Elements of Number Theory2 reviews John Stillwell Springer, 2002 Extremely well-motivated and clear introduction + Illuminating and down to earth This is a very pleasant introduction to number theory. Each chapter is preceded by a preview and concluded by a discussion to make the main ideas clear and well-motivated and to show how things fit in the big picture by discussing the historical development. The book starts with the very basics and ...             Naive Lie Theory (Undergraduate Texts in Mathematics) John Stillwell Springer, 2008 In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary ...             Numbers and Geometry1 review John Stillwell Springer, 1997 A starting point for independent mathematical explorers This is a book on elementary mathematics that treats its readers as curious human beings rather than intellectually spineless fools that must be drilled. There are excellent explanations of a lot of mathematics--some common, some unusual--and there are exercises that are actually interesting. Even ...             Geometry of Surfaces3 reviews John Stillwell Springer, 1995 Geometry from an isometry group point of view + Excellent book + Interesting advanced undergraduate course The three basic geometries of constant curvature are the Euclidean (zero curvature), spherical (positive curvature) and hyperbolic (negative curvature). These may be studied through their isometries (chapters 1, 3, 4, respectively). This is pretty. Other than these three "planes" one may obtain ...             The Four Pillars of Geometry (Undergraduate Texts in Mathematics)3 reviews John Stillwell Springer, 2005 A textbook for that geometry course you wish existed + Fine for School + Makes the connections, simply, readably This nice book contains many things that every mathematics student should know (but don't). Chapters 1-2 are on Euclid. The main ideas are picked out very nicely, in welcome contrast to the usual "let ABCD..."-style books. Chapters 3-4 on linear algebra in geometry will probably be skimmed by most ...             Elements of Algebra3 reviews John Stillwell Springer, 2001 The great insights of algebra free of silly formalism + Great Book for Reading Today there is a dangerously firm consensus on what should constitute the abstract algebra courses. Authors have been given the freedom to forget all about motivation. They often begin chapters by claiming that "it is necessary to..." and then they give the usual hyperabstract definitions and ...             Classical Topology and Combinatorial Group Theory3 reviews John Stillwell Springer, 1995 Does not deformation retract onto Munkres et al. + An introduction well worth reading + An accessible introduction to low-dimensional topology. This is a wonderfully intellectual, semi-historical approach to classical topology. Chapter 0 gets some fundamentals out of the way. Chapter 1 is very intriguing and contains lots of ideas. First we are given a taste of the Riemann surfaces of complex analysis. These are complemented by the ...             Yearning for the Impossible: The Surprising Truths of Mathematics9 reviews John Stillwell AK Peters, Ltd., 2006 Many of the mathematical ideas once considered impossible + Ideal Book for understanding Ideal + Excellent overview of many less "traditional" topics + Excellent             Mathematics and its History4 reviews John Stillwell Springer, 2004 An intellectually satisfying history of mathematics + Relationship between algebra and geometry + concise and well written summary of mathematics + see below             Mathematics and its History4 reviews John Stillwell Springer, 2004 An intellectually satisfying history of mathematics + Relationship between algebra and geometry + concise and well written summary of mathematics + see below             Yearning for the Impossible: The Surprising Truths of Mathematics9 reviews John Stillwell AK Peters, Ltd., 2006 Many of the mathematical ideas once considered impossible + Ideal Book for understanding Ideal + Excellent overview of many less "traditional" topics + Excellent             Geometry of Surfaces3 reviews John Stillwell Springer, 1995 Geometry from an isometry group point of view + Excellent book + Interesting advanced undergraduate course The three basic geometries of constant curvature are the Euclidean (zero curvature), spherical (positive curvature) and hyperbolic (negative curvature). These may be studied through their isometries (chapters 1, 3, 4, respectively). This is pretty. Other than these three "planes" one may obtain ...             Elements of Algebra3 reviews John Stillwell Springer, 2001 The great insights of algebra free of silly formalism + Great Book for Reading Today there is a dangerously firm consensus on what should constitute the abstract algebra courses. Authors have been given the freedom to forget all about motivation. They often begin chapters by claiming that "it is necessary to..." and then they give the usual hyperabstract definitions and ...             Naive Lie Theory (Undergraduate Texts in Mathematics) John Stillwell Springer, 2008 In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary ...             Numbers and Geometry1 review John Stillwell Springer, 1997 A starting point for independent mathematical explorers This is a book on elementary mathematics that treats its readers as curious human beings rather than intellectually spineless fools that must be drilled. There are excellent explanations of a lot of mathematics--some common, some unusual--and there are exercises that are actually interesting. Even ...             Elements of Number Theory2 reviews John Stillwell Springer, 2002 Extremely well-motivated and clear introduction + Illuminating and down to earth This is a very pleasant introduction to number theory. Each chapter is preceded by a preview and concluded by a discussion to make the main ideas clear and well-motivated and to show how things fit in the big picture by discussing the historical development. The book starts with the very basics and ...             The Four Pillars of Geometry (Undergraduate Texts in Mathematics)3 reviews John Stillwell Springer, 2005 A textbook for that geometry course you wish existed + Fine for School + Makes the connections, simply, readably This nice book contains many things that every mathematics student should know (but don't). Chapters 1-2 are on Euclid. The main ideas are picked out very nicely, in welcome contrast to the usual "let ABCD..."-style books. Chapters 3-4 on linear algebra in geometry will probably be skimmed by most ...             Classical Topology and Combinatorial Group Theory3 reviews John Stillwell Springer, 1995 Does not deformation retract onto Munkres et al. + An introduction well worth reading + An accessible introduction to low-dimensional topology. This is a wonderfully intellectual, semi-historical approach to classical topology. Chapter 0 gets some fundamentals out of the way. Chapter 1 is very intriguing and contains lots of ideas. First we are given a taste of the Riemann surfaces of complex analysis. These are complemented by the ...