Analysis: Foundations of Analysis

Barnier, William and Feldman, Norman. Introduction to Advanced Mathematics Englewood Cliffs, NJ: Prentice Hall, 1990.

Bittinger, Marvin L. Logic, Proof, and Sets, Reading, MA: Addison-Wesley, 1982. Second Edition.

Feferman, Solomon. The Number Systems: Foundations of Algebra and Analysis, New York, NY: Chelsea, 1989. Second Edition.

* Fendel, Daniel and Resek, Diane. Foundations of Higher Mathematics: Exploration and Proof Reading, MA: Addison-Wesley, 1990.

* Gardiner, A. Infinite Processes: Background to Analysis New York, NY: Springer-Verlag, 1982.

Gleason, Andrew M. Fundamentals of Abstract Analysis Boston, MA: Jones and Bartlett, 1991.

** Landau, Edmund G.H. The Foundations of Analysis, New York, NY: Chelsea, 1951, 1966. Third Edition.

Lightstone, A.H. Symbolic Logic and the Real Number System: An Introduction to the Foundations of Number Systems New York, NY: Harper and Row, 1965.

Lucas, John F. Introduction to Abstract Mathematics, New York, NY: Ardsley House, 1990. Second Edition.

Smith, D.; Eggen, M.; and St.~Andre, R. A Transition to Advanced Mathematics, Pacific Grove, CA: Brooks/Cole, 1990. Third Edition.

** Solow, Daniel. How To Read and Do Proofs: An Introduction to Mathematical Thought Processes, New York, NY: John Wiley, 1982, 1990. Second Edition.

Analysis: Elementary Real Analysis

Aliprantis, Charalambos D. and Burkinshaw, Owen. Principles of Real Analysis New York, NY: Elsevier Science, 1981.

* Apostol, Tom M. Mathematical Analysis, Reading, MA: Addison-Wesley, 1974. Second Edition.

* Bartle, Robert G. Elements of Real Analysis, New York, NY: John Wiley, 1976. Second Edition.

Binmore, K.G. Mathematical Analysis: A Straightforward Approach, New York, NY: Cambridge University Press, 1977, 1981. 2 Vols.

Burkill, John C. A First Course in Mathematical Analysis New York, NY: Cambridge University Press, 1978.

Goffman, Casper. Real Functions, Boston, MA: Prindle, Weber and Schmidt, 1967. Revised Edition.

* Goldberg, Richard R. Methods of Real Analysis, New York, NY: John Wiley, 1976. Second Edition.

Kolmogorov, Andrei N. and Fomin, S.V. Introductory Real Analysis Mineola, NY: Dover, 1975.

Protter, Murray H. and Morrey, C.B. A First Course in Real Analysis New York, NY: Springer-Verlag, 1977.

Rosenlicht, Maxwell. Introduction to Analysis Mineola, NY: Dover, 1986.

** Ross, Kenneth A. Elementary Analysis: The Theory of Calculus New York, NY: Springer-Verlag, 1980.

** Royden, H.L. Real Analysis, New York, NY: Macmillan, 1968, 1988. Third Edition.

*** Rudin, Walter. Principles of Mathematical Analysis, New York, NY: McGraw-Hill, 1953, 1976. Third Edition.

Smith, Kennan T. Primer of Modern Analysis New York, NY: Springer-Verlag, 1983.

Wheeden, Richard L. and Zygmund, Antoni. Measure and Integral: An Introduction to Real Analysis New York, NY: Marcel Dekker, 1977.

Analysis: Advanced Real Analysis

Akhiezer, N.I. The Classical Moment Problem New York, NY: Hafner Press, 1965.

Beals, R. Advanced Mathematical Analysis New York, NY: Springer-Verlag, 1973.

* Bishop, Errett and Bridges, Douglas S. Constructive Analysis New York, NY: Springer-Verlag, 1985.

*** Boas, Ralph P., Jr. A Primer of Real Functions, Washington, DC: Mathematical Association of America, 1972, 1981. Third Edition.

Burkill, John C. The Lebesgue Integral New York, NY: Cambridge University Press, 1951.

Caratheodory, C. Algebraic Theory of Measure and Integration, New York, NY: Chelsea, 1986. Second English Edition.

Fischer, Emanuel. Intermediate Real Analysis New York, NY: Springer-Verlag, 1983.

*** Gelbaum, Bernard R. and Olmsted, John M.H. Theorems and Counterexamples in Mathematics New York, NY: Springer-Verlag, 1990. (Former title: Counterexamples in Analysis.)

