Syllabus Supplement
Supplementary Reading in Mathematical Economics
This is an idiosyncratic collection of supplemental resources for Econ-705.
Supplementary Software
Python
Students interested in attempting the homework problems in Python should look at `Python 101`_ and then:
_ Python 101: https://python101.pythonlibrary.org/
- Mathematics for the Digital Age and Programming in Python; ch. 2, 3, 9
- A Primer on Scientific Programming with Python, ch. 1
- Economic Dynamics: Theory and Computation, ch. 2
Consider downloading the free (for academic use) Enthought Deployment Manager. (This includes the NumPy, Matplotlib and SciPy libraries.)
Additional Useful Texts
A small amount of required reading from these texts is listed on the syllabus. Aside from this, the following texts are “recommended reading” only if you are interested in pursuing specific topics beyond the scope of this course. These books include the following:
- An Introduction to Mathematical Analysis for Economic Theory and Econometrics
[Corbae.Stinchcombe.Zeman-2009-PrincetonUP] (errata: 1 | 2),
- Economic Dynamics: Theory and Computation
- Mathematics for Econometrics
- Foundations of Mathematical Economics
- Mathematical Methods and Models for Economists
- Mathematics for Economists
- Concavity and Optimization in Microeconomics
Finally, you can find a variety of free texts at http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html, and we may refer to
- Introduction to Real Analysis
Prerequisite Readings
Complete the following readings before the first week of class. In addition, please read Chapter 2 of my Mathematica Introduction. and [Torrence.Torrence-2019-CambridgeUP] ch. 1 and 2.
Why Use Math in Economics?
Week 0 (Background)
Required
Recommended
[Hoy-2001-MITPress] ch. 1;
The Structure of Economic Models
Week 0 (Background)
Required
[Chiang.Wainwright-2005-Irwin] ch.2,3;
Recommended
Functions: Exponents, Logarithms, and Polynomials
Week 0 (Background)
Required
[Simon.Blume-1994-WWNorton] ch.2,5; Appendix A2, A3;
Functions: Trigonometry and Complex Numbers
Week 0 (Background)
Required
[Simon.Blume-1994-WWNorton] ch.2,5; Appendix A2, A3;
Calculus Basics
Week 0 (Background)
[Simon.Blume-1994-WWNorton] ch.2-4;
Recommended:
- Active Calculus
by Matthew Boelkins pre-calc, univariate calculus, and multivariate calculus. https://activecalculus.org/
Logic and Proofs
- Foundations of Mathematical Economics, ch. 1.1
- How to Prove It: A Structured Approach, ch. 1–3
- Applied Discrete Structures, ch. 3
[Doerr.Levasseur-2021-Lulu]
More Logic
Babbay, Dov M. and C. J. Hogger and J. A. Robinson (eds), 1995, Handbook of Logic in Artificial Intelleigence and Logic Programming vol. 4 (isbn: 85379103)
Cleave, John P. A Study of Logics (Oxford : Clarendon Press ; New York : Oxford University Press, 1991) ISBN: 0198532113
Sets
Introductory level resources:
[Litvin.Litvin-2010-Skylight] ch. 5, 6, 8, 12.4, 13, 14.3
[Klein-2001-AddisonWesley] ch. 2;
[Hoy-2001-MITPress] ch. 2;
Intermediate level resources:
- Applied Mathematics for Database Professionals, ch. 4
- Economic Dynamics: Theory and Computation appendix A.1.1
Functions in Math and Computing
Week 0
Required
- How to Prove It: A Structured Approach
- Foundations of Mathematical Economics ch. 2.1
Recommended
[Torrence.Torrence-2019-CambridgeUP] ch. 3.1, 3.2, 3.5, 3.6;
[Stachurski-2009-MITPress] appendix A.1.2;
[Klein-2001-AddisonWesley] ch. 2;
