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Advanced Mathematics (ECO-630)
- Instructor Name: Dr. Rubina Ilyas & Ms. Farah Naz
- Credit Hours: 3
- PIDE School of Economics (PSE)
- E-mail: [email protected], [email protected]
- Office Hours: 08:00 AM-04::00PM (Monday through Friday)
Prerequisites For this Course:
None
Text Book(s):
- Basic Mathematics for Economists, Mike Rosser https://rupertstudies.weebly.com/uploads/9/5/8/4/9584887/basic.mathematics.for.economists_-_rosser.rootledge_2003_second.edition.pdf
- Mathematical Methods for Economic Analysis , Paul Scweinzer https://www.researchgate.net/publication/228760692_Mathematical_Methods_for_Economic_Analysis
- Mathematical Analysis for Economists by R. G. D. Allen
- https://archive.org/details/mathematicalanal033535mbp/page/n5/mode/2up?view=theater
- Mas-Colell, Andreu, Michael Whinston, and Jerry Green (MG). Microeconomic Theory. New York, NY: Oxford University Press, 1995.
- de la Fuente (2000), “Mathematical Methods and Models for Economists”, Cambridge University Press.
- Chiang, Alpha C. and Wainwright, Kevin, Fundamental Methods of Mathematical Economics, McGraw Hill Education; Fourth Edition, July 2017
Reference Book(s):
None
Course Description
This course introduces essential mathematical methods used in economic analysis, focusing on their application to theoretical and applied problems. It covers functions, optimization, dynamic analysis, linear programming, and game theory with hands-on practice. The content emphasizes translating economic models into mathematical form to develop analytical and problem-solving skills. It provides a strong foundation for advanced economic research and coursework.
Course Objectives
- Equip students with essential mathematical tools to analyze and solve economic problems.
- Provide hands-on training in applying mathematical methods to both theoretical and applied economics.
- Develop the ability to translate economic models into mathematical form for rigorous analysis.
- Build a foundation for advanced research by integrating mathematical techniques with economic applications.
Learning Outcomes
By the end of this course, students will be able to:
- Understand and apply specific mathematical tools relevant to economic theory and applications.
- Formulate economic problems using mathematical models and derive solutions analytically.
- Utilize optimization, linear programming, and dynamic analysis (including hyperbolic discounting and time-inconsistent preferences) to address intertemporal economic questions.
- Apply game theory concepts to strategic decision-making scenarios in economics.
- Develop the mathematical foundation necessary for research in advanced economics courses.
Lecture Plan
| Session | Topic | Readings
(Book Chapters/pages/Research papers/Handouts/Web links including video links |
Activities
Quizzes/Assignments/Term papers |
Instructor
(If multiple instructors are teaching a course, mention instructor’s name for each module/session |
| Module # 1: Theory of numbers | ||||
| 1 | Intervals, Real Number Line | Handouts/ppt | Hands on practice | Dr. Rubina |
| Module # 2: Cartesian Plan | ||||
| 2 | Zero to Three dimensional shapes, Plots | Chapter 2, Mathematical Methods for Economic Analysis, Paul Scweinzer | Hands on practice | Dr. Rubina |
| Module # 3: Functions | ||||
| 3 | All Types of functions, Functions and Curves | Chapter 4, Basic Mathematics for Economists, Mike Rosser |
Dr. Rubina |
|
| 4-5 | Functions and Diagrams in Economics Theory | Chapter 5, Mathematical Analysis for Economists, R. G. D. Allen | ||
| 6 | Limit and Continuity of Functions (Graphical Approach) | Assignmnet#1 | ||
| Module # 4: Straight Lines and Quadratics | ||||
| 7 | All types of lines and quadratics, Zeroes of Functions | Applications in Economics | Dr. Rubina | |
| Module # 5: Inequalities | ||||
| 8 | Interval solution of Inequalities | Applications in Economics | Dr. Rubina | |
| Module # 6: Calculus and Application to Economic Theory | ||||
| 9-10 | Total derivatives, Partial derivatives | Chapter 8, Basic Mathematics for Economists, Mike Rosser | Hands on practice. |
Ms. Farah Naz |
| 11-13 | Applications of derivatives in Economic Theory | Chapter 6, Mathematical Analysis for Economists, R. G. D. Allen | Hands on practice. | |
| 14-15 | Application of Derivatives: Monopoly Problems in Economics Theory, Problems of duopoly | Chapter 8, Mathematical Analysis for Economists, R. G. D. Allen | Quiz#1 | |
| 16 | MID TERM EXAM | |||
| Module #7: Optimization | ||||
| 17 | Unconstrained Optimization with one and more variables. | Chapter 8, Basic Mathematics for Economists, Mike Rosser | Hands on practice. |
Ms. Farah Naz |
| 18-19 | Convex Optimization in consumer and producer theory | Chapter 2 and Chapter 5, Microeconomic Theory, Mas-Colell, Andreu, Michael Whinston, and Jerry Green | Hands on practice. | |
| 20 | Dynamic Optimization and its application in Basic Model of Job search Hyperbolic Discounting |
Chapter 13, Mathematical Methods and Models for Economists, de la Fuente | Hands on practice.
Assignment#2 |
|
| Module # 8: Difference Equations | ||||
| 21 | 1st order difference Equations | Chapter 8, Mathematical Methods for Economic Analysis, Paul Scweinzer | Hands on practice. |
Ms. Farah Naz |
| 22 | Higher order difference Equations | Hands on practice. | ||
| 23 | Equilibrium conditions | |||
| Module #9: Linear Programming and Game Theory | ||||
| 24 | Basic Concepts | Chapter 5, Basic Mathematics for Economists, Mike Rosser
& Chapter 21 and 22, Fundamental Methods of Mathematical Economics, Chiang, Alpha C. and Wainwright, Kevin |
Hands on practice. |
Dr. Rubina/Ms. Farah Naz |
| 25-26 | Formulation of Linear Programming Problem | Hands on practice. | ||
| 27 | Basic Feasible solution and optimal solution | Hands on practice. | ||
| 28-29 | Simplex method and Graphical Methods | Hands on practice. | ||
| 30 | Concept of Duality and Game Theory | |||
| 31 | Game Theory (– two-person zero sum game – pure and mixed strategies – graphical solution of m x 2 game and 2 x n game) | Quiz#2 | ||
| 32 | Final Exam | |||
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