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Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered.

The text opens with an introduction to basic logic and set theory, setting students up to succeed in the study of analysis. Each section is followed by graduated exercises that both guide and challenge students. The author includes examples and...

Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject.

Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to...

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincare conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP...

If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.

Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more....

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis.

There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth...