Luis F. Moreno received his B.A. in mathematics at Rensselaer Polytechnic Institute in 1973, an M.S. in mathematics education at State University of New York, Albany in 1976, and an M.A. in mathematics at State University of New York, Albany in 1982. He belongs to the Mathematical Association of America (Seaway Section 2nd vice-chair in 2000) and New York State Mathematics Association of Two-Year Colleges, being campus liaison for both organizations. He teaches at Broome Community College where, besides the standard undergraduate courses through linear algebra and real analysis, he has taught courses in statistics, statistical quality control, and logic.

• 0. Paradoxes?1. Logical Foundations2. Proof, and the Natural Numbers3. The Integers, and the Ordered Field of Rational Numbers4. Induction and Well-Ordering 5. Sets6. Functions7. Inverse Functions 8. Some Subsets of the Real Numbers9. The Rational Numbers Are Denumerable10. The Uncountability of the Real Numbers11. The Infinite 12. The Complete, Ordered Field of Real Numbers13. Further Properties of Real Numbers 14. Cluster Points and Related Concepts15. The Triangle Inequality16. Infinite Sequences17. Limits of Sequences18. Divergence: The Non-Existence of a Limit19. Four Great Theorems in Real Analysis20. Limit Theorems for Sequences21. Cauchy Sequences and the Cauchy Convergence Criterion22. The Limit Superior and Limit Inferior of a Sequence23. Limits of Functions24. Continuity and Discontinuity25. The Sequential Criterion for Continuity26. Theorems About Continuous Functions27. Uniform Continuity28. Infinite Series of Constants29. Series with Positive Terms30. Further Tests for Series with Positive Terms 31. Series with Negative Terms 32. Rearrangements of Series33. Products of Series 34. The Numbers e and γ 35. The Functions exp x and ln x36. The Derivative37. Theorems for Derivatives 38. Other Derivatives 39. The Mean Value Theorem 40. Taylor's Theorem 41. Infinite Sequences of Functions42. Infinite Series of Functions43. Power Series44. Operations with Power Series45. Taylor Series46. Taylor Series, Part II 47. The Riemann Integral48 The Riemann Integral, Part II49. The Fundamental Theorem of Integral Calculus50. Improper Integrals51. The Cauchy-Schwarz and Minkowski Inequalities52. Metric Spaces53. Functions and Limits in Metric Spaces54. Some Topology of the Real Number Line55. The Cantor Ternary SetAppendices A-FAnnotated BibliographySolutions to Odd-Numbered ExercisesIndex

The title of this book suggests a friendly tone and a gentle introduction to real analysis. This does indeed seem to be the case, as the book's size and reader-friendly layout suggest… The annotated bibliography will be appreciated by both the instructor and by interested students." - CMS Notices