zakimath’s blog

Abstract Algebra:

1. Abstract Algebra, 2nd Edition; Pierre Antoine Grillet; Springer; 2007.
2. Abstract Algebra, 3rd Edition; I.N. Herstein; Prentice-Hall; 1996.
3. Abstract Algebra, 3rd Edition; David S. Dummit and Richard M. Foote; John Wiley & Sons, Inc.; 2004.
4. Advanced Modern Algebra; Joseph J. Rotman; Prentice Hall; 2003.
5. A First Course in Abstract Algebra, 6th Edition; John B. Fraleigh; Addison-Wesley, 2000.
6. Algebra; Thomas W. Hungerford; Springer; 1974.
7. Algebra: An Approach via Module Theory; William A. Adkins and Steven H. Weintraub; Springer; 1999.
8. Algebra, rev 3rd Edition; Serge Lang; Springer, 2002.
9. Algebra, 3rd Edition; Saunders Mac Lane & Garrett Birkhoff; American Mathematical Society, 1999.
10. Applications of Abstract Algebra with MAPLE; Richard E. Klima, Neil Sigmon, and Ernest Stitzinger; CRC Press; 1999.
11. Schaum’s Outline of Theory and Problems of Abstract Algebra, 2nd Edition; Frank Ayres and Lloyd R. Jaisingh; McGraw-Hill; 2004.
12. Undergraduate Algebra, 3rd Edition; Serge Lang; Springer; 2005.

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Algorithm, Computation, and Complexity Theory:

1. Algebraic Complexity Theory; Peter Burgisser; Michael Clausen, and M. Amin Shokrollahi; Springer; 1997.
2. Algorithms; Robert Sedgewick; Addison-Wesley; 1983.
3. Algorithms and Theory of Computation Handbook; Edited by Mikhail J. Atallah; CRC Press; 1999.
4. Complexity and Cryptography: An Introduction; John Talbot and Dominic Welsh; Cambridge University Press; 2006.
5. Complexity Theory and Cryptology: An Introduction to Cryptocomplexity; Jorg Rothe; Springer; 2005.
6. Complexity Theory: Exploring the Limits of Efficient Algorithms; Ingo Wegene; Springer; 2005.
7. Computational Complexity: A Modern Approach; Sanjeev Arora and Boaz Barak; Cambridge University Press; 2009.
8. Introduction to Algorithms, 2nd Edition; Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein; MIT Press; 2002.

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Category Theory:

1. Categories and Functors; Bodo Pareigis; Academic Press; 1970.
2. Categories for the Working Mathematician, 2nd Edition; Saunders Mac Lane; Springer; 1998.
3. Handbook of Categorical Algebra Vol.1 and 2: Basic Category Theory; Francis Borceux; Cambridge University Press; 1994.
4. Theory of Categories; Barry Mitchell; Academic Press; 1965.

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Computational Algebraic Geometry and Commutative Algebra:

1. A Singular: Introduction to Commutative Algebra; Gert-Martin Greuel and Gerhard Pfister; Springer; 2008.
2. Commutative Algebra with a View Toward Algebraic Geometry; David Eisenbud; Springer.
3. Computational Commutative Algebra 1 and 2; Martin Kreuzer and Lorenzo Robbiano; Springer; 2005.
4. Computing in Algebraic Geometry: A Quick Start using SINGULAR; Wolfram Decker and Christoph Lossen; Springer, 2006.
5. Grobner Bases: A Computational Approach to Commutative Algebra; Thomas Becker and Volker Weispfenning; Springer; 1993.
6. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition; David Cox, John Little, and Donal O’Shea; Springer; 2007.
7. Introduction to Algebraic Geometry; Brendan Hassett; Cambridge University Press; 2007.
8. Undergraduate Commutative Algebra; Miles Reid; Cambridge University Press; 1995
9. Using Algebraic Geometry, 2nd Edition; David Cox, John Little, and Donal O’Shea; Springer; 2005.

