Bibliografía de Matemática

S. Axler, Linear Algebra Done Right, 3rd ed, Springer, 2015
W. Greub, Linear Algebra, Springer 1975.
J. Hefferon, Linear Algebra. Accessible online a: http://joshua.smcvt.edu/linearalgebra/
A. Kostrikin, Y. Manin. Linear algebra and Geometry. Gordon and Breach Science Publishers, Amsterdam 1989. (Segona edició: 1997.)
G. Strang, Linear algebra and its applications.4th ed, Thomson, 2006

Funciones de variable real

M. Spivak. Calculus. Càlcul Infinitesimal. Ed. Reverté, Barcelona 1995.
R. Larson, R. P. Hostetler, B. Edwards. Cálculo I. Ediciones Pirámide. 2002.
W. Rudin. Principios de Análisis Matemático. Ed. McGraw-Hill. 1980.

Fundamentos de las matemáticas

M. Aigner i G. M. Ziegler, Proofs from The Book. Springer Verlag, 1999.
A. Cupillari, The nuts and bolts of proofs. Elsevier Academic Press, 2005.
P.J. Eccles, An introduction to mathematical reasoning, numbers, sets and functions. Cambridge University Press, Cambridge, 2007.
D.C. Ernst, An Introduction to Proof via Inquiry-Based Learning. Northern Arizona University 2017

Análisis matemático

W. Rudin. Principios de Análisis Matemático. McGraw-Hill, Mèxic, 1981.
G. P. Tolstov. Fourier Series, Edover Publications, New York, 1976.

Cálculo en diversas variables y optimización

Estructuras algebraicas

David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd. Edition, Wiley, 2003.
J.B. Fraleigh. A First course in abstract algebra. Pearson Education, 7th Edition, 2014. Review: https://www.maa.org/press/maa-reviews/abstract-algebra
T. W. Hungerford, Abstract Algebra, Brooks/Cole, 2013. Review:
https://www.maa.org/press/maa-reviews/abstract-algebra-an-introduction

Geometría lineal

Euclides, «Elementos de Geometría»
D. Hilbert, «Grundlagen der Geometrie»
R. Hartshorne, «Geometry: Euclid and beyond»

Análisis complejo y de Fourier

R. Burckel, Introduction to classical complex Analysis, vol I, Academic Pres, 1979.
W. Rudin, Análisi Real y Complexo, Alhambra, 1979
S. Saks et A. Zygumund, Fonctions Analytiques, Massin et Cie, 1970.
M. Stein, R: Shakarchi, Complex Analysis, Princeton University Press, 2003.

Ecuaciones diferenciales y modelización I

G.F. Simmons. Ecuaciones diferenciales con aplicaciones y notas históricas. Mc Graw-Hill, 1977.
H. Ricardo. Ecuaciones diferenciales: una introducción moderna. Editorial Reverté, Barcelona, 2008.
D.G. Zill. Ecuaciones diferenciales con aplicaciones de modelado. International Thomson Editores, México, 2001.
M. W. Hirsch , S. Smale, R. Devaney. Differential Equations, Dynamical Systems: An Introduction to Chaos. Elsevier, 2003.
M. Guzmán. Ecuaciones diferenciales ordinarias. Ed. Alhambra, Madrid, 1978.
G. Fulford, P. Forrester, A. Jones. Modelling with differential and difference equations. Cambridge University Press, New York, 1997.
P. Blanchard, and R.L. Devaney. Differential Equations. G.R. Hall, 2002. Traduït al castellà: «Ecuaciones Diferenciales». International Thomson Editores, México, 1999.
E. Boyce, y R.C. Di Prima. Ecuaciones Diferenciales y Problemas con Valores en la Frontera. Ed. Limusa, México, 1967.
R.L. Borrelli and C.S. Coleman. Differential equations: a modeling perspective. Prentice-Hall, 1987.
M. Braun. Ecuaciones diferenciales y sus aplicaciones. Grupo Editorial Iberoamérica. México, 2000.