*** Gillman, Leonard and Jerison, Meyer. Rings of Continuous Functions New York, NY: Springer-Verlag, 1976.

Grenander, Ulf and Szeg o, Gabor. Toeplitz Forms and Their Applications New York, NY: Chelsea, 1984.

** Halmos, Paul R. Measure Theory New York, NY: Springer-Verlag, 1974.

Hardy, G.H. Divergent Series New York, NY: Oxford University Press, 1949.

* Hewitt, Edwin and Stromberg, Karl R. Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable New York, NY: Springer-Verlag, 1969, 1975.

Karlin, Samuel and Studden, W. Tchebycheff Systems New York, NY: John Wiley, 1966.

Moise, Edwin E. Introductory Problem Courses in Analysis and Topology New York, NY: Springer-Verlag, 1982.

Munkres, James R. Analysis on Manifolds Reading, MA: Addison-Wesley, 1991.

Munroe, Marshall E. Introduction to Measure and Integration, Reading, MA: Addison-Wesley, 1971. Second Edition.

*** Polya, George and Szeg o, Gabor. Problems and Theorems in Analysis, New York, NY: Springer-Verlag, 1972, 1976. 2 Vols.

Stromberg, Karl R. Introduction to Classical Real Analysis Belmont, CA: Wadsworth, 1981.

Taylor, Angus E. General Theory of Functions and Integration Mineola, NY: Dover, 1985.

* Wagon, Stan. The Banach-Tarski Paradox New York, NY: Cambridge University Press, 1985.

Analysis: Fourier Analysis

Chandrasekharan, Komaravolu. Classical Fourier Transforms New York, NY: Springer-Verlag, 1989.

Chihara, T.S. An Introduction to Orthogonal Polynomials New York, NY: Gordon and Breach, 1978.

Davies, B. Integral Transforms and their Applications, New York, NY: Springer-Verlag, 1978, 1985. Second Edition.

* Dym, H. and McKean, H. Fourier Series and Integrals New York, NY: Academic Press, 1972.

Edwards, Robert E. Fourier Series: A Modern Introduction, New York, NY: Springer-Verlag, 1979, 1982. 2 Vols., Second Edition.

Jackson, Dunham. Fourier Series and Orthogonal Polynomials Washington, DC: Mathematical Association of America, 1941.

* Korner, T.W. Fourier Analysis New York, NY: Cambridge University Press, 1988.

Rogosinski, Werner. Fourier Series, New York, NY: Chelsea, 1962. Second Edition.

Seeley, Robert T. An Introduction to Fourier Series and Integrals Reading, MA: W.A. Benjamin, 1966.

** Stein, E.M. and Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces Princeton, NJ: Princeton University Press, 1971.

* Szeg o, Gabor. Orthogonal Polynomials, Providence, RI: American Mathematical Society, 1975. Fourth Edition.

* Titchmarsh, Edward C. Introduction to the Theory of Fourier Integrals London: Oxford University Press, 1948.

Widder, David V. An Introduction to Transform Theory New York, NY: Academic Press, 1971.

** Wiener, Norbert. The Fourier Integral and Certain of its Applications New York, NY: Cambridge University Press, 1933, 1988.

*** Zygmund, Antoni. Trigonometric Series New York, NY: Cambridge University Press, 1968, 1988.

Analysis: Fractals

* Barnsley, Michael. Fractals Everywhere New York, NY: Academic Press, 1988.

** Devaney, Robert L. An Introduction to Chaotic Dynamical Systems, Redwood City, CA: Benjamin Cummings, 1986, 1989. Second Edition.

* Devaney, Robert L. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics Reading, MA: Addison-Wesley, 1990.

* Devaney, Robert L. and Keen, Linda, eds. Chaos and Fractals: The Mathematics Behind the Computer Graphics Providence, RI: American Mathematical Society, 1989.

Edgar, G.A. Measure, Topology, and Fractal Geometry New York, NY: Springer-Verlag, 1990.

Falconer, Kenneth J. The Geometry of Fractal Sets New York, NY: Cambridge University Press, 1985, 1986.

* Lauwerier, Hans. Fractals: Endlessly Repeated Geometrical Figures Princeton, NJ: Princeton University Press, 1991.

*** Mandelbrot, Benoit. The Fractal Geometry of Nature New York, NY: W.H. Freeman, 1982.

* Peitgen, Heinz-Otto and Richter, P.H. The Beauty of Fractals: Images of Complex Dynamical Systems New York, NY: Springer-Verlag, 1986.

