A Transition to Advanced Mathematics

by Douglas Smith, Maurice Eggen, Richard St. Andre

Successfully addressing the frustration many students feel as they make the transition from beginning calculus to a more rigorous level of mathematics, A Transition to Advanced Mathematics provides a firm foundation in the major ideas needed for continued work in the discipline. The authors guide students to think and to express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. With their proven approach, Smith, Eggen, and St. Andre introduce students to rigorous thinking about sets, relations, optional functions and cardinality, and present introductions to modern algebra and analysis with sufficient depth to capture some of their spirit and characteristics. Addressing the needs of different students, A Transition to Advanced Mathematics includes exercises of varying difficulty for each section and provides worked-out answers to selected problems. With its straightforward style, logical topic sequence, exceptionally clear writing, well-chosen examples, illustrations, and historical notes, this unparalleled text will improve mathematical fashion, thereby giving your students a solid understanding of the material most useful for advanced courses.

Genres: Mathematics, Textbooks, Reference, Nonfiction, Stem

344 pages, Hardcover

First published January 1, 1983

Reviews

[Madhumita · Rating 3 out of 5]

It was a good supplement to my class, but some of the proofs were a bit difficult to understand without prior knowledge or explanations.

[Jimyanni · Rating 3 out of 5]

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.

[Ryan Pennell · Rating 4 out of 5]

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.

[Isaac · Rating 4 out of 5]

A good range of exercises with good difficulty when needed.

[Alex · Rating 5 out of 5]

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.

[Debra · Rating 4 out of 5]

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.

[Ahmed Sakr · Rating 5 out of 5]

Very simple yet useful

[Gabs · Rating 5 out of 5]

😃👍

[Curtis Penner · Rating 5 out of 5]

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.