Genetic Recombination and Gene Mapping

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Bozeman Science

Bozeman Science

Күн бұрын

Пікірлер: 607
@Tomozaurus
@Tomozaurus 9 жыл бұрын
I swear these videos are 100% times better than the actual lectures from my university-run units. They should just show these.
@mack_raymond
@mack_raymond 8 жыл бұрын
I have done the majority of my learning on KZbin, for free and in half the time as in lecture. Yet I am paying enormous amounts of money for tuition. This is sad. The only redeeming quality of the school system that I can find is that it pressures me into learning the material for exams. If I didn't have that pressure, perhaps I wouldn't be bothered to learn the material.
@shadowkisss1958
@shadowkisss1958 8 жыл бұрын
funny you mention that cause we are mostly put on to watch his videos in my grade 12 Biology classes
@theongraham3394
@theongraham3394 7 жыл бұрын
A million times better than my lecturer!
@megha7564
@megha7564 7 жыл бұрын
Tom Parker def
@jessrider2711
@jessrider2711 7 жыл бұрын
Agreed. I've already learned more from him in a week than this entire semester.
@samaalnassiry7541
@samaalnassiry7541 4 жыл бұрын
I haven't watched Bozeman science since my senior year of HS AP biology class. Here I am, 5 years later in college watching him again. Thanks for getting me one degree and on the way to the second.
@LXRY
@LXRY 3 жыл бұрын
im in senior year ap bio right now lol. good luck on your next degree!
@kirillkondrachov4864
@kirillkondrachov4864 9 жыл бұрын
Exam tomorrow, and I now understand all of this. Bless your soul.
@karinabuhaya5878
@karinabuhaya5878 5 жыл бұрын
good luck! hope u did well back then
@fernsader9261
@fernsader9261 5 жыл бұрын
​@@karinabuhaya5878 unfortunately he's not with us anymore because of this class
@keishabencosme8491
@keishabencosme8491 4 жыл бұрын
Same here
@AlmostAnything
@AlmostAnything 5 жыл бұрын
HELPFUL ? IT WAS WAS MORE THAN HELPFUL
@rheannesantos458
@rheannesantos458 4 жыл бұрын
trueee
@hydrogenperoxide7244
@hydrogenperoxide7244 2 жыл бұрын
The fact that i understand more about the whole chapter in this 10 minute video than my one and a half hour of lecture is amazing
@jsscmoran
@jsscmoran 9 жыл бұрын
Dear Lord... i learned more in this video than in two lectures ...thank you
@mayabalaji1020
@mayabalaji1020 10 жыл бұрын
Mr. Anderson, Thank you so much for taking the time to post some of the most helpful science videos on youtube! Your time means the world!!
@blessdog5392
@blessdog5392 8 жыл бұрын
Blows off his homework. FIres up his pipe, and figures the whole thing out. Studivent was bad 2 the bone
@sohoyankee66
@sohoyankee66 7 жыл бұрын
I'm running out and buying a pipe. Maybe then I'll understand this. :-)
@crownofall
@crownofall 7 жыл бұрын
Sounds like me only i prefer a cigarette
@NobleVagabond2552
@NobleVagabond2552 6 жыл бұрын
Sounds like me right now except I’m just high af tryna study, all I’m saying tho, Alfred sparked the la
@Jo-gj2nr
@Jo-gj2nr 6 жыл бұрын
It’s 1 AM the night before my AP bio exam, my bio teacher has spent the entire semester talking about her kids instead of teaching us, I want to thank you for being my bio teacher
@steff4413
@steff4413 4 жыл бұрын
Jo how did you do
@joebangles9951
@joebangles9951 4 жыл бұрын
We need to know, how'd it go
@Jo-gj2nr
@Jo-gj2nr 4 жыл бұрын
@@joebangles9951 got a three lol
@kurdweeb599
@kurdweeb599 3 жыл бұрын
@@Jo-gj2nr out of?
@Jo-gj2nr
@Jo-gj2nr 3 жыл бұрын
@@kurdweeb599 5, so not so bad
@lauramorganti4129
@lauramorganti4129 5 жыл бұрын
Just wanted to say thank you. I watched this video the night before my genetics exam because I was so confused and I scored 100% 😂🙌🏼
@zoemccall2473
@zoemccall2473 3 ай бұрын
I was first introduced to your videos as a freshman in high school, during my neuroscience class, and now I'm a freshman in college and I still like coming back to your channel:)
@skennedy918
@skennedy918 8 жыл бұрын
I always use Bozeman science when I am stuck on something from a lecture at uni, helps me understand it in a better light and furthers my learning greatly.
