CiNii 図書 - Transition to analysis with proof

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 illustrations that appeal to the visual side of analysis. The accessible structure of the book makes it an ideal refence for later years of study or professional work. Combines the author's previous works Elements of Advanced Mathematics with Foundations of Analysis Combines logic, set theory and other elements with a one-semester introduction to analysis. Author is a well-known mathematics educator and researcher Targets a trend to combine two courses into one

Chapter 1 Basic Logic
Chapter 2 Methods of Proof
Chapter 3 Set TheoryChapter 4 Relations and Functions
Chapter 5 Essential Number Systems Chapter 6 Sequences
Chapter 7 Series of Numbers
Chapter 8 Basic Topology Open and Closed Sets
Chapter 9 Limits and Continuity of Functions
Chapter 10 Differentiation of Functions
Chapter 11 The Integral
APPENDIX: Construction of The Weierstrass Nowhere Differentiable Function
Chapter 12 Sequences and Series of Functions
APPENDIX: Proof of the Weierstrass Approximation Theorem
Chapter 13 Elementary Transcendental Functions APPENDIX I Elementary Number Systems Table NotationGlossary Bibliography, Index

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Transition to analysis with proof

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