Welcome to the ECOMATH x LBYMATH Webpage!

Shortened course syllabi

What you see in this webpage is a shortened version of the course syllabi for Mathematical Economics (ECOMATH) and Mathematical Economics Laboratory (LBYMATH) available in Animospace.

Basic information

  1. You are enrolled in both ECOMATH and LBYMATH V24.
  2. The prerequisites of both courses are ECOCAL2 and LBYCALC.
  3. ECOMATH and LBYMATH are co-requisites.
  4. ECOMATH is one of the prerequisites to MIC1ECO, MAC1ECO, ECONSTA.
  5. We meet for ECOMATH Mondays 1245-1415 face-to-face and Thursdays 1245-1415 synchronously (unless otherwise informed).
  6. We meet for LBYMATH Mondays 1615-1715 face-to-face.
  7. We have two websites: one at Animospace and one here. I maintain a course diary here.
  8. Passing mark is 60%.

Course description

ECOMATH

This course serves as an introduction to mathematics for economic analysis at the undergraduate level. The course discusses concepts on linear algebra, optimization and tools for comparative statics. Topics include determinants of matrices and matrix inversion, systems of linear equations, unconstrained and constrained optimization. The course also covers economic applications from consumer and production theory.

LBYMATH

The course aims to discuss how to solve computational problems in economics using mathematical software. Students will be introduced to mathematical software packages, such as Mathematica, MATLAB, and/or Python, that are convenient, powerful, and practical to mathematical economic analysis.

Main textbook

We will be using the following textbook (abbreviated as EMEA):

Sydsæter, K., Hammond, P., & Strøm, A. (2012). Essential Mathematics for Economic Analysis (4th ed.). Pearson Education Limited. Borrow from Internet Archive.

Course outline

Below is a tentative course outline and we may have to adjust, depending on the circumstances.

Weeks Topics Readings from EMEA
1-3 Single-variable optimization Chapter 8
4-6 Two-variable optimization Chapter 13
7-9 Constrained optimization Chapter 14
10-12 Matrix algebra Chapters 15 and 16

LBYMATH follows the same scheduling as ECOMATH, but some of the most essential aspects of Python will be introduced in the first meetings.

References

ECOMATH

The following references have physical copies available at the DLSU Library Reserve Section, 8th Floor of the Henry Sy Hall and most are also available for digital borrowing through the Internet Archive.

Pemberton, M. & Rau, N. (2016). Mathematics for Economists: An Introductory Textbook (4th ed.). Manchester University Press. Borrow from Internet Archive.

Harrison, M. & Waldron, P. (2011). Mathematics for Economics and Finance. Routledge.

Klein, M. W. (2002). Mathematics for Economists: An Introductory Textbook (2nd ed.). Pearson Education Inc. Borrow from Internet Archive.

Hess, P. N. (2002). Using Mathematics in Economic Analysis (2nd ed.). Pearson Education Inc. Borrow from the Internet Archive.

Hoy, M., Livernois, J., McKenna, C., Rees, R., & Stengos, T. (2001). Mathematics for Economics (2nd ed.). The MIT Press. Borrow from Internet Archive.

Sydsæter, K. & Hammond, P. (1995). Mathematics for Economic Analysis. Pearson Education Inc. Borrow from Internet Archive.

The following references are more recent, meaning they come from the past five years. But we do not necessarily have physical or digital access to the newest editions, even if they may be available in the market. Of course, there are exceptions.

Margalit, D., Rabinoff, J. & Williams, B. (2024). Interactive Linear Algebra (UBC ed.). Visit online textbook draft.

Hoy, M., Livernois, J., McKenna, C., Rees, R., & Stengos, T. (2022). Mathematics for Economics (4th ed.). The MIT Press.

Sydsæter, K., Hammond, P., Strøm, A., & Carvajal, A. (2021). Essential Mathematics for Economic Analysis (6th ed.). Pearson Education Limited.

Because of accreditation requirements, I am compelled to brush aside my modesty and refer to the following materials which may still be relevant for the current course:

Pua, A. A. Y. (2024). Integral Calculus for Economic Analysis. Visit online textbook draft.