@haleythompson2615
@haleythompson2615 27 күн бұрын
actually BEYOND helpful. Literally had a 104 fever for a week and missed this in my lab and lecture at uni - final exam is tmrw and the assignments didnt help at all. Got desperate and won the lottery with this video my goodness thank you!!
@UdyKumra
@UdyKumra 8 жыл бұрын
The only thing I'm going to remember after the AP exam: if you blow off your homework you might make a groundbreaking discovery.
@vanshpatel9461
@vanshpatel9461 6 жыл бұрын
Udy Kumra usohy
@ShimiVa
@ShimiVa 5 жыл бұрын
"and i hope that was helpful" yes, yes it was! way more than the 2 hours i had in class today! thanks!! you're amazing!
4 жыл бұрын
This video helped me a lot. I just have to consider some issues about the distance of B-A and A-D. Thinking of it mathematically the distance between B-D from the given data is equal to 55 map units which on that note it should be independently assorted. It must have been 10 map units between A-D which would make total sense and the reordering of the gene map. I have to thank you Bozeman for letting us think critically and curiously
@joshuawhittaker1233
@joshuawhittaker1233 2 жыл бұрын
Your thinking is great, but in reality, his example is OK. It is possible (maybe even likely) there is a mistake and as a teacher he meant to give a simple example that added up nicely, but I think the numbers reveal the reality of genetic mapping. At 8:57 he says "relative map distance", because recombination frequencies accurately tell the ORDER of genes on a chromosome relative to one another, but do not always accurately tell the exact DISTANCE. In other words, sometimes the math doesn't add up. Reasons for numbers that don't add up are several. Double crossovers can result in incorrect distance calculations. Also, not all areas of the chromosome cross-over equally. Some areas are hotspots that have more recombination, and some areas like the centromeres have almost none. The farther apart genes are, the more opportunities there are for inaccuracy in distance calculations based on recombination frequency. Side note: Another obvious reason the numbers don't always add up, though not related to this exact problem, is that some human chromosomes are 200+ map units. This method can only calculate up to 50 map units because recombination frequency can't go over 50%. Genes that are over 50 map units apart on a chromosome will all map as 50% RF. In such a case, we would need more genes to compare that are closer together, or modern gene sequencing techniques. Also see Khan academy (bottom section of article): www.khanacademy.org/science/biology/classical-genetics/chromosomal-basis-of-genetics/a/linkage-mapping
@Xelth4
@Xelth4 2 жыл бұрын
@@joshuawhittaker1233 why cant the distance of the chromosome be higher than 50 map units and the recombination frequency between 2 genes must ne lower than 50% ? Not even exactly 50? Why if it's exactly 50, it means that the genes are in different chromosomes?
@whitakerhoskins
@whitakerhoskins 9 жыл бұрын
B to A should be 15 map units
@A169JB
@A169JB 9 жыл бұрын
+Whitaker Hoskins thanks i did pause and i couldnt figure it out...
@deltav9
@deltav9 9 жыл бұрын
+Whitaker Hoskins Realistically you are right but the recombinant frequencies come from a sample which means there is a range of error
@OShawna23
@OShawna23 8 жыл бұрын
Whitaker Hoskins why
@thea16able
@thea16able 7 жыл бұрын
Thanks I thought I was going crazy
@sierraslyh6743
@sierraslyh6743 7 жыл бұрын
so, when you look at the math behind the gene mapping, one would expect the distance from B-A and A-D to add up to the distance between B-D since A is just a point in between B and D. however, when you look at the numbers 30+25 does not equal 40. hope that helps
@crosbywhittington4879
@crosbywhittington4879 3 жыл бұрын
Mr.Bozemen you are truly godsent. I stg you a single-handedly getting me through college science at this point. I hope your pillow is always cold on both sides.
@Tomteluva82
@Tomteluva82 9 жыл бұрын
most pedagogic teacher ever, awesome video
@vasenainaiteqe7847
@vasenainaiteqe7847 8 жыл бұрын
I have my genetics exam tomorrow and this video has really help in thoroughly understanding Chromosomal Inheritance and recombination. Vinaka Fiji Islands
@Tamang4CA
@Tamang4CA 10 жыл бұрын
for the last gene mapping part. if B to C is 45%, isn't it impossible for A - B (30%) and A-D (25%) to be bigger than 45%?
