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The subject description:

 2. Algebra
    Groups and their representations (except as specified in 5 and 7). 
    Rings, algebras and modules (except as specified in 7). Algebraic K-theory. Category theory. 
    Computational algebra and applications.
    Connections with sections 1, 3, 4, 5, 6, 7, 14, 15.




Algebra: Introductory Surveys

Allenby, R.B.J.T. Rings, Fields and Groups: An Introduction to Abstract Algebra New York, NY: Edward Arnold, 1983.

    • Artin, Michael. Algebra Englewood Cliffs, NJ: Prentice Hall, 1991.

Bhattacharya, P.B.; Jain, S.K.; and Nagpaul, S.R. Basic Abstract Algebra New York, NY: Cambridge University Press, 1986.

      • Birkhoff, Garrett and Mac Lane, Saunders. A Survey of Modern Algebra, New York, NY: Macmillan, 1965, 1977. Fourth Edition.

Burnside, William Snow and Panton, Arthur William. The Theory of Equations with an Introduction to the Theory of Binary Algebraic Forms, Mineola, NY: Dover, 1960. 2 Vols.

Burton, D. Abstract Algebra Dubuque, IA: William C. Brown, 1988.

  • Childs, Lindsay. A Concrete Introduction to Higher Algebra New York, NY: Springer-Verlag, 1979.

Dean, Richard A. Classical Abstract Algebra New York, NY: Harper and Row, 1990.

  • Fraleigh, John B. A First Course in Abstract Algebra, Reading, MA: Addison-Wesley, 1976, 1989. Fourth Edition.
    • Gallian, Joseph A. Contemporary Abstract Algebra, Lexington, MA: D.C. Heath, 1986, 1990. Second Edition.

Goldstein, Larry J. Abstract Algebra: A First Course Englewood Cliffs, NJ: Prentice Hall, 1973.

+* Herstein, I.N. Abstract Algebra, New York, NY: Macmillan, 1986, 1990. Second Edition.

Hillman, Abraham P. and Alexanderson, Gerald L. A First Undergraduate Course in Abstract Algebra, Belmont, CA: Wadsworth, 1973, 1988. Fourth Edition.

  • Hungerford, Thomas W. Abstract Algebra: An Introduction Philadelphia, PA: Saunders College, 1990.

Kostrikin, A.I. Introduction to Algebra New York, NY: Springer-Verlag, 1982.

Lang, Serge. Undergraduate Algebra New York, NY: Springer-Verlag, 1987.

Marcus, Marvin. Introduction to Modern Algebra New York, NY: Marcel Dekker, 1978.

McCoy, Neal H. and Janusz, Gerald J. Introduction to Modern Algebra, Boston, MA: Allyn and Bacon, 1960, 1987. Fourth Edition.

Pinter, Charles C. A Book of Abstract Algebra New York, NY: McGraw-Hill, 1982.


Constructive and Computational Algebra

Barbeau, Edward J. Polynomials New York, NY: Springer-Verlag, 1989.

Connell, Ian. Modern Algebra: A Constructive Approach New York, NY: Elsevier Science, 1982.

  • Dobbs, David E. and Hanks, Robert. A Modern Course on the Theory of Equations Washington, NJ: Polygonal, 1980.
  • Humphreys, J.F. and Prest, M.Y. Numbers, Groups, and Codes New York, NY: Cambridge University Press, 1989.

Mines, Ray; Richman, Fred; and Ruitenburg, Wim. A Course in Constructive Algebra New York, NY: Springer-Verlag, 1988.

Sims, Charles C. Abstract Algebra: A Computational Approach New York, NY: John Wiley, 1984.


Applied Algebra

Birkhoff, Garrett and Bartee, Thomas C. Modern Applied Algebra New York, NY: McGraw-Hill, 1970.

  • Dornhoff, Larry L. and Hohn, Franz E. Applied Modern Algebra New York, NY: Macmillan, 1978.

Laufer, Henry B. Discrete Mathematics and Applied Modern Algebra Boston, MA: Prindle, Weber and Schmidt, 1984.

  • Lidl, Rudolf and Pilz, Gunter. Applied Abstract Algebra New York, NY: Springer-Verlag, 1984.

Lipson, John D. Elements of Algebra and Algebraic Computing Reading, MA: Addison-Wesley, 1981.

    • Mackiw, George. Applications of Abstract Algebra New York, NY: John Wiley, 1985.