Pua, A. A. Y. (2023). Piecewise Interpolation, Numerical Differentiation, and Numerical Integration. Retrieved from https://apsacad.neocities.org/numerical-2023-10-05.html.

LBYMATH

The references and the main textbook in ECOMATH are useful for LBYMATH. In addition, the following references are very recent and useful for exploration:

Tsukada, M., Kobayashi, Y., Kaneko, H., Takahasi, S. E., Shirayanagi, K., & Noguchi, M. (2024). Linear algebra with Python: Theory and Applications. Springer.

Sargent, T. J. & Stachurski, J. (2024). Python Programming for Economics and Finance. Visit the online textbook website.

Sargent, T. J. & Stachurski, J. (2024). A First Course in Quantitative Economics with Python. Visit the online textbook website.

Sargent, T. J. & Stachurski, J. (2024). Intermediate Quantitative Economics with Python. Visit the online textbook website.

Walls, P. (2022). Mathematical Python. Visit the online textbook website.

Because of accreditation requirements, I am compelled to brush aside my modesty and refer to the following material which may still be relevant for the current course. This reference is more appropriate for the Julia programming language but the material can be mapped into Python.

Pua, A. A. Y. (2023). Piecewise Interpolation, Numerical Differentiation, and Numerical Integration. Retrieved from https://apsacad.neocities.org/numerical-2023-10-05.html.

Software and connection to LBYMATH

The course is taught in an integrated manner with the laboratory co-requisite course LBYMATH. Although the focus of LBYMATH is the use of Python in ECOMATH, we may have occasion to use Desmos, Excel, Maxima, Julia, or Wolfram Alpha. Depending on the software used, you may be expected to know some code, some algorithms, and some setup for the course requirements.

Course requirements

ECOMATH

  1. Group quizzes (20%)
  2. Group homework assignments (10%)
  3. Long exams 1, 2, and 3 (weighted as 18%, 24%, and 28%, respectively): These requirements are timed and scheduled in advance. They are tentatively set on 2024-05-27, 2024-07-08, and 2024-07-29.

LBYMATH

  1. Peer and self-evaluation for the class exercises (10%)
  2. Long exams 1, 2, and 3 (weighted as 30%, 30%, and 30%, respectively): These requirements are timed and scheduled in advance. They are tentatively set on 2024-05-27, 2024-07-08, and 2024-07-29.

Class policies

Be guided by the student handbook regarding conduct and attendance. Additional policies may be given in class, if necessary. The biggest hurdle of any student is the inability to read, comprehend, and follow instructions. Make sure to keep yourself informed.

Refer to full syllabus for exam policy, late homework policy, and other policies related to online sessions.

Course diary

Long Exam 03, 2024-07-29, face-to-face

Lecture 19, 2024-07-25, online

Lab 8, 2024-07-22, face-to-face

  1. More practice involving Chapter 14
  2. Implementing KKT in SymPy
  3. Matrices

Lecture 18, 2024-07-22, face-to-face

Lecture 17, 2024-07-18, online

  1. Recap if the motivation for nonlinear programming problems with inequality constraints
  2. Recipe aka the KKT conditions: Finding solutions to KKT conditions involves a different style of solving systems of equations and inequalities
  3. What makes the recipe different from the Lagrange multiplier method
  4. The meaning behind the phrase complementary slackness
  5. Worked on Section 14.8 Examples 1 and 2
  6. Visualization of Section 14.8 Example 2
  7. Checking sufficient conditions
  8. Notes

Lab 7, 2024-07-15, face-to-face

  1. Use SymPy to set up and check Section 14.1 Examples 1 and 3.
  2. Use SymPy to check second-order conditions for both examples.
  3. To do: Rework Example 3 by incorporating the assumptions oon the parameters of the model.

