When I developed this series I never expected to see it on the Internet more than 40 years later. It gives me great pleasure to see that my work is now helping a new generation of students, many of whom were not yet born when the series was developed. I truly appreciate your taking the time to write to me and telling you how much the course is helping you.
Thanks for the very kind compliment. I have always tried to live up to the advice that says “Never think so much of your subject that you neglect your subjects!” Another one of my favorites is “People don’t care how much you know until they know how much you care”. It may seem extremely self-centered but I am very pleased at the number of personal email messages I am receiving by viewers who tell me how much they appreciate the course.
Dear Shu'aib, Messages such as yours make me feel much younger than my 84 years. As I’ve commented several times before, it is a great feeling to know that work I did over 40 years ago is still continuing to help people. I send you my best wishes.
Thanks for your kind words. My own belief is that the type of teachers we had then is pretty much the same as it is now. The huge difference is that we can now clone the best (that is, video them and upload their lectures) and have them teach globally. It is a whole new world in that respect and it amazes an old guy like me.
I had to chuckle at your unique compliment. I am pleased that you are enjoying my course. It is a wonderful feeling, especially in my old age, to see someone learning from a lecture series I developed over 40 years ago. Thanks for taking the time to write.
This is truly the greatest maths related playlist ever, as someone who only had done maths uptill high school and all of a sudden had to solve problems related to complex numbers later on in life, this playlist was truly a gift to humanity. Thank you Sir Herbert Gross, you will always be remembered. 🙏
I just saved this to my "EPIC" playlist. This was an EPIC lecture. I'm an MD PhD and practicing academic neurosurgeon that went to Cal and I have seen thousands of lectures in person and online on a multitude of topics and this lecture goes into my Hall of Fame.
Time independent Lectures. Honestly speaking, Professor Herbert belongs to the League of Leibnitz, Euler and Einstein.Geniuses like him with such ability to present such a topic as this in such lucid manner are seldom seen. I am very sure, mit would not have found a replacement. "Men may come, Men may go, but Herbert Gross is a jewel in the Crown"
Thanks again! The original intent of the complex variable segment of "Calculus Revisited" was to give viewers an overview of the subject and thus (hopefully) to make it easier for them to internalize a more formal, in-deo\pth course. I am very pleased that this seems to have happened in your case. Good luck in your upcoming exam!!!
it saddens my heart when I see people who have chosen profession as teachers and they are so kind and gentle in their words but do not get acknowledgement or are treated badly.
Holy shit! Hebert Gross is the clearest,most articulate, and most eloquent math teacher I've ever heard/had. Absorbing this material was so fast, easy and organic. Thank you for the course!
Dr. Professor Herbert Gross is easily the best professor of mathematics ever. His videos still remain to this day (2017) the very best of the best. That is not said to diminish in any way whatsoever the other math videos that have been produced by so many other great professors. It would be very wise of any math student to get as much instruction from as many learned math prof's as possible. And with TH-cam, etc., we all have the capability of doing that. But the start and the end of math education in America is and will always be with Prof. Gross. Thank you so much Dr. Gross for your contribution to humanity. It is so crystal clear that you deeply care, and have always cared, and will always care. Dr. Gross is, and has always been. and will always be a true Mensch.
Thank you Major for writing such a tribute to me. I hope that when my time comes to be eulogized, the speaker will be as eloquent as you. Having said that, I want to reinforce what you said about the Internet. More specifically, as well received as my lectures have been, they have still generated “dislikes” from some viewers. It is nice to know that those who don’t like my lectures will be able to find many alternatives to my approach, some of which might resonate with them. It is my opinion that the Internet will eventually revolutionize how we teach. In my own case, I feel blessed that the Internet “cloned” me, at least in the sense that it will enable the 42 year old Herb Gross in the videos to continue teaching even when the present 88 year old Herb Gross.
Thanks for your kind words! My subjective point of view is that for every student, especially the millions who do not intend to pursue a math/science/technology - oriented career, it is far more important for them to learn to understand the logical structure of mathematics and the critical thinking that it involves than to memorize how to ”plug in” numbers to equations.