[Chiang.Wainwright-2005-Irwin] ch.2,3;
de la Fuente 1;
Probability and Counting
- Introduction to Probability
[Grinstead.Snell-2003-AMS] ch.1,2 https://open.umn.edu/opentextbooks/textbooks/21
- Introduction to Econometrics
[Hansen-2021-self]_, ch. 1–3 https://www.ssc.wisc.edu/~bhansen/probability/ Chaper 1: Basic Probability Theory, Chaper 2: Random Variables, Chaper 3: Parametric Distributions
Linear Algebra
An Introduction to Matrix Algebra
Week 0
Required
[Simon.Blume-1994-WWNorton] ch. 6, 7, 8, 9, 10, 11, 26;
[Dhrymes-2013-Springer] ch. 1;
Recommended
- Foundations of Mathematical Economics ch. 3.1, 3.5
[Simon.Blume-1994-WWNorton] ch. 26,27,28,12;
[Klein-2001-AddisonWesley] ch. 4,5;
[Litvin.Litvin-2010-Skylight] ch 14.2
Elementary Matrices
- Video: Elementary Matrices
- Video: Elementary Matrices and Inverses
More Matrix Algebra
- Video: LU Decomposition
- Video: LU Decomposition
- The Extraordinary SVD
The Comparative Statics of Linear Models
Week 0
Required
[Simon.Blume-1994-WWNorton] ch. 6, 7, 8, 9, 26;
[Klein-2001-AddisonWesley] ch. 4,5;
Recommended
- Fundamental Methods of Mathematical Economics ch.5
Introduction to Game Theory
Osborne, Matin, and Ariel Rubinstein, A Course in Game Theory (MIT Press 1994) isbn 0-262-15041-7
Owen, Gullermo, 1999, Discrete Mathermatics and Game Theory (Kluwer) isbn 0-7923-8511-X
Linear Algebra: Core Theory
Understanding Linear Algebra by David Austin is an open textbook.
Strang, Gilbert, Linear Algebra & Its Applications 4th ed. (or later) (Harcourt College Publishers)
Linear Algebra by Jim Hefferon
Topical Readings
The following readings are not required except to the extent discussed in class. They provide some supplementary resources for those who want them.
Binary Relations
Basic Concepts
- How to Prove It: A Structured Approach, ch.4
[Velleman-2019-CambridgeUP] offers an extremely accessible introduction to binary relations.
- An Introduction to Mathematical Analysis for Economic Theory and Econometrics, ch.2
[Corbae.Stinchcombe.Zeman-2009-PrincetonUP] offers an introduction that emphasizes consumer theory.
- Building Blocks for Theoretical Computer Science, ch. 6-9
[Fleck-2013-Self] introduces binary relations from a CS perspective.
- Models in Microeconomic Theory, ch. 1-2
Applications
- Collective Choice and Social Welfare
[Sen-1970-HoldenDay] applies binary relations to the analysis of social choice.
Further Concepts
- Foundations of Mathematical Economics
[Carter-2001-MITPress] ch. 1.2 (Ordered Sets) and 1.6 (Preference Relations) and 2 (Functions).
- Applied Discrete Structures, ch. 6 (relations) and 7 (functions)
- Group Theory: Important Preliminaries
Video by Steven Roman: https://www.youtube.com/watch?v=ehqJeSGtv_4
- Partially Ordered Sets and Indicator Functions
Video by Richard Southwell: https://www.youtube.com/watch?v=Y_QaYRwkT2c (Note: in this video, indicator functions have a range of {F,T} instead of {0,1}.)
Computational Applications
- Types and Programming Languages, ch. 2
- Applied Mathematics for Database Professionals, ch. 4
[Haan.Koppelaars-2007-Apress] introduce binary relations in the context of relational databases.
Discrete Math
- Applied Discrete Structures
[Levasseur.Doerr-2021-Lulu]_ is an open textbook.
GARP
Introduction to Real Analysis
- Principles of Mathematical Analysis
[Rudin-1976-McGrawHill] is a lovely short introduction for the mathematically inclined.