Algebra: Advanced Surveys

+* Bourbaki, Nicolas. Elements of Mathematics: Algebra, New York, NY: Springer-Verlag, 1989, 1990. 2 Vols.

    • Cohn, Paul M. Algebra, New York, NY: John Wiley, 1974, 1982. 2 Vols., Second Edition.

+*** Herstein, I.N. Topics in Algebra, New York, NY: John Wiley, 1975. Second Edition.

+* Hungerford, Thomas W. Algebra New York, NY: Springer-Verlag, 1974.

+* Jacobson, Nathan. Lectures in Abstract Algebra, New York, NY: Springer-Verlag, 1953, 1975. 2 Vols.

+*** Jacobson, Nathan. Basic Algebra I and II, New York, NY: W.H. Freeman, 1974, 1989. Second Edition.

Kostrikin, A.I. and Shafarevich, Igor R., eds. Algebra I: Basic Notions of Algebra New York, NY: Springer-Verlag, 1990.

  • Lang, Serge. Algebra, Reading, MA: Addison-Wesley, 1965, 1984. Second Edition.

Ledermann, Walter and Vajda, Steven, eds. Algebra New York, NY: John Wiley, 1980. Handbook of Applicable Mathematics, Volume I.

+*** Mac Lane, Saunders and Birkhoff, Garrett. Algebra, New York, NY: Chelsea, 1988. Third Edition.

+*** van der Waerden, B.L. Algebra, New York, NY: Springer-Verlag, 1991. (Original title: Modern Algebra.)


Group Theory

Aschbacher, Michael. The Finite Simple Groups and Their Classification New Haven, CT: Yale University Press, 1980.

    • Budden, F.J. The Fascination of Groups New York, NY: Cambridge University Press, 1972.
  • Burn, R.P. Groups: A Path to Geometry New York, NY: Cambridge University Press, 1985, 1987.

Conway, John Horton, et al. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups New York, NY: Clarendon Press, 1985.

  • Curtis, Charles W. and Reiner, Irving. Methods of Representation Theory with Applications to Finite Groups and Orders New York, NY: John Wiley, 1981.
  • Curtis, Charles W. and Reiner, Irving. Representation Theory of Finite Groups and Associative Algebras New York, NY: John Wiley, 1962.

Dixon, J.D. Problems in Group Theory New York, NY: Blaisdell, 1967.

Feigelstock, S. Additive Groups of Rings Brooklyn, NY: Pitman, 1983.

Fuchs, L. Abelian Groups New York, NY: Academic Press, 1970.

  • Gorenstein, Daniel. The Classification of Finite Simple Groups New York, NY: Plenum Press, 1983.
    • Gorenstein, Daniel. Finite Simple Groups: An Introduction to Their Classification New York, NY: Plenum Press, 1982.

Grove, L.C. and Benson, C.T. Finite Reflection Groups, New York, NY: Springer-Verlag, 1985. Second Edition.

      • Hall, Marshall, Jr. The Theory of Groups, New York, NY: Chelsea, 1973. Second Edition.

Hall, Marshall, Jr. and Senior, J.K. Groups of Order $2^n(n eq 6)$ New York, NY: Macmillan, 1964.

Hill, Victor E. Groups, Representations, and Characters New York, NY: Hafner Press, 1975.

Johnson, D.L. Presentations of Groups New York, NY: Cambridge University Press, 1976.

  • Kaplansky, Irving. Infinite Abelian Groups, Ann Arbor, MI: University of Michigan Press, 1969. Revised Edition.
  • Kurosh, Alexander G. The Theory of Groups, New York, NY: Chelsea, 1960, 1970. 2 Vols., Second Edition.
    • Ledermann, Walter. Introduction to Group Characters, New York, NY: Cambridge University Press, 1977, 1987. Second Edition.
      • Rotman, Joseph J. An Introduction to the Theory of Groups, Needham Heights, MA: Allyn and Bacon, 1965, 1984. Third Edition.

Scott, William R. Group Theory Mineola, NY: Dover, 1987.

Serre, Jean-Pierre. Linear Representations of Finite Groups New York, NY: Springer-Verlag, 1977.

Weinstein, Michael. Examples of Groups Washington, NJ: Polygonal, 1977.

  • Weyl, Hermann. The Classical Groups: Their Invariants and Representatives Princeton, NJ: Princeton University Press, 1946.