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Discrete Mathematics and Combinatorics:

1. A First Course in Discrete Mathematics; Ian Anderson; Springer; 2001.
2. Analytic Combinatorics; Philippe Flajolet and Robert Sedgewick; Cambridge University Press; 2009.
3. An Introduction to Combinatorics; Alan Slomson; Chapman & Hall; 1991.
4. Discrete Mathematics: Elementary and Beyond; L. Lovász, J. Pelikán, and K. Vesztergombi; Springer; 2003.
5. Discrete Mathematics Using a Computer, 2nd Edition; John O’Donnell, Cordelia Hall and Rex Page; Springer; 2006.
6. Handbook of Discrete and Combinatorial Mathematics; Kenneth H. Rosen, et.al; CRC-Press; 2000.
7. Invitation to Discrete Mathematics, 2nd Edition; J. Matousek and Jaroslav Nesetril; Oxford University Press; 2008.
8. Schaum’s Outline of Discrete Mathematics, 3rd Edition; Seymour Lipschutz and Marc Lars Lipson; McGraw-Hill; 2007.

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Elliptic Curves:

1. Advanced Topics in the Arithmetic of Elliptic Curves; Joseph H. Silverman; Springer-Verlag; 1994.
2. Elliptic Curves; Anthony W. Knapp; Princeton University Press; 1992.
3. Elliptic Curves, 2nd Edition; Dale Husemöller; Springer; 2004.
4. Elliptic Curves: A Computational Approach; Susanne Schmitt and Horst G. Zimmer; Walter de Gruyter; 2003.
5. Elliptic Curves and Their Applications to Cryptography: An Introduction; Andreas Enge; Kluwer Academic Publisher; 1999.
6. Elliptic Curves: Number Theory and Cryptography, 2nd Edition; Lawrence C. Washington; Chapman & Hall/CRC; 2008.
7. Handbook of Elliptic and Hyperelliptic Curve Cryptography; Edited by Henri Cohen & Gerard Frey; Chapman & Hall/CRC; 2006.
8. Rational Points on Elliptic Curves; Joseph H. Silverman and John Tate; Springer; 1992.
9. The Arithmetic of Elliptic Curves, 2nd Edition; Joseph H. Silverman; Springer; 2009.

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Field and Galois Theory:

1. Exploratory Galois Theory; John Swallow; Cambridge University Press; 2004.
2. Field Arithmetic, 2nd Edition; Michael D. Fried and Moshe Jarden; Springer; 2005.
3. Galois Theory; Emil Artin and Arthur N. Milgram; University of Notre Dame Press; 1971.
4. Introduction to Finite Fields and Their Applications; Rudolf Lidl and Harald Niederreiter; Cambridge University Press; 1986.

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Graph Theory:

1. Algebraic Graph Theory; Chris Godsil and Gordon Royle; Springer; 2001.
2. Graph Theory; J.A. Bondy and U.S.R. Murty; Springer; 2008.
3. Graph Theory; Frank Harary; Addison-Wesley; 1969.
4. Graph Theory, Electronic Editon; Reinhard Diestel; Springer-Verlag; 2000.
5. Handbook of Graph Theory; Edited by Jonathan L. Gross and Jay Yellen; CRC Press; 2003.
6. Introduction to Graph Theory, 4th Edition; Robin J. Wilson; Addison Wesley Longman; 1972.

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Group Theory:

1. A Course in Group Theory; John F. Humphreys; Oxford University Press; 1996.
2. An Introduction to the Theory of Groups, 4th Edition; Joseph J. Rotman; Springer; 1995.
3. Combinatorial Group Theory; Roger C. Lyndon and Paul E. Schupp; Springer; 1977.
4. Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations; Wilhelm Magnus, Abraham Karrass & Donald Solitar; Dover Publications; 1976.
5. Handbook of Computational Group Theory; Derek F. Holt, Bettina Eick, and Eamonna A. O’Brien; Chapman & Hall/CRC; 2005.
6. The Theory of Finite Groups: An Introduction; Hans Kurzweil Bernd Stellmacher; Springer; 2004.

