A Comprehensive Textbook of Classical Mathematics

1. Front Matter

   Pages i-xxix

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2. The Language of Mathematics

   1. Front Matter

      Pages 1-1

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   2. Descriptive Theory of Sets

      • H. B. Griffiths, P. J. Hilton

      Pages 3-17

   3. Functions: Descriptive Theory

      • H. B. Griffiths, P. J. Hilton

      Pages 18-37

   4. The Cartesian Product

      • H. B. Griffiths, P. J. Hilton

      Pages 38-49

   5. Relations

      • H. B. Griffiths, P. J. Hilton

      Pages 50-61

   6. Mathematical Induction

      • H. B. Griffiths, P. J. Hilton

      Pages 62-70

3. Further Set Theory

   1. Front Matter

      Pages 71-72

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   2. Sets of Functions

      • H. B. Griffiths, P. J. Hilton

      Pages 73-87

   3. Counting, and Transfinite Arithmetic

      • H. B. Griffiths, P. J. Hilton

      Pages 88-102

   4. Algebra of Sets, and the Propositional Calculus

      • H. B. Griffiths, P. J. Hilton

      Pages 103-120

4. Arithmetic

   1. Front Matter

      Pages 121-121

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   2. Commutative Rings and Fields

      • H. B. Griffiths, P. J. Hilton

      Pages 123-135

   3. Arithmetic Mod m

      • H. B. Griffiths, P. J. Hilton

      Pages 136-145

   4. Rings with Integral Norm

      • H. B. Griffiths, P. J. Hilton

      Pages 146-161

   5. Factorization Into Primes

      • H. B. Griffiths, P. J. Hilton

      Pages 162-170

   6. Applications of the Theory of HCF’s

      • H. B. Griffiths, P. J. Hilton

      Pages 171-177

5. Geometry of ℝ3

   1. Front Matter

      Pages 179-180

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   2. Vector Geometry of ℝ3

      • H. B. Griffiths, P. J. Hilton

      Pages 181-202

   3. Linear Algebra and Measure in ℝ3

      • H. B. Griffiths, P. J. Hilton

      Pages 203-240

arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree.

• Arithmetic
• Mathematik
• algebra
• calculus
• equation
• function
• mathematics
• theorem
• variable

• University of Southampton, Southampton, England

  H. B. Griffiths

• Case Western Reserve University, Cleveland, USA

  P. J. Hilton

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