I'd like to stop for a moment because god bless this teacher ! If we had more people like him we could change the world. The material is clean only important information, step by step with empathy undrdtanding of the student needs.. Amazing. I just wonder if its just the teacher or the university thats better than mine..
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
Great Teacher. Hig school math fresh up in one hour. Easy to unterstand. This is the perfect test to check if your english and math knowleged is good enough for higer education. The whole course prepair you to study at University. Do not ask WHY! Learn it for the exam.
AHHHHHHHHHHHHHH this teacher is such a genious!! I need a teacher like him all my life!! Thank you sooo much @UCIOpen for putting out this video for us!! love love love this channel ❤
@@yydd4954 Well, mathematical economics could be defined as the condensation of economic theory and economic ideas in mathematical models, rather than in, say, essays. An example of mathematical economics is how the money multiplier is modeled with a geometric series. The money multiplier can be and has been discussed in economics essays and books, but it is only once the concept is mathematically modeled that we can talk about the multiplier being part of mathematical economics. That is, economic concepts can be expressed in different ways and mathematical economics is one of them. So mathematical economics is just a way of “doing” economics Mathematics for economics relates to the set of mathematical techniques commonly used by economists within mathematical economics (e.g. Lagrange multipliers)
Yeah ,we completed successfully and we reached here in harmburg ,they interviewed as to know our educational or training statues afterwards they if you are educated you are different thing ,you deserve Racism ,bewitching, byforce running you mad etc in harmburg here from 2016 to date ,together with lawyers, behord workers etc even our lives as take. They opened as to all people etc pls u can think of. So please forward for me .I have packed else where hmmm. One camp mattkamp in billstedt.
Sooo! All this time spent, it was just on simultaneous equation. Just high school stuff lol. Well good explanation, a good base to build on. Thank you and I think you are the best lecturer
Hahaha... love the Catepillar Question in a famous children book " Why you are HERE?" Me, had economy 101 lecture before and now just take this class as a hybrid function out of academic purpose, but for a realistic one in the life in COVID time. LOLOL
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.
Allow me put the lecture outline in this thread since this time stamp is already pretty useful for future reference. :) Lecture Outline: 1. Examples of math use / Building intuitions 1.1 Depreciation 1.2 Money multiplier and the geometric series 1.3 Graphing lines to build on intuition 2. Solving Systems of Linear Equations 2.1 Types of solutions to systems of linear equations: Unique, none or infinite 2.2 Ways to solve: Graphical, substitution and elimination method 2.3 Degenerate cases: Parallel lines and same line 3. Linear systems in n-variables 3.1 Just-identified equations: no. of equations = no. of variables. (Note: Substitution and elimination method are appropriate) 3.2 Overdetermined equations: no. of equations > no. of variables (Note: Substitution and elimination method are appropriate) 3.3 Underdetermined equations: no. of equations < no. of variables (Note: Define a parameter to present the solution)
I remember back in 2013, I was travelling to New Zealand in order to study at uni. I started studying economics and I went to TH-cam and I found this video. I never watched it until the end except by today. Thank you so much.
It's so weird, I happened to stumble upon this video and they use the textbook written by the acting chair of economics at my university and my math econ course this past semester used it as well (naturally). Go figure, finals are done and here I am, watching lectures of classes I've already done.
I’ve watched MIT Professor Gilbert Strang’s lectures on linear algebra and I’ve enrolled in Georgia Tech’s linear algebra course on edX. This is the most meticulous and easy to understand course for me.
Love this professor's pedagogical style! Is there any chance you could rename the the videos in this playlist to include the titles of the topics discussed in each lecture? That would make it a lot more convenient for people to navigate through these lectures... Thanks!
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.
Thinking about a Masters in Economics after watching this realizing I really like what he is teaching after 10 years out of secondary school. PhD after that leads to a nice teaching career 👍 nice 9-5
we tteach SAT test in spain and we love your video here.. what are you drinking.....we like the calculus parts.. some kids are scared by vocabulary and notation..
I wish you were my professor.. You're awesome! Thank you so much for putting this out there for the world to see. That's the way education should be, regardless of the level..
51:34 could have changed my whole life...Im 35, finally went back and finished my undergrad in 2017, went for my masters at a decent school, but unfortunately I failed miserably... in the meanwhile, and not necessarily related nor unrelated, I lost everything I had....these days im emotionally and financially bankrupt and truly contemplating ending it all. Ironically if I just knew enough math, I would have finished my Master's in another country where I was studying and could have had job opportunities to stay there, make money, live and most importantly be happy. But that's not how this sad pathetic story goes
@@refersonu I truly appreciate your msg. I wish I could respond by saying doing much better dude, but unfortunately can only say im doing worse. But your msg made me fucking happy which hasn't happened for a long time and for that I say thank u bro, and wish u all the fucking best
@@jqn8361 kindness & caring of "strangers" for human beings whom have no benefit, is in fact the only reason I personally haven't completely lost my faith in this misery we call "life"... I truly appreciate the msg, Icertainly take ur suggestion in regards to Aurelius, tho Im more of a Schopenhauer, Nietzsche, Dostoevsky and more recently david benatar kind of guy.
