I learned the Modern Algebra 28 years ago in the very university of "The Last Theorem of Fermat" in Toulouse, France (Classe Préparatoire aux Grandes Écoles, Lycée Pierre de Fermat - Mathématiques Supérieures et Mathématiques Spéciales). These were the 'darkest' years of my study life when we slogged for 2 years learning the abstract Modern Algebra and Analysis. The French are "Maths lovers", given 100+ streets in Paris are named after their mathematicians.
I remembered the Maths were taught in the form of arcane and boring Axioms/Theorems. starting from Set Theory (Ensemble), Group (Groupe), Ring (Anneaux), Field (Corps), Vector Space (Éspace Vectorielle), Affine Space(Éspace Affine), Matrix, Topology, etc. The toughest Grandes Écoles Entrance Exams (Concours) demanded the students master these maths abstract concepts in order to solve difficult maths questions in long-hour written and oral Papers. Many bright top students, after scoring brilliant results to enter the prestigious École Polytechniques (the one which failed twice Évariste Galois!), shied away from Maths in their life later because of this "Maths Phobia". What a shame and waste of maths talents.
After reading The "Unknown Quantity", I always ask "If only these Maths were taught in the similar interesting way", we could have actually loved and enjoyed it in our entire life.
Derbyshire has introduced many 'revolutionary' Maths teaching ideas:
1) Group, Ring (Ideal) and Field are presented in a non-traditional reversed order of all Maths text books. He said: "Field is a more common place kind of thing than a Group, and therefore easier to comprehend." I agree 100% when I read this book without any difficulty to follow.
2) Many enlightening 'tips' e.g. NZQRC (Nine Zulu Queens Rule China), help my teenage children grasp instantly the intrinsic Number Theory over a dinner talk.
3) 'Vector Space' was presented in a refreshing manner, without bothering us with the difficult theorem, which helps us understand the linear (in)dependence, hence linear algebra and its importance in application.
4) Chapter 8 "The Fourth Dimension" on Hamilton's Quaternions (1,i,j,k) and the intriguing story of the discovery (page 151) at Brougham Bridge on one Monday, 16th Oct, 1843.
5) Why x is the predominant used unknown variable in equations (Chapter 5, Page 93), because the french printer ran short of letters (y and z are commonly used in French language).
6) The reason behind the eccentric choice of letters (a,h,b,g,f,c, skipping i and e) for coefficients in conic equation: ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 was uncovered in the matrix on Page 245 (another maths tip: "All hairy guys have big feet") and Page 248 (homogeneous coordinates).
7) The Yin-Yang view of Geometry vs Algebra. Geometry is for Space and Algebra for Time (Sequence of transformations).
I had spent my entire 1 week holidays in end December till 1 Jan 2007 reading this book. No regret of time wisely spent. I urge all who are "curious nonmathematicians" to follow me.
This book has cured my 28-year Modern Maths Phobia!
Cornelius
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Fascinating History of Algebra
Fascinating History of Algebra"Unknown Quantity: A Real and Imaginary History of Algebra" by John DerbyshireReaders who enjoyed "Prime Obsession" will find "Unknown Quantity" irresistible. In this very readable text John Derbyshire covers the broad history of modern algebra. The history starts four thousand years ago in Egypt and Mesopotamia.The author tells the lives of the men and women who created modern algebra. Their stories are fascinating.The people who make up the history of algebra include (from the photographic plates after page 184):01 - Otto Neugebauer - found algebra in old Babylonian tablets02 - Hypatia03 - Omar Khayyam - wrote poetry and tackled the cubic equation04 - Girolamo Cardano - found a general solution for the cubic05 - Francois Viete - separated things sought from things given06 - Rene Descartes - algebrized geometry07 - Sir Isaac Newton - saw symmetry in solutions08 - Gottfried von Leibniz - found relief for his imagination09 - Joseph-Louis Lagrange - carried symmetry forward10 - Paulo Ruffini - believed the quintic was unsolvable11 - Augustin-Louis Cauchy - made an "arithmetic" of permutations12 - Niels Abel - proved Ruffini right13 - Evariste Galois - found permutation groups in equations14 - Arthur Cayley - abstracted the group idea15 - Ludwig Sylow - delved into the structure of finite groups16 - Camille Jordan - wrote the first book on groups17 - Sir William R. Hamilton - found a new algebra18 - Herman Grassman - explored vector spaces19 - Bernard Riemann - launched two geometric revolutions20 - Edwin A. Abbot - took us to Flatland21 - Julius Plucker - based his geometry on lines not points22 - Sophus Lie - mastered continuous groups23 - Felix Klein - mastered the group-ification of geometry24 - Henri Poincare - algebraized topology25 - Eduard Kummer - used algebra on Fermat's Last Theorem26 - Richard Dedikind - discovered ideals27 - David Hilbert - a geometry of tables, chairs and beer mugs28 - Emmy Noether - pulled it all together29 - Solomon Lefschetz - harpooned a whale30 - Oscar Zariski - refounded algebraic geometry31 - Saunders Mac Lane - attained a higher level of abstraction32 - Alexander Grothendieck: - as if summoned from the voidJust as before, the author takes a field of mathematics interesting for expert and layman alike. This is a very fresh perspective on the history of algebra.See Also:Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in MathematicsI thoroughly enjoyed and highly recommend "Unknown Quantity."
Top reviews from other countries
- Charles stewartReviewed in the United Kingdom on March 30, 2015
Good balance of history and detail for the amateur
- GrowltigerReviewed in the United Kingdom on March 12, 2010
An unusual distribution
- Dennis MobberleyReviewed in the United Kingdom on February 10, 2018
Very Worth Your While
- ab..cReviewed in the United Kingdom on September 29, 2007
express train show concerning the history of Algebraic developments
