Syllabus

Last modified: 25 November 2021

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: [Litvin.Litvin-2010-Skylight]
A Primer on Scientific Programming with Python, ch. 1: [Langtangen-2009-Springer]
Economic Dynamics: Theory and Computation, ch. 2: [Stachurski-2022-MITPress]

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. In addition, you can find a variety of free texts at http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html.

Introductory

The Student's Introduction to Mathematica: A Handbook for Precalculus, Calculus, and Linear Algebra: [Torrence.Torrence-2019-CambridgeUP]
Mathematical Methods for Economics: [Klein-2001-AddisonWesley]

Intermediate

Fundamental Methods of Mathematical Economics: [Chiang.Wainwright-2005-Irwin]
Mathematics for Economists: [Hoy.etal-2022-MITPress]

Advanced

Foundations of Mathematical Economics: [Carter-2001-MITPress]
Mathematical Methods and Models for Economists: [Fuente-1999-CambridgeUP],
An Introduction to Mathematical Analysis for Economic Theory and Econometrics: [Corbae.Stinchcombe.Zeman-2009-PrincetonUP] (errata: 1 | 2),
Economic Dynamics: Theory and Computation: [Stachurski-2022-MITPress]
Mathematics for Econometrics: [Dhrymes-2013-Springer]
Concavity and Optimization in Microeconomics: [Madden-1986-Blackwell]

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

[Simon.Blume-1994-WWNorton] ch.1;

Recommended

[Klein-2001-AddisonWesley] ch.1;
[Chiang.Wainwright-2005-Irwin] ch.1;
[Hoy.etal-2022-MITPress] ch. 1;

The Structure of Economic Models

Week 0 (Background)

Required

[Chiang.Wainwright-2005-Irwin] ch.2,3;

Recommended

https://cosmosmagazine.com/mathematics/why-x-marks-unknown-0

Logic and Proofs

Introduction to Logic and Proofs

Applied Discrete Structures, ch. 3: [Doerr.Levasseur-2021-Lulu]
Foundations of Mathematical Economics, ch. 1.1: [Carter-2001-MITPress]
How to Prove It: A Structured Approach, ch. 1–3: [Velleman-2019-CambridgeUP]

A Concise Introduction to Logic: by Craig DeLancy is freely available online.

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

Logic, Sets, and Recursion: [Causey-2005-JonesBartlett]
First-Order Logic: [Smullyan-1995-Dover]
Logic of Mathematics: A Modern Course of Classical Logic: [Adamowicz.etal-1997-Wiley]

Sets

Introductory level resources:

Sets, Numbers, and Functions: [Hoy.etal-2022-MITPress] ch. 2
Sets, Numbers, and Proofs: [Simon.Blume-1994-WWNorton], appendix A1

[Klein-2001-AddisonWesley] ch. 2;

Intermediate level resources:

Logic and Sets (!): [Velleman-2019-CambridgeUP], ch.1 and ch.2
Elements of Set Theory: [Ok-2007-PrincetonUP] ch. A.1
Applied Mathematics for Database Professionals: [Haan.Koppelaars-2007-Apress], ch. 4
Sets and Logic; Functions: [Stachurski-2022-MITPress], appendix A.1.1; A.1.2
Applied Discrete Structures, ch. 1, 2, 4: [Doerr.Levasseur-2021-Lulu]
Applied Mathematics for Database Professionals, ch. 1, 2: [Haan.Koppelaars-2007-Apress] ch. 1, 2;

Recommended Advanced Discussion:

An Introduction to Mathematical Analysis for Economic Theory and Econometrics, ch. 1: [Corbae.Stinchcombe.Zeman-2009-PrincetonUP]

Probability and Counting

Counting

Counting: [Hammack-2018-self] ch.3

Probability

Introduction to Probability: [Grinstead.Snell-2003-AMS] ch.1,2 https://open.umn.edu/opentextbooks/textbooks/21
Introduction to Econometrics: [Hansen-2022a-PrincetonUP], ch. 1–3 https://www.ssc.wisc.edu/~bhansen/probability/ Chaper 1: Basic Probability Theory, Chaper 2: Random Variables, Chaper 3: Parametric Distributions

