pt. 1. Numbers and equations -- Lesson 1. What algebra is -- Lesson 2. Equations and their solutions -- Lesson 3. Where algebra comes from -- Lesson 4. Why algebra is important -- Lesson 5. Numerical solution of equations -- pt. 2. formulaic approach to equations -- Lesson 6. Combinatoric solutions I: quadratic equations -- Lesson 7. Combinatoric solutions II: cubic equations -- pt. 3. Resolvents -- Lesson 8. From combinatorics to resolvents -- Lesson 9. search for resolvents -- pt. 4. Abstract algebra -- Lesson 10. Existence and constructibility of roots -- Lesson 11. breakthrough: Galois theory -- Epilogue: modern algebra -- App. Some facts about plynomials.
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"Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors." "Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, this book is excellent for mathematics courses of the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics."--Jacket.