Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.
Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. Option A:chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.
Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces.
Mathematical Analysis, Volume I was written by Dr. Elias Zakon of the University of Windsor and submitted to the Open Textbook Challenge by Dr. Bradley Lucier of Purdue University. According to the preface, "One of [the] main objectives is updating the undergraduate analysis as a rigorous postcalculus course... [without losing] contacts with classical texts still widely in use."
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