** Peitgen, Heinz-Otto and Saupe, Dietmar, eds. The Science of Fractal Images New York, NY: Springer-Verlag, 1988.

Preston, Chris. Iterates of Maps on an Interval New York, NY: Springer-Verlag, 1983.

** Schroeder, Manfred R. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise New York, NY: W.H. Freeman, 1990.

Analysis: Introductory Complex Analysis

*** Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, New York, NY: McGraw-Hill, 1966, 1979. Third Edition.

Bak, Joseph and Newman, Donald J. Complex Analysis New York, NY: Springer-Verlag, 1982.

* Boas, Ralph P., Jr. Invitation to Complex Analysis New York, NY: Birkhauser, 1987.

Burckel, Robert B. An Introduction to Classical Complex Analysis New York, NY: Academic Press, 1979.

Cartan, Henri. Theory of Analytic Functions of One or Several Complex Variables Reading, MA: Addison-Wesley, 1983.

** Conway, John B. Functions of One Complex Variable, New York, NY: Springer-Verlag, 1973, 1978. Second Edition.

Heins, Maurice. Complex Function Theory New York, NY: Academic Press, 1968.

* Knopp, Konrad. Theory of Functions, Mineola, NY: Dover, 1945, 1947; 1968. 2 Vols.

Markushevich, A.I. The Theory of Analytic Functions: A Brief Course Moscow: MIR, 1983.

Narasimhan, R. Complex Analysis in One Variable New York, NY: Birkhauser, 1985.

Nehari, Zeev. Introduction to Complex Analysis, Boston, MA: Allyn and Bacon, 1968. Revised Edition.

Nevanlinna, Rolf and Paatero, V. Introduction to Complex Analysis Reading, MA: Addison-Wesley, 1969.

* Polya, George and Latta, Gordon. Complex Variables New York, NY: John Wiley, 1974.

Analysis: Advanced Complex Analysis

* Caratheodory, C. Theory of Functions of a Complex Variable, New York, NY: Chelsea, 1958. 2 Vols.

Davis, Philip J. The Schwarz Function and Its Applications Washington, DC: Mathematical Association of America, 1974.

Fisher, Stephen D. Complex Variables, Belmont, CA: Wadsworth, 1986, 1990. Second Edition.

Grauert, H. and Fritzsche, K. Several Complex Variables New York, NY: Springer-Verlag, 1976.

** Henrici, Peter. Applied and Computational Complex Analysis, New York, NY: John Wiley, 1974--86. 3 Vols.

* Hille, Einar. Analytic Function Theory, New York, NY: Chelsea, 1973. 2 Vols.

Jones, William B. and Thron, Wolfgang J. Continued Fractions: Analytic Theory and Applications Reading, MA: Addison-Wesley, 1980.

*** Krantz, Steven G. Complex Analysis: The Geometric Viewpoint Washington, DC: Mathematical Association of America, 1990.

* Littlewood, J.E. Some Problems in Real and Complex Analysis Lexington, MA: D.C. Heath, 1968.

* Nehari, Zeev. Conformal Mapping Mineola, NY: Dover, 1979.

Price, G. Baley. An Introduction to Multicomplex Spaces and Functions New York, NY: Marcel Dekker, 1991.

* Remmert, Reinhold. Theory of Complex Functions New York, NY: Springer-Verlag, 1991.

*** Rudin, Walter. Real and Complex Analysis, New York, NY: McGraw-Hill, 1974, 1987. Third Edition.

** Saks, S. and Zygmund, Antoni. Analytic Functions, New York, NY: American Elsevier, 1952, 1971. Third Edition.

Smith, Kennan T. Power Series from a Computational Point of View New York, NY: Springer-Verlag, 1987.

* Springer, George M. Introduction to Riemann Surfaces Reading, MA: Addison-Wesley, 1957.

** Titchmarsh, Edward C. Theory of Functions, New York, NY: Oxford University Press, 1939. Second Edition.

Wermer, John. Banach Algebras and Several Complex Variables, New York, NY: Springer-Verlag, 1976. Second Edition.

* Weyl, Hermann. The Concept of a Riemann Surface Reading, MA: Addison-Wesley, 1964.

*** Whittaker, Edmund T. and Watson, G.N. A Course of Modern Analysis, New York, NY: Cambridge University Press, 1958, 1963. Fourth Edition.