- Introduction to Real Analysis
[Trench-2003-Pearson] (open textbook)
- Mathematical Analysis
- An Introduction to Mathematical Analysis for Economic Theory and Econometrics
Sequences
- Sequences and Series: An Introduction to Mathematical Analysis
Video: Sum n Positive Squares by Mathematical Visual Proofs
Topology
- Topology without Tears
[Morris-2020-Topology] (http://www.topologywithouttears.net/);
Optimization
- Foundations of Mathematical Economics
- Optimization and Stability Theory for Economic Analysis
- A Class Of Methods For Solving Nonlinear Simultaneous Equations
Dennis, J.E., Jr., Schnabel, R.B. (1981): A New Derivation Of Symmetric Positive Definite Secant Updates. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M., eds., Nonlinear Programming 4, 1980. Academic Press, New York, NY, 167–199
C.G. Broyden On the Discovery of the “Good Broyden” Method Journal Mathematical Programming Volume 87, Number 2 / April, 2000 Pages 209-213
Dynamic Programming
- On the Differentiability of the Value Function in Dynamic Models of Economics
- Economic Dynamics: Theory and Computation
Supplementary Topics
Numerical Methods
- Numerical Methods That Work
- Numerical Methods in Economics
- Economic Dynamics: Theory and Computation
Learning
- Learning and Expectations in Macroeconomics
- Convergence of Least-Square Learning Mechanisms in Self-Referential Linear Stochastic Models
- Learning, Estimation, and the Stability of Rational Expectations
Logic
Details
Acton, Forman S. (1997) Numerical Methods That Work. New York: Harper & Row for the Mathematical Association of America.
Adams, Malcolm R. (2012) Sequences and Series: An Introduction to Mathematical Analysis. : Self published. http://www.math.uga.edu/~adams/
Battalio, Raymond C., et al. (1973) A Test of Consumer Demand Theory Using Observations of Individual Consumer Purchases. Western Economic Journal 11, 411--428.
Beavis, Brian, and Ian Dobbs. (1990) Optimization and Stability Theory for Economic Analysis. Cambridge, UK: Cambridge University Press.
Benveniste, L. M., and J. A. Scheinkman. (1979) On the Differentiability of the Value Function in Dynamic Models of Economics. Econometrica 47, 727--732.
Bray, M. (1982) Learning, Estimation, and the Stability of Rational Expectations. Journal of Economic Theory 26, 318--39.
Broyden, C.G. (1965) A Class Of Methods For Solving Nonlinear Simultaneous Equations. Mathematics of Computation 19, 577--593.
Carter, Michael. (2001) Foundations of Mathematical Economics. Cambridge, MA: MIT Press.
Causey, Robert L. (2005) Logic, Sets, and Recursion. : Jones & Bartlett Learning.
Chellas, Brian F. (1980) Modal Logic : An Introduction. : Cambridge University Press.
Chiang, Alpha C., and Kevin Wainwright. (2004) Fundamental Methods of Mathematical Economics. New York: McGraw-Hill/Irwin.
Corbae, Dean, Maxwell B. Stinchcombe, and Juraj Zeman. (2009) An Introduction to Mathematical Analysis for Economic Theory and Econometrics. Princeton, NJ: Princeton University Press.
Dhrymes, Phoebus J. (2013) Mathematics for Econometrics. New York: Springer-Verlag.
Doerr, Al, and Ken Levasseur. (2021) Applied Discrete Structures. : Lulu.
Evans, George W., and Seppo Honkapohja. (2001) Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press.
Fleck, Margaret M. () Building Blocks for Theoretical Computer Science. : Self published. http://mfleck.cs.illinois.edu/building-blocks/
de la Fuente, Angel. (1999) Mathematical Methods and Models for Economists. Cambridge, UK: Cambridge University Press.
Grinstead, Charles M., and J. Laurie Snell. (2003) Introduction to Probability. : American Mathematical Society. https://open.umn.edu/opentextbooks/textbooks/21
de Haan, Lex, and Toon Koppelaars. (2007) Applied Mathematics for Database Professionals. Berkeley, CA: Apress.
Hoy, Michael. (2001) Mathematics for Economists. Cambridge, MA: MIT Press.
Judd, Kenneth L. (1998) Numerical Methods in Economics. Cambridge, MA: MIT Press.
Klein, Michael W. (2001) Mathematical Methods for Economics. Boston, MA: Addison-Wesley.