Rings and Ideals

Cohn, Paul M. Free Rings and Their Relations, New York, NY: Academic Press, 1985. Second Edition.

  • Goodearl, K.R. and Warfield, R.B., Jr. An Introduction to Noncommutative Noetherian Rings New York, NY: Cambridge University Press, 1989.
  • Herstein, I.N. Rings with Involution Chicago, IL: University of Chicago Press, 1976.
      • Herstein, I.N. Non-Commutative Rings Washington, DC: Mathematical Association of America, 1968.
  • Jacobson, Nathan. The Structure of Rings, Providence, RI: American Mathematical Society, 1964. Revised Edition.

Jans, J. Rings and Homology New York, NY: Holt, Rinehart and Winston, 1964.

    • Kaplansky, Irving. Fields and Rings, Chicago, IL: University of Chicago Press, 1969, 1974. Revised Second Edition.

Kostrikin, A.I. and Shafarevich, Igor R., eds. Algebra II: Non-Commutative Rings, Identities New York, NY: Springer-Verlag, 1991.

  • Lambek, Joachim. Lectures on Rings and Modules, New York, NY: Chelsea, 1976. Second Edition.
  • McConnell, J.C. and Robson, J.C. Noncommutative Noetherian Rings New York, NY: John Wiley, 1988.

McCoy, Neal H. Rings and Ideals Washington, DC: Mathematical Association of America, 1948.

McCoy, Neal H. The Theory of Rings New York, NY: Chelsea, 1973.

Passman, Donald S. The Algebraic Structure of Group Rings Melbourne, FL: Robert E. Krieger, 1985.

  • Robinson, Abraham. Numbers and Ideals San Francisco, CA: Holden-Day, 1965.

Rowen, Louis Halle. Polynomial Identities in Ring Theory New York, NY: Academic Press, 1980.

  • Rowen, Louis Halle. Ring Theory, New York, NY: Academic Press, 1988. 2 Vols.
  • Sharpe, David. Rings and Factorization New York, NY: Cambridge University Press, 1987.

Small, Lance W. Noetherian Rings and Their Applications Providence, RI: American Mathematical Society, 1987.

Stenstrom, Bo. Rings of Quotients: An Introduction to Methods of Ring Theory New York, NY: Springer-Verlag, 1975.


Fields and Galois Theory

  • Adamson, Iain T. Introduction to Field Theory, New York, NY: Cambridge University Press, 1982. Second Edition.
  • Artin, Emil. Galois Theory, Notre Dame, IN: University of Notre Dame Press, 1966. Second Revised Edition.

Brawley, Joel V. and Schnibben, George E. Infinite Algebraic Extensions of Finite Fields Providence, RI: American Mathematical Society, 1989.

+* Edwards, Harold M. Galois Theory New York, NY: Springer-Verlag, 1984.

    • Gaal, Lisl. Classical Galois Theory with Examples, New York, NY: Chelsea, 1973, 1988. Fourth Edition.

Garling, D.J.H. A Course in Galois Theory New York, NY: Cambridge University Press, 1986.

      • Hadlock, Charles R. Field Theory and Its Classical Problems Washington, DC: Mathematical Association of America, 1978.

Lang, Serge. Cyclotomic Fields I and II, New York, NY: Springer-Verlag, 1978--80, 1990. Second Edition.

  • Lidl, Rudolf and Niederreiter, Harald. Introduction to Finite Fields and Their Applications New York, NY: Cambridge University Press, 1986.
  • Lieber, Lillian R. Galois and the Theory of Groups: A Bright Star in Mathesis Brooklyn, NY: Galois Institute of Mathematics and Art, 1961.
  • McCarthy, Paul J. Algebraic Extensions of Fields, New York, NY: Chelsea, 1976. Second Edition.

+Rotman, Joseph J. Galois Theory New York, NY: Springer-Verlag, 1990.

+*** Stewart, Ian. Galois Theory, New York, NY: Chapman and Hall, 1989. Second Edition.


Category Theory

  • Barr, Michael; and Wells, Charles. Category Theory for Computing Science Hemel Hemstead, UK: Prentice Hall International, 1990.

Blyth, T.S. Categories White Plains, NY: Longman, 1986.

  • Herrlich, Horst and Strecker, George E. Category Theory: An Introduction, Berlin: Heldermann Verlag, 1979. Second Edition.

Lambek, Joachim and Scott, P.J. Introduction to Higher Order Categorical Logic New York, NY: Cambridge University Press, 1986, 1988.

    • Mac Lane, Saunders. Categories for the Working Mathematician New York, NY: Springer-Verlag, 1971.

Pareigis, B. Categories and Functors New York, NY: Academic Press, 1970.


Universal Algebra

Burris, Stanley and Sankappanavar, H.P. A Course in Universal Algebra New York, NY: Springer-Verlag, 1981.

  • Cohn, Paul M. Universal Algebra Norwell, MA: D. Reidel, 1981.
  • Gratzer, George. Universal Algebra, New York, NY: Springer-Verlag, 1979. Second Edition.


K-Theory

Bass, Hyman. Algebraic $K$-Theory Redwood City, CA: Benjamin Cummings, 1968.

Silvester, John R. Introduction to Algebraic $K$-Theory New York, NY: Chapman and Hall, 1981.


Special Topics

Artin, Emil. Geometric Algebra New York, NY: John Wiley, 1957.

  • Bachmann, Friedrich; Schmidt, Eckart; and Garner, Cyril W.L. n-gons Toronto: University of Toronto Press, 1975.
  • Halmos, Paul R. Lectures on Boolean Algebras New York, NY: Springer-Verlag, 1974.

Meldrum, J.D.P. Near-rings and Their Links with Groups Brooklyn, NY: Pitman, 1985.

Monk, J. Donald and Bonnet, Robert, eds. Handbook of Boolean Algebras, Amsterdam: North-Holland, 1989. 3 Vols.

  • Montgomery, Susan, et al., eds. Selected Papers on Algebra Washington, DC: Mathematical Association of America, 1977.

Sikorski, R. Boolean Algebras New York, NY: Springer-Verlag, 1960.



Linear Algebra: Elementary

    • Anton, Howard. Elementary Linear Algebra, New York, NY: John Wiley, 1973, 1991. Sixth Edition.
    • Banchoff, Thomas F. and Wermer, John. Linear Algebra Through Geometry New York, NY: Springer-Verlag, 1983.

Bloom, David M. Linear Algebra and Geometry New York, NY: Cambridge University Press, 1979.

  • Curtis, Charles W. Linear Algebra: An Introductory Approach, New York, NY: Springer-Verlag, 1984. Fourth Edition.

Damiano, David B. and Little, John B. A Course in Linear Algebra San Diego, CA: Harcourt Brace Jovanovich, 1988.

Fraleigh, John B. and Beauregard, Raymond A. Linear Algebra, Reading, MA: Addison-Wesley, 1990. Second Edition.

  • Greub, Werner. Linear Algebra, New York, NY: Springer-Verlag, 1975. Fourth Edition.

Grossman, Stanley I. Elementary Linear Algebra, Philadelphia, PA: Saunders College, 1980, 1991. Fourth Edition.

Jacob, Bill. Linear Algebra New York, NY: W.H. Freeman, 1990.

  • Kumpel, P.G. and Thorpe, John A. Linear Algebra with Applications to Differential Equations Philadelphia, PA: Saunders College, 1983.
  • Lang, Serge. Introduction to Linear Algebra, New York, NY: Springer-Verlag, 1986. Second Edition.

Leon, Steven J. Linear Algebra with Applications, New York, NY: Macmillan, 1980, 1986. Third Edition.

Lipschutz, Seymour. Schaum's Solved Problems Series: 3000 Solved Problems in Linear Algebra New York, NY: McGraw-Hill, 1989.

  • Noble, Ben and Daniel, James W. Applied Linear Algebra, Englewood Cliffs, NJ: Prentice Hall, 1969, 1988. Third Edition.

O'Nan, Michael and Enderton, Herbert B. Linear Algebra, San Diego, CA: Harcourt Brace Jovanovich, 1990. Third Edition.

  • Rorres, Chris and Anton, Howard. Applications of Linear Algebra, New York, NY: John Wiley, 1977, 1984. Third Edition.

Rothenberg, Ronald I. Linear Algebra with Computer Applications New York, NY: John Wiley, 1983.

Smith, Larry. Linear Algebra New York, NY: Springer-Verlag, 1978.

      • Strang, Gilbert. Linear Algebra and Its Applications, San Diego, CA: Harcourt Brace Jovanovich, 1988. Third Edition.

Towers, David A. Guide to Linear Algebra Houndmills, England: Macmillan Education, 1988.

  • Tucker, Alan. A Unified Introduction to Linear Algebra: Models, Methods, and Theory New York, NY: Macmillan, 1988.