Analysis: Functional Analysis

Beauzamy, Bernard. Introduction to Banach Spaces and Their Geometry Amsterdam: North-Holland, 1982.

Berberian, Sterling K. Introduction to Hilbert Space, New York, NY: Chelsea, 1976. Second Edition.

Bollobas, Bela. Linear Analysis New York, NY: Cambridge University Press, 1990.

Bridges, Douglas S. Constructive Functional Analysis Brooklyn, NY: Pitman, 1979.

Dieudonne, Jean. Treatise on Analysis, New York, NY: Academic Press, 1969--88. 7 Vols.

* Dunford, Nelson and Schwartz, Jacob T. Linear Operators, New York, NY: John Wiley, 1958, 1963. Parts I and II.

Flett, T.M. Differential Analysis: Differentiation, Differential Equations, and Differential Inequalities New York, NY: Cambridge University Press, 1980.

Gamelin, Theodore W. Uniform Algebras New York, NY: Chelsea, 1984.

* Gel'fand, Israel M., et al. Generalized Functions, New York, NY: Academic Press, 1964--68. 5 Vols.

* Gel'fand, Israel M.; Raikov, D.A.; and Shilov, G.E. Commutative Normed Rings New York, NY: Chelsea, 1964.

Goffman, Casper and Pedrick, George. A First Course in Functional Analysis, New York, NY: Chelsea, 1983. Second Edition.

Grothendieck, A. Topological Vector Spaces New York, NY: Gordon and Breach, 1973.

Halmos, Paul R. Introduction to Hilbert Space New York, NY: Chelsea, 1951.

Halmos, Paul R. A Hilbert Space Problem Book, New York, NY: Springer-Verlag, 1982. Second Edition.

* Hille, Einar and Phillips, R.S. Functional Analysis and Semi-Groups Providence, RI: American Mathematical Society, 1957.

* Hoffman, Kenneth. Banach Spaces of Analytic Functions Mineola, NY: Dover, 1980.

Kirillov, A.A. and Gvishiani, A.D. Theorems and Problems in Functional Analysis New York, NY: Springer-Verlag, 1982.

* Liusternik, L. and Sobolev, V. Elements of Functional Analysis New York, NY: Frederick Ungar, 1961.

Lorch, Edgar R. Spectral Theory New York, NY: Oxford University Press, 1962.

Nachbin, Leopoldo. Introduction to Functional Analysis: Banach Spaces and Differential Calculus New York, NY: Marcel Dekker, 1981.

* Naimark, M.A. Normed Rings Groningen: Wolters-Noordhoff, 1960.

** Riesz, Frigyes and Nagy, Bela Sz. Functional Analysis Mineola, NY: Dover, 1990.

** Rudin, Walter. Functional Analysis New York, NY: McGraw-Hill, 1973.

* Taylor, Angus E. and Lay, David C. Introduction to Functional Analysis, New York, NY: John Wiley, 1958, 1980. Second Edition.

** Yosida, Kosaku. Functional Analysis, New York, NY: Springer-Verlag, 1965, 1980. Sixth Edition.

Young, Nicholas. An Introduction to Hilbert Space New York, NY: Cambridge University Press, 1988.

Analysis: Operator Theory

Arveson, William. An Invitation to $C^*$-Algebras New York, NY: Springer-Verlag, 1976.

** Banach, Stefan. Theory of Linear Operators New York, NY: Elsevier Science, 1987.

Brown, Arlen and Pearcy, Carl. Introduction to Operator Theory I: Elements of Functional Analysis New York, NY: Springer-Verlag, 1977.

Gohberg, Israel and Goldberg, Seymour. Basic Operator Theory New York, NY: Birkhauser, 1981.

* Kadison, Richard V. and Ringrose, John R. Fundamentals of the Theory of Operator Algebras, New York, NY: Academic Press, 1983. Vol. I: Elementary Theory.

* Kato, Tosio. Perturbation Theory for Linear Operators, New York, NY: Springer-Verlag, 1976. Second Edition.

Analysis: Calculus of Variations

Ioffe, A.D. and Tihomirov, V.M. Theory of Extremal Problems Amsterdam: North-Holland, 1979.

Krasnov, M.L.; Makarenko, G.I.; and Kiselyov, A.I. Problems and Exercises in the Calculus of Variations Moscow: MIR, 1984.

* Troutman, John L. and Hrusa, W. Variational Calculus with Elementary Convexity New York, NY: Springer-Verlag, 1983.

