The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book ...
Read More
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Read Less
Add this copy of The Foundations of Mathematics to cart. $5.97, very good condition, Sold by Wonder Book - Member ABAA/ILAB rated 5.0 out of 5 stars, ships from Frederick, MD, UNITED STATES, published 1977 by Oxford University Press, USA.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Very Good. Very Good condition. A copy that may have a few cosmetic defects. May also contain light spine creasing or a few markings such as an owner's name, short gifter's inscription or light stamp.
Add this copy of The Foundations of Mathematics to cart. $12.97, very good condition, Sold by ThriftBooks-Reno rated 5.0 out of 5 stars, ships from Reno, NV, UNITED STATES, published 2015 by Oxford University Press.
Add this copy of The Foundations of Mathematics to cart. $16.32, very good condition, Sold by Halcyon Books rated 4.0 out of 5 stars, ships from LONDON, LONDON, UNITED KINGDOM, published 1977 by Oxford University Press, USA.
Add this copy of The Foundations of Mathematics to cart. $19.60, good condition, Sold by GW Spokane Books rated 5.0 out of 5 stars, ships from Spokane, WA, UNITED STATES, published 2015 by Oxford University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Condition: GOOD-Used with some wear from use. May include stickers on cover, missing or wear to dustcover, inside cover, spine, slight curled corners, stains, and wear to the fore edge. All orders ship via UPS Mail Innovations-MAY TAKE UP TO 10 BUSINESS DAYS from first scan to be delivered.
Add this copy of The Foundations of Mathematics to cart. $19.60, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2015 by Oxford University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!
Add this copy of The Foundations of Mathematics to cart. $20.96, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2015 by Oxford University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!
Add this copy of The Foundations of Mathematics to cart. $26.74, good condition, Sold by FirstClassBooks rated 4.0 out of 5 stars, ships from Little Rock, AR, UNITED STATES, published 2015 by Oxford University Press.