@halamilktea
@halamilktea 4 жыл бұрын
A-B would be 15% right
@azuretea7534
@azuretea7534 3 жыл бұрын
agree
@chickenwang8786
@chickenwang8786 3 жыл бұрын
yeah I noticed that also
@GalaticGarden
@GalaticGarden 3 жыл бұрын
i wish you well.7 years ago wow
@GM-hi2sp
@GM-hi2sp 3 жыл бұрын
Please answer this question .....
@desertman33
@desertman33 9 жыл бұрын
I've taken a number of courses with this concept and did well enough on the tests, but it was only as I watched this video that it really began to truly make sense
@orangecaprinun
@orangecaprinun 4 ай бұрын
It is customary to like your video before it even starts at this point, THANK YOU SO MUCH Prof!
@cosmiccaravan9408
@cosmiccaravan9408 4 жыл бұрын
THOSE VIDEOS HAVE ACTUALLY HELPED ME UNDERSTAND AT ONCE ALL THE THINGS MY UNIVERSITY TEACHERS FAILED TO EXPLAIN CLEARLY! THANK YOU SO MUCH!
@MacyCathleen
@MacyCathleen 9 жыл бұрын
Don't know what I would have done without your videos and Khan academy this quarter! Thank youuuu!
@rev2505
@rev2505 6 жыл бұрын
This less than 10 minute video just helped me understand what my teacher tried to teach me in a 1.5 hour lecture.
@tomvolpe6562
@tomvolpe6562 10 жыл бұрын
Great video! Two comments. 1) 50% recombination doesn't necessarily imply the genes you're mapping are on different chromosomes. The could just be far apart on the same chromosome or have a recombination hot spot between them. 2) When you discuss recombination between the b and vg you have a green box labeled recombination and red boxes above and below labeled no recombination. I know what you mean but students may think that there is no recombination occurring in these regions. It may be but you just can't see it with the alleles you are tracking. Thanks again for all your hard work making these videos. They are extremely helpful.
@yvonnechiletmarch798
@yvonnechiletmarch798 6 жыл бұрын
yes it does, as a chromatic only represent 50%, so if its more than this is means its not in the same chromatid and therefore chromosome after recombination
@rgudduu
@rgudduu 4 жыл бұрын
recombination is always checked pairwise, is it? Say, i want to find that final mapping of 4 genes a,b,c,d. So we do pairwise, taking 2 phenotypes at a time, and carefully choosing the corresponding flies?
@Xelth4
@Xelth4 2 жыл бұрын
I didnt understand ur second one
@charityann27
@charityann27 8 жыл бұрын
you and the amoeba sisters have helped me out a lot this semester
@lianafeng7074
@lianafeng7074 5 жыл бұрын
Mr. Anderson is my lifesaver every time 🙌🏻🙌🏻
@jennifermccarty7272
@jennifermccarty7272 8 жыл бұрын
I am so thankful I stumbled upon your channel, this video in particular. My praxis biology content exam is coming up and your videos are a blessing!
@emiliaarif
@emiliaarif 10 жыл бұрын
whats life without paul andersen... thank u paul ^^
@ladinonyc
@ladinonyc 7 жыл бұрын
For someone like me. Besides reading the text book( which I don't get) to later watch a video.Your video helped give me a better image of whats been spoken about in class.Thank you.
@amandashirley990
@amandashirley990 10 жыл бұрын
The problem you give at the end does not make sense. If the correct order is BADC, as you state, the distance between B-A that you list as 30 mu, and A-D you have listed as 25 mu combined give a combined distance of 55, which would signify that the genes B & D are probably not listed on the same chromosome, and no where near the listed 40 mu's apart. I think the distance between B-A was supposed to have read as 15, not 30, in which case the problem is correct, and the idea that there are 40 map units between B & D is sound.
@georgeofhamilton
@georgeofhamilton 10 жыл бұрын
Arjune Giri Amanda Shirley Maybe he wanted to give us an example of an anomaly of statistics and make us see that this idea still works.
@OKELLAK
@OKELLAK 9 жыл бұрын
+Amanda Shirley Or maybe he just made a mistake. It happens.