Great stuff!
Thanks for sharing.
Prof is going ham on that chalkboard
Thank you..
Deep.
😂Goodluck man.
Just Brilliant
I'd like to stop for a moment because god bless this teacher ! If we had more people like him we could change the world.
The material is clean only important information, step by step with empathy undrdtanding of the student needs.. Amazing. I just wonder if its just the teacher or the university thats better than mine..
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
Thank you🙇♀️
Thank you man!
Thank you so much
Naa, bro. You really did me a big one. Thanks a whole lot! 🔥
I’d highly recommend putting the video in 1.25x to 1.75x speed. It’s much better and sounds like a more normal pace
brilliant, brilliant, brilliant
Thank u UCI
This is by far the most clear and precise lecture ever. Salute 🫡
-3 workers in economics means you need to hire 3 workers and once you've hired them, you'd have no workers at all. 😅
51:04 indifference curve
Great Teacher. Hig school math fresh up in one hour. Easy to unterstand. This is the perfect test to check if your english and math knowleged is good enough for higer education. The whole course prepair you to study at University. Do not ask WHY! Learn it for the exam.
AHHHHHHHHHHHHHH this teacher is such a genious!! I need a teacher like him all my life!! Thank you sooo much @UCIOpen for putting out this video for us!! love love love this channel ❤
This prof has a really nice way with him.
This professor made mathematical economics a lovely course
He sure is good :) However, mathematical economics is different from mathematics for economics!
@@jqn8361 elaborate plz
I know it's different
But how exactly?
@@yydd4954 Well, mathematical economics could be defined as the condensation of economic theory and economic ideas in mathematical models, rather than in, say, essays. An example of mathematical economics is how the money multiplier is modeled with a geometric series. The money multiplier can be and has been discussed in economics essays and books, but it is only once the concept is mathematically modeled that we can talk about the multiplier being part of mathematical economics. That is, economic concepts can be expressed in different ways and mathematical economics is one of them. So mathematical economics is just a way of “doing” economics
Mathematics for economics relates to the set of mathematical techniques commonly used by economists within mathematical economics (e.g. Lagrange multipliers)
Yeah ,we completed successfully and we reached here in harmburg ,they interviewed as to know our educational or training statues afterwards they if you are educated you are different thing ,you deserve Racism ,bewitching, byforce running you mad etc in harmburg here from 2016 to date ,together with lawyers, behord workers etc even our lives as take. They opened as to all people etc pls u can think of. So please forward for me .I have packed else where hmmm. One camp mattkamp in billstedt.
you have made math very interesting subject
Perfect!
i want to see all of this think it get me
28:34
😂I'm having fun now.
1:16:56
This is so cool ,the video at 1.75 x speed the chalk goes ratatata which is such a satisfying noise haha
Sooo! All this time spent, it was just on simultaneous equation. Just high school stuff lol.
Well good explanation, a good base to build on. Thank you and I think you are the best lecturer
The lecturer is amazing at simplifying.
He's a good teacher and has good personality
This man seems smart, he should teach
Being fast
This professor has an unusual gift for turning the complex into simple ideas. This is genius.
Best math professor I've ever seen
Unicoos from Spain and JulioProfe from Colombia are even better but this one is not bad!
Search for QUADRATIC EQUATIONS by Crunching Numbers
Very informative sir
Hahaha... love the Catepillar Question in a famous children book " Why you are HERE?"
Me, had economy 101 lecture before and now just take this class as a hybrid function out of academic purpose, but for a realistic one in the life in COVID time. LOLOL
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.
How can I find the lectures of the earlier chapters (1-6)?
This playlist starts from chapter 7.
Allow me put the lecture outline in this thread since this time stamp is already pretty useful for future reference. :)
Lecture Outline:
1. Examples of math use / Building intuitions
1.1 Depreciation
1.2 Money multiplier and the geometric series
1.3 Graphing lines to build on intuition
2. Solving Systems of Linear Equations
2.1 Types of solutions to systems of linear equations: Unique, none or infinite
2.2 Ways to solve: Graphical, substitution and elimination method
2.3 Degenerate cases: Parallel lines and same line
3. Linear systems in n-variables
3.1 Just-identified equations: no. of equations = no. of variables.
(Note: Substitution and elimination method are appropriate)
3.2 Overdetermined equations: no. of equations > no. of variables
(Note: Substitution and elimination method are appropriate)
3.3 Underdetermined equations: no. of equations < no. of variables
(Note: Define a parameter to present the solution)
Thank you from the future! 🙏🏽
Thank you so much😘😘😘
thanks
Fix those sliding mechanisms for the boards!
53:00
Intelligent guy of thinking about the problem of learning and why people fail. But his noices of breathing...
Garcia Lisa Garcia Kevin Harris Brenda
good work
Teachers like this are the ones that give me hope and increase my love of mathematics
THIS MAN IS A FANTASTIC TEACHER!! ❤️👏👏❤️
I remember back in 2013, I was travelling to New Zealand in order to study at uni. I started studying economics and I went to TH-cam and I found this video. I never watched it until the end except by today. Thank you so much.
