Challenging Problems in Algebra

Al Posamentier is currently Dean of the School of Education and Professor of Mathematics Education at Mercy College, New York. He is Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was for 40 years. He is the author and co-author of more than 55 mathematics books for teachers, secondary and elementary school students, and the general readership. Dr. Posamentier is also a frequent commentator in newspapers and journals on topics relating to education. Alfred S. Posamentier: Math's Champion Dr. Alfred S. Posamentier, Professor Emeritus of Mathematics Education at New York's City College and, from 1999 to 2009, the Dean of City College's School of Education, has long been a tireless advocate for the importance of mathematics in education. He is the author or co-author of more than 40 mathematics books for teachers, students, and general readers including The Fascinating Fibonacci Numbers (Prometheus, 2007) and Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers (Prometheus, 2009). His incisive views on aspects of mathematics education may often be encountered in the Letters columns and on the op-ed pages of The New York Times and other newspapers and periodicals. For Dover he provided, with co-author Charles T. Salkind, something very educational and also fun, two long-lived books of problems: Challenging Problems in Geometry and Challenging Problems in Algebra, both on the Dover list since 1996. Why solve problems? Here's an excerpt from a letter Dr. Posamentier sent to The New York Times following an article about Martin Gardner's career in 2009: "Teachers shouldn't think that textbook exercises provide problem-solving experiences — that's just drill. Genuine problem solving is what Mr. Gardner has been espousing. Genuine problem solving provides a stronger command of mathematics and exhibits its power and beauty. Something sorely lacking in our society."

• IntroductionPreparing to Solve a ProblemSECTION I First Year Algebra1. Posers: Innocent and Sophisticated2. Arithmetic: Mean and Otherwise3. Relations: Familiar and Surprising4. Bases: Binary and Beyond5. "Equations, Inequations, and Pitfalls"6. Correspondence: Functionally Speaking7. Equations and Inequations: Traveling in Groups8. Miscellaneous: Curiosity CasesSECTION II Second Year Algebra9. Diophantine Equations: The Whole Answer10. Functions: A Correspondence Course11. "Inequalities, More or Less"12. Number Theory: Divide and Conquer13. Maxima and Minima: Ups and Downs14. Quadratic Equations: Fair and Square15. Systems of Equations: Strictly Simultaneous16. Algebra and Geometry: Often the Twain Shall Meet17. Sequences and Series: Progression Procession18. Logarithms: A Power Play19. Combinations and Probability: Choices and Chances20. An Algebraic PotpourriAnswersAppendices