Estadística

Casella, G..and Berger, R. (2002) . Statistical Inference, 2º ed. Wadsworth, Belmont, CA.
Casella, G., Berger, R. and Santana, D. (2002). Solutions Manual for Statistical Inference, Second Edition.
Morris H. Degroot, Mark J. Schervish, Probability and Statistics , https://es1lib.org/book/3606887/3d12fd?id=3606887&secret=3d12fd
Millar, R. (2011). Maximum Likelihood Estimation and Inference. Wiley.
Rossi, Richard,Mathematical Statistics: An Introduction to Likelihood Based Inference, https://onlinelibrary.wiley.com/doi/book/10.1002/9781118771075
https://syndetics.com/index.aspx

Das Gupta («2008) «Asymptotic Theory of Statistics and Porbability», Springer.
J.A.Rice (2007), Mathematicla Statistics and data analysis, 3rd Ed, Duxbury/Thomson
Versani, J. «Using R for introductory Statistics», Taylor and Francis.
M. Kendall and A. Stuart (1983). “The Advanced Theory of Statistics”.Griffin and Co. Limited, London.
Lehman, E.L. and Romano (2005, 3rd Ed.), J.P, «Testing Statistical Hypotheses», Springer
C.R. Rao (1973). “Linear Statistical Inference and its Applications”. Wiley, London.
M.L. Rizzo (2007). «Statistical computing with R». Computer Science and Data Anal Cysis Series». Chapman & Hall / CRC
Williams, D. (2001) «Weighihg the Odds», Cambridge University Press.

Álgebra commutativa

W. A. Adkins, S. H. Weintraub, Algebra, An Approach via Module Theory. Springer, New York, 1992.
A. Altman, S. Kleiman, A Term of Commutative Algebra. Worldwide Center of Mathematics, LLC, 2012.
M. Atiyah, I. Macdonald, Introducción al álgebra conmutativa. Ed. Reverté, Barcelona, 1968.
P. M. Cohn, Algebra, vol 2. Second Ed. John Wiley and Sons, New York, 1989.
D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry. Springer, New York, 2004.
B. Hartley, T. O . Hawkes, Rings, modules and linear algebra. Chapman and Hall, London 1983.
N. Jacobson, Basic Algebra I, Basic Algebra II. W. H. Freeman and Company, New York, 1989.
E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Birkhäuser, New York, 2013.
S. Lang, Algebra. Aguilar, Madrid, 1977.
J.S. Milne, A Primer of Commutative Algebra, 2009.
O. Zariski, P. Samuel, Commutative Algebra I, II, Van Nostrand, Princeton (1958, 1960).

Análisis armónico

E. Stein and R. Shakarchi, «Fourier Analysis, an introduction», Princeton Lectures in Analysis, Priceton Univresity Press 2007
Gasquet-Witomski, «Fourier Analysis and applications». Springer-Verlag, 1999.
S. Mallat, «A wavelet tour of signal processing», Academic Press, 1999

Aritmética

W. Stein, Elementary Number Theory: Primes, Congruences, and Secrets, Springer-Verlag, Berlin, 2008.
J.-P. Serre, A Course in Arithmetic, GTM7, Springer, 1973.
N.Koblitz, A Course in Number Theory and Cryptography, GTM114, Springer, 1994.
I.N. Stewart, D.O. Tall, Algebraic Number Theory, Chapman and Hall, 1979.
Z.I. Borevich y I.R. Shafarevich, Number Theory, Academic Press, 1966.
L.J. Mordell, Diophantine Equations, Academic Press, 1969.
J. Neukirch, Algebraic number theory, Springer-Verlag 1999.

Ecuaciones en derivadas parciales

L. C. Evans, Partial Differential Equations. Graduate Studies in Mathematics 19. AMS, 1998.
F. John, Partial Differential Equations. Springer-Verlag, 1980.
J. Ockendon, S. Howison, A. Lacey, A. Movchan. Applied partial differential equations. Oxford University Press, 2003.
Y. Pinchover, J. Rubinstein. An Introduction to Partial Differential Equations. Cambridge, 2005.
M. Renardy, R.C. Rogers. An Introduction to partial differential equations. Springer, 2004.
S. Salsa, Partial Differential Equations in action: from modelling to theory. Springer, 2008.
W. A. Strauss. Partial Differential Equations: An Introduction. John Wiley & Sons,1992.
A.N. Tijonov, A.A. Samarsky. Ecuaciones de la física matemática. Mir, 1983.
E.H. Zauderer. Partial differential equations of applied mathematics. Wiley-Interscience, 2006

