This channel is about helping you learn math. I've got full playlists for Discrete Math, Linear Algebra, Calculus I-IV and Differential equations, as well as many more videos on cool math topics or about learning effectively.
I am an Assistant Teaching Professor teaching mathematics at the University of Victoria, in Canada. I completed my PhD in a fun branch of math called Algebraic Topology at the University of Toronto. Many of the videos on this channel were filmed during my time as an Assistant Professor, Educator at the University of Cincinnati.
Mathematics is a journey we can all participate in. My videos can help support you, give you tools, and show you some of beauty and power of mathematics. But ultimately it is a journey we must travel together, so make sure you don't JUST watch my videos. Ask questions, try problems, and do as much math as you can on your own too!
As your explanation went along it seemed to be going faster and faster. It probably didn't seem like that to you because you already completely understand the whole subject. As you're going faster and faster, you're also giving the student less and less time to take in all the information and make sense ot it. At a certain point during your video it almost becomes cartoon like as the information flows faster and faster. At that point, the whole purpose of the video is gone. Then it just sounds like a bunch of random information that doesn't relate to anything. I'm sure it doesn't sound that way to you, but to the person watching, it's just Charlie Brown's teacher. Blah, blah, blah, blah, blah! That is why it's difficult for many students to learn math. These same ideas apply to subjects other than math, too.
Great video Dr. Question: we decomposrd the matrix and then took the inverse of these decompositions. Is it always true that there exists an inverse of each submatrix of the decomposition?
Thank you so much, I don’t like my linear algebra course, they don’t show me this beauty; so well explained, I’m gonna start doing harder in the subject, thanks.
I am currently taking an advanced Linear Algebra course at the University of New Brunswick in Fredericton as part of my declared minor. Your explanation is an essential concept to understand the tenets of linear transformations, that eventually is a requirement for understanding advance topics such as the non-commutative geometry.
That is sooo coooll!!!! Linear algebra isn't taught so intuitively in India, it's just largely algebraic without really going onto linear transformations and what they actually mean. It's taught more computationally, through adjoints, cramer's rule etc + a litle bit of geometry on what the planes do, but not what the operations themselves encode. Seeing such a fresh perspective on it is so amazing!
That'd be fun! I guess since gaussian elimination gets generalized to computing a grobner basis the geometric intuition would probably be animated in the linear case first, not quite sure what good pictures there are in the general non-linear case off the top of my head.
No human is writing such an ambigous math problem (unless the goal is to be ambiguous). Therefore this math question is in fact the equivalent to the quintessential english class question "what did the author mean by __"
Nice demonstration. You show it, but don't really say it, and I think it could do with saying: a shear operation, applied to a line, is a rotation of that line. The two operations are indistinguishable, when applied to a line that goes to infinity in both directions (except some rotations of 90 degrees cannot be accomplished by a shear tied to particular axes). That'd tie the two parts of the video together nicely.
This video is like catnip for mathcats and I love it. Thanks for making this video. Our imagination is the only limit there is. Right now, I'm studying chemistry but I really miss those days when I used to watch your set theory videos for hours and those helped me a lot but I still don't understand anything about ordered pairs or n-tuples. I mean, I know its to represent the order but my heart doesn't accept it. I want a truly satisfying reason for it. Usually wikipedia does satisfy but this it didn't. So, can you please make a really long and detailed video about ordered pair. Thanks if you have read my comment. You(and few other amazing folks) are the reason I love math unconditionally!
"Thank you so much! I want to ask you how we can study math effectively. I mean, no one really explains the simple things, like how to understand definitions or theorems properly. How do you learn math? What steps do you take? Can you provide a roadmap to clarify the path (what should I start with)? Thanks in advance!"
I like what I call "the rabbit hole" method. If your teacher is telling you something you don't understand keep asking "but why" going deeper and deeper into the rabbit hole until you get something you really understand deeply and them climb back out. Basically don't allow yourself to just be mimicing what I do in a video or what a teacher does, make sure YOU really understand it.
