The Elements of Advanced Mathematics, Second Edition Steven G. Krantz,
Publisher: Chapman & Hall/CRC
ISBN: 1584883030
Edition: Paperback; 2002-01-18
Summary:
The gap between the rote, calculational learning mode of calculus and
ordinary differential equations and the more theoretical learning
mode of analysis and abstract algebra grows ever wider and more
distinct, and students' need for a well-guided transition grows with
it. For more than six years, the bestselling first edition of this
classic text has helped them cross the mathematical bridge to more
advanced studies in topics such as topology, abstract algebra, and
real analysis. Carefully revised, expanded, and brought thoroughly up
to date, the Elements of Advanced Mathematics, Second Edition now
does the job even better, building the background, tools, and skills
students need to meet the challenges of mathematical rigor,
axiomatics, and proofs.New in the Second Edition:·Expanded
explanations of propositional, predicate, and first-order logic,
especially valuable in theoretical computer science·A chapter that
explores the deeper properties of the real numbers, including
topological issues and the Cantor set·Fuller treatment of proof
techniques with expanded discussions on induction, counting
arguments, enumeration, and dissection·Streamlined treatment of
non-Euclidean geometry·Discussions on partial orderings, total
ordering, and well orderings that fit naturally into the context of
relations·More thorough treatment of the Axiom of Choice and its
equivalents·Additional material on Russell's paradox and related
ideas·Expanded treatment of group theory that helps students grasp
the axiomatic method·A wealth of added exercises
Applied optimal estimation
(written by Technical staff, the Analytic sciences corporation; ed. by Arthur Gelb; principal authors Arthur Gelb; ISBN: 0262570483;
(hft.); 100% match)
•
Calculus
(Elgin H. Johnston, Jerold C. Mathews; ISBN: 0321006828;
100% match)
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