Introduction to Mathematical Analysis I - 3rd Edition

Video lectures explaining problem solving strategies are available Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels of difficulty. Hints and solutions to selected exercises are available in the back of the book. For each section, there is at least one exercise with hints or fully solved. For those exercises, besides the solutions, there are explanations about the process itself and examples of more general problems where the same technique may be used. The last chapter contains additional topics. These include topological properties of the real line, generalizations of the extreme value theorem and more contemporary topics that expand on the notions of continuity or optimization. Lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. Print on DemandStandard print copy (paperback)Premium print copy (hardcover) Adopt/Adapt If you are an instructor adopting or adapting this PDXOpen textbook, please help us understand your use by filling out this formhttps://pdxscholar.library.pdx.edu/pdxopen/1048/thumbnail.jp

Pure Σ2\Sigma_2-Elementarity beyond the Core

We display the entire structure ${\cal R}_2$ coding $\Sigma_1$- and $\Sigma_2$-elementarity on the ordinals. This will enable the analysis of pure $\Sigma_3$-elementary substructures.Comment: Extensive rewrite of the introduction. Mathematical content of sections 2 and 3 unchanged, extended introduction to section 2. Removed section 4. Theorem 4.3 to appear elsewhere with corrected proo

Introduction to papers on the modeling and analysis of network data

Introduction to papers on the modeling and analysis of network dataComment: Published in at http://dx.doi.org/10.1214/10-AOAS346 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Equity and economic theory: reflections on methodology and scope

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples

Making proofs without Modus Ponens: An introduction to the combinatorics and complexity of cut elimination

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Equity and economic theory: reflections on methodology and scope.

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples.Fairness; Equity; Distributive justice;