References References
Many of the references listed here were used in preparing the original 1980's version of this book. In most cases, the mathematics that they contain is still worth reading for further background. Many can be found online, in university libraries or used bookstores. A few references more current references have been added.
[1]
Allenby, R.B.J.T, Rings, Fields and Groups, Edward Arnold, 1983.
[2]
Appel, K., and W. Haken, Every Planar Map Is 4-colorable, Bull, Am. Math. Soc. 82 (1976): 711-12.
[3]
Arbib, M. A., A. J. Kfoury, and R. N. Moll, A Basis for Theoretical Computer Science, New York: Springer-Verlag, 1981.
[4]
Austin, A. Keith, An Elementary Approach to NP-Completeness American Math. Monthly 90 (1983): 398-99.
[5]
Beardwood, J., J. H. Halton, and J. M. Hammersley, The Shortest Path Through Many Points Proc. Cambridge Phil. Soc. 55 (1959): 299-327.
[6]
Ben-Ari, M, Principles of Concurrent Programming, Englewood Cliffs, NJ: Prentice-Hall, 1982.
[7]
Berge, C, The Theory of Graphs and Its Applications, New York: Wiley, 1962.
[8]
Bogart, Kenneth P, Combinatorics Through Guided Discovery, 2005.
Note
This book may be freely downloaded and redestributed under the terms of the GNU Free Documentation License (FDL), as published by the Free Software Foundation.
[9]
Bronson, Richard, Matrix Methods, New York: Academic Press, 1969.
[10]
Busacker, Robert G., and Thomas L. Saaty, Finite Graphs and Networks, New York: McGraw-Hill, 1965.
[11]
Connell, Ian, Modern Algebra, A Constructive Introduction, New York: North-Holland, 1982.
[12]
Denning, Peter J., Jack B. Dennis, and Joseph L. Qualitz, Machines, Languages, and Computation, Englewood Cliffs, NJ: Prentice-Hall, 1978.
[13]
Denning, Peter J, Multigrids and Hypercubes. American Scientist 75 (1987): 234-238.
[14]
Dornhoff, L. L., and F. E. Hohn, Applied Modern Algebra, New York: Macmillan, 1978.
[15]
Even, S, Graph Algorithms, Potomac, MD: Computer Science Press, 1979.
[16]
Fisher, J. L, Application-Oriented Algebra, New York: Harper and Row, 1977.
[17]
Ford, L. R., Jr., and D. R. Fulkerson, Flows in Networks, Princeton, NJ: Princeton Univesity Press, 1962.
[18]
Fraleigh, John B, A First Course in Abstract Algebra, 3rd ed. Reading, MA: Addison-Wesley, 1982.
[19]
Gallian, Joseph A, Contemporary Abstract Algebra, D.C. Heath, 1986.
[20]
Gallian, Joseph A, Group Theory and the Design of a Letter-Facing Machine, American Math. Monthly 84 (1977): 285-287.
[21]
Hamming, R. W, Coding and Information Theory, Englewood Cliffs, NJ: Prentice-Hall, 1980.
[22]
Hill, F. J., and G. R. Peterson, Switching Theory and Logical Design, 2nd ed. New York: Wiley, 1974.
[23]
Hofstadter, D. R, Godel, Escher, Bach: An Eternal Golden Braid, New York: Basic Books, 1979.
[24]
Hohn, F. E, Applied Boolean Algebra, 2nd ed. New York: Macmillan, 1966.
[25]
Hopcroft, J. E., and J. D. Ullman, Formal Languages and Their Relation to Automata, Reading, MA: Addison-Wesley, 1969.
[26]
Hu, T. C, Combinatorial Algorithms, Reading, MA: Addison-Wesley, 1982.
[27]
Knuth, D. E, The Art of Computer Programming. Vol. 1, Fundamental Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1973.
[28]
Knuth, D. E, The Art of Computer Programming. Vol. 2, Seminumerical Algorithms, 2nd ed., Reading, MA: Addison-Wesley, 1981.
[29]
Knuth, D. E, The Art of Computer Programming. Vol. 3, Sorting and Searching, Reading, MA: Addison-Wesley, 1973.
[30]
Knuth, D. E, The Art of Computer Programming. Vol. 4A, Combinatorial Algorithms, Part 1, Upper Saddle River, New Jersey: Addison-Wesley, 2011.
[31]
Kulisch, U. W., and Miranker, W. L, Computer Arithmetic in Theory and Practice, New York: Academic Press, 1981.
[32]
Lipson, J. D, Elements of Algebra and Algebraic Computing, Reading, MA: Addison-Wesley, 1981.
[33]
Liu, C. L, Elements of Discrete Mathematics, New York: McGraw-Hill, 1977.
[34]
O'Donnell, Analysis of Boolean Functions.
Note
A book about Fourier analysis of boolean functions that is being developed online in a blog.
[35]
Ore, O, Graphs and Their Uses, New York: Random House, 1963.
[36]
Parry, R. T., and H. Pferrer, The Infamous Traveling-Salesman Problem: A Practical Approach Byte 6 (July 1981): 252-90.
[37]
Pless, V, Introduction to the Theory of Error-Correcting Codes, New York: Wiley-Interscience, 1982.
[38]
Purdom, P. W., and C. A. Brown, The Analysis of Algorithms, Holt, Rinehart, and Winston, 1985.
[39]
Quine, W. V, The Ways of Paradox and Other Essays, New York: Random House, 1966.
[40]
Ralston, A, The First Course in Computer Science Needs a Mathematics Corequisite, Communications of the ACM 27-10 (1984): 1002-1005.
[41]
Solow, Daniel, How to Read and Do Proofs, New York: Wiley, 1982.
[42]
Sopowit, K. J., E. M. Reingold, and D. A. Plaisted The Traveling Salesman Problem and Minimum Matching in the Unit Square.SIAM J. Computing, 1983,12, 144–56.
[43]
Standish, T. A, Data Structure Techniques, Reading, MA: Addison-Wesley, 1980.
[44]
Stoll, Robert R, Sets, Logic and Axiomatic Theories, San Francisco: W. H. Freeman, 1961.
[45]
Strang, G, Linear Algebra and Its Applications, 2nd ed. New York: Academic Press, 1980.
[46]
Tucker, Alan C, Applied Combinatorics, 2nd ed. New York: John Wiley and Sons, 1984.
[47]
Wand, Mitchell, Induction, Recursion, and Programming, New York: North-Holland, 1980.
[48]
Warshall, S, A Theorem on Boolean Matrices Journal of the Association of Computing Machinery, 1962, 11-12.
[49]
Weisstein, Eric W. Strassen Formulas, MathWorld--A Wolfram Web Resource, http://mathworld.wolfram.com/StrassenFormulas.html.
[50]
Wilf, Herbert S, Some Examples of Combinatorial Averaging, American Math. Monthly 92 (1985).
[51]
Wilf, Herbert S. generatingfunctionology, A K Peters/CRC Press, 2005
Note
The 1990 edition of this book is available at https://www.math.upenn.edu/~wilf/DownldGF.html
[52]
Winograd, S, On the Time Required to Perform Addition, J. Assoc. Comp. Mach. 12 (1965): 277-85.
[53]
Wilson, R., Four Colors Suffice - How the Map Problem Was SolvedPrinceton, NJ: Princeton U. Press, 2013.