Transition to Advanced Mathematics

This text provides an introduction to proofs with a view towards algebra and analysis, as well as practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. It is written by Danilo R. Diedrichs and Stephen Lovett and follows the curriculum guide recommended by the Committee on the Undergraduate Program in Mathematics (CUPM).

Format: Hardback
Length: 538 pages
Publication date: 27 May 2022
Publisher: Taylor & Francis Ltd

This comprehensive and cutting-edge text goes beyond the traditional scope of a transition course, providing an in-depth introduction to proofs with a focus on algebra and analysis. It not only serves as a foundational guide for students embarking on upper-level mathematics coursework but also immerses undergraduate students in the contemporary world of mathematics.

The authors adhere to the recommendations outlined in the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, emphasizing the importance of cognitive goals and a broad perspective in modern mathematics programs. Part I of the text offers a thorough exploration of logic and set theory, serving as a solid foundation for proof methods that are applicable to various branches of mathematics, including analysis, topology, algebra, and probability.

To enhance the learning experience, the authors incorporate numerous illustrated examples, drawing upon concepts that students are likely already familiar with. This approach minimizes the need for lengthy discussions about proof techniques and allows students to focus on understanding and applying the concepts effectively. Additionally, an appendix provides an annotated rubric with feedback codes, aiding in the assessment of proof writing skills.

Part II of the text delves into the context and culture aspects of the transition into modern mathematics. It explores 21st-century mathematics, including the current mathematical culture, career opportunities, and the evolving nature of the field. Students are introduced to the history and philosophical issues of mathematics, which provide a deeper understanding of the discipline's development. They also learn valuable skills for approaching, reading, and learning from journal articles and other primary sources, essential for advancing their mathematical knowledge.

Furthermore, Part II covers mathematical writing and typesetting in LaTeX, a widely used software for scientific and technical documentation. This practical aspect equips students with the necessary tools to communicate their ideas and results in a professional manner.

In summary, this text offers a comprehensive and engaging introduction to proofs, combining theoretical foundations with practical skills and cultural insights. It caters to students preparing for advanced mathematics coursework and provides them with the tools they need to excel in the contemporary mathematical landscape. Whether you are a student seeking to deepen your understanding of proof techniques or a professional looking to expand your knowledge in modern mathematics, this text is an invaluable resource.

Weight: 958g
Dimension: 163 x 244 x 36 (mm)
ISBN-13: 9780367494445