Possible Beneficial Audiences
- College students who have taken courses in calculus, differential equations, and perhaps linear algebra, may be unprepared for the more advanced courses of real analysis, abstract algebra, and number theory that lie ahead. (If you cannot negate a logical sentence, you are probably not ready for prime time.) Although the basic calculus et al. sequence is important for developing a rounded background in mathematics as well as developing problem‐solving skills, most calculus courses are not intended to prepare the student for advanced mathematics. Few students, after going through the basic sequence, are even familiar with the basic language of mathematics, such as the sentential and predicate logic. If a student is to develop skills for reading, analyzing, and appreciating mathematical arguments and ideas, knowledge of the basic language of mathematics is a must.
- Mathematics teachers and math education students will hopefully find this book a valuable aid for teaching an inspiring and exciting introduction to mathematics that goes beyond the basics. The large and varied collection of historical notes and varied problems at the end of each section should be worth the “price of admission” alone.
- Bright high school students with good backgrounds and a strong interest in mathematics will hopefully fall in love with this book, all the way from the “Important Note” inserts to the exciting problem sets.
- Scientists, engineers, and out‐of‐practice others in the professional workforce, who are discovering the mathematics they learned long ago is not adequate for their current needs, will benefit by spending some time with this book. This book might even show self‐study individuals just how uncomplicated and enjoyable mathematics can be, possibly at variance from their college days, and in fact might develop newly found mathematical confidence.
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