I want to learn mathematics from the base principles from scratch...?

Question

I can handle college mathematics in the normal way , but i still feel uncomfortable with the technique....

Are their any books , that could teach me from the very basics, not just what is true , but how they were found to be true and why they are true.

by from the basics i mean the basics- such as addition and multiplication

i mean i want to know the basic concept on which mathemtics is based.

Answer 1

Very interesting question. There's no single answer, but I'd recommend an eclectic selection of the following:

'The Universal History of Numbers,' by Idrish Shah

'Just Six Numbers' by Martin Rees

Almost anything by Martin Gardner, who writes a back page for the Scientific American and has a way of tickling one's mathematical funny-bone

Find a local bookstore and look for Pelican books on Mathematics; in the 1960s and 70s they did a superb series of histories and biographies, mostly out of print now but well worth looting.

'Fermat's Last Theorem,' by Simon Singh - a very good science writer indeed.

Someone whose name I can't remember wrote a book called 'Mathematics Made Difficult,' which might appeal to the frame of mind you're expressing - raising questions like 'are you sure we know what we mean when we say 'and?''

Or you could try 'Godel, Escher, Bach', by Douglas Hofstader, which is a wonderfully synthetic book (in the best, original sense of the word 'synthetic.).

You have an interesting journey ahead of you. I hope you find it fun. I'll set you a short written test in about a week's time.

Lots of love. This kind of discontent is one of the requiments fort a future Nobel Prize winner.

Answer 2

Your question seems rather broad - all I can tell you (from your additional details) is that multiplication is "repeated addition."

I think what you may want is a foundation in algebra. You see, when we learn mathematics in grade school, we usually get to see how one number and another number do "this" when given an operation, so we really only learn the results of adding, subtracting, etc. those given numbers.

In algebra, we learn more general concepts and mathematical properties through the use of variables (a, b, c, etc.), and then we sometimes see examples with numbers to see that the concepts apply.

One thing to learn about math is that you learn how to approach things logically. You learn the general concepts, such as the derivation of a particular formula (and the thought processes that went into that discovery), and then pick a "real world" scenario (specific measurements, numbers, etc.) to see that the concept works.

My guess is that you should pick up a book on basic algebra and see if you understand the ideas within.

Answer 3

Good question. The basics aren't easy though. You might want to start by looking into the basics of set theory. Here's a link.

http://en.wikipedia.org/wiki/Set_theory

Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described. It is (along with logic and the predicate calculus) one of the axiomatic foundations for mathematics, allowing mathematical objects to be constructed formally from the undefined terms of "set" and "set membership". It is in its own right a branch of mathematics and an active field of mathematical research.

Answer 4

Basics:
Addition
1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
1+6=7
1+7=8
1+8=9
1+9=10
1+10=11
Multiplication
1x1=1
1x2=2
1x3=3
1x4=4
1x5=5
1x6=6
1x7=7
1x8=8
1x9=9
1x10=10
You may get dizzy by studying these but dont give up.

Answer 5

You need to study Sir Issac Newton. He was they guy that changed mathematics into what we know it as today.