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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.
- A new mini-section in Chapter 1 on mathematical writing style that describes good practices and some of the special characteristics that distinguish the way mathematics is communicated. Besides advice on what to include in a proof and what to leave out, this short section offer tips on the use of symbols and other details that help in writing clear, readable proofs.
- An expanded section on strategies for constructing proofs follows the introductory sections on methods of proof and the discussion on writing style. This section summarizes basic proof methods and includes more than sixty exercises involving proofs.
- A new section, Section 3.4, on modular arithmetic, and a new Section 4.7 on limits of functions and continuity of real functions.
- Revised Sections, 2.6 on combinatorial counting and Section 4.6 on sequences provide the most current content.
- The authors follow a logical development of topics, and write in a readable style that is consistent and concise. As each new mathematical concept is introduced the emphasis remains on improving students' ability to write proofs.
- Worked examples and exercises throughout the text, ranging from the routine to the challenging, reinforce the concepts.
- Proofs to Grade exercises test students' ability to distinguish correct reasoning from logical or conceptual errors.
- A flexible organization allows instructors to expand coverage or emphasis on certain topics and include a number of optional topics without any disruption to the flow or completeness of the core material.-
2. Sets and Induction.
3. Relations and Partitions.
6. Concepts of Algebra.
7. Concepts of Analysis
Answers to selected exercises.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Complete Solutions Manual on Instructor Companion Website for A Transition to Advanced Mathematics, 8th