- Видео 143
- Просмотров 17 044
Dr. Loveless Teaches Math
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Добавлен 26 сен 2023
I am a professor at the University of Washington that has taught over 20,000 students in math over 20+ years. Students have asked me if I can share some of my review videos more publicly so I am making this channel mainly for the purpose of helping students at the University of Washington do better in their math courses.
The second goal of this channel is selfish. I'll use it as a personal release, a chance to enjoy and share the little I know about math without dealing with the challenges of exams, grades, and disgruntled students. Please keep this space positive, let's not worry if we (or I) make mistakes, I really just hope this channels brings some joy to your (and my) day.
The third goal is to share the beauty in mathematics. My research, before I got so busy teaching, was in number theory and combinatorics, but my interests range broadly (sports, games, etc). I have a huge list of ideas, some goofy, some boring, but I hope a few are enlightening.
The second goal of this channel is selfish. I'll use it as a personal release, a chance to enjoy and share the little I know about math without dealing with the challenges of exams, grades, and disgruntled students. Please keep this space positive, let's not worry if we (or I) make mistakes, I really just hope this channels brings some joy to your (and my) day.
The third goal is to share the beauty in mathematics. My research, before I got so busy teaching, was in number theory and combinatorics, but my interests range broadly (sports, games, etc). I have a huge list of ideas, some goofy, some boring, but I hope a few are enlightening.
My favorite integrals (part 3) - The Bell Curve and a Polar Trick
This video discusses the classic result from probability that the integral of e^(-x^2) from - infinity to infinity approaches the square root of pi. Check it out!
Time Stamps:
00:00 Intro
00:32 Bell Curve Integrals
01:30 Why the integration is hard and how to use Taylor Series
02:29 Writing as a double integral
03:44 Converting to polar coordinates
05:27 Talk like a pirate!
07:27 Finishing the Integral
08:34 Closing Comments
Time Stamps:
00:00 Intro
00:32 Bell Curve Integrals
01:30 Why the integration is hard and how to use Taylor Series
02:29 Writing as a double integral
03:44 Converting to polar coordinates
05:27 Talk like a pirate!
07:27 Finishing the Integral
08:34 Closing Comments
Просмотров: 4
Видео
White Elephant Gift Exchanges (part 2) - How to Cheat with Alliances
Просмотров 102 часа назад
This video asks some questions about what happens in a white elephant give exchange when most of the presents are horrible and there is only one or two that are good. This leads me to some questions that I hope you find interesting. Perhaps you can take this "research" problem farther. Also, please don't really cheat your family in a white elephant game, that would be rude (unless it is your si...
White Elephant Gift Exchanges (part 1) - Intro to Fair Division
Просмотров 92 часа назад
Here I explain the rules we use in our family white elephant gift exchange that we do each year. I use this as a chance to introduce the idea of "fair division" and a chance to gift thanks to my family. Please watch this fully before checking out part 2 where I give practical advice on how to cheat by using alliances, ha. But please don't actually do that. Mostly this video hopefully introduces...
Circles and Lines and the Goal of UW Precalculus
Просмотров 237 часов назад
In this video I work through an old Math 120 final exam related to circles and lines. The video is also about the goal of precalculus at UW which is to build up multi-step problem solving skills so that you are more prepared for future math courses that require applied math skills. Time Stamps: 00:00 Intro 00:24 Some Math 120 Background 00:45 Preparing for Exams in Math 120 01:30 Systematic App...
Circle/Cylinder Area via Toilet Paper and Frisbees
Просмотров 557 часов назад
There is a very easy way to remember the formula for the surface area of a cylinder that just requires toilet paper. I hope this helps you remember it (and makes you think of my class every time you use the bathroom, sorry). In this video, I also recap where the number "pi" comes from (using Frisbees) and I derive the area of a circle. So a few general circle and cylinder facts. Mostly I wanted...