Hi Everyone. When I was a young man going to university in the 70's there were many of my lecturers that had the same enthusiasm and delivery that Herb did. They were dedicated professionals who loved what they did and they were good at it. Just like you see here with Herb, I was lucky enough to have Maths and Physics professors who knew how to teach a subject, because they really understood the material, and knew how to put it across. Thanks Herb.
The first ten minutes of this class is enough for every student to get rid of all the mechanical crap that is teached on high school (and colleges) with respect to complex numbers. We all know that Prof. Gross put a lot of effort to organize these classes and all were worth with.
Hi Alan, From my subjective point of view your comment is very interesting. More specifically, my complex variable mini-course was meant only to help a student get an idea of what the subject was about before enrolling in a full-fledged course. The same was true about my mini-courses in differential equations and linear algebra. So it is extremely pleasing that someone at your level found it to be valuable. Thank you for taking the time to write.
This is my favorite series of educational mathematics videos. Thank you MIT for making this series available to the general public for free...........
Thanks Gus One of the great things about the potential of the Internet is that it can make a master teacher available to any student in any location and in any point of time. In essence it may allow us to clone mater teachers. In addition such a delivery system is time-independent, meaning that the viewers are not restricted by the lock-step pace of the traditional school class room.
"When the student is ready the master will appear" ... These lectures, with the amazing responses they are generating, are the perfect example of that! It's amazing how you tie so much together without letting the main points get lost in details ... best introduction I've seen after several undergrad and grad level courses.
+Jon Hofmann Thankyou Jon. My “game plan” in all of my video courses is to use the lectures to emphasize the “great ideas” and the accompanying written material to highlight the “nuts and bolts”. My feeling is that it is my lectures that drive the rest of my wok. I should point out that TH-cam has only the videos but to make use of the course’s written materials one has to go to the OpenCourseWare website.
Hi Ron, If color had been an option at the time I would have preferred it. However we went with what we had and I feel very happy that so many viewers were pleased with what the final outcome was. My guess is that people who are visiting the OCW website are looking primarily for good content and it doesn’t matter whether what the delivery system is. I often gave a talk that was entitled “Delivering Stale Donuts in a Rolls Royce Doesn’t Make the Donuts Any Fresher".
A number of viewers have asked me about the square root of a positive number. There are 2 numbers whose square is 4; namerly 2 and -2. Thus one should ask "What is the positive square root of 4?" or "What is the negative square root of 4?" When the sign isn't mentioned it is an agreed-upon convention that "What is the sqaure root of 4?" means "What is the postive square root of 4?"
These (and his other) lectures are excellent and Herb Gross is a legend for responding to youtube comments and emails until the very end. A few years before he died I emailed him thanking him for these lectures and mentioned that I live fairly close to him. He responded with something like "perhaps if you're nearby we could meet." I'm sure he was just being polite but I also couldn't pass up an opportunity to meet with a famous youtube celebrity, so I told him sure, I could meet at a park near you. Alas, he was probably busy and didn't respond again. I don't know if he had children but I can imagine the conversations between them: "Janet, can you call and check on dad? He's talking about going to meet some weirdo from youtube at the playground again!" So that's my story of how I maybe almost hung out with Herb Gross at the park but didn't.
Professor Gross, I am on a post-graduate course in complex variables and have previously covered much of the material in your course, Yet I found every one of your lectures full of new facets and insights which have further illuminated and enhanced my understanding of the subject. Like others who have posted comments, I have thoroughly enjoyed viewing your course. Thank you so much for these lectures and the superb clarity of your delivery.
Mr. Gross, I am in the final year of getting my Math undergraduate degree and I must say you are one of the best teachers I have had to date. You make otherwise difficult concepts easy to understand. Thank you for all your work!
+vysoc There is an adage that says “The music is not in the guitar”. In that context, a textbook is the guitar and the instructor is the person who is playing the guitar. In that sense it is a truism, in every walk of life, that some guitar players produce better music than others. On a personal note, in producing this calculus series, I did lots of practicing before I “playedany of the piece” in public.
Thank you for the kind words. I greatly appreciate them. I feel greatly honored by how well my work has been received even though it is almost 50 years since I produced the course.
