| Introductory real analysis can be an exciting course; it is the gateway to an impressive panorama of higher mathematics. But for all too many students, the excitement takes the form of anxiety or even terror; they are overwhelmed. For many, their study of mathematics ends one course sooner than they expected, and for many others, the doorways that should have been opened now seem rigidly barred. It shouldn’t have to be that way, and this book is offered as a remedy.
GOALS FOR INTRODUCTORY ANALYSIS
The goals of first courses in real analysis are often too ambitious. Students are expected to solidify their understanding of calculus, adopt an abstract point of view that generalizes most of the concepts, recognize how explicit examples fit into the general theory and determine whether they satisfy appropriate hypotheses, and not only learn definitions, theorems, and proofs but also learn how to construct valid proofs and relevant examples to demonstrate the need for the hypotheses. Abstract properties such as countability, compactness and connectedness must be mastered. |
|
|
 | | Handbook of Discrete and Combinatorial MathematicsI like the book's format. There are glossaries at the beginning of each chapter. Each subsection begins with definitions and goes on to facts, then algorithms (boxed and in pseudo -code), lists of mathematical objects, illuminating pictures, examples, lists of applications, and, finally, bibliography and web sources. This handbook will appeal both... | | Construction MathematicsA truly introductory level mathematics text, written specifically for students of building and construction
. Focuses on construction topics not found in traditional technician-level mathematics textbooks - essential for students learning how to apply mathematics in building and construction
. Content matched to the... |
Advanced CalculusNew publisher! Corrected version! Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This... | | Brownian Motion Calculus
Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver... | | All the Mathematics You Missed But Need to Know for Graduate School"Point set topology, complex analysis, differential forms, the curvature of surfaces, the axiom of choice, Lebesgue integration, Fourier analysis, algorithms, and differential equations.... I found these sections to be the high points of the book. They were a sound introduction to material that some but not all graduate students will... |
|
