A Transition to Advanced Mathematics

by Douglas Smith, Maurice Eggen, Richard St. Andre

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

Genres: Mathematics, Textbooks, Reference, Nonfiction, Stem

416 pages, Hardcover

First published January 1, 1983

About the author

Douglas Smith is a multi-award-winning author described by Library Journal as “one of Canada's most original writers of speculative fiction.”

His latest work is the multi-award-winning YA urban fantasy trilogy, The Dream Rider Saga (The Hollow Boys, The Crystal Key, and The Lost Expedition). Other books include the urban fantasy novel, The Wolf at the End of the World; the collections, Chimerascope, Impossibilia, and La Danse des Esprits (translated); and the writer's guide Playing the Short Game: How to Market & Sell Short Fiction.

His short fiction has appeared in the top markets in the field, including The Magazine of Fantasy & Science Fiction, Amazing Stories, InterZone, Weird Tales, Baen’s Universe, Escape Pod, On Spec, and Cicada.

Published in 27 languages, Doug is a 4-time winner of Canada's Aurora Award, most recently in 2023 for The Hollow Boys, as well as the juried IAP Award for the same book. He's been a finalist for the Astounding Award, CBC's Bookies Award, Canada's juried Sunburst Award, the juried Alberta Magazine Award for Fiction, and France's juried Prix Masterton and Prix Bob Morane.


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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.