Decision Making Under Risk

Attitudes, Traits, and Actions: Dispositional Prediction of Behavior in Personality and Social Psychology: Ajzen, I. (1987) , in L. Berkowitz (ed) Advances in Experimental Social Psychology 20, 1-63. San Diego: Academic Press.
Le Comportement de l'Homme Rationel Devant le Risque,: Allais, A. (1953) Critique des Postulates et Axioms de l'Ecole americaine, Econometrica 21, 503-546.
Beyond Microeconomics: conflict among interests in a multiple self as a determinant of value: Anslie, G. (1982) , in J. Elster (ed) The Multiple Self. Cambridge: Cambridge University Press.
Alternative Approaches to the Theory of Choice in Risk-Taking Situations: Arrow, K. (1951) , Econometrica 19, 404-37.
Nonconsequentialist Decisions: Baron (1994) , Behavioral and Brain Sciences 17, 1-42.
Biases in the quantitative measurement of values for public decisions: Baron, J. (1997) , Psychological Bulletin 122, 72-88.
The Economic Way of Looking at Behavior: Becker, G. (1993) , Journal of Political Economy, 101, 385-409.
Specimen Theoriae Novae th Mensura Sortis: Bernoulli, D. (1738) , Commentarii Academiae Scientiarum Imperiales Petropolitanae 5, 175-192.
Measuring values of extra-market goods: are indirect measures biased?: Bishop, R.; Heberlein, T. (1979) American Journal of Agricultural Economics 61, 926-930.
Estimating willingness to pay: an experiment: Bohm, P. (1972) , European Economic Review 3, 111-130.
Commodity Specification and the Framing of Contingent-Valuation Questions: Boyle, K. (1989) , Land Economics 65, 57-63.
Starting Point Bias in Contingent Valuation Bidding Games: Boyle, K.; Bishop, R.; Welsh, M. (1985) , Land Economics 61, 188-94.
The Role of Question Order and Respondent Experience in Contingent-Valuation Studies: Boyle, K.; Welsh, M.; Bishop, R. (1993) , Journal of Environmental Economics and Management 25, Part 2, S80-S99.
Do Biases in Probability Judgment Matter in Markets? Experimental Evidence: Camerer, C. (1987) , American Economic Review 77, 981-997.
Progress in Behavioral game Theory: Camerer, C. (1998) , Journal of Economic Perspectives, forthcoming.
Contingent Valuation and Revealed Preference Methodologies: Comparing the Estimates for Quasi-Public Goods: Carson, R. et al (1994) , University of California, San Diego Department of Economics Working Paper 94-07.
Referendum contingent valuation estimates: sensitivity to the assignment of offered values: Cameron, T.; Huppert, D. (1991) , Journal of the American Statistical Association 86, 910-918.
The Foundations of Utility: Chipman, J. (1960) , Econometrica 28, 193-224.
Restructuring: Constructive Processing of Information Displays in Consumer Choice: Coupey, E. (1994) , Journal of Consumer Research 21, 83-89.

Deaton, A.; Muellbauer, J. (1980) Economics and Consumer Behavior, Cambridge University Press: Cambridge.

Debreu, G. (1959) Theory of Value, Wiley: New York.

Inconsistent Trade-offs Between Attributes: New Evidence in Preference Assessment Biases: Delquie, P. (1993) , Management Science 39, 1382-1395.

Desvousges, W.; Johnson, R.; Dunford, R.; Boyle, K.; Hudson, S.; Wilson, N. (1992) Measuring Nonuse Damages using Contingent Valuation: An Experimental Evaluation of Accuracy. RTI Monograph 93-1: Research Triangle NC.

Contingent Valuation: Is Some Number Better than No Number?: Diamond, P.; Hausman, J. (1994) Journal of Economic Perspectives; 8, 45-64.

Davidson, D.; Suppes, P. (1957) Decision Making, Stanford: Stanford University Press.

Festinger, L. (1957) A Theory of Cognitive Dissonance, Stanford: Stanford University Press.

Fisher, I. (1930) The Theory of Interest, New York: Macmillan.

Fischoff, B. ; Welch, N. (1998), Construal Processes in Preference Assessment, Journal of Risk and Uncertainty.

The Role of Moral Sentiments in the Theory of Intertemporal Choice: Frank, R. (1992) , in G. Loewenstein and J. Elster (eds) Choice over Time, New York: Russell Sage Foundation.
Rethinking Rational Choice: Frank, R. (1990) , in R. Friedland and A. Robertson (eds) Beyond the marketplace: Rethinking economy and society. Sociology and Economics: Controversy and Integration series, New York: Aldine de Gruyter, 1990, pages 53-87.
Duration neglect in retrospective evaluations of affective episodes: Fredrickson, B.; Kahneman, D. (1993) , Journal of Personality and Social Psychology 65, 45-55.
The Utility Analysis of Choices Involving Risk: Friedman, M.; Savage, L. (1948) , Journal of Political Economy 56, 279-304.
The Importance of Routines for the Performance of Everyday Activities: Garling, T. (1992) , Scandinavian Journal of Psychology 33, 170-177.
When Do Stated Preferences (SP) Predict Actual Behavior?: Garling, T.; Gillholm, R. (1998) Working Paper, Goteborg University.
Pennies a Day: Increasing Consumer Compliance Through Temporal Re-Framing: Gourville, J. (1996) , Harvard University Working Paper.
Referendum Contingent Valuation, Anchoring, and Willingness to Pay for Public Goods: Green, D.; Jacowitz, K.; Kahneman, D.; McFadden, D. (1998) , Energy and Resources Journal
Economic Theory of Choice and the Preference Reversal Phenomena: Grether, D.; Plott, C. (1979) , American Economic Review 69, 623-638.
Measures of Cognitive Functioning in the AHEAD Study: Hertzog, R.; Wallace, R. (1996) , Journal of Gerontology 52B, 37-48.
Valuing Public Goods with the Contingent Valuation Method: A Critique: Harrison, G. (1992) , Journal of Environmental Economics and Management 23, 248-57.
Melioration: A Theory of Distributed Choice: Herrnstein,R.; Prelec, D. (1991) , Journal of Economic Perspectives 5, 137-156.
Measures of Cognitive Functioning in the AHEAD Study: Hertzog, R.; Wallace, R. (1996) Journal of Gerontology 52B, 37-48.
Ventures, Bets, and Initial Prospects: Hildreth, C. (1974) , in M Balch et al (eds) Essays on Economic Behavior Under Uncertainty, North Holland, 99-122.
Time-Consistent Preferences and Consumer Self-Control: Hoch, S. (1991) , Journal of Consumer Research 17, 492-507.
An Independent Sample Test of Yea-Saying and Starting Point Bias in Dichotomous-Choice Contingent Valuation: Holmes, T.; Kramer, R. (1995) , Journal of Environmental Economics and Management 29, 121-32.
Adding Asymmetricaly Dominated Alternatives: Violations of Regularity and the Similarity Hypothesis: Huber, J.; Payne, J.; Puto, C. (1982) , Journal of Consumer Research 9, 90-98.