@@DrTrefor Thanks to many internet resources, especially the ones you're providing, that rabbit hole method is a lot more doable. Thank you for everything you do.
What is most remarkable is that a text can make up a function where you take the derivative, square it, add one, take the square root, and end up with something you can actually find an anti-derivaitve of in closed form. That is why all the examples in any text look so weird. What about x^3 - 3x or just sine
"Pre-calculus" needs to be abolished as a class and replaced with algebra-for-calculus and trigonometry-for-calculus, both full-semester classes. Students who are comfortable with algebra, can move directly into trigonometry. Students who are comfortable with trigonometry can just take algebra.
Thank you. I've watched many of your videos and taken many math classes. You are a top notch teacher. I wish I wasn't a broke student because I would buy you lunch. Seriously your content has changed the trajectory of many of my grades.
I'm very happy to see a math professor rightly calling out these problems as fundamentally uninteresting, rather than certain OTHER channels (perhaps pictured in this video) that seem to relish in the clicks generated by viral order-of-operations nonsense.
Amazing explanation sir! There's this idea I thought of to solve homogenous equations with linear coefficients (for second order this is, this can be extended to higher order for sure). It is a bit inefficient, but I've learnt only first orders ODEs, so this is really my first exposure to higher order ODEs. Say we have the differential equation y'' + ay' + by = 0 what I did was substitute h(x) = (y' + Ay) h'(x) = y'' + Ay' Say our equation is h' + Bh = 0 y'' + (A+B)y' + ABy = 0 A+B = a, AB = b, which will take us to the same complex roots, real and distinct etc. cases. h = e^-Bx + c y' + Ay = e^-Bx + c1 IF = e^(Ax) d(e^Ax y) = e^(A-B)x + c1 e^Ax e^Ax y = [e^(A-B)x]/(A-B) + c1/A e^Ax + c2 y = [e^-Bx]/(A-B) + c1/A + c2 e^(-Ax) = c1 e^(-Bx) + c2 e^(-Ax) + c3 If we set c1, c2 = 0, y = c3 can only be a solution if c3 = 0, hence c3 = 0 y = c1 e^-Bx + c2 e^-Ax, whcih gives the same output as assuming y = e^rt and solving for r The method of assuming e^rx as a solution, and using linear combination of solutions is a much quicker method for sure, this is just something I had to work around cuz we needed to show working and we only knew first order ODEs at that point.
THIS IS WHAT IS WRONG WITH OUR MATH AND SCIENCE COMPETENCY OF STUDENTS IN THIS COUNTRY. THE CURRICULUM WAS BEEN SO DILUTED THAT STUDENTS TODAY ARE BEHIND THE REST OF THE WORLD. TRIGONOMETRY USED TO BE A FULL YEAR. NOW AT MOST IT IS A CHAPTER. THOSE WHO ARGUE NOW STUDENTS ARE TAKING PRECALCULUS IN HIGH SCHOOL. I TUTOR THESE STUDENTS. THESE CLASSES ARE JUST WATERED DOWN ALGEBRA TWO. THIS ISSUE GOES FAR BEYOND MATH AND SCIENCE. CURRICULUMS ON MANY SUBJECTS ARE WATERED DOWN OR KEY COURSES ARE ELIMINATED ALL TOGETHER AS WE EXPECT LESS NOT MORE. PATHETIC!!!
I converted to cylindrical coordinates, performed the integration, and got 18pi/8, which is approximately 7.07. By looking at the volume and visualizing a 1×1×1 cube based on the coordinate system, it looks like about 7 blocks of that size might fit inside. Is my answer correct? Thanks for a great video!
I understand the constraint is the equation of a circle, where 𝑔(𝑥,𝑦)=0 and increases in the direction outside the circle. I don't understand how a local max/min would be found "inside" the circle with the way this is being used. The min/max is only found on the circumference of the circle in the following picture. Whereas, if the equation for the circle were modified so all points inside and on circumference were g(x,y) = c, then min/max would be found inside as well.