@noirritnibedita7565
@noirritnibedita7565 7 жыл бұрын
but I got BADC where A should be 10 units distant from D,here it is shown as 25!
@dma67111
@dma67111 7 жыл бұрын
noirrit nibedita no its 15mu Total 50mu..longest b-c 45mu So b-a + a-d + d-c (5%) = 45mu and on a 50mu chromosome
@mouzicanat
@mouzicanat 7 жыл бұрын
You can't combine the percentages. Assume they never relate in any way.
@faramund9865
@faramund9865 5 жыл бұрын
8:59 There's an issue now though because now B and A aren't 30% apart!
@sashadecosta3537
@sashadecosta3537 10 ай бұрын
you get it! you have one the internet for today! congrats! hahah! holy cow what a mistake to have been made! omg, could never have been me!
@raj10fat
@raj10fat 9 жыл бұрын
Explanation was crystal clear, understood the concept. Thanks Paul. Kudos
@phillipkrayterman3008
@phillipkrayterman3008 5 жыл бұрын
Actually just saved my life. You made a hard concept easy to grasp for anyone. Thanks!
@Joelpenda
@Joelpenda 10 жыл бұрын
Thank you Professor.You make things really simple and easy to understand.
@jorgeaguilar5809
@jorgeaguilar5809 8 жыл бұрын
OMFG I hope one day I can be as skilled as you to teach science, your videos are GOLD :D
@LK-cc4uj
@LK-cc4uj Жыл бұрын
You are such a great instructor. The visuals were so helpful as well. Thank you!!
@ztzexplorer
@ztzexplorer 3 жыл бұрын
A-B is 15 m.u., not 30. Your sequence of B-A-D-C is right though. But thank you Mr. Anderson. You're an amazing teacher. I use your videos all the time to reinforce concepts in the minds of my AP Bio students. If only I had your talent!
@joshuawhittaker1233
@joshuawhittaker1233 2 жыл бұрын
In reality, his example is OK. It is possible (maybe even likely) there is a mistake and as a teacher he meant to give a simple example that added up nicely, but I think the numbers reveal the reality of genetic mapping. At 8:57 he says "relative map distance", because recombination frequencies accurately tell the ORDER of genes on a chromosome relative to one another, but do not always accurately tell the exact DISTANCE. In other words, sometimes the math doesn't add up. Reasons for numbers that don't add up are several. Double crossovers can result in incorrect distance calculations. Also, not all areas of the chromosome cross-over equally. Some areas are hotspots that have more recombination, and some areas like the centromeres have almost none. The farther apart genes are, the more opportunities there are for inaccuracy in distance calculations based on recombination frequency. Side note: Another obvious reason the numbers don't always add up, though not related to this exact problem, is that some human chromosomes are 200+ map units. This method can only calculate up to 50 map units because recombination frequency can't go over 50%. Genes that are over 50 map units apart on a chromosome will all map as 50% RF. In such a case, we would need more genes to compare that are closer together, or modern gene sequencing techniques. Also see Khan academy (bottom section of article): www.khanacademy.org/science/biology/classical-genetics/chromosomal-basis-of-genetics/a/linkage-mapping
@kingfisher32
@kingfisher32 5 жыл бұрын
I was confused by my teacher’s lecture today but now I understand the topic!
@itsmemargarette9836
@itsmemargarette9836 3 жыл бұрын
This is how you properly explain Genetic Recombination and Mapping. By watching this, I was able to FULLY understand it!! Bye Universities. LOL
@sameepthakuri9550
@sameepthakuri9550 5 жыл бұрын
I guess studying at one of best university in the world doesn’t necessarily mean you have access to one of the best teachers in the world . Thank you for this
@pris3675
@pris3675 6 жыл бұрын
This is super helpful great job Mr Andersen! Sincerely student trying to pass HL bio
@hebahamood362
@hebahamood362 2 жыл бұрын
my HS teachers traumatized me by making us watch you all the time but I'm so glad I got over it! woohoo ty very helpful
@Sabibi420
@Sabibi420 3 жыл бұрын
I was going over my lecture material for like an hour and was stuck on the recombination frequencies, I'd almost lost all hope until I found this video. You explained it all so well I can finally understand it now, thanks!
@rajbhakta9432
@rajbhakta9432 8 жыл бұрын
Hey Paul, I noticed at 9:06 that A was placed closer to B when it should be closer to D. Great video by the way, helped a lot!
