Reviews for College Mathematics

The average rating for College Mathematics based on 2 reviews is 3.5 stars.

Review # 1 was written on 2014-04-05 00:00:00 Pham Thuan Many people think of mathematics as the operations like addition, subtraction, multiplication or division, or the complicated models used in calculus, linear modeling or differential equations. But mathematics embodies conceptual tools that are as important to understanding math as any other branch of the science. In this work, the authors lay out the concepts of conceptual mathematics in a way that is very understandable to students and to self-learners. Conceptual mathematics is sort of the bridge between philosophical logic and math, so the student is exposed to concepts much more than operational mathematics. Such concepts as the associative theorems, distributions and other items of set theory are discussed. This book is a very good introduction to many of the concepts of conceptual mathematics that many students pick up as they study other areas of math, such as algebra or geometry. Because these concepts are hidden behind other, more specific operations, the student never really learns the concepts as such. I would imagine that many people who think that they are not good at math are simply lacking the conceptual ideas that are taught in this book. It would be interesting to teach these concepts implicitly to a group of adults who hate math and see if they make mathematics more understandable to them. If so, then this topic really should be taught to more people who feel that they don't have the aptitude to master math. Overall I would recommend this book to anyone who wants a better understanding of the conceptual underpinnings of math.

Review # 2 was written on 2014-08-27 00:00:00 Raul Gudino A real gem. More than an introduction to categories, if you stick with it this is an introduction to topos theory, and more generally an invitation to Lawvere-space. In other words, the treatment is largely synthetic (as opposed to analytic). Brouwer's fixed point theorem is a lovely payoff 1/3rd of the way through, and the Lawvere fixed point theorem that comes later, even better – if the treatment of dynamical systems etc. wasn't a thrill enough for the reader of what is in some respects a thoroughly elementary book. The philosophy and power of categorical thinking is also made abundantly clear. Towards the end (eg. section on connected component functor), the presentation gets a little sketchy and would benefit from supplementation from other sources, but overall a model of pedagogy and highly recommended!