Marvelous and magnificent professor actually Many Thanks
I’m horrible with math but have an old Applied Economics BA and I wish I had a math teacher like him!
After watching for half an hour 30:24 is the point from where your perception about math and about this lecture changes.
yeah me too.. after watching that little demonstration, im sold, im finishing this course (hopefully).. great teacher!
Thomas Cynthia Miller Larry Lewis Maria
3:06
Great lecture thanks sir
It's so weird, I happened to stumble upon this video and they use the textbook written by the acting chair of economics at my university and my math econ course this past semester used it as well (naturally).
Go figure, finals are done and here I am, watching lectures of classes I've already done.
Where do you work now?
I’ve watched MIT Professor Gilbert Strang’s lectures on linear algebra and I’ve enrolled in Georgia Tech’s linear algebra course on edX. This is the most meticulous and easy to understand course for me.
FYI- money multiplier is a fallacy. Banks don't lend reserves :)
Richard Werner and Michael Hudson are my heroes too!
Love this professor's pedagogical style! Is there any chance you could rename the the videos in this playlist to include the titles of the topics discussed in each lecture? That would make it a lot more convenient for people to navigate through these lectures... Thanks!
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.
This is how i would like to learn all my subjects, with all the abstraction and generalization.
Thank you :)
Brilliant lecturer and superb course..
Thinking about a Masters in Economics after watching this realizing I really like what he is teaching after 10 years out of secondary school. PhD after that leads to a nice teaching career 👍 nice 9-5
Did you do a bachelor in economics before? Or another field?
@@multiVgames yes in mathematics
we tteach SAT test in spain and we love your video here.. what are you drinking.....we like the calculus parts.. some kids are scared by vocabulary and notation..
This is exactly the kind of material I was looking for. Thanks, UCI!
Thanks a lot for this course, you are really good at building concepts from the simplest form
OMG this guy is amazing! Thank you Sir
👍
Great lecturer. I wish there were more of you around!
thats why i dont wanna major in economics
I absolutely love you
I can't thanks you guys enough for this
He is an amazing teacher. I wish all teachers knew how to share knowledge and passion like this.
Thank you for sharing UCI!
I wish you were my professor.. You're awesome! Thank you so much for putting this out there for the world to see. That's the way education should be, regardless of the level..
Great lecture and amazing professor
Who is from India😁
What a great course! Cuts right to the meat and potatoes
A cheat sheet is a reference sheet
Thanks a lot for making this open source.
Powerful tuition am really learning for my course
I enjoyed this
Hats off this professor's pedagogical style! My simple request is that all lectures should be titled.Thanks in advance.
where are the other lectures?
@@arkamukherjee4027 on the website, the link is in the video description :)
This Teacher is just GREAT. Thanks for posting this !!
Thanks for your advices,best Teacher
Shout out to Dave Gibbons
brilliant man
it is good
51:34 could have changed my whole life...Im 35, finally went back and finished my undergrad in 2017, went for my masters at a decent school, but unfortunately I failed miserably... in the meanwhile, and not necessarily related nor unrelated, I lost everything I had....these days im emotionally and financially bankrupt and truly contemplating ending it all. Ironically if I just knew enough math, I would have finished my Master's in another country where I was studying and could have had job opportunities to stay there, make money, live and most importantly be happy. But that's not how this sad pathetic story goes
I hope you are o.k. now, bro.
@@refersonu I truly appreciate your msg. I wish I could respond by saying doing much better dude, but unfortunately can only say im doing worse. But your msg made me fucking happy which hasn't happened for a long time and for that I say thank u bro, and wish u all the fucking best
@@joecorbet8120 stay strong, Joe. Read Marcus Aurelius’ Meditations 😊 All the best
@@jqn8361 kindness & caring of "strangers" for human beings whom have no benefit, is in fact the only reason I personally haven't completely lost my faith in this misery we call "life"...
I truly appreciate the msg, Icertainly take ur suggestion in regards to Aurelius, tho Im more of a Schopenhauer, Nietzsche, Dostoevsky and more recently david benatar kind of guy.
@@joecorbet8120 I hope things are better for you now!
very helpful, the concept of teaching from very basics is great!
A cheat sheet has the formulas written on them and notes
Amazing teacher!
I NEEDED THIS COURSE THANK YOU !
thx
You allow for a cheat sheet. I had one. I used highlighters
skip the first 19 min is just about the syllabus but the rest is worth watching
Thanks for sharing. Looking forward for next lectures
EN ESPAÑOL ?
Awesome lectures. Can't thank this channel enough.
At 37:22 he starts teaching from the book. Section 7.1, Solving Systems of Linear Equations.
[chalkboard rumbles]
You great!
Brazilian greetings.
Very interesting introduction. I enjoyed learning the practical aspects of economics with simple maths shown. Thank you UC Irvin!
The homework questions aren't available anymore can someone help ????
Thank You sir❤❤
Yeah please include the titles of the topics discussed in each lecture!! Big help! Thanks :-)
i find it quite enjoyable and fun, compared the ones i have to attend each and everyday....