Supplementary Reference Material

 

Our book addresses essential topics at the intermediate level in set theory in Chapter 1, abstract algebra (resp. algebraic structures) in Chapter 2, linear algebra and matrix algebra in Chapters 3 and 4, metric spaces (resp. real analysis and topological structures) in Chapter 5, Banach and Hilbert spaces (resp. functional analysis) in Chapter 6, and linear operators (resp. functional analysis) in Chapter 7. Since each one of these topics constitutes a subject in its own right, references for supplementary reading are provided at the end of each chapter. Some of these were selected because they are classic books on the subject under discussion while others provide an especially good exposition of the material on hand. In the following, in addition to the references cited in our book, we enumerate some additional material which the reader may find useful for further study of the addressed topics.

 

References for Chapter 1 include [1]-[3].

 

References for Chapter 2 include [4]-[7]. For more recent texts on abstract algebra refer, e.g. to [8]-[10].

 

References for Chapters 3 and 4 include [11]-[16]. For more recent references on linear algebra and matrix algebra, the reader may wish to consult, e.g. [17]-[21].

 

References for Chapter 5 include [22]-[25] and [29]. For more recent references on real analysis (resp. metric spaces) the reader may want to consult, e.g. [26]-[28].

 

References for Chapters 6 and 7 include [29]-[40]. For more recent references on functional analysis the reader may want to consult, e.g. [41]-[43].

 

References

 

[1] A.M. Gleason, Fundamentals of Abstract Analysis, Reading, MA., Addison- Wesley Publishing Co., 1966.

 

[2] P.R. Halmos, Nave Set Theory, Princeton, N.J., D. Van Nostrand Co., 1960.

 

[3] F. Hausdorff, Mengenlehre, New York, Dover Publications, Inc., 1944.

 

[4] G. Birkhoff and S. MacLane, A Survey of Modern Algebra, New York, The Macmillan Company, 1965.

 

[5] C.B. Hanneken, Introduction to Abstract Algebra, Belmont, CA., Dickensen Publishing Co., 1968.

 

[6] N. Jacobsen, Lectures in Abstract Algebra, New York, D. Van Nostrand Co., 1951.

 

[7] S.T. Hu, Elements of Modern Algebra, San Francisco, Holden Day, Inc., 1965.

 

[8] D.S. Dummit and R.M. Foote, Abstract Algebra, New York, John Wiley & Sons, 2003.

 

[9] I.N. Herstein, Abstract Algebra, 3rd Edition, New York, John Wiley & Sons, 1996.

 

[10] J.B. Fraleigh, A First Course in Abstract Algebra, 6th Edition, Reading, MA., Addison-Wesley Publishing Co., 1999.

 

[11] P.R. Halmos, Finite Dimensional Vector Spaces, Princeton, N.J., D. Van Nostrand Co., 1958.

 

[12] K. Hoffman and R. Kunze, Linear Algebra, Englewood Cliffs, N.J., Prentice- Hall, 1971.

 

[13] S. Lipschutz, Linear Algebra, New York, Mc Graw-Hill Book Co., 1968.

 

[14] B. Noble, Applied Linear Algebra, Englewood Cliffs, N.J., Prentice-Hall, Inc., 1969.

 

[15] R.E. Bellman, Introduction to Matrix Algebra, New York, Mc Graw-Hill Book Co., 1970.

 

[16] F.R. Gantmacher, Theory of Matrices, vol. 1 and 2, New York, Chelsea Publishing Company, 1959.

 

[17] W.H. Greub, Linear Algebra, 4th Edition, New York, Springer-Verlag, 1981.

 

[18] L. Smith, Linear Algebra, New York, Springer-Verlag, 1998.

 

[19] S. Lang, Linear Algebra, 3rd Edition, Springer-Verlag, 2004.

 

[20] T.S. Shores, Applied Linear Algebra and Matrix Analysis, New York, Springer-Verlag, 2006.

 

[21] R. Steven, Advanced Linear Algebra, New York, Springer-Verlag, 2005.

 

[22] E.T. Copson, Metric Spaces, Cambridge, England, Cambridge University Press, 1968.

 

[23] H.L. Royden, Real Analysis, New York, The Macmillan Company, 1965.

 

[24] A.E. Taylor, General Theory of Functions and Integration, New York, Blaisdell Publishing Co., 1965.

 

[25] J. Kelly, General Topology, Princeton, N.J., D. Van Nostrand Co., 1955.

 

[26] H.L. Royden, Real Analysis, 3rd Edition, Englewood Cliffs, N.J., Prentice-Hall, 1988.

 

[27] W. Rudin, Real and Complex Analysis, New York, Mc Graw-Hill Book Co., 1987.

 

[28] G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd Edition, New York, John Wiley & Sons, 1999.

 

[29] A.N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis, vol. 1 and 2, Albany, N.Y., Graylock Press, 1957.

 

[30] L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Linear Spaces, New York, The Macmillan Company, 1964.

 

[31] P.R. Halmos. Introduction to Hilbert Space, New York, Chelsea Publishing Co., 1957.

 

[32] L.A. Liusternik and V.J. Sobolev, Elements of Functional Analysis, New York, Frederick Ungar Publishing Co., 1961.

 

[33] A.E. Taylor, Introduction to Functional Analysis, New York, John Wiley & Sons, Inc., 1958.

 

[34] K. Yosida, Functional Analysis, Berlin, Springer-Verlag, 1965.

 

[35] N. Dunford and J. Schwarz, Linear Operators, Parts 1 and 2, Reading MA., Addison-Wesley Publishing Co., 1964.

 

[36] E. Hille and R.S. Phillips, Functional Analysis and Semigroups, Providence, R.I., American Mathematical Society, 1957.

 

[37] A.W. Naylor and G.R. Sell, Linear Operator Theory in Engineering and Science, New York, Holt, Rinehart and Winston, 1971.

 

[38] A.V. Balakrishnan, Applied Functional Analysis, New York, Springer-Verlag, 1976.

 

[39] R.F. Curtain and A.J. Pritchard, Functional Analysis in Modern Applied Mathematics, London, Academic Press, 1977.

 

[40] L. Collatz, Functional Analysis and Numerical Mathematics, New York, Academic Press, 1966.

 

[41] E. Kreyszig, Introductory Functional Analysis with Applications, New York, John Wiley & Sons, 1978.

 

[42] J.B. Conway, A Course in Functional Analysis, 2nd Edition, New York, Springer-Verlag, 1990.

 

[43] E. Zeidler, Applied Functional Analysis: Main Principles and Their Applications, New York, Springer-Verlag, 1995.