Lecture 16, 2024-07-15, face-to-face

  1. Recap of everything we have done for the Lagrange method
  2. Moved on to Section 14.3 where multiple stationary points of the Lagrangian can occur
  3. Worked on a visualization and geometric interpretation of Section 14.3
  4. Pointed out how to check sufficient conditions (did not develop the argument anymore)
  5. Motivated the case of inequality constraints in Section 14.8

Lecture 15, 2024-07-11, online

  1. Completed the argument as to why the Lagrange multiplier has a very neat interpretation
  2. Worked on some examples and exercises
  3. Visualization of the Lagrange method and using that as a stepping stone to understand why the Lagrange method works
  4. Develop the analytical argument as to why the recipe looks the way it does
  5. Notes

Long Exam 02, 2024-07-08, face-to-face

Coverage for ECOMATH: Chapters 8 and 13

Coverage for LBYMATH: Everything until Lab 6

Lecture 14, 2024-07-04, online

  1. Introduced constrained optimization and contrasted with what was taught before
  2. You have actually done some form of constrained optimization in previous chapters! Refer to the substitution method in Section 14.1 Example 1 and Section 13.5 Exercise 3.
  3. Introduce the recipe for Lagrange’s method.
  4. Worked on some examples and made connections with future topics in the majors
  5. Motivated the point of introducing the Lagrange multiplier
  6. Notes

Lab 6, 2024-06-18, face-to-face

  • Discussed the motivation for studying Section 13.7 Exercise 5

  • Discussed the workflow to solve Section 13.7 Exercise 5 by hand and how to transfer to SymPy

  • Setup portion

from sympy import *
p, w, r = symbols('p w r', real = True, positive = True)
K, L = symbols('K L', real = True, positive = True)
pi = symbols('pi', real = True)
Q = Function('F')(K, L)
pi = p*Q-w*L-r*K
  • Distinguish between regular inputs \((K, L)\) with optimal inputs \((K^*, L^*)\)
Kstar = Function('K')(w,r,p)
Lstar = Function('L')(w,r,p)
  • Target for this code is to derive expressions for \(\partial K^*/\partial w\) (call this x) and \(\partial L^*/\partial w\) (call this y):
x, y = symbols('x y', real = True)
eq1 = Derivative(Derivative(pi, K).doit().subs({K:Kstar, L:Lstar}), w).doit().subs({Derivative(K, w).subs({K:Kstar, L:Lstar}):x, Derivative(L, w).subs({K:Kstar, L:Lstar}):y})
eq2 = Derivative(Derivative(pi, L).doit().subs({K:Kstar, L:Lstar}), w).doit().subs({Derivative(K, w).subs({K:Kstar, L:Lstar}):x, Derivative(L, w).subs({K:Kstar, L:Lstar}):y})
solve([eq1, eq2], [x, y])

Lecture 13, 2024-06-18, face-to-face

NOTE: This is a Tuesday with a Monday schedule!!

  1. Group quiz 04
  2. Worked mainly on the envelope theorem
  3. Group HW02
  4. Reading assignment for the coming meetings: Sections 14.1 to 14.5

Lecture 12, 2024-06-13, online

  1. Extending the extreme value theorem to functions of two variables

  2. Short discussion on convex sets vs closed and bounded sets (contrast between Sections 13.2 and 13.5)

  3. Worked out Section 13.5 Exercise 3: some details are left to students to complete

  4. Extensions of Sections 13.1-13.5 to functions of three or more variables

  5. Reading assignment for next meeting: Sections 13.5, 13.6 (Focus on “A Useful Result”), 13.7, 14.1

  6. Practice exercises: Section 13.5 Example 1, all Exercises (except 5d, 7)

  7. Notes

Lab 5, 2024-06-10, face-to-face

  1. Mostly reviewed the material for Lab 4
  2. More LaTeX stuff introduced
  3. Worked on Section 13.3 Exercise 1, made plots using the plotting templates in Lab 4
  4. To do: Section 13.3 Exercise 3