Hurd, M. (1998), Anchoring Effects in the HRS: Experimental and Non-Experimental Evidence, Journal of Risk and Uncertainty.

Consumption and Savings Balances of the Elderly: Experimental Evidence on Survey Response Bias: Hurd, M; McFadden, D.; Chand, H.; Gan, L.; Merrill, A.; Roberts, M. (1997) , National Bureau of Economic Research Working Paper.
Measuring Non-use Value of Environmental Goods Using the Contingent Valuation Method: Problems of Information and Cognition and the Application of Cognitive Questionnaire Design Methods: Hutchinson, G.; Chilton, S.; Davis, J. (1995) , Journal of Agricultural Economics 46, 97-112.
When More Pain is Preferred to Less: Kahneman, D.; Fredrickson, D.; Schreiber, C.; Redelmeier, D. (1993) , Psychological Science 4, 401-405.
Valuing Public Goods: The Purchase of Moral Satisfaction: Kahneman, D.; Knetsch, J. (1992) , Journal of Environmental Economics and Management 22, 57-70.
Experimental Tests of the Endowment Effect and the Coase Theorem: Kahneman, D.; Knetsch, J.; Thaler, R. (1990) , Journal of Political Economy 98, 1325-1348.
The Endowment Effect, Loss aversion, and Status Quo bias: Kahneman, D.; Knetsch, J.; Thaler, R. (1991) , Journal of Economic Perspectives 5, 193-206.
Economists have Preferences, Psychologists Have Attitudes: An Analysis of Dollar Responses to Public Issues: Kahneman, D.; Ritov, I.; Schkade, D. (1998) , Princeton University Working Paper.

Kahneman, D.; Slovic, P.; Tversky, A., eds (1982) Judgment Under Uncertainty: Heuristics and Biases, Cambridge: Cambridge University Press.

Subjective Probability: A Judgment of Representativeness: Kahneman, D.; Tversky, A. (1972) , Cognitive Psychology 3, 430-451.
On the Psychology of Prediction: Kahneman, D.; Tversky, A. (1973) , Psychological Review 80, 237-251.
Intuitive Prediction: Biases and Corrective Procedures: Kahneman, D.; Tversky, A. (1979) , Studies in Management Science 12, 313-327.
On the Study of Statistical Institutions: Kahneman, D.; Tversky, A. (1982) , Cognition 11, 123-141.
Choices, Values, and Frames: Kahneman, D.; Tversky, A. (1984) , American Psychologist 39, 341-350.

Keynes, J. (1921) A Treatise on Probability, New York: Macmillan.

Knight, F. (1921) Risk, Uncertainty, and Profit, New York: Houghton-Mifflin.

Larrick (1993) Organizational Behavior and Human Decision Processes.

Frames of Mind in Intertemporal Choice: Lowenstein, G. (1988) , Management Science 34, 200-214.
Out of control: Visceral Influences on Behavior: Lowenstein, G. (1996) , Organizational Behavior and Decision Processes 65, 272-92.
Wouldn't It Be Nice? Predicting Future Feelings: Lowenstein, G.; Schkade, D. (1998) in E. Diener, N. Schwartz, and D. Kahneman (eds) Hedonic Psychology: Scientific Approaches to Enjoyment, Suffering, and Well-Being. New York: Russell Sage Press.
Adaptive Behavior and Economic Theory: Lucas, R. (1987) , in R. Hogarth and M. Reder (eds) Rational Choice: The Contrast Between Economics and Psychology. Chicago: University of Chicago Press.
Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty: Machina, M. (1989) , Journal of Economic Literature 32, 1622-1668.
Rational Behavior, Uncertain Prospects, and Measurable Utility: Marschak, M. (1950) , Econometrica 18, 111-141.
On Some Facets of Betting: McFadden, D. (1974) , in M Balch et al (eds) Essays on Economic Behavior Under Uncertainty, North Holland, 99-122.
Econometric Models of Probabilistic Choice: McFadden, D. (1981) , in C. Manski & D. McFadden (eds) Structural Analaysis of Discrete Data with Econometric Applications, Cambridge: MIT Press.
Contingent valuation and social choice: McFadden, D. (1994) , American Journal of Agricultural Economics 76, 689-708.
Computing Willingness-to-Pay in Random Utility Models: McFadden, D. (1997) , in R. Hartman and J. Moore (eds), Essays in Honor of John Chipman, forthcoming.
Das Unsicherheitsmoment in der Wertlehre betrachtungen im Anschluss an das sogenannte Petersburger Spiel: Menger, K. (1934) , Zeitschrift fuir Nationalokonomis Band V, Heft 4, 459-485.
Economics and the Social Sciences: Papandreou, A. (1960) , Economic Journal 60, 715- 723.
Behavioral Decision Research: A Constructive Process Perspective: Payne, J., Bettman, J.; Johnson, E. (1992) , Annual Review of Psychology 43, 87-131.