Loveless Law of the C's - Remembering your Trig Derivatives
Просмотров 147 часов назад
The "Loveless Law of the C's" sounds like something someone would say on a pirate ship. I made up that saying years ago and would like to trademark it, ha. It is just a goofy way to help you remember that the derivatives of any trig functions that start with the letter "c" will be negative (while the others will be positive). Ultimately, you just need to know all these derivatives very, very we...
Trick to Remember the Area of a Trapezoid with Examples involving Labeling Graphs
Просмотров 107 часов назад
Labeling areas of regions is an important skill you will need in integral calculus. In precalculus, we attempt to give you practice with this skill by having you find areas of regions. And that often requires you remember the area of a trapezoid. In this video, I'll review how to remember that formula and how to use it to find the patterns for some "accumulated" areas. Time Stamps: 00:00 Intro ...
An Interesting Infinite Sum (Basel Problem and Euler) which I plan to never think about again, ha.
Просмотров 13512 часов назад
I give the famous proof given by Euler for the fact that the sum of the inverse squares is equal to pi^2 / 6. This is one of the facts that sparked my interest in math and led me down a path to study lots of infinite sums. Looking back I think this was a bottomless pit where I wasted a lot of valuable time, ha. So this is interesting, but also a warning to not dig too deep. The tools are intere...
Why Divisibility Tricks Work and How you can Make Your Own
Просмотров 2714 часов назад
Here I recap various divisibility "tricks" for checking divisibility for any of the numbers from 2 to 20. More importantly, I explain why these "tricks" work and how they really are just about congruences (i.e. remainders) and how the various numbers relate to the number 10. I use several interesting numbers that I pulled from "real life" (like dividing up a giant bin of cheeseball, ha). Then I...
My Favorite Integrals (part 2): a student over-complication
Просмотров 5214 часов назад
I encountered this unique integration while grading a final exam. A "clever" way to integrate x^3. Time Stamps: 00:00 Intro 00:49 Why is this one of my favorite integrals? 01:02 Encounter this in my grading 01:28 What just happened?!? 01:58 A Substitution? 02:45 I'll never forget this!
My Favorite Integrals (part 1): Integrating x^x
Просмотров 44516 часов назад
This video discusses one of the most interesting integrations I have ever come across. Then I discuss how I tried (and failed) to generalize the results. Hope you find this interesting and maybe this helps get students interested in Taylor series and an unusual (but fun) application. And perhaps you can finish my research and publish a paper with me? Let me know in the comments if you have an i...
Intro to Congruences - My Mom Stole from 4th Graders??
Просмотров 3221 час назад
This video introduces the idea of "congruences". It is intended as a primer for other videos where I will talk about interesting (in my opinion) facts from math and number theory. But mostly this is a chance to thank my mom (and grandma) for being a great teachers and giving me the gift of a love of learning. My mom was a wonderful 4th grade teacher and she did NOT steal from her students, but ...
An Unsolved Problem Related to 2+2=2x2, where sums and products meet (A Journey in Generalization)
Просмотров 2521 час назад
Many years ago I created this small exploratory project on situations when the sum of positive whole numbers is equal to the product of the same numbers. As we generalize our results and find solutions, we learn that it leads to some unsolved problems. I'm so happy I found this old project and please to share it more broadly. I hope some of you can find the current research on this project as I...
0 = 1 Math is Wrong, Stop Watching this Video
Просмотров 52День назад
Here I give several examples proving that 0 = 1 and that math is wrong and you are wasting your time studying math and watching this, ha. Time Stamps: 00:00 Intro 00:16 What I Say In Class 00:42 Three Basic Arithmetic Examples 02:32 Can you find the error? Let me know in the comments. 03:27 Errors with Squares 04:59 An Example from Calculus 06:42 Let me know of more examples you find.
A Man Was Killed for Finding an Irrational Number? (the square root of 2)
Просмотров 23День назад
In this video, I prove that the square root of 2 is irrational and gives some (likely untrue) history. Then I talk a bit about other interesting facts about this number including what is called a continued fraction. Time Stamps: 00:00 Intro 00:43 About Rational Numbers 01:49 Length of the Diagonal of a Square 02:47 Hippasus of Metapontum Died for this?!? 03:33 Proof that the Square Root of 2 is...