This is probably the single greatest introductory lecture to any mathematical subject I have ever encountered. It's conceptually clear, mathematically precise and beautifully explained by someone who clearly both knows exactly what he's talking about and who he's speaking to. And I absolute love how carefully Prof. Herbert words his statements. If every mathematics teacher in the world taught like Prof. Herbert Gross, we'd all be mathematicians right now.
Thanks for that very complimentary comment. Although I appreciate the gift I have for teaching I believe that much of the credit for this course belongs to my “boss” Harold Mickley, who allowed me to take as much time as I needed to produce a script with which I was satisfied (in this case the script was the prewritten “green boards”). In addition to that, whenever a video was completed, he and I would go over it line by line to ensure that there were no major glitches in it (we let minor verbal and written typos go because correcting them meant redoing the entire lecture). In short, I think I would have done a decent job regardless but with Harold’s expertise to help guide me, the series has become sort of a cult classic. My only regret is that Harold passed away before he had a chance to read the kind comments that viewers such as you have written!
I belong to PhD in chemistry, but always more interested in mathematics and physics...complex analysis has great importance in quantum mechanics (or chemistry). I loved the way of your teaching and the flow in which you poured the concepts in my mind. Kudos sir...thankew
My friends always say that complex number is difficult to visualize, and I thought so as well, but this video clears it up so well with those examples. Thank you.
I was in need of a refresher on complex numbers for a project at work, as it's been some years since I've last had to work with them, and I have to say I'm quite pleased I stumbled upon this splendid lecture series. Wow. If only my original complex analysis professor had been as succinct as yourself, Herb Gross, perhaps I might have retained it far better. Thank you so very much.
I was searching for resources to understand more of complex variables and I happened to stumble upon this. Herbert Gross, you are truly a great teacher, I ended up enjoying this video. I felt like I was learning for the fun of it when I was watching this, rather than studying for the sake of understanding the confusion I have in class. This video is truly "old but gold". Thank you for these amazing lectures.
Thanks for your kind words. In my opinion the difference between work and play is the degree of enjoyment rather than the degree of difficulty. In that sense it is not contradictory for students to learn and have fun simultaneously! I am pleased that you seem to have done both.
I was genuinely shocked to see the actual professor from these lectures, Professor Herbert Gross, taking the time to reply to individual comments on this video. I just wanted to say thanks for taking the time to interact, continue to teach and spread mathematics to the public even after all of this time. I'm working on my first assignment for a Math 300 level course in Analysis of Complex Variables and am finding this helpful. It's very nice to know MIT and yourself have made these resources available for students. It's much appreciated. Thank you Professor Gross!
Thank you for the very kind words. I continue to be amazed by well-received these videos are even from students who are taking calculus for the first time. When the videos were made over 40 years ago, they were meant to be a review for practicing engineers and scientists who wanted to refresh their calculus backgrounds. Out of respect and appreciation for the viewers who have taken the time to comment I feel it is appropriate for me to acknowledge them while I still can As I approach the age of 85, I realize that I might not be able to do acknowledge these comments much longer but I feel very good knowing that these videos will go on helping others even when I am no longer here.
@@hgross3comcast Rest In Peace, Sir!!! Your works speak for you when even you are not around here among us. My sincere respect for everything you have done for us!!!
You are the best mathematics professor I have ever seen. Your explanations are very clear and easy to follow. I could have gone much farther if you had been my teacher. I have always loved math from a distance and watching your lectures has brought it into a much sharper focus for me. Thank You!
Prof. Gross, Thank you for producing these videos. I am a chemical engineer and theorist, I watch your video series at least once a year as a refresher in the "game" of mathematics. Whenever I meet a person, whom is interested in improving their understanding of mathematics, I recommend your videos. You do a wonderful job of presenting the true beauty of mathematics.