Linear Algebra: Advanced

  • Brown, William C. A Second Course in Linear Algebra New York, NY: John Wiley, 1988.

Dieudonne, Jean. Linear Algebra and Geometry Boston, MA: Houghton Mifflin, 1969.

  • Gel'fand, Israel M. Lectures on Linear Algebra Mineola, NY: Dover, 1989.

Gohberg, Israel; Lancaster, Peter; and Rodman, L. Invariant Subspaces of Matrices with Applications New York, NY: John Wiley, 1986.

      • Halmos, Paul R. Finite-Dimensional Vector Spaces New York, NY: Springer-Verlag, 1968, 1974.
    • Herstein, I.N. and Winter, David J. Matrix Theory and Linear Algebra New York, NY: Macmillan, 1968, 1988.
      • Hoffman, Kenneth and Kunze, Ray. Linear Algebra, Englewood Cliffs, NJ: Prentice Hall, 1971. Second Edition.

Jarvinen, Richard D. Finite and Infinite Dimensional Linear Spaces: A Comparative Study in Algebraic and Analytic Settings New York, NY: Marcel Dekker, 1981.

  • Kaplansky, Irving. Linear Algebra and Geometry: A Second Course New York, NY: Chelsea, 1974.
    • Lang, Serge. Linear Algebra, New York, NY: Springer-Verlag, 1987. Third Edition.

Shilov, G.E. Linear Algebra Englewood Cliffs, NJ: Prentice Hall, 1971.



Matrix Theory

Beezer, Rob, A First Course in Linear Algebra, licensed under GFDL.

    • Berman, Abraham and Plemmons, Robert J. Nonnegative Matrices in the Mathematical Sciences New York, NY: Academic Press, 1979. ISBN 0-12-092250-9
  • Davis, Philip J. Circulant Matrices New York, NY: John Wiley, 1979.

Gantmacher, Felix. Matrix Theory, New York, NY: Chelsea, 1959. 2 Vols.

A. Graham, Nonnegative Matrices and Applicable Topics in Linear Algebra, John Wiley&Sons, New York, 1987.

Graybill, Franklin A. Introduction to Matrices with Applications in Statistics Belmont, CA: Wadsworth, 1969.

Hefferon, jim, Linear Algebra(Online textbook)

Henryk Minc, Nonnegative matrices, John Wiley&Sons, New York, 1988, ISBN 0-471-83966-3

  • Horn, Roger A. and Johnson, Charles R. Matrix Analysis New York, NY: Cambridge University Press, 1985.

Householder, Alston S. The Theory of Matrices in Numerical Analysis New York, NY: Blaisdell, 1964.

Iohvidov, I.S. Hankel and Toeplitz Matrices and Forms: Algebraic Theory New York, NY: Birkhauser, 1982.

Johnson, Charles R., ed. Matrix Theory and Applications Providence, RI: American Mathematical Society, 1990.

    • Lancaster, Peter and Tismenetsky, Miron. The Theory of Matrices, New York, NY: Academic Press, 1985. Second Edition with Applications.
  • Marcus, Marvin and Minc, Henryk. Survey of Matrix Theory and Matrix Inequalities Boston, MA: Allyn and Bacon, 1964.
  • Minc, Henryk. Nonnegative Matrices New York, NY: John Wiley, 1988.

Muir, Thomas. A Treatise on the Theory of Determinants Mineola, NY: Dover, 1933.

Newman, Morris. Integral Matrices New York, NY: Academic Press, 1972.

Perlis, Sam. Theory of Matrices Reading, MA: Addison-Wesley, 1952.

Pullman, N.J. Matrix Theory and its Applications: Selected Topics New York, NY: Marcel Dekker, 1976.

Wedderburn, J.H.M. Lectures on Matrices Mineola, NY: Dover, 1934, 1964.


Linear Algebra: Special Topics

  • Campbell, S.L. and Meyer, C.D., Jr. Generalized Inverses of Linear Transformations Brooklyn, NY: Pitman, 1979.

Goodbody, A.M. Cartesian Tensors: With Applications to Mechanics, Fluid Mechanics and Elasticity New York, NY: Halsted Press, 1982.

    • Greub, Werner. Multilinear Algebra, New York, NY: Springer-Verlag, 1978. Second Edition.

Roman, Steven. The Umbral Calculus New York, NY: Academic Press, 1984.

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