A Calculus Exam From When I was a Student (I missed graphing a region!)
Просмотров 157День назад
A Calculus Exam From When I was a Student (I missed graphing a region!)
Dr. Loveless Reads Rate My Professor (Thank You Students, Some Personal Thoughts & a Plea for Help)
Просмотров 325День назад
Dr. Loveless Reads Rate My Professor (Thank You Students, Some Personal Thoughts & a Plea for Help)
Pancake Cutting Part 4: Cutting n-Dimensional Hyperspheres into Thirds
Просмотров 16День назад
Pancake Cutting Part 4: Cutting n-Dimensional Hyperspheres into Thirds
Pancake Cutting Part 2: Cut a Pancake into Thirds (Trig. Substitution)
Просмотров 33День назад
Pancake Cutting Part 2: Cut a Pancake into Thirds (Trig. Substitution)
Pancake Cutting Part 1: Intro and a Puzzle
Просмотров 27День назад
Pancake Cutting Part 1: Intro and a Puzzle
Roots of Unity Saved My Dad's Life (Imaginary Numbers are life and death?)
Просмотров 210День назад
Roots of Unity Saved My Dad's Life (Imaginary Numbers are life and death?)
Fundamental Theorem of Calculus Part 1 Final Recap
Просмотров 18514 дней назад
Fundamental Theorem of Calculus Part 1 Final Recap
Work, Work, Work Lifting "Stacks of Books"
Просмотров 9714 дней назад
Work, Work, Work Lifting "Stacks of Books"
Work, Work, Work on Lifting "Leaky Buckets" and Ropes
Просмотров 10214 дней назад
Work, Work, Work on Lifting "Leaky Buckets" and Ropes
Other Exact Values of Trig (Video 1? Want More?)
Просмотров 2214 дней назад
Other Exact Values of Trig (Video 1? Want More?)
My Calculus Students Hate Donuts and the Theorem of Pappus
Просмотров 22914 дней назад
My Calculus Students Hate Donuts and the Theorem of Pappus
dude, just say that is the feyrman's method
What is the feyrman's method? Curious. If I'm using any method for anything that would be interesting that would be surprising, ha. I suspect that anything I'm reporting on has likely already been done, I am not an active researcher only reporting on fun things from 20 years of teaching to share with my students and family. So this channel is really only a release for me, a chance to do something other than worry about grades and teaching (I teach 1200+ students a year and don't get to do research). So any method that I overlap with is purely by accident.
@ emm, Isa method that we use when nothing of calc. 2 methods works Feyrman born May 11, 1918, New York, New York, U.S.-died February 15, 1988 Os Angles California) is an old method btw
And thanks for teaching maths, people needs people like you (Bc most people think that this is extremely difficult) , but I don’t think so
you mean Feynman as in Richard Feynman, one of the greatest physicists of the 20th century
Oh yes, Feynman. He does speak on how teaching something is one of the best ways to learn it. Sorry, when I saw Feyrman I thought maybe that was someone else who did this integral. I didn't understand you were talking about my comment on learning by teaching (I should have known you meant Feynman). Thanks all!
9:57 still watching lol, these taylor series sound fun to learn in math 126... x^x is just such a fascinating function to do stuff with!
Lovely, the start of Taylor series (error bounds) in Math 126 is a bit dry, but things pick up by the end. Unfortunately you don't get to do very many examples that I would call "fun", but I hope by making a few videos like this it will make it easier for you to enjoy that part of Math 126.
Thank you Dr.Loveless! Took the 125 this quarter and it’s a really interesting class (as a math class lol). The office hours and ta are really helpful and your resources helped me a lot in preparing for the exam!
