eBook ISBN:  9781470430306 
Product Code:  CHEL/354.H.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $67.50 
eBook ISBN:  9781470430306 
Product Code:  CHEL/354.H.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $67.50 

Book DetailsAMS Chelsea PublishingVolume: 354; 1961; 631 ppMSC: Primary 12; 40
At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten.
In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discussions of techniques of solving quadratic and cubic equations, as well as some discussion of fourthorder equations. There are also detailed treatments of partial fractions, the method of undetermined coefficients, and synthetic division.
The book is ostensibly an algebra book; however, it covers many topics that are found throughout today's curriculum:
 calculus and analysis: infinite series, partial fractions, undetermined coefficients, properties of continuous functions,
 number theory: continued fractions,
 probability: basic results in probability.
Though the book is structured as a textbook, modern mathematicians will find it a delight to dip into. There are many gems that have been overlooked by today's emphasis on abstraction and generality. By revisiting familiar topics, such as continued fractions or solutions of polynomial equations, modern readers will enrich their knowledge of fundamental areas of mathematics, while gaining concrete methods for working with their modern incarnations. The book is suitable for undergraduates, graduate students, and researchers interested in algebra.
ReadershipUndergraduates, graduate students, and research mathematicians interested in algebra.

Table of Contents

Chapters

Chapter 1. The natural numbers–counting, addition, and multiplication

Chapter 2. Subtraction and the negative

Chapter 3. Division and fractions

Chapter 4. Irrational numbers

Chapter 5. The imaginary and complex numbers

Chapter 6. Preliminary considerations

Chapter 7. The fundamental operations

Chapter 8. Simple equations in one unknown letter

Chapter 9. Systems of simultaneous simple equations

Chapter 10. The division transformation

Chapter 11. Factors of rational integral expressions

Chapter 12. Highest common factor and lowest common multiple

Chapter 13. Rational fractions

Chapter 14. Symmetric functions

Chapter 15. The binomial theorem

Chapter 16. Evolution

Chapter 17. Irrational functions. Radicals and fractional exponents

Chapter 18. Quadratic equations

Chapter 19. A discussion of the quadratic equation. Maxima and minima

Chapter 20. Equations of higher degree which can be solved by means of quadratics

Chapter 21. Simultaneous equations which can be solved by means of quadratics

Chapter 22. Inequalities

Chapter 23. Indeterminate equations of the first degree

Chapter 24. Ratio and proportion. Variation

Chapter 25. Arithmetical progression

Chapter 26. Geometrical progression

Chapter 27. Harmonical progression

Chapter 28. Method of differences. Arithmetical progressions of higher orders. Interpolation

Chapter 29. Logarithms

Chapter 30. Permutations and combinations

Chapter 31. The multinomial theorem

Chapter 32. Probability

Chapter 33. Mathematical induction

Chapter 34. Theory of equations

Chapter 35. The general cubic and biquadratic equations

Chapter 36. Determinants and elimination

Chapter 37. Convergence of infinite series

Chapter 38. Operations with infinite series

Chapter 39. The binomial, exponential, and logarithmic series

Chapter 40. Recurring series

Chapter 41. Infinite products

Chapter 42. Continued fractions

Chapter 43. Properties of continuous functions


Reviews

The author has arranged a great variety of classical, elementary material in a very original manner, which every college student or grammarschool master can still considerably profit from, even so in these days.
Zentralblatt MATH 
From a review of the previous edition:
This book contains more than would seem possible from the title ... the author demonstrates that he is taking pains to bring scientific rigor into accord with pedagogical considerations.
translation of Jahrbuch Database review cited in Zbl. Reviews


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At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten.
In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discussions of techniques of solving quadratic and cubic equations, as well as some discussion of fourthorder equations. There are also detailed treatments of partial fractions, the method of undetermined coefficients, and synthetic division.
The book is ostensibly an algebra book; however, it covers many topics that are found throughout today's curriculum:
 calculus and analysis: infinite series, partial fractions, undetermined coefficients, properties of continuous functions,
 number theory: continued fractions,
 probability: basic results in probability.
Though the book is structured as a textbook, modern mathematicians will find it a delight to dip into. There are many gems that have been overlooked by today's emphasis on abstraction and generality. By revisiting familiar topics, such as continued fractions or solutions of polynomial equations, modern readers will enrich their knowledge of fundamental areas of mathematics, while gaining concrete methods for working with their modern incarnations. The book is suitable for undergraduates, graduate students, and researchers interested in algebra.
Undergraduates, graduate students, and research mathematicians interested in algebra.

Chapters

Chapter 1. The natural numbers–counting, addition, and multiplication

Chapter 2. Subtraction and the negative

Chapter 3. Division and fractions

Chapter 4. Irrational numbers

Chapter 5. The imaginary and complex numbers

Chapter 6. Preliminary considerations

Chapter 7. The fundamental operations

Chapter 8. Simple equations in one unknown letter

Chapter 9. Systems of simultaneous simple equations

Chapter 10. The division transformation

Chapter 11. Factors of rational integral expressions

Chapter 12. Highest common factor and lowest common multiple

Chapter 13. Rational fractions

Chapter 14. Symmetric functions

Chapter 15. The binomial theorem

Chapter 16. Evolution

Chapter 17. Irrational functions. Radicals and fractional exponents

Chapter 18. Quadratic equations

Chapter 19. A discussion of the quadratic equation. Maxima and minima

Chapter 20. Equations of higher degree which can be solved by means of quadratics

Chapter 21. Simultaneous equations which can be solved by means of quadratics

Chapter 22. Inequalities

Chapter 23. Indeterminate equations of the first degree

Chapter 24. Ratio and proportion. Variation

Chapter 25. Arithmetical progression

Chapter 26. Geometrical progression

Chapter 27. Harmonical progression

Chapter 28. Method of differences. Arithmetical progressions of higher orders. Interpolation

Chapter 29. Logarithms

Chapter 30. Permutations and combinations

Chapter 31. The multinomial theorem

Chapter 32. Probability

Chapter 33. Mathematical induction

Chapter 34. Theory of equations

Chapter 35. The general cubic and biquadratic equations

Chapter 36. Determinants and elimination

Chapter 37. Convergence of infinite series

Chapter 38. Operations with infinite series

Chapter 39. The binomial, exponential, and logarithmic series

Chapter 40. Recurring series

Chapter 41. Infinite products

Chapter 42. Continued fractions

Chapter 43. Properties of continuous functions

The author has arranged a great variety of classical, elementary material in a very original manner, which every college student or grammarschool master can still considerably profit from, even so in these days.
Zentralblatt MATH 
From a review of the previous edition:
This book contains more than would seem possible from the title ... the author demonstrates that he is taking pains to bring scientific rigor into accord with pedagogical considerations.
translation of Jahrbuch Database review cited in Zbl. Reviews