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A Transition to Advanced Mathematics
TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.
372 pages, Hardcover
First published January 1, 1983
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Displaying 1 - 9 of 9 reviews
June 22, 2021
It was a good supplement to my class, but some of the proofs were a bit difficult to understand without prior knowledge or explanations.
April 17, 2012
Three stars seems a bit low, but four definitely would be too high for this book. My copy is the seventh edition; the picture seems to be of the sixth edition. I'm given to understand that there are many differences between editions for this book, enough so that they really should be rated separately. As such, keep in mind that this review is for the seventh edition only.
On the good side, this book seems to have a good variety of exercises to work, from easy to extremely challenging; unlike some reviewers, I consider this a feature, not a bug. And if there aren't solutions to all (or even half) of the problems, it is a fair defense to point out that in a book of this sort, there may be many possible solutions to the same problem, and it would be doing students a disservice to provide "the" solution. Still, I'll agree with the reviewers who complain that the "the second half of this proof is left as an exercise for the student" copout is the lazy author's way out.
The real problem with this book, however, is that even more so than most math textbooks (which is saying something) the explanations are impenetrable for someone who isn't already fluent in the language of math. I was fortunate enough to have a good prof, who was able to explain concepts clearly and with a translation to standard english; as such, concepts that were impenetrable when I read them prior to class made perfect sense by the time class was finished. But not everyone is so fortunate; the value of a math textbook is that if the student doesn't understand something in the lecture, he/she can supplement the lecture with the textbook. My suspicion is that anyone trying to do that with this book would be left at least as baffled as they were before reading it.
And no, it doesn't help that it's outrageously overpriced.
On the good side, this book seems to have a good variety of exercises to work, from easy to extremely challenging; unlike some reviewers, I consider this a feature, not a bug. And if there aren't solutions to all (or even half) of the problems, it is a fair defense to point out that in a book of this sort, there may be many possible solutions to the same problem, and it would be doing students a disservice to provide "the" solution. Still, I'll agree with the reviewers who complain that the "the second half of this proof is left as an exercise for the student" copout is the lazy author's way out.
The real problem with this book, however, is that even more so than most math textbooks (which is saying something) the explanations are impenetrable for someone who isn't already fluent in the language of math. I was fortunate enough to have a good prof, who was able to explain concepts clearly and with a translation to standard english; as such, concepts that were impenetrable when I read them prior to class made perfect sense by the time class was finished. But not everyone is so fortunate; the value of a math textbook is that if the student doesn't understand something in the lecture, he/she can supplement the lecture with the textbook. My suspicion is that anyone trying to do that with this book would be left at least as baffled as they were before reading it.
And no, it doesn't help that it's outrageously overpriced.
December 10, 2018
I really liked this book. It went into full detail for logic, proofs and a introduction to Analysis. I am very thankful that I read this book as it helped me greatly for my Analysis course.
December 13, 2021
A good range of exercises with good difficulty when needed.
December 27, 2022
This is the book I recommend all of my students wishing to get into higher level mathematics. It's a short breezy introduction to logic, set theory and proof writing which doesn't waste the readers time. All of the examples are well chosen and valuable, and there are just the right number of exercises.
December 27, 2023
It has a great variety for introduction to advanced math topics, but the proofs left a little to be desired. Not as complete as I feel proofs should be.
January 19, 2025
Very simple yet useful
September 20, 2024
Completed the first edition. It was 160 pages, which is the proper length. Mr. Smith wrote with clarity and provided hints to how to prove theorems. there was extensive problems with selected problems having answers in the back.
Displaying 1 - 9 of 9 reviews