Langtangen, Hans Petter. (2009) A Primer on Scientific Programming with Python. : Springer.
Litvin, Maria, and Gary Litvin. (2010) Mathematics for the Digital Age and Programming in Python. Andover, MA: Skylight Publishing.
Madden, Paul. (1986) Concavity and Optimization in Microeconomics. : Blackwell Publishers.
Marcet, Albert, and Thomas J. Sargent. (1989) Convergence of Least-Square Learning Mechanisms in Self-Referential Linear Stochastic Models. Journal of Economic Theory 48, 337--68.
Martin, Carla D., and Mason A. Porter. (2012) The Extraordinary SVD. The American Mathematical Monthly 119, 838-851. https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.119.10.838
Morris, Sidney A. (2020) Topology without Tears. urlhttp://www.sidneymorris.net/: Self published. http://www.topologywithouttears.net/
Osborne, Martin J., and Ariel Rubinstein. (2020) Models in Microeconomic Theory. Cambridge, UK: Open Book Publishers. https://www.openbookpublishers.com/product/1159
Peters, Hans, and Peter Wakker. (1994) WARP Does Not Inply SARP for More Than Two Commodities. Journal of Economic Theory 62, .
Pierce, Benjamin C. (2002) Types and Programming Languages. ** , .
Rosen, Kenneth H. (2011) Discrete Mathematics and Its Applications. Columbus, OH: McGraw-Hill Education.
Rudin, Walter. (1976) Principles of Mathematical Analysis. New York: McGraw-Hill.
Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.
Sen, Amartya. (1970) Collective Choice and Social Welfare. San Francisco: Holden-Day.
Simon, Carl P., and Lawrence Blume. (1994) Mathematics for Economists. New York: W.W. Norton & Company, Inc..
Smullyan, Raymond M. (1995) First-Order Logic. : Dover.
Stachurski, John. (2009) Economic Dynamics: Theory and Computation. Cambridge, MA: MIT Press.
Torrence, Bruce F., and Eve A. Torrence. (2019) The Student's Introduction to Mathematica(R): A Handbook for Precalculus, Calculus, and Linear Algebra. : Cambridge University Press.
Trench, William F. (2003) Introduction to Real Analysis. : Digital Commons (originally Pearson Education). http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml
Velleman, Daniel J. (2006) How to Prove It: A Structured Approach. Cambridge, UK: Cambridge University Press.
Velleman, Daniel J. (2019) How to Prove It: A Structured Approach. Cambridge, UK: Cambridge University Press.
Zakon, Elias. (2019) Mathematical Analysis. West Lafayette, IN: The Trilla Group. https://math.libretexts.org/@go/page/19020
Zofia Adamowicz, Pawel Zbierski. (1997) Logic of Mathematics: A Modern Course of Classical Logic. : John Wiley & Sons.
Benveniste, A. and M. Metivier and P. Priouret, 1990, Adaptive Algorithms and Stochastic Approximations (Springer-Verlag)
Fractals for the Classroom : Complex Systems and Mandelbrot Set by Heinz-Otto Peitgen (Editor), Hartmut Jurgens, Dietmar Saupe, Evan M. Maletsky Vol 2 (September 1992) Springer Verlag; ISBN: 0387977228 (PLEASE NOTE THIS IS VOLUME 2!)
Hoy, Micahel et al., 2001, Mathematics for Economists (Cambridge, MA: MIT Press) isbn: 0-262-08294-2
Golub, Gene H. and Charles F. Van Loan, 1996, Matrix Computations (Johns Hopkins Series in the Mathematical Sciences) Johns Hopkins Univ Pr; ISBN: 0801854148
Hiriart-Urruty, Jean-Baptiste, and Claude Lemarechal, Convex Analysis and Minimization Algorithms I: Fundamentals, Comprehensive Studies in Mathematics, vol. 305 (NY: Springer, 1993)
Horn, Roger A. and Charles R. Johnson (Editor), 1990, Matrix Analysis Cambridge Univ Press; ISBN: 0-521-30586-1
Horn, Roger A. and Charles R. Johnson (Editor), 1994, Topics in Matrix Analysis Cambridge Univ Press; ISBN: 0521467136
Hayashi, Fumio, 2000, Econometrics (Princeton, NJ: Princeton University Press) isbn: 0-691-01018-8
Gourieroux, Christian and Joann Jasiak, 2001, Financial Econometrics (Princeton, NJ: Princeton University Press) isbn: 0-691-08872-1
Metcalf, Michael and John K. Reid, 1996, The F Programming Language (Oxford University Press) isbn: 850026-2 Chow, Gregory C., 1996, Dynamic Economics: Organization by the Lagrange Method (Oxford: Oxford University Press)
Beavis, Brian, and Ian Dobbs, Optimization and Stability Theory for Economic Analysis (Cambridge: Cambridge University Press, 1990). (Used only as a reference on mathematical techniques.)
