Best Math Textbooks? (Mainly choosing between AoPS and DM)

[Guest Powermaniac7]

Hi,

 

Well I'm new here but everytime I did a google search regarding "Best Math Textbooks" or "Art of Problem Solving or New Elementary Math (or Discovering Maths)" I would get conversations on this site. The only problem is I never did seem to find a definitive answer or something that basically decided for me which was the better choice.

 

To add a little background information, I'm a year 11 student in South Australia. That is planning on re-learning/reinforcing what I've already learnt with some textbooks that are hopefully really good. As currently the textbooks available here in Australia are horrible and I've been a sick kid thus there are holes in my knowledge. Let alone I suffer from what I like to call "Use it or Lose it" where either I use the concept weekly or monthly otherwise I forget how to use it.

 

I've recently just finished what we call Math Studies A which covers:

 

Statistics

• centre of a distribution

• spread of a distribution

• sampling

• normal distribution

Geometry and Mensuration

• right angled triangle geometry

• solving non-right angled triangles

2-D Coordinate Geometry

• distance formula, ratio, equations of straight

lines

• equations of circles

• inverse functions

 

Then I go onto study Math Studies B which covers:

 

 

Quadratics and other Polynomials

• The quadratic function

• Quadratic algebra

• Cubics and Quartics

Models of Growth

• Linear functions

• Exponential functions

Logarithms

• Rules, solving exponential equations

• Using Binomial Theorem

Functions and Graphs

• Linking algebraic and graphical representations

of a relationship

• Sketching of linear, quadratic and other

functions

• Graphs of cubic polynomials

 

And Math Studies C:

 

 

Planar Geometry

• Similar Triangles and Congruence

• Circle Properties

• Cyclic Quadrilaterals

Vectors

• Operations

• Component Form

• Unit Vectors

• Vector Projection

Periodic Phenomena

• Observing Periodic Behaviour

• Sine Function

• Cosine Function

• Trigonometric relationships

 

I listed that so you know where I'm at and might be able to relate it to whatever the curriculum is where you are. So yes I would like to know what is the 'best' mathematics textbooks. Or out of the Singapore Math Discovering Mathematics series or the Art of Problem Solving series which is the best.

 

Anyway thanks.

[Julie of KY]

I would recommend Art of Problem Solving.

 

The Singapore series is very good and probably closer to what you already do. Art of Problem Solving, however, will probably give a much better understanding of math as well as go deeper. I also think AoPS is easier for self learning. It is designed to be read and learned by a student and the solution manuals are great. The forums on the AoPS website are also a great source of help if needed.

 

A big difference is that the AoPS texts are each one subject rather than integrated like you are currently doing.

 

 

[Guest Powermaniac7]

Thank you Julie.

 

Would anyone else like to share there thoughts. As I would to make as informed as possible decision.

 

Leaning further and further towards AoPS although not sure which book to start with (got a rather small budget of $80 for now).

 

Thanks.

[jhschool]

take all the aops readiness tests and see what you are qualified to learn next.

http://www.artofproblemsolving.com/

get the books used. they are much cheaper. abebooks, homeschool classifieds, etc.

[Sebastian (a lady)]

Have you looked at the videos and online problems available from Art of Problem Solving in their Alcumus section? This might provide the instruction and practice you're looking for in self-study without using the textbooks. Another resource popular here for self-study is Khan Academy.