Math Proofs Demystified McGraw-Hill 2005

Elementary Number Theory - Clark

btw I got them off a torrent xP they're from the biiiig math torrent on torrentspy

]]>Positive, even/odd, divisible, functions, and relations are all very fimiliar terms, but I guess their meaning runs a little deeper than I realize.

]]>Let A be a set (need not be finite) and let ~ be an equivalence relation on A. Let f be a bijective function from A onto B.

(a) Prove that the equivalence classes partition A.

(b) Prove that there exists a unique equivalence relation on B which depends solely on ~ and f.

Please, no one else post solutions until bossk171 has done so.

]]>It's never a bad time to study number theory , if you can't find anything else to do, investigate that

How would I go about that? Do you know of any good books?

]]>Here's an applet that graphs them.

The x and y values are like an Ech-A-Sketch; each has its own equation.

http://www.ies.co.jp/math/java/calc/sg_para/sg_para.html]]>

As for a book for multi variable calculus, I'm not certain. The book I used was Calculus with Early Transcendentals by Stewart, but this book is big enough to take you through introductory and second semester calc, multi variable calculus, and even has a section on differential equations.

]]>I do know integration by parts, is integration around the axis when you have a curve spun around the axis and you have to find the volume of the solid it generates? If so, the I know that as well.

So I guess that means that I'm ready for "multi variable calculus." I have the very (very) basics of linear algebra down (up to and including inverse matrices), but I guess I could keep going in that.

What books (or websites) would you recommend to get me started on multi variable calc?

]]>Typically when you get into college, you have one to two more years of calculus before you get into pure maths. If you have covered integral calculus up to integration by parts, integration around the axis,and the like, then you would be ready for multi variable calculus and differential equations. You should also be studying introductory linear algebra and vector geometry during these. Once you finish multi variable calculus, you can move on to vector calculus, which is like vector geometry and multi variable calculus combined into one. This was my first 3 semesters of math courses.

This type of calculus typically falls under applied mathematics. It is what the engineers and the physicists use to do their work. On the other hand, there is pure mathematics. This starts off with an introduction to proofs. After that you can go into a variety of introductory subjects: Modern Algebra, Advanced Calculus (a pure (theoretical) approach to the real numbers), Combinatorics, Discrete math, Linear Algebra, and probably others I can't think of at this moment.

You can go right into proofs without learning calculus at the college level. Why my university requires differential equations and multi variable calculus for an intro to proofs class, I haven't got a clue. So it is really up to you. Myself, I love the pure mathematics, and I have a distaste for applied such as calculus.

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