Lecture 11, 2024-06-10, face-to-face

  1. Group quiz 03
  2. Worked on Section 13.4 Exercise 5 on duopoly

Lecture 10, 2024-06-06, online

  1. Discussed Examples 1, 2, and 4 of Section 13.4

  2. Reading assignment: Section 13.4, 13.5, 13.6 (Focus on “A Useful Result”), 13.7

  3. Practice exercises: All examples of Section 13.4, Exercises 1 to 3 and 5 of Section 13.4

  4. Notes

Lab 4, 2024-06-03, face-to-face

  1. Take up skipped material from Lab 3 about Taylor polynomials
  2. Lab 4
  3. Lab 4 self-evaluation form

Lecture 9, 2024-06-03, face-to-face

  1. Group quiz 02
  2. Discussed Sections 13.2 and 13.3: Pay attention to the similarities and differences between Chapter 8 and Chapter 13!
  3. Practice Exercises: All Examples and Exercises of Section 13.2, all Examples of Section 13.3, Exercises 1 to 5 of Section 13.3

Lecture 8, 2024-05-30, online

  1. Discussed Section 13.1

    • Pay attention to the notation of partial derivatives.
    • First order necessary conditions for a maximum or minimum
    • Used Desmos to plot bits and pieces of the function given in Section 13.1 Example 1: connections to shapes encountered in high school, e.g. parabolas, circles, ellipses
    • Spent time on traces and level curves of a surface
    • Section 13.1 Example 3: Interpreting first-order conditions

  2. Discussed first part of Section 13.2: Compare and contrast Theorems 13.1.1 and 13.2.1.

  3. To review functions of two variables, consider Sections 5.1 to 5.3 of the chapter Extensions to functions of two variables of my textbook draft in ECOCAL2 or Chapter 11 of EMEA.

  4. Reading assignment for next meeting: Sections 13.1, 13.2, 13.3

  5. Practice exercises: All examples and exercises of Sections 13.1

  6. Notes

Long Exam 01, 2024-05-27, face-to-face

What to bring for ECOMATH exam:

  1. Pens and extra pens
  2. Non-programmable scientific calculator
  3. University ID with picture

ECOMATH Coverage: Chapter 8 except “The Mean Value Theorem” in Section 8.4, and “More General Definition sof Concave and Convex Functions” in Section 8.7.

What to bring for LBYMATH exam:

  1. Pens and extra pens
  2. University ID with picture

LBYMATH Coverage: Everything, refer to this for what to practice on.

Lecture 7, 2024-05-23, online

  1. Mostly practiced exercises
  2. Notes

Lab 3, 2024-05-20, face-to-face

  1. Continue the remaining part of Lab 2

  2. Lab 3

  3. Practice for the upcoming long exam:

    • Redo the labs. Practice using Google Colab and Live SymPy Shell. For Google Colab you need to have from sympy import * at the beginning. If you want to plot graphs in Google Colab, you need to run from matplotlib import * at the beginning.
    • Skip Lab 3 “Understanding why optimization works”.
    • What we did not do in class but you should work on: Lab 1 Exercises 7, 11, and 13; Lab 3 Exercise 3C to 3E.
    • Practice making a notebook which will document the code and the answers to exercises you may find in EMEA or in the lab. Any example and exercise in EMEA or in the lab is fair game for the long exam.
    • Here1 is my answer to the basic notebook I asked you to make. Of course, there is more commentary here so that you could hopefully understand what went on.
    • When you do your practice: Try without looking at your notes or references. Try a version where you write down code from scratch. Try also to create code that is self-contained (all symbols defined for that particular set of code).

Lecture 6, 2024-05-20, face-to-face

  1. Group quiz 01: Covers reading assignment indicated in Lecture 5
  2. Wrap up curve sketching.
  3. Move on to inflection points and wrap up Chapter 8.
  4. Reading assignment for the next meeting: Read Chapter 8 once again.
  5. Practice exercises: All examples and exercises in Section 8.7 (skip Exercise 8) and Review Problems for Chapter 8.

Lecture 5, 2024-05-16, online

  1. Continue working on economic applications. Specifically, Section 8.5, Example 4 on optimization over two time periods

  2. What if there are multiple stationary points?

    1. Note that it is possible to have local maxima/minima but no global maxima/minima.
    2. Pay attention to the intervals for which you are asked to search for maxima/minima.
    3. Pay attention to the sign diagram and the alternative representation in the form of a table.
    4. The second derivative test can fail.