Payne, J.; Bettman, J., Schkade, D. (1998), Measuring Preferences in a Constructive World, Journal of Risk and Uncertainty, this issue.

Poulton, E. (1989) Bias in Quantifying Judgment. Hillsdale: Lawrence Erlbaum.

Poulton, E. (1994) Behavioral Decision Theory: A New Approach. New York: Cambridge University Press.

Values and principles: Some limitations on traditional economic analysis: Prelec, D. (1991) , in A. Etzioni & P. Lawrence (eds) Perspectives on Socioeconomics. London: M.E. Sharpe.
The red and the Black: Mental Accounting of Savings and Debt: Prelec, D.; Lowenstein, G. (1997) , MIT Working Paper.
Self-Deception and the Voter's Illusion,: Quattrone, G.; Tversky, A. (1986) in J. Elster (ed) The Multiple Self, Cambridge University Press.
Psychology and Economics: Rabin, M. (1996) , Journal of Economic Literature, forthcoming.
Truth and Probability: Ramsey, F. (1931) , in The Foundations of Mathematics and Other Logical Essays, Paul, Trench, Trubner.
The Relevance of Quasi-Rationality in Competitive Markets: Russell, T.; Thaler, R. (1988) , in D. Bell, H. Raiffa, & A. Tversky (eds) Decision Making: Descriptive, Normative, and Prescriptive Interactions, Cambridge University Press.
Status Quo Bias in Decision Making: Samuelson, W.; Zeckhauser, R. (1988) , Journal of Risk and Uncertainty, 1, 7-59.
How People Respond to Contingent Valuation Questions: A Verbal Protocol Analysis of Willingness to Pay for an Environmental Regulation: Schkade, D.; Payne, J (1994) , Journal of Environmental Economics and Management; 26, 88-109.
Willingness to Pay for Environmental Goods in Norway: A Contingent Valuation Study with Real Payment: Seip, K.; Strand, J. (1992) , Environmental and Resource Economics 2, 91-106.
Thinking Through Uncertainty: Nonconsequential Reasoning and Choice: Shafir, E.; Tversky, A. (1992) , Cognitive Psychology 24, 449-474.
The behavior of respondents in contingent valuation: evidence on starting bids: Silberman, J.; Klock, M. (1989) , Journal of Behavioral Economics, 18, 51-60.
Theories of Decision-Making in Economics and Behavioral Science: Simon, H. (1959) , American Economic Review 49, 253-283.
Choice in Context: Tradeoff Contrast and Extremeness Aversion: Simonson, I.; Tversky, A. (1992) , Journal of Marketing Research 29, 281-295.
An experimental comparison of three public good decision mechanisms: Smith, V. (1979) , Scandinavian Journal of Economics, 81, 198-215.
Public Good Provision and Public Bad Prevention: The Effect of Framing: Sonnemans, J.; Schram, A.; Offerman, T. (1994) , University of Amsterdam working paper.
Learning in and about Complex Systems: Sterman, J. (1994), System Dynamics Review 10, 291--330.
Process Descriptions of Decision Making: Svenson, O. (1979), Organizational Behavior and Human Performance 23, 86--112.
On the Modeling of Human Choices in Descriptive Behavioral Decision Theory: Svenson, O. (1996), Stockholm University Working Paper.
Principles of Economics: Taussig, F. (1912) Macmillan.
Mental Accounting and Consumer Choice: Thaler, R. (1985) , Marketing Science 4, 199-214.
Savings, Fungability, and Mental Accounts: Thaler, R. (1990), Journal of Economic Perspectives 4, 193-205.
Quasi-Rational Economics: Thaler, R. (1991) Russell Sage Foundation.
Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice: Thaler, R. and Johnson, E. (1990), Management Science, 36, 643--660.
Neglect of Stimulus Information in a Two-choice Task: Tune, G. (1966), Journal of General Psychology 74, 231--236.
On the Elicitation of Preferences: Descriptive and Prescriptive Considerations: Tversky, A. (1977), in Bell, D., Kenney, R., and Raiffa, H., eds., Conflicting Objectives in Decisions, Wiley: New York.
Weighing Risk and Uncertainty: Tversky, A. and Fox, C. (1995), Psychological Review 102, 269--283.
Belief in the Law of Small Numbers: Tversky, A. and Kahneman, D. (1971), Psychological Bulletin 76, 105--110.
Judgment under Uncertainty: Heuristics and Biases: Tversky, A. and Kahneman, D. (1974) Science, 185, 1124--1131.
The Framing of Decisions and the Psychology of Choice: Tversky, A.; Kahneman, D. (1981) , Science 211, 453-458.
Loss Aversion in Riskless Choice: A Reference-Dependent Model: Tversky, A.; Kahneman, D. (1991) , Quarterly Journal of Economics 107, 1039-1061.
Advances in Prospect Theory: Cumulative Representations of Uncertainty: Tversky, A.; Kahneman, D. (1992) , Journal of Risk and Uncertainty 5, 297-323.
The Causes of Preference Reversal: Tversky, A.; Slovic, P.; Kahneman, D. (1990) , American Economic Review 80, 204-217.
The Disjunction Effect in Choice Under Uncertainty: Tversky, A.; Shafir, E. (1992) , Psychological Science 3, 305-309.
Contingent Weighting in Judgment and Choice: Tversky, A.; Sattath, S.; Slovic, P. (1988) , Psychological Review 95, 371-384.
Theory of Games and Economic Behavior: von Neumann, J. and Morgenstern, O. (1947) Princeton University Press.
Giving Respondents Time to Think in Contingent Valuation Studies: A Developing Country Application: Whittington, D. et al. (1992), Journal of Environmental Economics and Management 22(3), 205-225.