@komals.6881
@komals.6881 6 жыл бұрын
Sir you are the best teacher for genetics i would say.. Your vedios have helped me a lot. Thank you so much.
@drvir
@drvir 5 жыл бұрын
*videos
@farhanaahmed7163
@farhanaahmed7163 9 жыл бұрын
I was so confused in the lecture, this video has helped me so much, all your videos explain perfectly! Thank you very much!
@matthew_bang
@matthew_bang 6 жыл бұрын
UC honors bio genetics class. Lectures didn't explain this and textbook didn't bother to explain either. You're my go-to source for bio videos
@aliyahstinard3038
@aliyahstinard3038 2 жыл бұрын
You made me understand in 10 minutes what my professor couldn't over 2 weeks
@Its2EZbaby
@Its2EZbaby 7 жыл бұрын
Very helpful, thank you so much. 1000% times better than my college professors could explain over the course of several lectures.
@katharina...
@katharina... 9 жыл бұрын
All excellent teachers should be required by law to make youtube videos :D Thank you for your time Mr Andersen, your contribution is invaluable!
@AsfandyarAfridi
@AsfandyarAfridi 9 жыл бұрын
U are the best teacher ever ...U made me look good
@FourtySven
@FourtySven 10 жыл бұрын
i feel bad for those fruit flies, everytime i make them in my green box i just put it outside and set them free
@leewonkim3533
@leewonkim3533 4 жыл бұрын
you are the uni lecturer we need but don't deserve
@zogfotpik8848
@zogfotpik8848 10 жыл бұрын
Man, this guy looks like Hank Green, and he lives in Montana also
@Tinuviel-gv4xm
@Tinuviel-gv4xm 9 жыл бұрын
+Jim Gibbs He is way better looking than Hank Green
@richarddenny8013
@richarddenny8013 9 жыл бұрын
There related
@richarddenny8013
@richarddenny8013 9 жыл бұрын
jk idk
@jenniferwang946
@jenniferwang946 4 жыл бұрын
Tinuviel 19715 oooooofff
@lancebryan56
@lancebryan56 7 жыл бұрын
ive been watching these videos since 11th grade AP bio and they're even helping me now in my 2nd year in undergrad :')
@faz1991
@faz1991 10 жыл бұрын
As soon as he said "Mr. Anderson" i thought of: "It's inevitable... Mr. Anderson...".
@jacobenright4184
@jacobenright4184 8 жыл бұрын
You're the man Mr Anderson
@SpycyWonton
@SpycyWonton 8 жыл бұрын
I understand the concept better now, thank you! The only confusing part was the math in the RF example, the numbers don't add up.
@fmar105
@fmar105 9 жыл бұрын
You explain so many different topics well!
@GodisGris1
@GodisGris1 6 жыл бұрын
This was so helpful! I love that you actually used an example och how to solve it
@zujamongullie6544
@zujamongullie6544 4 жыл бұрын
After watching Nth number of video on this. Finally I landed on this!!!! And it cleared all my doubt. I feel like I have attained enlightenment. Thank you so much sir
@judyleatherman7563
@judyleatherman7563 3 ай бұрын
Mr Anderson, I am a genetics professor, and you have great videos, I appreciate you and like to provide additional resources like yours for my students to learn genetics! But you've got an error on this one--each chromosome is NOT 50 cM. The percent recombinants are not related to the full length of the chromosome. Some long chromosomes are 200+ cM, and once genes are 50 cM apart, they simply act like they are unlinked.
@rhettwilliams4996
@rhettwilliams4996 7 жыл бұрын
You just saved my grade for finals. Bless your soul.
@taladiv3415
@taladiv3415 4 жыл бұрын
Well done dear contributor Paul Andersen!
@cosmiccrystaldreams
@cosmiccrystaldreams 7 жыл бұрын
Amazing video! Explained it in a way that was easy to understand and had excellent visuals to match. Keep more videos coming!
@gazw9933
@gazw9933 9 жыл бұрын
Damn. Mr Anderson, you make some of the trickier aspects of my degree so easy to learn. Your videos are an asset to my learning. Thank you. And to answer your question. Yes. It was helpful 👍👍
@ananyasuri1223
@ananyasuri1223 4 жыл бұрын
Omg I don’t have words to explain about this video....I saw a lot and lot of videos but finally understood it .....thanks
@krystelnavarro1223
@krystelnavarro1223 8 жыл бұрын
You are a great teacher and speaker! Thanks for the videos!