  3. Usefulness of the first and second derivatives for curve sketching

  4. Reading assignment for next meeting: Sections 8.6 and 8.7

  5. Practice exercises: all examples and exercises in Sections 8.6 (skip Exercise 7)

  6. Notes

Lab 2, 2024-05-13, face-to-face ONLINE

  1. Continue the remaining part of Lab 1.
  2. Lab 2
  3. Self-evaluation form

Lecture 4, 2024-05-13, face-to-face ONLINE

  1. Discuss aspects of group HW01

  2. Continue economic applications

    • Section 8.3, Example 2 on average cost minimization (not total cost minimization!)
    • Section 8.3, Example 3 on comparative statics

  3. Move away from the focus of Sections 8.1 to 8.3 where there is only one candidate extreme point. Discuss the extreme value theorem and how it can be used in more complicated situations.

  4. Reading assignment for next meeting: Sections 8.5, 8.6, and 8.7

  5. Practice exercises: all examples and exercises in Sections 8.4 (except Example 3 and Exercises 5(c) and 6), 8.5

  6. Notes

Lecture 3, 2024-05-09, online

  1. Paying attention once again to what the Theorems 8.1.1, 8.2.1, and 8.2.2 are actually saying and what they are not saying

  2. Formulate definitions of increasing and decreasing functions in terms of the first derivative, concave and convex functions in terms of the second derivative

  3. How to find maxima and minima more systematically armed with the second derivative?

  4. Section 8.3, Example 1(b) on profit maximization

  5. Reading assignment for next meeting: Sections 8.3, 8.4, and 8.5

  6. Practice exercises: All exercises and examples in Sections 8.1, 8.2, 8.3

  7. Notes

  8. Group HW01

Lab 1, 2024-05-06, face-to-face ONLINE

  1. Quickly introduce syllabus, then jump in to our first lab.

  2. Learn basic syntax for plotting and symbolic computation.

  3. Bring textbook examples to the computer and check your answers.

  4. Self-evaluation form for Lab 1

Lecture 2, 2024-05-06, face-to-face ONLINE

  1. Using non-calculus arguments to find maxima and minima, writing down arguments

  2. How to find maxima and minima more systematically

    • Pay attention to the vocabulary used. Stationary points and critical points seem to be used interchangeably.2 But they are not the same in other textbooks, see for example Paul’s Online Notes.
    • This distinction affects conclusions of Section 8.1, Figure 3.
    • Why is Theorem 8.1.1 called a necessary first-order condition?
    • What is the distinction between necessary and sufficient conditions?

  3. “Foreshadowing”: Local maximum, inflection point

  4. If first-order condition is only necessary, how do we check if we have a maximum or a minimum? Focused on the geometric picture first.

    • Formulate a definition of when a function is increasing and decreasing over some interval. (Move to Lecture 3, for now emphasize the geometric meaning)
    • Why is the first derivative involved here?

  5. Section 8.2, Example 1

  6. Reading assignment: Sections 8.1, 8.2, 8.3, 8.7 (focus on “More general definitions of concave and convex functions”), 8.4 (skip “The Mean Value Theorem”), 8.5

  7. Notes

Lecture 1, 2024-05-02, online

  1. Course administration:

    • Must enroll in the corresponding lab course with section code V24!
    • Deadline for dropping course: May 8 with 90% refund, May 15 with 50% refund, May 29 with no refund
    • Deadline for withdrawal from course: May 30 to June 29 with no refund

  2. Advice:

    1. Forget what you know about study habits.
    2. How to write an email

  3. Formulate definitions for maxima and minima of functions of one variable.

  4. How to find maxima and minima by starting with simple examples: constant functions, piecewise linear functions, and quadratic functions

  5. How do you write a correct and presentable solution to an exercise? Refer to Section 8.1, Example 1 for a possible “template”.

  6. Reading assignment: Sections 8.1, 8.2, 8.3, 8.7 (focus on “More general definitions of concave and convex functions”)

  7. Notes

Footnotes

  1. You may have to right-click and click on “Save Link As” or “Save Target As”. Then save to a place you can access and find.↩︎

  2. You do not see this in the 2nd edition of the book.↩︎