Harville, David A., 1997, Matrix Algebra from a Statistician's Perspective (Springer)
Schott, James R., 1996, Matrix Analysis for Statistics (Wiley)
Dhrymes, Phoebus J., 2000, Mathematics for Econometricians 3rd Edition (Springer)
Levy, Haim and Moshe Levy and Sorin Solomon, 2000, Microscopic Simulation of Financial Markets (New York: Academic Press) isbn: 0-12-445890-4
Novshek, William, 1993, Mathematics for Economists (New York: Academic Press) isbn: 0-12-522575-x
Wichers, Robert, 1996, A Theory of Individual Behavior (New York: Academic Press) isbn: 0-12-748450-7
Dhrymes, Phoebus, 1998, Time Series, Unit Roots, and Cointegration (New York: Academic Press) isbn: 0-12-214695-6
Neftci, Salih N., 2000, An Introduction to the Mathematics of Financial Derivatives, 2nd Ed (New York: Academic Press) isbn: 0-12-515392-9
Nerlove, Marc and David M. Grether and Jose L. Varvalho, 1995, Analysis of Economic Time Series: A Synthesis (New York: Academic Press) isbn: 0-12-515751-7
Yaffee, Robert and Monnie McGee, 2000, Introduction to Time Series Analysis and Forecasting: with Applications of SAS and SPSS (New York: Academic Press) isbn: 0-12-767870-0
Watt, David A. and Brown, Deryck F., Programming Language Processors in Java: Compilers & Interpreters Feb. 2000 Prentice-Hall. New Jersey. ISBN: 0130257869
Mak, Ronald L. Writing Compilers and Interpreters: An Applied Approach Using C++ 2nd ed. July 1996 John Wiley & Sons, Incorporated ISBN 0471113530
Konrad Knopp, 1990, Theory and Application of Infinite Series (New York: Dover) isbn: 0486661652
Moore, James C., Mathematical methods for economic theory vols. 1 & 2 . Studies in Economic Theory,vol. 9 & 10. Heidelberg and New York:Springer,1999.Pp. xii,414. ISBN 3 540 66235 9
Merz, Thomas, 2000, The PostScript and PDF bible 2nd Edition.
Fractals and Chaos : An Illustrated Course by Paul S. Addison
Advances in Computational Economics, vol.14, 2000, (Boston: Kluwer Academic) ISBN 0-7923-8665-5
Powers, Daniel A., 2000, Statistical Methods for Categorical Data Analysis (New York: Academic Press) isbn: 0-12-563736-5
Billot, Antoine, 1995, Economic theory of Fuzzy Equilibria: An Axiomatic Analysis 2nd edition (Heidelberg: springer) isbn 3-540-60200-3
Driscoll, Daniel, 1995, Strengthening Policy Analysis: Econometric Tests Using SPSS/PC+, SAS PC, & GAUSS-386 Microcomputers in Policy Research Ser., Vol. 2 (Washington, DC: International Food Policy Research Institute) ISBN 0896293300
Ericsson and Irons, 1994, Exogeneity, Oxford University Press.
