Bridge to Higher Mathematics by Sam Vandervelde (PDF)

Description

This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐We used this as a textbook in a college proof’s class. I remember it being challenging occasionally, but it was a good book.

⭐great

⭐I’ve been a math professor for nearly 20 years, and have struggled to find the right text for the “bridge course.” I’ve juggled several competing philosophies: keep the level of rigor high, keep the text short, include problem-solving philosophies, etc. The main difficulty is that it is hard to keep the level of rigor high without making the problems and exercises pretty dry and trivial. You run the risk of teaching students to write elegant proofs about nothing, and the even graver risk that your students end up not really knowing what mathematics is all about.I’ve come to the realization that rigor, while important, is useless in a vacuum; it is essential to have a rich mathematical experience.This is where Vandervelde’s book truly excels. He doesn’t avoid rigor, but he completely avoids dry logical games. His text is a book about Mathematics itself, and his primary goal is to bring it to life and make things FUN. When I say “fun,” I don’t mean silly or fluffy. Vandervelde’s creative problems and examples are fascinating and truly imaginative. The student is immediately engaged, and thus is motivated to argue rigorously, because the content is truly interesting.If you think that truth tables are essential, you’ll hate this book. But if you think that mathematics, while rigorous, should be suffused with ingenuity, beauty, and FUN, you’ll love Vandervelde’s book.

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