Dear Raul, Thank you for the very kind words (as well as for your endorsement of my work). It is greatly appreciated. I am particularly pleased that you refer others to my work, especially since I worry that people who might benefit the most from my work might not even know that it exists! With that in mind, there is a favor that I would like to ask of you. More specifically, except for the 5 years that I spent developing and producing the MIT “Calculus Revisited” video series, the rest of my teaching career was devoted to helping math-phobic adults overcome their fear of basic mathematics. Upon my retirement in 2003, I began developing my own website (www.mathasasecondlanguage.org) where all my work in arithmetic and algebra is available for anyone to use free of charge. I am hoping that you will let others know about the website because, as I mentioned above, I worry that people will not know that the website exists (especially since I don’t have the same name recognition as MIT!!) In any event, thanks again for your comment and I send you my best wishes and warmest regards!!
This video was so amazing. The energy of the delivery and the content itself was amazing. As a mechanical engineering student I tend to learn things in a very intuitive and visual manner, which is why complex numbers always scared me. But the way the real implications of the imaginary numbers were discussed, made me understand it in a heart beat. Can't wait to finish rest of the Lectures, and thank you so much for going through the trouble of recording them!
Thank you so much for posting these videos!! I love how you teach math! Your passion really shows and you make it very easy to understand. I'm a new undergraduate, very passionate about math, and these are the types of lectures I've been looking for for months! I think your integration of teaching the beautiful big concepts of mathematics along with the precise/practical problems is just the right balance and I wish the education system in America would do it this way. Thanks again so much!
Thanks Ashwith. It's an example that illustrates that there is nothing imaginary about "imaginary" numbers. In my mind it is results such as this that make mathematics a true liberal arts course that transcends its value to only math/science majors.
Prof. Gross, your classes are a great success among students and instructors in Joinville, SC, Brazil. Yes, we must be carefull as you are, to explain students that there is a difference between Euler´s formula e^(iθ):=cosθ+isinθ , and (e)^(iθ), understood as the irrational number e raised to a complex power, which can have infinite different values. Many, many thanks.
Mr Herb you are a real hero! I am an applied math graduate student (close to graduation) and I find your videos very clear, enjoyable, and humorous! I am taking 8xxx complex analysis course this semester sucking the life out of me, but I love math because it will help me solve real world problems!
Thanks, Michael. Making these videos was a labor of love then; and now it is pure love that I feel when read all the nice messages the videos have elicited. I have been amply rewarded by the show of support I have received from viewers like you.
Herb, i want to say THANK YOU very much for this amazing lecture. i finished my engineering without really understanding why do we need complex numbers and i always felt overwhelmed with it. but not after this video
+Doaa Al-Otoom You're very welcome. Making the videos was a labor of love for me and I am delighted that the course is helping you and, hopefully, many others.
Mr. Gross, I want to thank you whole heartedly for your presentation on these videos. You make the topics easier for me to swallow and at the same time being amazed by the content itself I have the feeling that of course I can concquer this. Although the course is from some years in the past, the topic is still very much the same I suppose. What more mathematical marvels await me?! I can only study this as a hobby for my age has reached a point that pursuing a job or even a carreer would make me my own laughingstock. This be as it may, often wishing I found this interest earlier in life, I can't help but being amazed at every new topic I am learning and ultimatily understanding. Once again, thank you! Sincerely yours, Jurgen Koopman - Holland, Vianen
THE STUDENTS ARE IN A GREAT NEED FOR ONLINE LECTURES FOR COMPLEX ANALYSIS (with theorem-proof kind), i beg you MIT put something like that online,there is so much calculus in R courses and so little in C on the other side this is a great insight into subject and a lecturer does an amazing job,thank you for sharing this :)
HG You are a great professor. So humble personality and clarity of presentation!! And sense of humor. It's a privilege to watch this video on complex numbers which half of people don't even understand, but mechanically do it.
I have had many great instructors in my many, many years as a student and take great pride in my in my day-in and night-out work as a university mathematics professor. In fact sometimes I even find myself believing that I'm really good at what I do, due primarily in part that I love doing it! I have always appreciated the balance of craftsmanship and creativity which must be sought in order to improve as an educator, and it wasn't until a few hours ago when I for the first time followed one of the links to one of professor Gross' lectures on complex line integration that it became clear to me that not only do I have A LOT of room for improvement, but also that perfection IS possible!!Your instruction is almost as humbling as it is inspirational. It has given me chills (not kidding) to consider how much your 34 minute lecture enhanced my understanding, and helped bridge connections among so many areas of complex analysis, calculus and beyond. You are without exaggeration THE BEST TEACHER I'VE EVER SEEN IN MY ENTIRE LIFE! :-D Thank you Professor Herbert Gross! BRAVO!