Weinstock, Robert. Calculus of Variations with Applications to Physics and Engineering Mineola, NY: Dover, 1974.

Analysis: Inequalities

** Beckenbach, Edwin F. and Bellman, Richard E. An Introduction to Inequalities Washington, DC: Mathematical Association of America, 1975.

Beckenbach, Edwin F. and Bellman, Richard E. Inequalities, New York, NY: Springer-Verlag, 1961, 1965. Second Edition.

*** Hardy, G.H.; Littlewood, J.E.; and Polya, George. Inequalities, New York, NY: Cambridge University Press, 1952, 1988. Second Edition.

* Kazarinoff, Nicholas D. Analytic Inequalities New York, NY: Holt, Rinehart and Winston, 1961.

Korovkin, P.P. Inequalities Moscow: MIR, 1975, 1986.

Marshall, Albert W. and Olkin, Ingram. Inequalities: Theory of Majorization and Its Applications New York, NY: Academic Press, 1979.

Tong, Y. L. Probability Inequalities in Multivariate Distributions New York, NY: Academic Press, 1980.

Analysis: Harmonic Analysis

** Ash, J.M., ed. Studies in Harmonic Analysis Washington, DC: Mathematical Association of America, 1976.

Helson, Henry. Harmonic Analysis Belmont, CA: Wadsworth, 1991.

* Katznelson, Yitzhak. An Introduction to Harmonic Analysis, Mineola, NY: Dover, 1976. Second Edition.

Loomis, Lynn H. An Introduction to Abstract Harmonic Analysis New York, NY: Van Nostrand Reinhold, 1953.

* Rudin, Walter. Fourier Analysis on Groups New York, NY: John Wiley, 1990.

Analysis: Lie Groups and Symmetric Spaces

* Adams, J. Frank. Lectures on Lie Groups Chicago, IL: University of Chicago Press, 1982.

** Chevalley, Claude. Theory of Lie Groups Princeton, NJ: Princeton University Press, 1946.

Dieudonne, Jean. Special Functions and Linear Representations of Lie Groups Providence, RI: American Mathematical Society, 1980.

Helgason, Sigurdur. Groups and Harmonic Analysis New York, NY: Academic Press, 1984.

* Helgason, Sigurdur. Differential Geometry, Lie Groups, and Symmetric Spaces New York, NY: Academic Press, 1978.

Montgomery, Deane and Zippin, Leo. Topological Transformation Groups Melbourne, FL: Robert E. Krieger, 1974.

Sugiura, Mitsuo. Unitary Representations and Harmonic Analysis: An Introduction New York, NY: Halsted Press, 1975.

* Terras, Audrey. Harmonic Analysis on Symmetric Spaces and Applications, New York, NY: Springer-Verlag, 1985, 1988. 2 Vols.

Analysis: Nonstandard Analysis

* Davis, Martin D. Applied Nonstandard Analysis New York, NY: John Wiley, 1977.

Hurd, Albert E. and Loeb, Peter A. An Introduction to Nonstandard Real Analysis New York, NY: Academic Press, 1985.

** Robinson, Abraham. Non-standard Analysis Amsterdam: North-Holland, 1966.

Stroyan, K.D. and Luxemburg, W.A.J. Introduction to the Theory of Infinitesimals New York, NY: Academic Press, 1976.

Analysis: Special Functions

* Akhiezer, N.I. Elements of the Theory of Elliptic Functions Providence, RI: American Mathematical Society, 1990.

Andrews, George E. $q$-Series: Their Development and Applications in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra Providence, RI: American Mathematical Society, 1986.

** Artin, Emil. The Gamma Function New York, NY: Holt, Rinehart and Winston, 1964.

* Bailey, W.N. Hypergeometric Series New York, NY: Hafner Press, 1972.

** Erdelyi, Arthur, et al. Higher Transcendental Functions, New York, NY: McGraw-Hill, 1952. 2 Vols.

* Fine, Nathan J. Basic Hypergeometric Series and Applications Providence, RI: American Mathematical Society, 1988.

Gasper, G. and Rahman, M. Basic Hypergeometric Series New York, NY: Cambridge University Press, 1990.

* Olver, F.W.J. Asymptotics and Special Functions New York, NY: Academic Press, 1974.

Rivlin, Theodore J. Chebyshev Polynomials, New York, NY: John Wiley, 1974, 1990. Second Edition.

Wang, Z.X. and Guo, D.R. Special Functions Teaneck, NJ: World Scientific, 1989.