Mathematics, Form and FunctionThis book is intended to describe the practical and conceptual origins of Mathematics and the character of its development - not in historical terms, but in intrinsic terms. |
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abelian groups abstract addition algebraic angle arithmetic axiomatic axioms bijection calculations called cardinal number Chapter circle complex numbers composite congruence construction continuous convergence coordinates corresponding cotangent curvature curve cyclic groups defined derivative described determined differential dimensional dimensions elements equation Euclidean geometry example field Figure finite formula function f Galois given group G hence holomorphic function homomorphism idea infinite inner product integral interval inverse isomorphism least upper bound magnitudes manifold Mathematics matrix means metric space modulo multiplication natural numbers normal subgroup number theory objects open set operations ordered pairs ordered set ordinal orthogonal path Peano postulates permutation plane polynomial positive proof properties rational numbers real numbers Riemann surface rigid motion rotation rules scalar segment sequence set theory smooth functions sphere structure subgroup subsets symmetry tangent theorem tion topological space transformation group triangle unique values variable vector space zero