Simulated Draws

Darts, Dice, and Coins: by Keith Schwarz explains Vose's alias method. https://www.keithschwarz.com/darts-dice-coins/

Binary Relations

Basic Concepts

Relations: [Velleman-2019-CambridgeUP] ch.4 offers an extremely accessible introduction to binary relations.
Relations: [Velleman-2006-CambridgeUP] ch.4 covers transitive closure.
Relations: [Ok-2007-PrincetonUP] ch. A.1.2, A.1.3, A.1.4 offers a condensed overview.
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: [Osborne.Rubinstein-2020-OpenBook]

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): [Doerr.Levasseur-2021-Lulu]
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: [Pierce-2002-MIT]
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: [Doerr.Levasseur-2021-Lulu] is an open textbook.
Discrete Mathematics and its Applications, 8th Edition,: Rosen, Kenneth H. McGraw-Hill, Inc., New York, 2019. http://www.mhhe.com/rosen/

GARP

Foundations of Economic Analysis: [Samuelson-1947-HarvardUP]
WARP Does Not Inply SARP for More Than Two Commodities: [Peters.Wakker-1994-JET]

Functions

Basics of Functions

Functions: [Velleman-2019-CambridgeUP] ch. 5
Mathematics for Economists: [Simon.Blume-1994-WWNorton] ch. 5 (covers exponents and logarithms)
Foundations of Mathematical Economics ch. 2.1: [Carter-2001-MITPress]
Functions: [Abramson-2022-OpenStax] ch. 1

Injectivity and Surjectivity

Video: Intuitive Introduction to Category Theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0

Functions: Polynomials

Foundations of Mathematical Economics: [Carter-2001-MITPress] ch 4.4
Recommended:: Bezier Curves by Paul Bourke

Functions: Exponents and Logarithms

Functions: Trigonometry and Complex Numbers

Video: Visualizing Six Trigonometric Functions via Unit Circle: by Jack L. Jackson II

[Simon.Blume-1994-WWNorton] ch.2,5; Appendix A2, A3;

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: [Zakon-2019-Trilla]
An Introduction to Mathematical Analysis for Economic Theory and Econometrics: [Corbae.Stinchcombe.Zeman-2009-PrincetonUP]

Sequences

Introductory

Sequences, Series, and Limits: [Hoy.etal-2022-MITPress] ch. 3

Intermediate

Sequences and Series: An Introduction to Mathematical Analysis: [Adams-2012-Sequences]
Convergent Sequences: [Binmore-1982-CambridgeUP] ch. 4

Videos

Video by Trefor Bazett: Limits of Sequences, Limit laws & Function Representations

Videos by Wrath of Math: Definition of the Limit of a Sequence and Connecting Function Limits and Sequence Limits

Video: Sum n Positive Squares by Mathematical Visual Proofs

Basic Topology

Topology without Tears: [Morris-2020-Topology] (http://www.topologywithouttears.net/);

Videos

Video by Dr. Peyam: Compactness

Basic Calculus

Limits, Continuity, and Derivatives

Basic Introduction to Calculus

Introduction to Calculus: [Abramson-2022-OpenStax] ch. 12

Introduction to Calculus

Derivatives and Differentials: [Simon.Blume-1994-WWNorton] ch.2-4;
Active Calculus: by Matthew Boelkins pre-calc, univariate calculus, and multivariate calculus. https://activecalculus.org/

Univariate Optimization

Mathematics for Economists, ch. 13, 14, 17, 29: [Simon.Blume-1994-WWNorton]

Linear Algebra

Vector Spaces

Mathematics for Economists, ch. 10, 11: [Simon.Blume-1994-WWNorton]

An Introduction to Matrix Algebra

Introduction to Linear Algebra: [Simon.Blume-1994-WWNorton] ch.6

[Dhrymes-2013-Springer] ch. 1;

Recommended

Foundations of Mathematical Economics ch. 3.1, 3.5: [Carter-2001-MITPress]

[Simon.Blume-1994-WWNorton] ch. 26,27,28,12;
[Klein-2001-AddisonWesley] ch. 4,5;
[Litvin.Litvin-2010-Skylight] ch 14.2

Video: Matrix Multiplication in Excel: https://www.youtube.com/watch?v=nhtKTKdx86I

Elementary Matrices

Systems of Linear Equations: [Simon.Blume-1994-WWNorton] ch.7
Matrix Algebra: [Simon.Blume-1994-WWNorton] ch.8
Video: Elementary Matrices: http://www.youtube.com/watch?v=7H3JFH3IjB0
Video: Elementary Matrices and Inverses: https://www.youtube.com/watch?v=BGE5Y6TXPUQ

