Customer Reviews

An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)

5 star:		(2)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

I really appreciate "An accompaniement to higher mathematics", because it presents a great amount of stuff concerning the technique of proof. The first chapter present why examples are so importants by showing how to test definitions, how to construct good and bad examples and how to test the validity of a theorem by the mean of extreme example. The material in this chapter is basic and easy to follow. The second chapter is about the infirmal language and some technics of proof. First, it presents the logic behind the proofs. Also, this chapter presents technics such as induction, proof by case, differents forms of proof based on implication. The third chapter is about the use of quantifier in the proof. It shows how to use and when to use quantifier. Also how to find the structure of a proof. Why I find this book interresting ? First the book is full of exercises of different kind (set, function, analysis, ...and the forth chapter contain laboratories that give you again plenty of exercises), It is written clearly, the author give a lot of advice about proofs, I find the book very suitable to undergraduted, I find the style of writting of the book very motivating. This book is definitely a good one but it is not perfect. I found some of the exercises too easy (about 30 % of the exercises), I don't think that this book is suitable for graduate student but it may help in the way you work proofs and problems. Also this book give me some help in analysis course. I recommend this book for anyone who want to learn the basic and more about proofs.

This is simply a great text for introducing undergraduate students to the basics of upper-level mathematics. Stresses the importance of examples and definitions in proof discovery. While probably inappropriate for graduate students, it makes a great primary text for any first course in proofs at the undergraduate level and is written primarily to students in this situation. Overall, the book seems to be extremely appreciated by students transitioning from calculus to upper-level mathematics.