion). Here's a part of the list I used which is sufficient for Spivak (or Stewart, Courant, Apostol).

NCERT Books

Basic Mathematics by Serge Lang

Geometry by Kiselev (volume 1: planimetry) or by Lang (and Gene Murrow - highly recommended) or by Harold Jacobs but I recommend Lang's Geometry the most

Algebra by Gelfand

Trigonometry by Gelfand

Go through all of those and you'll be ready for Spivak. This also gives me the sense that you are serious for learning math in a rigorous way, which is exactly what these books are for. "For Dummies" and such books, including high school books except NCERT and Singapore, are written by crackpots. Best of luck!

Bobbym, not on the job?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,398

Yes, they expect answers and refuse to wait years. They just get someone else.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

**Online**

**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

ShivamS wrote:

Patternman:

That's fantastic! You seem really enthusiastic about learning mathematics and I think you'll be very successful. I can go on and on about how I think the education system is nonsense. Their method: formula/trick, memorize, ace the exam. Method of the books I recommended: intuition, derivation, prove, remarks which works so much better. Take your time, but work at a steady pace. Spivak in one year is a reasonable and definitely doable goal.Note that you will need more than NCERT to move to Spivak (in my opinion). Here's a part of the list I used which is sufficient for Spivak (or Stewart, Courant, Apostol).

NCERT Books

Basic Mathematics by Serge Lang

Geometry by Kiselev (volume 1: planimetry) or by Lang (and Gene Murrow - highly recommended) or by Harold Jacobs but I recommend Lang's Geometry the most

Algebra by Gelfand

Trigonometry by GelfandGo through all of those and you'll be ready for Spivak. This also gives me the sense that you are serious for learning math in a rigorous way, which is exactly what these books are for. "For Dummies" and such books, including high school books except NCERT and Singapore, are written by crackpots. Best of luck!

Bobbym, not on the job?

I have done an AMC and Out of 24 questions I got 4 wrong and 4 questions I couldn't answer. Of the ones I didn't answer 1 was about the calender because I don't know how many days are in each month, and the other was something on magic triangles. I don't know what magic triangles are. These AMC papers can be fun but I feel strapped for time. A few of the problems can be done in 1 minute but the majority take me around 5 minutes to do. That's 2 hours to do 1 paper and then probably 45 minutes to review it adding their solution methods to my repertoire. So I may only do 2 papers a week or something from now on. I'm happy that a couple of my solutions weren't on their list also.

As for those books I don't know if I'll buy them. The art of problem solving videos give tips for methods of solving problems rather than just giving you the rules and facts. That is how the videos taught and the excerpts look the same. I'll go through the NCERT books 9, 10 and maybe 11 if I can find it anywhere. I'll do the occasional AMC problems and then probably buy the aops books bit by bit. If I bought them all it would cost me a small fortune of £284 if I can afford them. I'll definitely get the number theory book. Depending on how it goes and if I decide to go to university for a maths heavy degree then I might buy them and go through instead of the others you recommended.

Don't you recommend going through an easier calculus book before tackling Spivak's? I have heard of people getting A's for their A level mathematics in the UK but st with Struggling heavily with Spivak's. Does that book reveal your real mathematics aptitude because I spoke to someone who was going to do a maths degree but decided not to after reading that book.

"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: 3,640

AoPS teaches you the basics as well but I never told you to buy them. The ones I think you should read are the ones in my last post. They are, in my opinion, much better than AoPS and cost $5. Note that the NCERT books are available online for free. I don't recommend you do AMC problems right now - do them after the books I recommended. It is often said to go through a calculus book before Spivak, but I disagree. If you have too much trouble with it, then read "First Course in Calculus" by Lang. Spivak prepares you for Real Analysis by Rudin. The person you spoke to was very stupid - math is a lot more then calculus.

*Last edited by ShivamS (2014-03-14 11:28:33)*

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

Actually I'm struggling to find those Sege Lang books for cheap. These are the prices I have found:

Basic Mathematics - Serge Lang £ 19.74

Geometry - Serge Lang £ 12.41

Algebra - Gefrand £ 15.51

Trigonometry - Gelfrand £20.06

Total = £69.82 = $116.10

I'm almost addicted to the AMC questions at this point. I just do them for fun. For me they're analogous to people that do word puzzles or sudoku on the train.

"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: 3,640

Try abebooks.com

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

Those prices on from abebooks.co.uk Serge Lang's boook on basic mathematics is going for twice the price of that on Amazon.co.uk. His Geometry book is around £18 more on other sites. Gelfrands boks are a bit more costly on Amazon too. So I might not be able to get anything for very cheap but at least these are cheaper than the aops books.

Do Serge Lang's books have any challenging questions or good tips like the aops videos do?

*Last edited by PatternMan (2014-03-15 06:39:06)*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Those books are much better then AoPS. They have problems much harder then AoPS.

http://www.abebooks.com/servlet/SearchResults?kn=serge+lang&tn=basic+mathematics

http://www.abebooks.com/servlet/BookDetailsPL?bi=10646454044&searchurl=kn%3Dalgebra%2Bgelfand%26amp%3Bsts%3Dt%26amp%3Bx%3D0%26amp%3By%3D0

http://www.abebooks.com/servlet/SearchResults?kn=geometry+serge+lang&sts=t&x=0&y=0

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

How are you doing with it?

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

ShivamS wrote:

How are you doing with it?