+Christopher Berghout Your glowing tribute makes me feel quite humble. To this day I recall the angst I experienced when Harold Mickley, the founding director of MIT’s Center for Advanced Engineering Study (CAES) told me that he wanted me to make a video version of my “Calculus Revisited” course. At the time, my only previous experience was teaching at a small community college and I worried about how my course would be perceived by those who were bona fide university professors. It was a huge leap forward from teaching Fellows in the privacy of a small classroom. Comments such as yours validate the time I spent, together with Harold, meticulously planning each lecture and reviewing the prewritten black boards (actually they were green) prior to my presenting each lecture. So thank you for the very kind words. Should you care to communicate with me further, please feel free to write to me at hgross3@comcast.net.
Oh,my god great professor,I am extremely lucky that I can hear professor's lecture,in the time of releasing from MIT,every sentence of the lecture is extremely inspiring,the treasure of professor's lecture will be internal,thanks again,it is great honor to watch lectures and comment on this.
This is really tremendous teaching ! The analogy presented at the beginning showing expansion of the integer number set to include fractions .... in order to find solutions for certain kinds of problems where it actually makes sense to have a solution.... is really brilliant and beautiful. Thanks so much! Many years have passed since this teaching took place but I've never seen it done better.
Thanks James. You’ve hit upon the “slippery slope” I was on in developing this course. On the one hand my presentations had to be relatively rigorous (at least rigorous enough so as to not make mathematicians weep); while at the same time it had to be sufficiently transparent to my target audience (namely, engineers and scientists who were coming to MIT for post graduate study) to hold their interest. And based upon the many comments I have seen, it seems that my approach helped a lot of viewers. At age 88 I am developing my own website (www.mathasasecondlanguage.org) where I am trying to bring this same approach to arithmetic and algebra. All of my work in those is being made available on the website for anyone to use free of charge. Thanks again for your kind words and I send you my best wishes and warmest regards.
Oh man. Are you the real Herbert Gross? I never thought I would get a real reply back! That's crazy! I have watched close to every lecture of yours that MIT has uploaded! You are an amazing lecturer. I've never seen an explanation as clear as yours anywhere else. This series on complex numbers and the "calculus revisted" in particular are fantastic. Thanks for making them!
I noticed Dr. Gross was in the comments, so I needed to thank you for all your fantastic lectures. You are a brilliant teacher with a natural ability to relate higher level math in clear and engaging ways.
Nielzen E Dear Nielzen, Thank you for the very kind words. While it might not address your comment directly, I am very pleased that OCW has effectively cloned me. More specifically, the fact that this video, at the time I am writing this, has had almost 126,000 views from viewers from around the world and since so many comments indicate that my videos have had aprofound positive impact on many students indicates that I have been a “virtual instructor” for many students. The reason I mention this is that my course is not alone not alone, While there is a lot of clutter on the internet there are many courses that have had the same effect as my course has had. So my thought is that the courses that are available on the internet are a game changer to how courses are currently taught. For better or for worse, the fact exists with respect to any video is that every viewer, in every location and at every point of time sees exactly the same thing! What could possibly be more systemic than this???
Professor Herbert Gross, you're lectures are amazing! I wish I discovered them before. I never realized I could get the expressions for cos(nA) and sin(nA) using complex numbers. That's brilliant (I do, however, feel a bit stupid now for not noticing this before :-( ). I would always do it the "hard" way using trigonometry. Thank you for these videos!
