A Transition to Advanced Mathematics, 8/e (Hardcover)

A TRANSITION TO ADVANCED MATHEMATICS helps students to bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors present introductions to modern algebra and analysis and place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

《進階數學過渡》幫助學生在微積分和進階數學課程之間建立橋樑。作為同類書籍中最成功的一本，第8版繼續為持續學習提供重要概念的堅實基礎，引導學生以數學的方式思考和表達自己，分析情況，提取相關事實並得出適當的結論。作者介紹了現代代數和分析，並始終強調提高學生閱讀和寫作證明的能力，以及培養他們對證明中常見錯誤的批判意識。概念清晰解釋並以詳細示例支持，而豐富多樣的練習則提供了對常規和更具挑戰性問題的全面練習。學生將對他們在後續課程中需要應用的數學推理類型有堅實的直覺，並更好地理解各種數學家如何處理和解決問題。