@danielec.7789
@danielec.7789 8 жыл бұрын
it's very helpful. Now I am prepared for my test tomorrow. Thanks
@tamaracoore6079
@tamaracoore6079 9 жыл бұрын
i love your videos so much, it gives me hope, I've been watching them since my freshman year now I'm a junior taking genetics, you helped me through BIO1 and 2 now i feel confident about genetics. -Thank you
@funnibunni500
@funnibunni500 10 жыл бұрын
Way better than my crappy genetics teacher at school. Thank you!
@jacobmarks2868
@jacobmarks2868 3 жыл бұрын
The best video on KZbin
@monagpal1842
@monagpal1842 8 жыл бұрын
We watch your videos in IB Bio HL, and they help a ton! Thanks so much!
@shawnagar3747
@shawnagar3747 2 жыл бұрын
Thank you So much KDB... Assisting on and off the Pitch
@lesoul700
@lesoul700 9 ай бұрын
Wow. What a crystal clear explanation. This is beauty. Thank you so much. Thank you.
@lesoul700
@lesoul700 9 ай бұрын
This helped me a lot!!!
@nancysohlberg8150
@nancysohlberg8150 4 жыл бұрын
Thank you so much! This illustration and connection is EXACTLY what I was looking for!
@rymunoz
@rymunoz 10 жыл бұрын
Thanks Mr. Anderson!!!! Your videos always help me!!
@madcowzrchewy
@madcowzrchewy 10 жыл бұрын
Thankyou for this! You're infinitely more helpful than the so called "teaching academics" at my university.
@lachlay01
@lachlay01 10 жыл бұрын
super helpful. I watch all your videos for uni. cheers
@meggietiffany9124
@meggietiffany9124 5 жыл бұрын
Thank you for being a more understandable source of teaching than my Actual university lecturers
@megha7564
@megha7564 7 жыл бұрын
Wow.. Such an explanation clear n crisp niiice
@neetapatel5092
@neetapatel5092 4 жыл бұрын
I am watching this amazing video in 2020👩‍🎓
@ChemistryBiologyBelalSir
@ChemistryBiologyBelalSir 8 жыл бұрын
Really awesome work would u mind if i take few snapshots and use it for my class ? thank you
@محمدعليمهدلي-ح6ق
@محمدعليمهدلي-ح6ق 6 ай бұрын
thanks so much what I admire about you lessons that they are deep and focus on the historical background and how did they figure out the thing you are explaining rather than just memorizing without understanding the origin
@Antweezy
@Antweezy 6 жыл бұрын
bless you. this was so much easier to follow than an hour long lecture
@yanghoward2201
@yanghoward2201 2 жыл бұрын
extremely helpful
@mashaelahmed1416
@mashaelahmed1416 10 жыл бұрын
why exactly arent u teaching at a top rated university ? my genetics prof. is the worst instructor anyone could have!! THANK YOU FOR THE VIDEOS!
@kenbessellieu8267
@kenbessellieu8267 10 жыл бұрын
Just in time for my final next week! Thank you so much, I owe my A in Bio this semester to you! :)
@SirJaxxSirJaxx
@SirJaxxSirJaxx 7 жыл бұрын
Wouldn't the range between A & B be 15%? Because if B to D is 40%, subtracting A's 25% should only allow 15 units left over between A & B and not the 30% you have listed.
@konstantinospanagiotopoulo2927
@konstantinospanagiotopoulo2927 5 жыл бұрын
Thank you Paul! I was looking for an explanation like this one! Great work thanks again :)
@e-miner-man
@e-miner-man 6 жыл бұрын
Thank you SO much
@alexbjjperez
@alexbjjperez 7 жыл бұрын
Making dummies like me smarter thanks this really helped me out for my genetics class.
@1212Brenda
@1212Brenda 8 жыл бұрын
I love you. These videos are so clear
@nancyjan25
@nancyjan25 7 жыл бұрын
I hate my professor after watching this. She made it into an engineering class. Thank you for making it simple !
@glassofwater3767
@glassofwater3767 6 жыл бұрын
Fantastic explanation
@peacelovejonas094
@peacelovejonas094 10 жыл бұрын
Your videos are so helpful! I finally understand this thank you!
@dilanhama9178
@dilanhama9178 9 жыл бұрын
I really enjoy your lectures.. In fact I am looking for them
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