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Homological Algebra:

1. A Course in Homological Algebra; P.J. Hilton and U. Stammbach; Springer; 1971.
2. An Elementary Approach to Homological Algebra; L.R. Vermani; Chapman & Hall; 2003.
3. Methods of Homological Algebra; Sergei I. Gelfand and Yuri I. Manin; Springer; 1996.

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Linear Algebra:

1. A Polynomial Approach to Linear Algebra; Paul A. Fuhrmann; Springer; 1996.
2. Advanced Linear Algebra, 2nd Edition; Steven Roman; Springer, 2005.
3. Handbook of Linear Algebra; Edited by Leslie Hogben; Chapman & Hall/CRC; 2007.
4. Linear Algebra, 2nd Edition; Kenneth Hoffman and Ray Kunze; Prentice-Hall; 1971.
5. Linear Algebra, 3rd Edition; Serge Lang; Springer; 1987.
6. Schaum’s Theory and Problems of Linear Algebra, 2nd Edition; Seymour Lipschutz; McGraw-Hill; 1991.

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Matrix and Generalized Inverse Theory:

1. Matrices Over Commutative Rings; William C. Brown; Marcel Dekker, Inc.; 1993.
2. The Theory of Generalized Inverses Over Commutative Rings; K.P.S. Bhaskara Rao; Taylor & Francis; 2002.

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Number Theory:

1. A Computational Introduction to Number Theory and Algebra; Victor Shoup; Cambridge University Press; 2008.
2. A Course in Number Theory and Cryptography, 2nd Edition; Neal Koblitz; Springer; 1994.
3. Elementary Number Theory and Cryptography; Maria Welleda Baldoni, Ciro Ciliberto, Giulia Maria Piacentini Cattaneo; Springer-Verlag; 2009.
4. Elementary Number Theory and Its Applications; Kenneth H. Rosen; Addison-Wesley; 1992.
5. Number Story: From Counting to Cryptography; Peter M. Higgins, Springer; 2008.
6. Number Theory for Computing, 2nd Edition; Song Y. Yan; Springer; 2002.
7. Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity, 5th Edition; Manfred Schroeder; Springer; 2009.

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Representation Theory:

1. Groups and Representations; J.L. Alperin with Rowen B. Bell; Springer; 1995.
2. Introduction to Lie Algebras and Representation Theory; James E. Humphreys; Springer-Verlag; 1972.
3. Representation Theory: A First Course; William Fulton & Joe Harris; Springer; 1991.
4. Representation Theory of Finite Groups: Algebra and Arithmetic; Steven H.Weintraub; American Mathematical Society; 2003.

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Ring and Module Theory:

1. A Course in Ring Theory; Donald S. Passman; American Mathematical Society; 2004.
2. Foundations of Module and Ring Theory: A Handbook for Study and Research; Robert Wisbauer; Gordon and Breach Science Publishers; 1991.
3. Rings and Categories of Modules, 2nd Edition; Frank W. Anderson and Kent R. Fuller; Springer-Verlag; 1992.

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Semigroup Theory:

1. An Introduction to Semigroup Theory; J.M. Howie; Academic Press; 1976.
2. Fundamentals of Semigroup Theory; J.M. Howie; Clarendon Press-Oxford; 2003.
3. The Algebraic Theory of Semigroups, Vol.2; A.H. Clifford and G.B. Preston; American Mathematical Society (AMS); 1967.

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Topology and Algebraic Topology:

1. Algebraic Topology; Allen Hatcher; Cambridge University Press; 2002.
2. Algebraic Topology; Edwin H. Spanier; McGraw-Hill; 1963;
3. Algebraic Topology: A First Course; William Fulton; Springer; 1995.
4. General Topology; John L. Kelley; Springer; 1955.
5. Lectures on Algebraic Topology; Sergey V. Matveev; European Math. Society;  2006.
6. Topology: A First Course; James R. Munkres; Prentice-Hall; 1974.
7. Topology, 2nd Edition; James R. Munkres; Prentice-Hall; 2000.