Lenguaje Matemático, Conjuntos y Números

TemaApuntesProblemasCapítulos ref.
1LógicaProblemasCh1 [1], Ch1,2,5,6,7 [3]
2ConjuntosProblemasCh2 [1], Ch3 [2], Ch3 [3]
3Relaciones (I), (II), AplicacionesCh3 [1], Ch3 [2], Ch8,9 [3]
4Estructuras algebraicasCh4 [1]
5$\mathbb{N}$, $\mathbb{Z}$ProblemasCh5 [1], Ch2,4 [2], Ch4 [3]
6$\mathbb{Q}$, $\mathbb{R}$Ch6 [1], Ch4 [2]
7$\mathbb{C}$Ch7 [1]

Bibliografía

  1. Delgado Pineda, M. y Muñoz Bouzo, M.J. Lenguaje matemático, conjuntos y números. 2nd Edition, Sanz y Torres.
  2. Tao, T. Analysis I. 4th Edition, Springer Singapore. DOI.
  3. Cummings, J. Proofs: A Long-Form Mathematics Textbook. Independently published. DOI.

Real Analysis I

UnitNotesProblemsChapter ref.
1$\mathbb{R}$Problems
2SequencesProblems
3SeriesProblems
4Topology in $\mathbb{R}$Problems
5Limits and continuityProblems
6DifferentiabilityProblems

Bibliography

  1. Abbott, S. Understanding Analysis. 2nd Edition, Springer New York, NY. DOI.
  2. Tao, T. Analysis I. 4th Edition, Springer Singapore. DOI.
  3. Cummings, J. Real Analysis: A Long-Form Mathematics Textbook. 2nd Edition, Independently published. DOI.
  4. Ross, K. A. Elementary Analysis. The Theory of Calculus. 2nd Edition, Springer New York, NY. DOI.

Real Analysis II

UnitNotesProblemsChapter ref.
1Riemann integralProblems
2Metric SpacesProblems
2Continuity in Metric SpacesProblems
3Sequences of functionsProblems
4Uniform convergenceProblems
5Series of functionsProblems
6Power seriesProblems

Bibliography

  1. Abbott, S. Understanding Analysis. 2nd Edition, Springer New York, NY. DOI.
  2. Tao, T. Analysis I. 4th Edition, Springer Singapore. DOI.
  3. Tao, T. Analysis II. 4th Edition, Springer Singapore. DOI.
  4. Cummings, J. Real Analysis: A Long-Form Mathematics Textbook. 2nd Edition, Independently published. DOI.
  5. Apostol, T. Mathematical Analysis. 2nd Edition, Pearson.

Multivariate Real Analysis (I, II)

UnitNotesProblemsChapter ref.
1Calculus in Several VariablesProblems
2Lebesgue measureProblems
2Lebesgue integralProblems

Bibliography

  1. Tao, T. Analysis II. 4th Edition, Springer Singapore. DOI.
  2. Apostol, T. Mathematical Analysis (2nd ed.). Pearson.

Functional Analysis

UnitNotesProblemsChapter ref.
1Banach spacesProblems
2$C[0,1]$Problems
3Hilbert spacesProblems
4Linear functionalsProblems
5Compact operatorsProblems

Bibliografía 1.

Measure Theory

UnitNotesProblemsChapter ref.
1Abstract measure spaceProblems
2Integration on a measure spaceProblems
3Product measuresProblems
4Absolute continuity of measuresProblems

Bibliography

  1. Tao, T. Analysis II. 4th Edition, Springer Singapore. DOI.
  2. Stein, E. M., & Shakarchi, R. (2005). Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press. DOI
  3. Royden, A. (1983) Real Analysis. 4th Edition, MacMillan, New York.