Guide to Learning Advanced Mathematics

Author: Yu Desheng / Zheng Huasheng (Editor-in-Chief)
Publisher:
Publish Date: 2003-08-01
Features: This book systematically elaborates on the issues of teaching and learning higher mathematics, divided into twelve chapters, based on the basic content of the "Higher Mathematics" (Fifth Edition) edited by Tongji University. Each chapter consists of four parts: teaching objectives, content summary, learning guidance, and ability testing. The teaching objectives are divided into four levels of competence: knowledge, comprehension, application, and analysis-synthesis, specifically outlining the basic requirements for higher mathematics teaching, enabling students to clarify learning objectives and enhance their initiative and purpose in learning. The content summary of each chapter uses a tree diagram to concisely summarize and generalize the content, helping students grasp the connections between knowledge and form a solid knowledge structure. The learning guidance focuses on the key and difficult points of the textbook, discussing mathematical ideas, mathematical methods, learning methods, and problem-solving methods, enabling students to broaden their horizons, deepen their understanding of knowledge, and grasp the learned knowledge from a higher level. The ability testing carefully selects test questions, including judgment, fill-in-the-blank, multiple-choice, problem-solving, and proof types, as well as problems corresponding to each level of competence (knowledge, comprehension, application, and analysis-synthesis). Each question is marked with the required level of competence to solve it. At the end of the book, the answers to the ability test questions are provided to help students consolidate their practice, conduct ability tests, and evaluate themselves, thereby clarifying their direction of effort. The book can serve as a teaching reference for higher mathematics courses in engineering and can also be used as review material for candidates preparing for postgraduate entrance examinations.