What are some good introductory books on number theory, combinatorics and algebra?

NUMBER THEORY AND COMBINATORICS

The Higher Arithmetic  -Davenport

Numbers: Rational and Irrational -Niven (NML)
    This book was written for bright high school kids along with
other books of the New Mathematical Library (published by the
Mathematical Association of America).  Of course very few high schools
actually use these fine books.  In California it's *illegal* to use
them as texts in public high schools!  In fact nearly all good books
are barred, in all subjects.  (cf Surely You're Joking, Mr. Feynman, by
Feynman).

Mathematics Of Choice -Niven (NML)
    Subtitled "How to count without counting", an introduction to
combinatorics.

Comtet, Louis, _Advanced_Combinatorics_, D. Reidel [Editor: "Riedel"
in the original] Publishing Company, 1974, page 235.

ALGEBRA

A Concrete Approach To Modern Algebra -Sawyer
    "Modern Algebra" is very different from high school algebra.

The Theory Of Equations  -V. A. Uspensky
     This on the other hand, picks up where high school algebra left
off.

Groups And Their Graphs -Grossman and Magnus (NML)
      Groups should not be confused with sets.  Groups are a sort of
algebraic structure.  The "graphs" referred to in the title are not
the type of graph you're thinking of either!

[ Editor: contributor not named in the source. ]

=================================================================
                    NONPARAMETRIC STATISTICS
                (Books on concepts and methods.)
=================================================================

Conover, W. J.
Practical nonparametric statistics / 2nd ed.  New York : Wiley,
c1980.

Daniel, Wayne W.,
Applied nonparametric statistics, Boston : Houghton Mifflin,
c1978.

Gibbons, Jean Dickinson,
Nonparametric statistical inference 2nd ed.  New York: M. Dekker,
c1985.

Pratt, John W.
Concepts of nonparametric theory, New York : Springer-Verlag,
c1981.

Puri, Madan Lal.
Nonparametric methods in general linear models, New York : Wiley,
c1985.

=================================================================

Would anyone like to offer a comparative review on the books above?
Short comments on the net might be nice also.

-- Walt Sakai  dual!proper!walt_sak@UCBVAX.BERKELEY.EDU

[ Editor: no reviews were found in the collected postings. ]

LATIN SQUARES

[ Editor: in reply to a combinatorics question about writing down the
pairs of integers from 1 to N in increasing order; the rest of the
question was cut in the collected reply. ]

The key words you want to be searching for are:
        skew latin squares
        mutually orthogonal latin squares
        higher dimensional latin squares

You'll find that the problem may be extended to more than pairs.
A good reference book is:

        Denes and Keedwell, Latin Squares and Their Applications,
        English Universities Press, 1974.

-- Jennifer Seberry <jennie@cs.adfa.oz>