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Basic Undergraduate Textbooks for Mathematics

  1. Abstract Algebra:
    1. 1. Fraleigh, J.B. 1994, A first course in abstract algebra, 5th edn, Addison-Wesley, Reading, Mass.
    2. 2. Hungerford, T.W. & SpringerLink (Online service) 1974, Algebra, Springer New York, New York, NY.
    3. 3. Herstein, I.N. 1975, Topics in algebra, 2nd edn, Wiley, New York.
    4. 4. Isaacs, I.M. 2009, Algebra: a graduate course, American Mathematical Society, Providence, R.I.
    5. 5. Dummit, D. S., & Foote, R. M. (1991). Abstract algebra. Englewood Cliffs, N.J., Prentice Hall.

  1. Linear Algebra:
    1. 1. Hoffman, K. & Kunze, R., 1971, Linear Algebra, 2nd Edition, Prentice Hall Inc., Upper Saddle River.
    2. 2. Curtis, M. L., & Place, P. 1990, Abstract linear algebra, Springer-Verlag, New York.
    3. 3. Jänich, K. 1994, Linear algebra, Springer-Verlag, New York.

  1. Algebraic Geometry and Topology:
    1. 1. Hartshorne, R. & SpringerLink (Online service) 1977, Algebraic Geometry, Springer New York, New York.
    2. 2. Cox, D.A., Little, J. & O'Shea, D. 2015, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Fourth edn, Springer International Publishing AG, Cham.
    3. 3. Hatcher, A., 2002, Algebraic topology, Cambridge University Press, New York.

  1. Calculus:
    1. 1. Buck, R.C. 2003, Advanced calculus, 3rd edn, Waveland Press, Long Grove, IL.
    2. 2. Spivak & Michael 2018, Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus, 1st edn, CRC Press Inc.

  1. Dynamical Systems:
    1. 1. Perko, L. 2013, Differential Equations and Dynamical Systems, Springer, New York, NY.

  1. Differential Geometry:
    1. 1. Carmo, M.P.d. 1976, Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, N.J.
    2. 2. Guillemin, V. & Pollack, A. 2010, Differential topology, AMS Chelsea Pub, Providence, R.I.
    3. 3. Milnor, J. W., 1965, Topology From the Differentiable Viewpoint, University Press of Virginia, Charlottesville.

  1. Mathematical Analysis:
    1. 1. Rudin, W. 1976, Principles of mathematical analysis, 3d edn, McGraw-Hill, New York.
    2. 2. Apostol, T.M. 1964, Mathematical analysis, 4th edn, Addison-Wesley Pub. Co, Reading, Mass.
    3. 3. Bartle, R. G., 1964, The elements of real analysis, Wiley, New York.
    4. 4. Royden, H. L. & Fitzpatrick P., 2018, Real Analysis, Pearson, New York, NY.
    5. 5. Pugh, C.C., 2015, Real Mathematical Analysis, Springer International Publishing AG, Cham.

  1. Complex Analysis:
    1. 1. Conway, J. B., 1978, Functions of One Complex Variable I, Springer New York, New York.
    2. 2. Conway, J. B., 1995, Functions of One Complex Variable II, Springer New York, New York.
    3. 3. Palka, B. P., 2012, An introduction to complex function theory, World Publishing Corporation, Beijing.
    4. 4. Busam, R. & Freitag, E. 2009, Complex analysis, Springer.

  1. Geometry and Topology:
    1. 1. Munkres, J. R., & Davis, L., 2018, Topology, Pearson Prentice Hall,Upper Saddle River, N.J.
    2. 2. Pressley, A., 2010, Elementary differential geometry, 2nd edn, Springer, New York.
    3. 3. Tu, L.W., 2011, Introduction to Manifolds, Springer New York, New York.