More Matrix Algebra

[Simon.Blume-1994-WWNorton] ch. 9, 10, 11, 26;

Video: LU Decomposition: http://www.youtube.com/watch?v=rhNKncraJMk
Video: LU Decomposition: http://www.youtube.com/watch?v=UlWcofkUDDU
The Extraordinary SVD: [Martin.Porter-2012-AMM]

Determinants and Inverses

Determinants and Inverses: [Hoy.etal-2022-MITPress] ch. 9
Determinants: [Simon.Blume-1994-WWNorton] ch.9 (Determinants) and 26 (Determinants)

Quadratic Forms

Quadratic Forms: [Hoy.etal-2022-MITPress] ch. 10.2
Quadratic Forms: [Simon.Blume-1994-WWNorton] ch. 13.3, 16

The Comparative Statics of Linear Models

Mathematics for Economists, ch. 6-9: [Simon.Blume-1994-WWNorton]

[Simon.Blume-1994-WWNorton] ch. 26;
[Klein-2001-AddisonWesley] ch. 4,5;

Fundamental Methods of Mathematical Economics ch.5: [Chiang.Wainwright-2005-Irwin]

Introduction to Game Theory

A Course in Game Theory: Osborne, Matin, and Ariel Rubinstein, (MIT Press 1994) isbn 0-262-15041-7
Discrete Mathermatics and Game Theory: Owen, Gullermo, 1999, (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

Multivariate Calculus

Basic Multivariate Calculus

Multivariate Calculus: [Hoy.etal-2022-MITPress] ch. 11
Calculus of Several Variables: [Simon.Blume-1994-WWNorton] ch. 14

Nonlinear Comparative Statics

Comparative Statics: [Hoy.etal-2022-MITPress] ch. 14
Implicit Functions: [Simon.Blume-1994-WWNorton] ch. 15

Eigensystems

Eigensystems: [Hoy.etal-2022-MITPress] ch. 10.1
Mathematics for Economists, ch. 23: [Simon.Blume-1994-WWNorton]

Multivariate Optimization

Foundations of Mathematical Economics: [Carter-2001-MITPress]
Optimization and Stability Theory for Economic Analysis: [Beavis.Dobbs-1990-CambridgeUP]

A Class Of Methods For Solving Nonlinear Simultaneous Equations: [Broyden-1965-MathComp]

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

On the Discovery of the “Good Broyden” Method: C.G. Broyden, Journal of Mathematical Programming Volume 87, Number 2 / April, 2000 Pages 209--213
Multivariate Optimization: [Hoy.etal-2022-MITPress] ch. 12
Mathematics for Economists, ch. 17-19: [Simon.Blume-1994-WWNorton]
Foundations of Mathematical Economics, ch. 5.1-5.3: [Carter-2001-MITPress]

Constrained Multivariate Optimization

Constrained Multivariate Optimization: [Hoy.etal-2022-MITPress] ch. 13, 15

Dynamic Programming

On the Differentiability of the Value Function in Dynamic Models of Economics: [Benveniste.Scheinkman-1979-Econometrica]
Economic Dynamics: Theory and Computation: [Stachurski-2022-MITPress]

Hamiltonian Dynamics

Introduction to Hamiltonian Dynamics in Economics: [Cass_Shell-1976_Cass_Shell]

Category Theory

The core online resource is nLab.

Introductory

Video: Intuitive Introduction to Category Theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0

Intermediate

Basic Category Theory for Computer Scientists: [Pierce-1991-MIT]

Econometrics and Statistics

An Introduction to Statistical Thinking: With Applications in Python: [James.etal-2023-Springer]
Toward A Formal Science Of Economics: The Axiomatic Method in Economics and Econometrics: Stigum,Bernt P.,

Programming Languages

Matlab, Python, Julia: What to Choose in Economics?: [Coleman.Lyon.Maliar.Maliar-2020-CompEcon]

R Language (Gnu S)

S Programming: Venables, W. N., 2000, (Springer)

Julia

Julia: A Fresh Approach to Numerical Computing: [Bezanson-2017-SIAM]
Economic Dynamics: Theory and Computation: [Stachurski-2022-MITPress]

Python

Economic Dynamics: Theory and Computation: [Stachurski-2022-MITPress]

PostScript

Knowledge of PostScript is no longer necessary for most economists. Draw with TikZ instead.

PostScript Drawing: An Economist’s Guide: [Isaac-2004-SSCR]
The PostScript and PDF bible 2nd Edition.: Merz, Thomas, 2000
PostScript Language Tutorial and Cookbook: Staff, Adobe Systems Inc., 1986,
Real World PostScript: Roth, Stephen F. ed. (Addison-Wesley, 1988).

Supplementary Topics

Numerical Methods

Numerical Methods That Work: [Acton-1997-HarperRow]
Numerical Methods in Economics: [Judd-1998-MITPress]
Economic Dynamics: Theory and Computation: [Stachurski-2022-MITPress]

Learning

Learning and Expectations in Macroeconomics: [Evans.Honkapohjaa-2001-PrincetonUP]
Convergence of Least-Square Learning Mechanisms in Self-Referential Linear Stochastic Models: [Marcet.Sargent-1989-JET]
Learning, Estimation, and the Stability of Rational Expectations: [Bray-1982-JET]

Details

[Abramson-2022-OpenStax]

Abramson, Jay. (2022) Precalculus. : OpenStax. https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(OpenStax)/01:_Functions

[Acton-1997-HarperRow]

Acton, Forman S. (1997) Numerical Methods That Work. New York: Harper & Row for the Mathematical Association of America.

