Math 4. Math for Economists. Lecture 01. Introduction to the Course 

00:00 Course information (topics, homework, quizzes, grading, schedule, textbook etc.) 06:00 Introduction: Why is there a maths for economics class (at UCI)? Who this course is for (it is especially for those who wish to go to graduate school) 10:50 Playing a clip from the movie, The Matrix --> "Downloading" information into your head 12:50 Dr Kronewetter's paedagogy - How to learn the content as quickly as possible 16:35 Dr Kronewetter's paedagogy - How to "download" math (into your head) --> Start with something very easy, and then build on it, increasing in difficulty/complexity. **Simple method**: when you have a complete solution for a problem, take a clean piece of paper and until you can do it completely by yourself (without looking at the original solution), you aren't ready to move on 19:59 Introduction: Why do economists need math? Often, topics in economics have to be put into mathematical terms in order to understand it. 24:10 The money multiplier: The amount of money that gets created after you create $1. (e.g. if the federal reserve makes $1, you end up with $10 in the economy). Example using simplistic model of $1: Fractional Reserve Bank keeps 10% of deposits, so they can only lend 90%. If the first loan is $1 and goes into the bank from the federal reserve, and because the bank keeps 10% of $1 (i.e. 10c), there is only 90c available to loan out to people and it goes out into the economy. Eventually some or all of it will go back into the bank, so the next loan will be 90c of that 90c (i.e. 0.9*0.9), and so on 28:24 The above pattern explained above (i.e. for the total loans) can be described by a geometric series 30:00 Formula for the money multiplier (1/f where f is the fractional reserve rate) 31:10 Goals for this class --> 1a) Survey of linear algebra, 1b) Survey of multivariable calculus, 2a) Mathematical maturity (not being intimidated by notation), 2b) Mathematical abstraction (thinking about things abstractly), 2c) Mathetmical generalisation, 2d) Proof-writing 3) Intuition (the mind stores details in pictures) 37:06 Solving systems of linear equations 38:40 Linear equation: can have any number of variables (n), but variables can only have powers of 1, and the coefficients can be any real number. Equations have an equal (=) sign 40:50 Levels of variables 1 variable e.g. x=2, or y=3 (a line) 2 variables e.g. 2x+y=1 (generalised: ax+by=c, where a,b & c are coefficents) 3 variables e.g. 2x+3y-z=6 (the third variable, z is projected from flat 2D) --> plane 44:37 Use of subscript in instances where there is more than 3 variables. Coefficients associated with these variables can also be labelled with indices 48:00 Examples of a non-linear equation: root(x)+y=3, 1/x-y=7, x^2+y^2=4 49:19 y=root(x) --> Law of Diminishing Returns 50:30 y=1/x (focusing on the positive x axis only) --> Indifference curve 52:30 "System" means there are multiple linear equations Possibilities: 1) Unique solution, 2) No solution, 3) Infinitely many solutions 54:10 Two variable system of linear equations --> applications include: supply & demand, equilibrium 1) Unique solution: 1 point which satisfies both equations 2) No solution: Parallel lines (do not intersect) 3) Infinitely many solutions: 2 overlapping lines (the same line) 57:40 Imagining the third dimension for the above scenarios 1) Unique solution: for two intersecting planes, the point where they meet now becomes a line in the 3rd dimension 2) No solution: 2 planes stacked on each other - they still do not intersect 3) Infinitely many solutions: the same plane 58:35 Examples of two variable systems of linear equations 01:02:24 Solving systems of linear equations 01:02:34 1) Graphical method (not effective for more complex situations) 01:04:20 2) Substitution method 01:07:20 3) Elimination method 01:10:56 Degenerate cases 01:10:58 2) Parallel lines - coefficents of x and y in both lines are multiples of each other. The same slope means they are parallel line (unless they are the exact same line). Because the constant number is not a multiple of both lines, we know they are parallel lines (rather than the same line). Algebraically, you get a nonsense answer when trying to solve this system. There are no solutions. 01:13:55 3) Same line - both lines have a multiple of each other that produces the exact same line. When you solve this algebraically, you get 0=0. Thus, there are infinitely many solutions. 01:17:00 Multivariable systems of linear equations. Two things to consider: 1) the number of equations, 2) the number of variables 01:17:48 Example using 3 variables and 3 equations 01:22:24 Degenerate case: Overdetermined system - situation where there are too many solutions (more equations than variables). Example using 3 equations and 2 variables 01:27:18 It's not always the case that overdetermined systems have no solution, but usually there isn't (at least in this course) 01:28:16 Underdetermined system - situation where there are not enough solutions (fewer equations than variables). Example using 1 equations and 2 variables. Every point on the line is a solution, so there are infinitely many solutions to this system. 01:32:04 (For the undetermined system, from previous example) we can present the solution using a parameter, t. The equations can be rewritten in terms of t, where t is any real number 01:34:28 Example of underdetermined system where there are 3 variables but only 2 equations. There are two planes which are intersecting and the goal is to find the line where they intersect (remember the point where they intersect is actually a line in the 3rd dimension). Parameterisation is used - 1 variable is set to equal t, and the equations can then be written in terms of t

This professor made mathematical economics a lovely course

As a note: the actual lecture starts at 20:00 (a bit earlier than that if you want to watch a clip of the Matrix movie) The lesson theme of "Solving Systems of Linear Equations" begins at 37:05 and if you have the book "Mathematics for Economists" by Hoy, Livernois, et al. then it is Chapter 7.

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At 37:22 he starts teaching from the book. Section 7.1, Solving Systems of Linear Equations.

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Syllabus material starts @ 19:51

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You might be able to understand an economic phenomenon without putting into mathematical terms, but you'll have immense difficulty COMMUNICATING such understanding to others. This is one principle reason why simplifying the understanding to mathematical equations is so popular. Understanding is deep. Math is relatively shallow in comparison.

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Search for QUADRATIC EQUATIONS by Crunching Numbers

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