Thank you for the very kind words, Phillip. I would say that the late Harold Mickley, the founding Director of MIT’s Center for Advanced Engineering Study (CAES), deserves the credit as well. I was 38 years old at the time, teaching at a community college and had only a B. A. degree when Harold recruited me to develop the “Calculus Revisited” program for CAES. I was overwhelmed by the faith he had in my ability. Had it not been for Harold, I would have been like the tree in the forest that fell with no one there to hear it. 45 years have passed since I completed that project and I am still in awe by how well the course has been received. Being able to work with Harold remains a major highlight of my professional career.
thank you Herb for your reply. I feel that it is your ability to leave NOTHING to the imagination that makes your Lectures so CLEAR and Concise. Toss in your moments of HUMOR and you have a HIT on your hands.. For example when you talked about the guy that had his feet in the oven and an Ice Pack on his head and HE claimed that on AVERAGE he was just fine.. LOL.. or how about when you mentioned the Guy that fell off the Empire State bldg and someone asked how he was doing and he responded with, SO FAR, SO GOOD.... lol... but it was your TIMING of those Humorous comment that were, well, TIMELY.. so THANK YOU... I'm still going through your videos.. I have to admit.. It is hard to believe that you only had a BA degree at the time you taped those lectures... Your grasp of the PURITY of Math and your way of Conveying it reflect the Magic and Talent in your Presentation.... By the way, I"m 63 years old and I'm FINALLY enjoying the chance to reLEARN Calculus and Physics without the pressure of getting Good Grades.. THANKS HERB..
Thank you for your in-depth response to my comment, The truth is that it was never my intention to become a mathematician. In fact my aspiration was to become a high school math teacher. In terms of a sports analogy, I preferred to become a coach than to become a player. However to become a good coach you have to understand the sport even better than most players do; and it was for that reason that I decided to enroll in a math Ph.D. program at MIT. In my 5th year at MIT, I was given the opportunity to become the founding math department chairperson at Corning (NY) Community College. The word “community” resonated with me and so began my full time 50 year teaching career. I never did complete my doctoral studies and I was able to get by with only my B.A. from Brandeis University. Through MIT‘s name recognition, I became known internationally by how well I taught calculus; but my “pride and joy” was teaching basic math to math-challenged adults with the hope of having them get over their fear of mathematics. In fact since my retirement in 2003 I have been busy developing my own website (www.mathasasecondlanguage.org) where all of my work in arithmetic and algebra is available for anyone to use free of charge. As an anecdotal aside, Harold Mickley really enjoyed my sense of humor but asked me to try to avoid telling jokes in the lectures because he anticipated that the average viewer would view a given video more than once and he was afraid they might become annoyed having to hear the same joke over and over. So what you are seeing with respect to my sense of humor is a very subdued Herb Gross. And now you know the rest of the story!!!
+Herb Gross Being a Physics graduate of some vintage, with real-life experience and occupation veering far from that discipline, it was sheer serendipity to have discovered these wonderful lectures on the 'Going Back to School' route. Thank you, Mr. Herbert Gross. I was also curious to know when these lectures were actually recorded - the black and white presentation gives these lectures a reverential polish. Bless you, Sir.
Dr. Herbert Gross, thank you for this teaching. You are a great teacher with a kind smile on your face. This lecture removed most of my confusions regarding complex variables. ☺
Your courses are helping me understand calculus and complex variables I'm almost through with my 1st year of Electronics and the math classes were challenging last semester so this semester i'm studying a lot more.. thanks Mr. Gross..
It has been over 40 years since I developed the course and I don't have total recall of what was included and what was omitted. My guerss is that if it isn't in the lecture on integrating complex valued functions it wasn't included in my work. My complex variable videos were meant to be an introduction to the subject rather than a complete course. It was intended as a "heads up" as to what the topic entailed.
Thank you, Gonzalo. It was like two different careers. In terms of a sports analogy, I played math at MIT but I coached math at the community college. I loved both jobs. And in that spirit I am as proud of the basic math material that I have made available on my own website (www.mathasasecondlanguage.org) as I am of the video courses I made for MIT.
Thanks R T What amazes me the most is that my video lectures are receiving the type of response that one would hopefully expect to receive for a good live lecture. It gives me hope that I will be able to teach others effectively even when I am no longer here. And now that I am in my 90th year, I find this thought to be particularly appealing!