[Adamowicz.etal-1997-Wiley]

Adamowicz, Zofia, Pawel Zbierski, and Pawe Zbierski. (1997) Logic of Mathematics: A Modern Course of Classical Logic. : John Wiley and Sons.

[Adams-2012-Sequences]

Adams, Malcolm R. (2012) Sequences and Series: An Introduction to Mathematical Analysis. : Self published. http://www.math.uga.edu/~adams/

[Battalio.etal-1973-WEJ]

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.Dobbs-1990-CambridgeUP]

Beavis, Brian, and Ian Dobbs. (1990) Optimization and Stability Theory for Economic Analysis. Cambridge, UK: Cambridge University Press.

[Benveniste.Scheinkman-1979-Econometrica]

Benveniste, L. M., and J. A. Scheinkman. (1979) On the Differentiability of the Value Function in Dynamic Models of Economics. Econometrica 47, 727--732.

[Bezanson-2017-SIAM]

Bezanson, Jeff, et al. (2017) Julia: A Fresh Approach to Numerical Computing. SIAM review 59, 65--98. https://doi.org/10.1137/141000671

[Binmore-1982-CambridgeUP]

Binmore, Ken. (1982) Mathematical Analaysis: A Straightforward Approach. : Cambridge University Press.

[Bray-1982-JET]

Bray, M. (1982) Learning, Estimation, and the Stability of Rational Expectations. Journal of Economic Theory 26, 318--39.

[Broyden-1965-MathComp]

Broyden, C.G. (1965) A Class Of Methods For Solving Nonlinear Simultaneous Equations. Mathematics of Computation 19, 577--593.

[Carter-2001-MITPress]

Carter, Michael. (2001) Foundations of Mathematical Economics. Cambridge, MA: MIT Press.

[Cass_Shell-1976_Cass_Shell]

CASS, DAVID, and KARL SHELL. (1976) "Introduction to Hamiltonian Dynamics in Economics". In Cass, David and Shell, Karl (Eds.) The Hamiltonian Approach to Dynamic Economics, : Academic Press.

[Causey-2005-JonesBartlett]

Causey, Robert L. (2005) Logic, Sets, and Recursion. : Jones and Bartlett Learning.

[Chiang.Wainwright-2005-Irwin]

Chiang, Alpha C., and Kevin Wainwright. (2005) Fundamental Methods of Mathematical Economics. New York: McGraw-Hill/Irwin.

[Coleman.Lyon.Maliar.Maliar-2020-CompEcon]

Coleman, Chase, et al. (2020) Matlab, Python, Julia: What to Choose in Economics?. Computational Economics , . https://doi.org/10.1007/s10614-020-09983-3

[Corbae.Stinchcombe.Zeman-2009-PrincetonUP]

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-2013-Springer]

Dhrymes, Phoebus J. (2013) Mathematics for Econometrics. New York: Springer-Verlag.

[Doerr.Levasseur-2021-Lulu]

Doerr, Al, and Ken Levasseur. (2021) Applied Discrete Structures. : Lulu.

[Dudewicz.VanDerMeulen-1981-JASA]

Dudewicz, Edward J., and Edward C. Van Der Meulen. (1981) Entropy-Based Tests of Uniformity. Journal of the American Statistical Association 76, 967-974. https://www.tandfonline.com/doi/abs/10.1080/01621459.1981.10477750

[Evans.Honkapohjaa-2001-PrincetonUP]

Evans, George W., and Seppo Honkapohja. (2001) Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press.

[Fleck-2013-Self]

Fleck, Margaret M. () Building Blocks for Theoretical Computer Science. : Self published. http://mfleck.cs.illinois.edu/building-blocks/

[Fuente-1999-CambridgeUP]

de la Fuente, Angel. (1999) Mathematical Methods and Models for Economists. Cambridge, UK: Cambridge University Press.

[Grinstead.Snell-2003-AMS]

Grinstead, Charles M., and J. Laurie Snell. (2003) Introduction to Probability. : American Mathematical Society. https://open.umn.edu/opentextbooks/textbooks/21

[Haan.Koppelaars-2007-Apress]

de Haan, Lex, and Toon Koppelaars. (2007) Applied Mathematics for Database Professionals. Berkeley, CA: Apress.

[Hammack-2018-self]

Hammack, Richard. (2018) Book of Proof. Richmond, VA: self published. https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

[Hansen-2022a-PrincetonUP]

Hansen, Bruce E. (2022) Probability and Statistics for Economists. Princeton, NJ: Princeton University Press. https://www.ssc.wisc.edu/~bhansen/probability

[Hoy.etal-2022-MITPress]

Hoy, Michael, et al. (2022) Mathematics for Economists. Cambridge, MA: MIT Press.

[Isaac-2004-SSCR]

Isaac, Alan G. (2004) PostScript Drawing: An Economist's Guide. Social Science Computer Review 22, 512--530.

[James.etal-2023-Springer]

James, Gareth, et al. (2023) An Introduction to Statistical Thinking: With Applications in Python. New York, NY: Springer.