I haven't been on for a while. I'm just going through geometry. I never did much of it. I am covering geometry and trigonometry together but not from the same book. I have been covering polygons, circle theoroms, trig ratios sin + cos rule, vectors etc. Once I am used to basic geometry and trig then going to check coordinate geometry. I'm rushing through at the moment but I plan to loop back on the material and go through harder questions. The questions I'm doing are generally easy and are just there to learn how to apply the rules properly. When I loop back on the material I'll hopefully cover questions like these and AMC ones.

http://www.mathisfunforum.com/viewtopic.php?id=20857&p=2

I haven't actually been using the books you recommended because I'm really tight on money right now. So I'm just using the subpar books from the library even if they don't give me a great understanding. Basic understanding is better than none for now.

*Last edited by PatternMan (2014-04-24 13:48:22)*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Ah. That's fine. Learn as much as you can now and then move on to the advanced level later. Just a word of caution that you will need more mathematical knowledge (likely) than you can attain from the books you are using prior to pursuing a math or physics degree (which is what you are plannin to do).

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

ShivamS wrote:

Ah. That's fine. Learn as much as you can now and then move on to the advanced level later. Just a word of caution that you will need more mathematical knowledge (likely) than you can attain from the books you are using prior to pursuing a math or physics degree (which is what you are plannin to do).

I should have more money for books later. Will those books you recommended suffice as enough mathematics education before a degree though?

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Most definitely. They will actually be more than the bare minimum you need.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

My copy of:

Basic Mathematics - Serge Lang

Geometry - Serge Lang

should arrive within 2 weeks. I'll probably go through them quickly and be done by mid - end of June. If I'm still passionate in the summer I'll finish the other buy and finish the other two. After that I'll either try move on to Spivak or revise all the basics. I need to have near mastery of everything upto the end of the 6th form curriculum because I plan to take the STEP exam next year. They cover pure mathematics, mechanics, and statistics.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

I think I asked this before but does anyone know a website or software I can use to graph functions? I want to experiment a lot with this precalculus before I go any further.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

hi PatternMan

Basic grapher here:

http://www.mathsisfun.com/data/function … c1=sqrt(x)

Introduction to calculus here:

http://www.mathsisfun.com/calculus/introduction.html

Theory:

http://www.mathsisfun.com/calculus/deri … ction.html

Excellent interactive gradient simulation:

http://www.mathsisfun.com/calculus/slop … point.html

Bob

*Last edited by bob bundy (2014-08-10 06:52:36)*

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,740

Apologies that I haven't been following this thread until now. Let's see if I've got this right:

You're in the UK and about to start A levels ?

What book(s) do your school / college use ?

What exam board ?

Is there a library nearby ? If you ask them to 'order' you a book they'll search around other libraries in the locality, track it down and get it for you (no cost). Then all you have to do is read it in three weeks

Bob

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

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Desmos is an easy to use, free and powerful online graphing calculator.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

Thank you so much ShivamS and Bob Bundy.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

Hello guys it's been a while. I have been very busy crash coursing the basics of the sciences. I'm learning physics now(classical mechanics). Kinematics, dynamics, newtons laws etc... It's algebra based not calculus based. I'm looking to transition to calculus very soon. I'm just going over logarithms and trigonometry stuff.

Is this the book right book? I will try to devour it in 2 weeks next month. I don't care if I can't do the problems as long as I understand the definitions, rules, applications etc....

http://www.ebay.co.uk/itm/Calculus-by-Michael-Spivak-third-Edition-/121459248987?pt=LH_DefaultDomain_3&hash=item1c47890f5b

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

PatternMan wrote:

Hello guys it's been a while. I have been very busy crash coursing the basics of the sciences. I'm learning physics now(classical mechanics). Kinematics, dynamics, newtons laws etc... It's algebra based not calculus based. I'm looking to transition to calculus very soon. I'm just going over logarithms and trigonometry stuff.

Is this the book right book? I will try to devour it in 2 weeks next month. I don't care if I can't do the problems as long as I understand the definitions, rules, applications etc....

http://www.ebay.co.uk/itm/Calculus-by-Michael-Spivak-third-Edition-/121459248987?pt=LH_DefaultDomain_3&hash=item1c47890f5b

That is the right book (by the way, it is available online and legally at https://archive.org/details/Calculus_643). Although, I'm pretty surprised you're covered precalculus/algebra already. However, even if you have a few gaps, you can fill them up later.

As for the problems, they are basically a must if you want to gain a good level of understanding. They're half the reason why Spivak is such a good book. Also, even if you put in about 8 hours a day, Spivak in 2 weeks is pretty ambitious.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 190

ShivamS wrote:

PatternMan wrote:Hello guys it's been a while. I have been very busy crash coursing the basics of the sciences. I'm learning physics now(classical mechanics). Kinematics, dynamics, newtons laws etc... It's algebra based not calculus based. I'm looking to transition to calculus very soon. I'm just going over logarithms and trigonometry stuff.

Is this the book right book? I will try to devour it in 2 weeks next month. I don't care if I can't do the problems as long as I understand the definitions, rules, applications etc....

http://www.ebay.co.uk/itm/Calculus-by-Michael-Spivak-third-Edition-/121459248987?pt=LH_DefaultDomain_3&hash=item1c47890f5b

That is the right book (by the way, it is available online and legally at https://archive.org/details/Calculus_643). Although, I'm pretty surprised you're covered precalculus/algebra already. However, even if you have a few gaps, you can fill them up later.

As for the problems, they are basically a must if you want to gain a good level of understanding. They're half the reason why Spivak is such a good book. Also, even if you put in about 8 hours a day, Spivak in 2 weeks is pretty ambitious.

To be fair I already knew most of elementary algebra. I just didn't understand it and needed to fill in lots of gaps. lol I just scanned through the online book. It will probably take me till next summer to go through this properly. But it doesn't seem that intimidating after going through Serge Lang's books. It seems to follow from there quite easily. I just feel maybe I should go through trigonometry and proofs in more detail first. Oh well good luck to me. xD

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