A Transition to Advanced Mathematics helps you bridge the gap between calculus and advanced math courses. The 8th edition, by Douglas Smith, continues to provide a firm foundation in major concepts needed for continued study. It guides you to think and express yourself mathematically—analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors present introductions to modern algebra and analysis, with continuous emphasis on improving your ability to read and write proofs, and developing critical awareness of common errors in proofs.

Concepts are clearly explained through detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. You will gain a solid intuition for the types of mathematical reasoning you’ll need to apply in later courses, and a better understanding of how mathematicians approach and solve problems. The book exposes you to a large number of examples and exercises that allow you to practice developing the skills needed to think and write like a mathematician.