[Judd-1998-MITPress]

Judd, Kenneth L. (1998) Numerical Methods in Economics. Cambridge, MA: MIT Press.

[Klein-2001-AddisonWesley]

Klein, Michael W. (2001) Mathematical Methods for Economics. Boston, MA: Addison-Wesley.

[Langtangen-2009-Springer]

Langtangen, Hans Petter. (2009) A Primer on Scientific Programming with Python. : Springer.

[Litvin.Litvin-2010-Skylight]

Litvin, Maria, and Gary Litvin. (2010) Mathematics for the Digital Age and Programming in Python. Andover, MA: Skylight Publishing.

[Madden-1986-Blackwell]

Madden, Paul. (1986) Concavity and Optimization in Microeconomics. : Blackwell Publishers.

[Marcet.Sargent-1989-JET]

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.Porter-2012-AMM]

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-2020-Topology]

Morris, Sidney A. (2020) Topology without Tears. urlhttp://www.sidneymorris.net/: Self published. http://www.topologywithouttears.net/

[Ok-2007-PrincetonUP]

Ok, Efe A. (2007) Real Analysis with Economic Applications. Princeton, New Jersey: Princeton University Press.

[Osborne.Rubinstein-2020-OpenBook]

Osborne, Martin J., and Ariel Rubinstein. (2020) Models in Microeconomic Theory. Cambridge, UK: Open Book Publishers. https://www.openbookpublishers.com/product/1159

[Peters.Wakker-1994-JET]

Peters, Hans, and Peter Wakker. (1994) WARP Does Not Inply SARP for More Than Two Commodities. Journal of Economic Theory 62, .

[Pierce-1991-MIT]

Pierce, Benjamin C. (1991) Basic Category Theory for Computer Scientists. Cambridge, MA: MIT Press.

[Pierce-2002-MIT]

Pierce, Benjamin C. (2002) Types and Programming Languages. ** , .

[Rosen-2011-McGrawHill]

Rosen, Kenneth H. (2011) Discrete Mathematics and Its Applications. Columbus, OH: McGraw-Hill Education.

[Rudin-1976-McGrawHill]

Rudin, Walter. (1976) Principles of Mathematical Analysis. New York: McGraw-Hill.

[Samuelson-1947-HarvardUP]

Samuelson, Paul A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.

[Sen-1970-HoldenDay]

Sen, Amartya. (1970) Collective Choice and Social Welfare. San Francisco: Holden-Day.

[Simon.Blume-1994-WWNorton]

Simon, Carl P., and Lawrence Blume. (1994) Mathematics for Economists. New York: W.W. Norton & Company, Inc..

[Smullyan-1995-Dover]

Smullyan, Raymond M. (1995) First-Order Logic. : Dover.

[Stachurski-2022-MITPress]

Stachurski, John. (2022) Economic Dynamics: Theory and Computation. Cambridge, MA: MIT Press.

[Torrence.Torrence-2019-CambridgeUP]

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-2003-Pearson]

Trench, William F. (2003) Introduction to Real Analysis. : Digital Commons (originally Pearson Education). http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml

[Uzawa-2014_Giorgi.Kjeldsen]

Uzawa, Hirofumi. (2014) "The Kuhn-Tucker Theorem in Concave Programming". In Giorgi, Giorgio and Kjeldsen, Tinne Hoff (Eds.) Traces and Emergence of Nonlinear Programming, : Springer Basel.

[Velleman-2006-CambridgeUP]

Velleman, Daniel J. (2006) How to Prove It: A Structured Approach. Cambridge, UK: Cambridge University Press.

[Velleman-2019-CambridgeUP]

Velleman, Daniel J. (2019) How to Prove It: A Structured Approach. Cambridge, UK: Cambridge University Press.

[Zakon-2019-Trilla]

Zakon, Elias. (2019) Mathematical Analysis. West Lafayette, IN: The Trilla Group. https://math.libretexts.org/@go/page/19020

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!)

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

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)

Levy, Haim and Moshe Levy and Sorin Solomon, 2000, Microscopic Simulation of Financial Markets (New York: Academic Press) isbn: 0-12-445890-4

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

Mak, Ronald L. Writing Compilers and Interpreters: An Applied Approach Using C++ 2nd ed. July 1996 John Wiley & Sons, Incorporated ISBN 0471113530

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

Fractals and Chaos : An Illustrated Course by Paul S. Addison

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

Ericsson and Irons, 1994, Exogeneity, Oxford University Press.

Mac Lane, Saunders, 1985 Mathematics: Form and Function, Springer-Verlag ISBN 0387962174 (libary cannot get it; it's out of print)

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

Ebbinghaus, H.-D., J. Flum, W. Thomas, Jorg Flum, W. Thomas, Ann S. Ferebee, Margit Mebmer Mathematical logic (Springer-Verlag)

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)

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)

Conrad, Jon M., 1999, Resource Economics, Cambridge University Press ISBN 0-521-64974-9

Lauwerier, Hans, 1992, Fractals (Princeton University Press)

Ruud, Paul A., 2000, An Introduction to Classical Econometric Theory (Oxford University Press)

Chambers, John M., 1998, Programming with Data (springer)

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.

Merton, Robert, 1992, Continuous Time Finance (Blackwell Publishers) isbn 0-631-18508-9