Dr. Loveless you made me so excited to come to class because you were always so full of joy and excitement. I loved this quarter in 125 - you are a teacher i will never forget
Dr. Loveless, I really appreciated everything you did in math 125 this quarter! You were quite literally the first professor I ever had in college and you have been so encouraging and I thought I was sooo doomed after my first two exams, but your encouragement to improve is something I will always be grateful for, and I really can't thank you enough. I hope you have an amazing future and a well-deserved break after all of your amazing videos and stuff you have put out! I think your #1 best piece of advice was to do multiple practice exams beforehand, as I had never thought to do anything like that before getting to college but it was 100% the most helpful thing for me to help me (hopefully) do really good on the final and pass your course! <3
Could you make a video about false proofs (stuff like proving 1=2) it's a topic i've always been interested in
Thanks for the suggestion. Does this video scratch that itch for you: ruclips.net/video/-St9G9zfnhU/видео.html
Thank YOU Dr. Loveless!
Hi Dr. Loveless, I took your math 125 course this quarter and i really enjoyed your teaching. Math isn’t something that comes to me naturally but the amount of effort you put in with the videos and extra resources have helped me greatly! Thanks for all your hard work and have a great break!
this is fascinating, thank you!
This is interesting. I am currently taking calc 2 at NMSU and we did not cover donuts. For volumes of rotation shell, disc, and washer methods were taught but we did not cover any donuts.
Thank goodness, I'm glad you still get to enjoy donuts, ha.
didn''t realize the e^(pi*i) = -1 formula actually had any uses.... thought it was just a fun little math thing... do we learn this in later calc courses?
Thanks for your question. I could talk about Euler and his formula for many, many hours, don't tempt me, ha. After you take Math 126 and learn about Taylor series, come back and I can derive Euler's formula for you. I think you mostly would encounter these ideas in a course in complex analysis which requires you to stick around math for a while. But maybe check out the book I mention. Thanks for watching.
Here's an interesting probability question for the game of Go Fish: If all players are honest and you shuffle perfectly, what are the odds that a player never has to "go fish" in an entire game?
Lovely, I should note I may be slow to make these videos, but I will add this to my list, might be a while before I get to it (I'm grading finals and have a long, long, long list of other goofy videos in mind), but I'll add this to my queue. Thanks.
thank you so much for making the work videos :)
You aren’t even teaching this class this quarter, but this video still helps so much 😭
Lovely, my department may ask me to teach Math 126 this summer due to a budget issue and they want me to get enrollment as high as possible, so you can help me by advertising Math 126 in the summer, I need at least 100 students, but more would be better. In other news check out my weird math videos as I'm having fun on those. Good luck on your final.
Should the dm/dt for the last question be -1/(1+t) since the mass is decreasing? Thank you for the video!
Yes, it should! Two mistakes in one video, darn it. Sorry, I'll need to remake this in the future, and thanks for pointing out the error.
thank you dr loveless! quick note though, 25-4.8 = 20.2, not 21.2 :) overall a very useful vidoe though
Haha, me no subtract good, thanks for pointing that out. I am not doing as careful checking in order to get these out quickly, so I really appreciate errors being pointed out in the comments and I'll polish these videos up in the future.
What is funny is that my final answer is still correct as I made another subtraction error in the next step to fix my error. Two wrongs did make a right, hurrah.
This freaked me out until I realized this uni's math 125 is different to my uni's math 125, linear algebra 💀
thank you doctor!
thank you
Thank you Dr. Loveless 🙏
Literally a life saver 🙏🏼
Hello Professor Loveless, I think you should look into Catan. It's a popular turn based strategy game that is fun to play with friends. Sincerely, a Math 126 fan.
Good suggestion, my family has played that one (a bit more Catan Junior as opposed to Catan). But they key is to find an interest, or weird, or funny math question to ask related to the game, have any ideas?
@@Dr.LovelessTeachesMath Well I spoke with some friends, and one of the things they mentioned was winning the game by gaining victory points from methods outside of building settlements and cities. Usually my friends do this by collecting development cards and hoarding them until the very end where they suddenly reveal they have a couple extra victory points that allows them the game. They also do this by attempting to build the longest road or acquire the largest army for bonus victory points. I guess my question is, aside from building settlements and cities, what is the best/fastest alternative way to gain victory points? Maybe it's not the best question to ask because Catan is just a bunch of probabilities and it would vary a lot depending how many resources you are able to take in but it could be interesting. Thank you!
