<< 1 >>
Rating: 
Summary: Disturbing to say the least
Review: Dear Authors of The Art of Mathematics:Hi, I don't know how to start this letter I am a friendly person who likes to build people up, and likes helping people I offered my help to a new friend, who just started attending SJSU Since she has no math background, she had to take a basic math course. I have a BS in Chemistry/Nuclear Physics from SJSU I have tutored hundreds of students, in mathematics, physics, chemistry,
spanish, etc And I had to warn so many students about the lack of touch with reality of some
college Professors, and their lack of guidance to students in how to prepare
themselves to succeed in college. For instance, I would warn them that organic chemistry is different than general
chemistry, and that usually college professors would never warn the students
that they are trying to cramp too much knowledge too soon, and specially with
organic chemistry, that they will be ill prepared if they didn't start studying
before they take the class I have helped in several University programs, like EOPS, Upward bound, Summer
Bridge, Alliance for minority participation, Minority engineering program, etc And I have met so many professors who are unhelpful and out of touch with the
reality of the difficulty of mastering any concepts For instance, electricity and magnetism, Maxwell's equations, etc,
Students get discouraged because they can't see what is going on, and no one
seems to remind them that what it took scholars decades to master, they are
asked to understand in a semester Well, when I went to help my new friend, and she shows me she has to prove
Cantor's method for ... I was shocked... I love mathematics, it is not my major, but I have loved the process of
reflexion that this science has brought to my mind But I find it SO DISTURBING that a friend who has never taken any geometry, or
trigonometry, or basic logic, etc, etc, is thrown into trying to prove something
that, again, it took scholars decades to understand I see it everywhere in the academic world It is SO EASY to forget how hard it is not to understand I read an article written in the seventies, in a journal of Chemistry, about the
margin of excellence The whole article was about how the margin of excellence was being lost, because
of the need to expose undergraduates to as much knowledge as possible (without a
true mastery or understanding of it) I think few students will have the courage to express their minds and/or able to
see that maybe the purpose of the book was the self agrandizemnt of its authors Students ask the professor for a deeper explananation, which the same professor
can't provide Then students find themselves regurgitating the answer given to them, and fake a
true understanding to pass the class I love mathematics, but just to see a water down introduction to deep concepts
of mathematics, and the exposure of these concepts to students who may or may
not have the intellectual skills (for the lack of formal mathematical classes)
is disturbing to me. Please, please, please, send spies into the classrooms of people taken this
course and be willing to hear the true opinions of students Best of life to you Sincerely
Rating: 
Summary: Gets to the heart of mathematics!
Review: I disagree strongly with the previous reviewer who found the text "disturbing." That person and his/her student friend missed the point entirely! This is not a textbook aimed at the traditional recipes for solving sets of mathematical problems. Rather, it is a survey of mathematical thought from ancient to modern times and the astonishing aspect is that it is within the grasp of all students to comprehend it! For example, we don't just learn the Pythagorean formula for right triangles and apply it to specific problems. We discover with hands on clarity WHY Pythagoras' theorem is true! What could be more elegant that Euclid's easily understood proof that there are infinitely many prime numbers? Moreover, we get to see those abstract notions put to great use in encryption without which even amazon.com would not be the great success that it is! All of this is comprehensible to any student willing to read the text and to participate in classroom discussion. The authors nurture creative thinking throughout keeping students alert to and on the lookout for patterns while encouraging them to try new methods of attacking problems. This is how REAL mathematics works! Also, they make it clear that mathematics is not a closed subject having solved all number problems. They provide many examples of problems that took centuries to solve (Fermat's Last Theorem) along with some that have yet to be cracked (Goldbach's Conjecture). Things really start to get interesting when the text delves into the nature of infinity. The authors set this up very cleverly, first, with an early introduction of a simple and innocent looking game which is eventually used as a stepping stone into Cantor's proof and, second, with a highly visual analogy of numbers on a conveyor belt used to compare the cardinality of sets. Finally, they treat the student to an infinity of infinities! The student cannot help but grasp the essence of the great ideas and appreciate the thinking that yielded such marvelous concepts. The text introduces many more areas of fascinating mathematics some which were touched on in earlier reviews here. I particularly enjoyed the discussions of the fixed point theorem as well probability and statistics in the final chapter where the student sees the need to question statistical data (polls). The student will acquire an appreciation of both the power and limitations of statistical inference. Will the student leave the course laden with mathematical techniques and skills that will allow them to solve systems of partial differential equations or to model nonequilibrium chemical processes or to design the first interstellar space probe? Of course not. They will leave the course as better thinkers and with a much greater appreciation of mathematics!
Rating: 
Summary: I disagree with the implied goal of this book
Review: I disagree with the implied goal of this book to give people who are unable and/or unwilling to learn mathematics an easy way to fulfill a mathematics requirement. When are mathematicians going to face the fact that not everyone can enjoy and do mathematics? Do we ask students to read Dr. Seuss in fulfillment of a literature requirement? The world is already filled with too many people who think they understand mathematics and who are practicing mathematics. The real challenge is to educate those who are able and willing to learn mathematics and ensure that mathematics is applied competently. But if one wants to make a buck selling mathematics books, this is the way to do it. I'm reminded of the quotation: "No one ever went broke underestimating the intelligence of the American people." - Attributed to H. L. Mencken
<< 1 >>
| 
