Are Math books for engineers are easier to understand than math books for mathematicians? I do not know the exact answer, because I have not studied math books for engineers, although I have the experience of teaching Higher Mathematics for Engineers 3 decades ago (only for a semester). To my memory, the textbook was published by Sichuan University (Press), yellow cover pages. This experience told me that I need not provide proof process for many mathematical theorems, listed in the textbook. Therefore, how to apply mathematics to engineering is the aim for Math books for engineers, if I am not wrong. The difficulty of math books for mathematician lie in the proof process, from a simple entity of the objective world to the mathematical theorem using only modus ponens. This process includes infinite beauty although it is hard to master such a beauty. I lectured Linear Algebra and Discrete Mathematics for many years for Computer Science students. However, I lectured each of them. Use projector? No. Use MOODLE or Google Classroom? No, Use MS PPT? No. Use whiteboard, No. I only used chalk to write what I kept in mind to the blackboard. I had not lecture notes available in class room, but it is at home, because I was trained to not use lecture notes, nor textbooks available for class teaching. Therefore, at that time, my time for preparing for 2 hours class teaching using head or mind is a few times more than today. This teaching experience of many years also trains me to keep what I lectured in mind, at least in terms of short terms memory. For example, I still use this mind method to write weekly teaching diary. For example, I wrote all the program codes for told my students of IT in class as a part of diary after class teaching. I was not the unique to class teaching without using textbooks or lecture notes. My professor, Jun Xi, was my role model at that time.
My student of IT asked me "I didn’t know that mathematician have their own text book, who wrote the math book for mathematician?" This is not an easy question. To my memory,
1. Walter Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill Education. is one of the best books. I studied the 1st edition of the book. I still use some method of the book for my research.
2. Kösaku Yosida (1995) Functional Analysis 6th ed. Edition. I studied its earlier edition. I used to obsess with it for some time.
More general, I studied a few books from the lists of 278 books,
https://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics.
I believe that the majority of them are for students of mathematics or Computer Science.
Finally, I believe that the 47 books of Springer listed at
https://www.springer.com/series/3242?detailsPage=titles
are all for mathematicians. I only studied 2 of them many years ago.
Finally, mathematics is a science of study of abstract concepts and their relations. How to abstract entity to a mathematical concept or counterpart from the physical world is a mathematical skill. For example, one has taken 1 year to develop an expert system. However, in mathematics, this expert system is equivalent to ES = , where K is a non-empty set, E is an operator or operators, it is an algebra. If we do not understand such a mathematical abstraction, then we cannot have an interest, lasting interest in studying mathematics or using mathematics. The current trend for the majority of people to say bye-bye to mathematics at the age of less than 20. This is a modern tragedy for modern society and future.
This is an answer to my students of Information Technology. It took me hours for retrospecting my experience of studying and teaching mathematics many years ago.
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