Repeating what I said to someone else below... I will add this to my list, might be a while before I get to it (I'm grading finals and have a long, long, long list of other goofy videos in mind), but I'll add this to my queue. And I'll find a quirky, funny, or odd way to ask a question that likely won't help you, but will make me laugh, which is what matters to me, ha.
Thank you for these review videos! I am not in any of your classes, but I am taking MATH125, and I appreciate immensely the amount of effort and information in these videos!
could you do something like this with work problems? I still feel confused on how to find the cross sections and what I label the top and bottom, thanks as always for the videos :)
How about this: ruclips.net/video/V8Zv2k2EnF4/видео.htmlsi=E3jDZgpfYIfusRpV
Great video sir 👍
Thank you so much for these review videos!
yall i think i might be cooked 😭😭🙏🙏
You can do it! Where are you stuck, let me know on the discussion board, I believe in you.
@@Dr.LovelessTeachesMath I WATCHED A LOT OF YOUR REVIEW VIDEOS AND I AM FEELING A LOT BETTER, I will not be scared to use the ed though if i need more help!
I study for my math final for 6 hours, and this is the enjoyment I need afterwards 😊
I think your method is good but I'm curious how well it extends. To see what I mean, here's a challenge. Show that with 1000 distinct decks of cards there are 843063174823101023549821871061481721122400 ways of making 15.
Thanks for watching. This is all for fun. I like to think about someone trying to shuffle 1000 decks, ha. There are sometimes ways to extract a coefficient of a polynomial or power series without fully expanding, I didn't think on that as I was able to expand in this case. With 1000 decks, I'd have to think on it more. How did you find my video? I am mostly posting for fun for family and friends. Surprised anyone else would watch (and stay awake), ha.
@@AndyLoveless-jj3cr I'm a big fan of cribbage and maths so somehow youtube knew to suggest your video to me. I thought the counting problem you were tackling was fun and I enjoyed following your progress in the mini-series. To solve 1000 decks, you can work over a quotient ring Q[x]/(x^16), which is a lot faster since it's just a 15-dimensional Q-algebra.
Born and raised Oregonian here. Manzanita is one of the few beaches that the tourists haven’t gotten to yet! 😂
Wow very interesting presentation and style… at least for those of us who like math. I think the channel is going to blow up. 🎉
This would be an introverts dream. Thanks for the video!
Let's go Max 🎉
thank you for the solutions! It's really helpful for the midterm
thank you! loveless bless me for midterm 2
great video
Note* @ 40:37 it's 3/9 = 1/3.
Yes, thanks for pointing that out, I didn't check my work, boo on me. My first term on my final answer of the last example is off by a factor of 3, sorry all. My correctly written solutions can be found in my exam solution here (problem 2(a)): sites.math.washington.edu/~aloveles/Math125Materials/w15m125e2solns.pdf
very high quality
do one where you dont know the answers already
Ha, good point. I made this particular entire video without the answers first... but I forgot to hit "record screen"... because I am an idiot. So then I redid the entire video again (which is painful to re-recorded the exact same thing again), but I was too lazy to erase the answers I had already written. I am prone to small typos. But I am not worried about getting 100% on these tests, I was never good at things like that. But I hope videos like this help you with how to approach exams. Hope these are helping.
@@Dr.LovelessTeachesMath vid is still helpful i am just wondering how long it would take a math prof to do
Subbed
thanks
u are so cool
This is certainly not true, but thanks anyway. Hope the videos are helping.
thank you!
Cool!
Videos going into depth for trig that is needed for calc 125 would be very helpful!
Thanks for the input. Trig plays a bit role later in Math 125 (sections 7.2 and 7.3). I'll review trig when we get there (and maybe make a few supplemental videos as well).
goated math prof!!!!!
Best teacher 💯
That's really interesting and ties in my own Analysis (real) class. I'd love to see more on it, with examples and useful formulas
Mr friend Anthony showed me this channel and I enjoy the videos, very interesting