This is not intended to be
free verse.
Writing each phrase on a separate line
facilitates rapid reading,
and everyone
is in a hurry
nowadays.
EXPERT OPINION on LATTICE THEORY
by LILLIAN R. LIEBER with drawings by HUGH G. LIEBER
GARRETT BIRKOFF (one of the originators of this theory - Head of the Department of Mathematics at Harvard University): This book is "a charming addition to the literature on lattice theory - to which it should win many converts and friends".
ERNEST NAGEL (a well-known logician and philosopher - Professor of Philosophy at Columbia University), agrees with the point of view expressed in this book, namely, that Science is NOT AMORAL, that this idea must be made EXPLICIT, and that this must be repeated over and over again, until everyone hears it and can examine and think about it, and NOT continue to repeat the CLICHÉS:
"Science is amoral", and
"Scientists are a menace bent on destroying mankind".
THESE CLICHÉS ARE FALSE!
Read the book and see if you AGREE!
Author(s): Lillian R. Lieber, Hugh G. Lieber
Publisher: Galois Institute of Mathematics and Art
Year: 1959
Language: English
Pages: 287
City: Brooklyn, N.Y.
Tags: Lattice Theory
Part I. The Nineteenth Century: The NEW FREEDOM.
Dedication....i
Table of Contents....ii
Acknowledgements....iv
Preface....vi
I. Introduction....1
II. Various kinds of ELEMENTS....7
III. Various kinds of OPERATIONS....22
IV. Various kinds of POSTULATES....34
V. Some interesting ALGEBRAS....46
VI. An Engaging Ring....57
VII. Summary of Part I....65
Part II. The Twentieth Century: The ATOMIC AGE of Mathematics: ORDER and STRUCTURE.
VIII. Something NEW: ORDER....68
IX. Partially Ordered SETS....78
X. POSETS (cont.)....90
XI. STRUCTURE of POSETS....98
XII. What is a LATTICE?....106
XIII. A Few Surprises!....118
XIV. Basic Characteristics of Lattices....126
XV. Mapping....126
XVI. The Mapping of LATTICES....142
XVII. From POSET to Boolean Algebra....147
XVIII. More than one Boolean Algebra!....155
XIX. Applications to Group Theory....167
XX. Applications to Geometry....177
XXI. A Few Useful Lattices....183
XXII. Affine and Projective Geometries....192
XXIII. Other Geometries....202
XXIV. Algebra of Algebras!....209
XXV. Try Your Skill....222
Part III. Behind the Scenes.
XXVI. METAmathematics....237
XXVII. The Duality Principle....245
XXVIII. Life, Liberty, and The Pursuit of Happiness....254
Appendix....254
I. Alternate Postulate Sets for a Group....267
II. A Proof in connection with p. 157....269
III. Some "SUBTLETIES"....270
IV. An Amusing Point....273
Bibliography....285
SPECIAL NOTE....287