Estadística Matemática

Rao, C. B., Touttenburg, H., Shalabh, Heumann, C.; Linear Models and Generalizations. 3rd edition, Springer, 2008.
Rawlings J. O, Pantula S. G , Dickey D. A.; Applied Regression Analysis. A Research Tool. Second Edition, Springer, 1999.
Rencher, A.C., Schaalje, G.B.; Linear Models in Statistics. Wiley-Interscience, 2008.
Seber, G., Lee, A.; Linear Regression Analysis. Wiley Series in Probability and Statistics, 2003.
Hay-Jahans C.; An R Companion to Linear Statistical Models. Chapman and Hall, 2012.
Faraway, J.; Linear Models with R. Chapman&Hall/CRC, 2005.
Faraway, J.; Extending the linear model with R. Chapman&Hall/CRC, 2006.
Vikneswaran; An R Companion to Experimental Design. https://cran.r-project.org/doc/contrib/Vikneswaran-ED_companion.pdf

McCullagh, P., Nelder, J. A.; Generalized Linear Models. Chapman&Hall, 1989.
Clarke, B. R.; Linear Models. The theory and applications of Analysis of Variance. Wiley Series in Probability and Statistics, 2008.
Sen, A., Srivastava, M.; Regression Analysis. Theory, Methods and Applications. Springer, 1990.
Christensen, R.; Advanced Linear Modelling. Springer, 2001.
Christensen, R.: Log-Linear Models. Springer, 1990.
Draper, N., Smith, H.; Applied regression Analysis. Wiley, 1998.
Chatterjee, S. & Price, B.; Regression Analysis by Example. Wiley-Interscience, third edition, 2000.
Scheffé, H.; The Analysis of Variance, 1999.
Montgomery, D.C., Peck, E., Vining, G.; Introduction to Linear Regression. Wiley Series in Probability and Statistics, 2001.

Geometría Riemanniana

Manfredo P. do Carmo, Riemannian Geometry. Birkhäuser, 1992.
Manfredo P. do Carmo, Geometría diferencial de curvas y superfícies. Alianza Universidad, 1990.
S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry. Springer-Verlag, 1990.
John M. Lee, Riemannian Manifolds: An introduction to curvature. Springer-Verlag, 1997.
M. Spivak, A Comprehensive Introduction to Diferential Geometry. Publish or Perish Inc, 1979.

Integración numérica

M. G. Larson, F. Benzgon: The finite element method: Theory, implementation and applications. Springer, 2013.
C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method. Dover, 2009.
R.M.M. Mattheij, S.W. Rienstra, J.H.M. ten Thije Boonkkamp: Partial Differential Equations. Modeling, Analysis, Computation. SIAM, 2005.

Topología de variedades

J. M. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics 218, Springer-Verlag, New York. xvii+ 631 pp. (https://link-springer-com.are.uab.cat/book/10.1007%2F978-1-4419-9982-5)
L. W. Tu, An introduction to manifolds. Universitext. Springer, New York, second edition, 2011. 384 pp. (https://link-springer-com.are.uab.cat/book/10.1007%2F978-1-4419-7400-6)
A. Hatcher, Algebraic topology. Cambridge University Press, Cambridge, 2002. xii+544 pp. (http://www.math.cornell.edu/~hatcher/AT/ATpage.html)
R. Bott and L.W. Tu, Differential forms in algebraic topology. Graduate Texts in Mathematics, 82. Springer-Verlag, New York-Berlin, 1982. xiv+331 pp.
M. W. Hirsch, Differential Topology. Graduate Texts in Mathematics 33, Springer-Verlag New York Heidelberg Berlin 1976. x + 222pp.
P. Michor, Topics in Differential Geometry, Graduate Studies in Mathematics 93. American Mathematical Society, Providence, RI, 2008. xii+494 pp. (https://www.mat.univie.ac.at/~michor/dgbook.pdf)