Mathematical Methods in Economics Dr. Vinci Chow vincichow@cuhk.edu.hk I Dr. Vinci Chow and His Elite Team • My office hour: https://www.econ.cuhk.edu.hk/booked/Web/sc hedule.php?sid=2 • Teaching Assistants: • Max Hong maxkhhong@cuhk.edu.hk • Stephanie Hou stephaine@link.cuhk.edu.hk • Jason Poon 1155143784@link.cuhk.edu.hk Course Structure • Weekly lectures • Attendance not mandatory • Lecture recordings in Cantonese and English will be available after class each week • (Almost) weekly assignments • One final exam Online Resources • Blackboard: https://blackboard.cuhk.edu.hk Textbooks Tutorial Time Slot Survey http://bit.ly/45AKgt2 Source: whatonearthcatalog.com ©xkcd ECONOMICS Mathematical Economics = Using mathematics to represent economic models Hate even more Econometrics = Statistical theory and data analysis Hate Why Math? ✓Clarity ✓Generalizability ✓It also looks cool Learning Outcomes Source: funnyjunk.com Learning Outcomes ✓ Familiar with basic mathematical tools such as matrix and differentiation Essssential to survival in the next 4 years ✓ Able to use computer programs to aid their analysis Useful for work Python • Python is an open-source, cross-platform programming language • Very intuition syntax, lots of extensions Quick Guide to Mathematical Symbols Constant Body weight = 50 + 5 × Ice−cream Variable Coefficient Variable These often need to be solved Quick Guide to Mathematical Symbols Parameter Coefficient 𝑦 = 𝑎 + 𝑏𝑥 Variable Variable o Variables are usually represented with 𝑥, 𝑦 and 𝑧 o Parameters and Coefficients are usually represented by 𝑎, 𝑏, 𝑐, … Types of Numbers -1, 0, 1, 2, 3,… Integers 2 3 13 689 27 2017 Fractions Rational Numbers = any number that be expressed as a fraction of integers e.g. 2 = 2 / 1 so it is a fraction of integers Types of Numbers Irrational Numbers = any number that cannot be expressed as a fraction of integers Types of Numbers Rational Numbers + Irrational Numbers = Real Numbers Question to ponder: What are fake numbers? ℝ Source: scimathmn.org Summation • The summation sign means summing up all the elements: 10 𝑎𝑖 = 𝑎1 + 𝑎2 + ⋯ + 𝑎10 𝑖=1 Product • The product sign means multiplying all the elements: 10 ෑ 𝑎𝑖 = 𝑎1 × 𝑎2 × ⋯ × 𝑎10 𝑖=1