Fausett, Laurene V., 1999. Applied numerical analysis using MATLAB (Upper Saddle River, NJ : Prentice Hall) ISBN: 0133198499
Mac Lane, Saunders, 1985 Mathematics: Form and Function, Springer-Verlag ISBN 0387962174 (libary cannot get it; it's out of print)
Mancosu, Paolo (ed), From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s (New York : Oxford University Press, 1998.) Call Number: QA8.6 .F757 1998
Pliska, Stanley R., 1997, Introduction to Mathematical Finance (Blackwell Publishers) isbn: 1-55786-945-6
Numerical methods in finance edited by L.C.G. Rogers and D. Talay (Cambridge ; New York : Cambridge University Press, 1997) ISBN: 0521573548
Salomon, D., 1999, Computer Graphics and Geometric Modeling (Springer) isbn: 0-387-98682-0
Sigmon, Kermit N., 1997, MATLAB Primer (5th ed. or more recent) (Boca Raton, FL: C R C Press LLC) ISBN 0849313058
Stroeker, R. J. and J. F. Kasshoek, 1999, Discovering Mathematics with Maple: an interactive exploration for mathematicians, engineers, and econometricians (Basel and Boston: Birkhauser) isbn: 0817660917
Van Loan, Charles F., 1997, Introduction to scientific computing: a matrix-vector approach using MATLAB (Upper Saddle River, N.J. : Prentice Hall) ISBN: 0131254448
Ebbinghaus, H.-D., J. Flum, W. Thomas, Jorg Flum, W. Thomas, Ann S. Ferebee, Margit Mebmer Mathematical logic (Springer-Verlag)
Rosen, Kenneth H. Discrete Mathematics and its Applications, Fourth Edition, McGraw-Hill, Inc., New York, 1999. isbn 0-07-289905-0
Loukides, Mike and Andy Oram. Programming with GNU software Sebastopol, CA : O'Reilly & Associates, c1997.
Pfaffenberger, Bryan, 1999, Linux Clearly Explained (New York: Academic Press) isbn: 0-12-553169-9
Freeman, Alan and Guglielmo Carchedi (eds), 1996, Marx and non-equilibrium economics (Cheltenhaum, UK ; Brookfield, US : Edward Elgar).
Chu, C. Y. Cyrus, 1998, Population Dynamics (Oxford University Press)
Dawid, Herbert, 1999, Adaptive Learning by Genetic Algorithms: Analytical Results and Applications to Econom8ic Models 2nd Ed (NY: Springer)
Staff, Adobe Systems Inc., 1986, PostScript Language Tutorial and Cookbook (Reading,Massachusetts: Addison Wesley Longman, Incorporated) ISBN 0201101793
Roth, Stephen F. ed. Real World PostScript (Addison-Wesley, 1988).
Davies, A. J. and Samuels, P., 1996, An Introduction to Computational Geometry for Curves & Surfaces Oxford Applied Mathematics and Computing Science Ser. (Oxford University Press, Incorporated)
Berg, Mark D., 1997, Computational Geometry: Algorithms and Applications (Springer-Verlag New York, Incorporated)
Farin, G., 1988, Curves and Surfaces for Computer Aided Geometric Design (New York: Academic Press)
Korsch, H.J. and J.J. Jodl, 1999, Chaos: A Program Collection for the PC (Springer)
Conrad, Jon M., 1999, Resource Economics, Cambridge University Press ISBN 0-521-64974-9
Lauwerier, Hans, 1992, Fractals (Princeton University Press)
Paeth, Alan W. (Editor) Graphics Gems V
Ruud, Paul A., 2000, An Introduction to Classical Econometric Theory (Oxford University Press)
Venables, W. N., 2000, S Programming (Springer)
Chambers, John M., 1998, Programming with Data (springer)
Stigum,Bernt P., Toward A Formal Science Of Economics : The Axiomatic Method in Economics and Econometrics HB71 .S825
Velupillai, K., 2000, Computable Economics (Oxford University Press) isbn 829527-8
Choquet, Gustave, 1983 Geometry in a Modern Setting Translated from the original French text: L'enseignement de la geometrie. London: Kershaw Publishing Company Limited.
Soper, Jean and Phil Hobbs, 1999, Mathematics for Economics and Business (Blackwell Publishers) isbn 0-631-21189-6
Merton, Robert, 1992, Continuous Time Finance (Blackwell Publishers) isbn 0-631-18508-9