 Algebra (Helena Peirse)

# Algebra

 Автор(ы): Helena Peirse 06.10.2007 Год изд.: 1970 Описание: This text is designed to give the student a background in the foundations of algebra and analysis. The algebra of symbolic logic and the concept of set are introduced early in the text so that the main definitional development of the complex number system flows easily from a set of postulates for the natural numbers. Important concepts are introduced when needed to provide better motivation through immediate usage. Thus, the approach is integrated for a greater continuity of ideas than would be possible if a course in sets were followed by a course in the number systems. Оглавление: Обложка книги. 1 LOGIC     Thales    1. Introduction    2. Statements and Connectives    3. Tautologies, Absurdities, and Contingencies    4. The Mathematics of Logic    5. Quantifiers    6. The Logic of Mathematics    7. A Simple Logical Discourse    8. Proof  2 SETS     Pythagoras    9. Sets and Subsets    10. Union and Intersection    11. Some Basic Properties    12. Complement    13. Power Set    14. Relations    15. Equivalence Relations    16. Functions    17. Operations  3 BOOLEAN ALGEBRA     Archimedes    18. Boolean Algebra    19. Logic    20. Switching Circuits  4 NATURAL NUMBERS     End of the Greek Era    21. Motivation    22. The Natural Numbers    23. Order    24. Subtraction and Division    25. Mathematical Induction    26. Exponents and Inequalities    27. Two More Principles    28. An Independent Postulate Set    29. The Peano Postulates    30. Cardinal Numbers and Addition    31. Cardinal Numbers and Multiplication  5 INTEGERS     Fibonacci    32. Ordered Pairs    33. Basic Properties    34. Inequality    35. Absolute Value    36. Mathematical Induction    37. The Integers  6 RATIONAL NUMBERS     Newton    38. Ordered Pairs    39. Identities    40. Subtraction and Division    41. Inequality    42. Miscellaneous Properties    43. The Field    44. Modular Arithmetic    45. Rings and Integral Domains  7 REAL NUMBERS     Gauss    46. Sequences and Limits    47. Cauchy Sequences    48. Equivalence, Addition, Multiplication    49. Basic Properties    50. Order    51. Completeness    52. Real Numbers    53. Dedekind Cuts  8 COMPLEX NUMBERS     Cauchy    54. Ordered Pairs    55. The Fundamental Theorem of Algebra  9 INFINITY AND BEYOND     Weierstrass    56. Infinity    57. Beyond Infinity    58. Cardinal Arithmetic    59. The March of the Ordinals    60. Three Paradoxes    61. Two Axioms  APPENDICES]   A. Umbugio    B. Proof of a Completeness Theorem    C. Synthetic Division    D. Proofs of Some Set Theorems  HINTS FOR SELECTED EXERCISES  ANSWERS FOR SELECTED EXERCISES  BIBLIOGRAPHY  INDEX  Формат: djvu Размер: 2454265 байт Язык: ENG Рейтинг: 225 Открыть: Ссылка (RU)