Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations;

Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems

From the reviews of the second edition:

Toth's 'Glimpses' offer selected material that connect algebra and geometry ... . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein's famous work on the quintic and the icosahedron. (Gunter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004)

The book is intended - and really manages it - to fill undergraduates with enthusiasm to reach the graduate level. ... the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. ... information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one. (G. Kowol, Monatshefte fur Mathematik, Vol. 141 (2), 2004)

The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. ... there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. ... the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003)

This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. ... Each of the chapters is a good read and the book adds up to a wholly appealing entity. ... It can be warmly recommended ... . I can well imagine that teachers ... as well as scientists ... will benefit from this carefully worked-out textbook. (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003)

* 'A Number is a multitude composed of units' (Euclid) * '..there are no irrational numbers at all' (Kronecker) * Rationality, Elliptic Curves and Fermat's Last Theorem * Algebraic or Transcendential? * Complex Arithmetic * Quadratic, Cubic, and Quartic Equations * Stereographic Projection * Proof of the Fundamental Theorem of Algebra * Symmetries of Regular Polygons * Discrete Subgroups of Iso(R^2) * Moebius Geometry * Complex Linear Fractional Transformations * 'Out of nothing I have created a new universe' (Bolyai) * Fuchsian Groups * Riemann Surfaces * General Surfaces * The Five Platonic Solids * Finite Moebius Groups * Detour in Topology: Euler-Poincare Characteristic * Detour in Graph Theory: Euler, Hamilton and the Four Color Theorem * Dimension Leap * Quaternions * Back to R^3! * Invariants * The Icosahedron and the Unsolvable Quintic * The Fourth Dimension * Appendices * Solutions for 100 Selected Problems * Index

NLS9781441929624

9781441929624

1441929622

Glimpses of Algebra and Geometry by Gabor Toth

New

Paperback

Springer-Verlag New York Inc.

2011-12-14

450

N/A

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

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