Thanks Ogechi. It has been over 40 years since I have even looked at complex variables so I must leave it to others to advise you about textbooks. However if you go to wwwocwmitedu and look under “supplementary resources” you will find “Calculus Revisited” listed under “mathematics”. My study guide, supplementary notes and lectures for my segment on complex variables are all available there. And if you Google “herb gross math” you will find other references to work that I’ve done.
MIT, I love you too! Very nice what you are doing. I am donating to the opencourse and I will ask my friends on facebook to donate too. This service is VERY great to humanity.
I never memorized a proof. Rather I would read the proof and make sure I understood it (even though I might not know how the author discovered it). I would then try to see why it was important and how it was to be used in what followed. I found that once I became comfortable with the theorem and its applications, the proof became easier for me to internalize. I hope this helps even a little!!
I don't think I am brilliant. However I do know that for over 50 years teaching has always been a labor of love for me;and messages such as yours give me much satisfaction. Thanks for taking the time to comment.
Thank you very much for explaining this so clearly. I'm learning this on my own because I'm switching careers (I'm an accountant). I've also noticed you're commenting on these lectures. You are an amazing human being! Thank you for helping us all in our quest to understand mathematics.
Thanks Scott. I guess I’m programmed to acknowledge anyone who takes the time to comment about my work and the influence it might have had on them. Comments such as yours serve to validate to me that it was well worth the time and effort it took for me to produce the calculus series. My current goal is to complete my own website (www.mathasasecondlanguage.com) where I am uploading all of my work in arithmetic and algebra for anyone to use free of charge. Once again, thanks for writing and I extend to you my very best wishes for success in all of your endeavors, especially in your change of careers.
Awesome lecture, absolutely awesome. If you read this Mr. Herb Gross, I want to thank you. You have succinctly and brilliantly 'uncovered' in 40 minutes what would otherwise have taken many long classes.
Thank you for the very kind words. I think they are words that would please every teacher; and I appreciate your having taken the time to comment. As a matter of common decency I try to respond to every message, except for those that in my mind don’t seem to require a response. I invite viewers to write to me directly at hgross3@comcast.net so that I don’t clutter this website with lengthy messages. Your comment reminded me of one of my favorite sayings, namely, “The job of a good teacher is not to cover ground but rather to uncover it”. And I am pleased that this happened when you watched my presentation. I hope this continues to happen as you continue to watch more of the presentations. Feel free to keep me informed of your progress. In the meantime I send you my best wishes
In “Memory of Herb Gross” A tribute to a great educator and great human being: www.ocw-openmatters.org/2020/06/10/in-memory-of-herb-gross/
When I developed this series I never expected to see it on the Internet more than 40 years later. It gives me great pleasure to see that my work is now helping a new generation of students, many of whom were not yet born when the series was developed.
I truly appreciate your taking the time to write to me and telling you how much the course is helping you.
is this you ?~
@@kumaran7971 he passed away bro
@@kumaran7971 This comment was from the real Herb Gross, who has passed away.
;-; my heart hurts
legendary
RIP Herbert Gross. Your lectures will continue inspiring students and educators, as they’ve always have.
He was such an amazing person as a teacher and as a person.May his soul rest in peace!!!
When did he die? He was alive 5 years ago, as I see some of his replies to comments under MIT videos.
@@pinklady7184 He passed away on May this year.
ah rip I remember when he was alive
@@99bits46 yes I remember too, like 9 months ago
Thanks for the very kind compliment. I have always tried to live up to the advice that says “Never think so much of your subject that you neglect your subjects!” Another one of my favorites is “People don’t care how much you know until they know how much you care”. It may seem extremely self-centered but I am very pleased at the number of personal email messages I am receiving by viewers who tell me how much they appreciate the course.
bro i've come here to learn, not to feel..
Dear Shu'aib,
Messages such as yours make me feel much younger than my 84 years. As I’ve commented several times before, it is a great feeling to know that work I did over 40 years ago is still continuing to help people.
I send you my best wishes.
Thanks for your kind words. My own belief is that the type of teachers we had then is pretty much the same as it is now. The huge difference is that we can now clone the best (that is, video them and upload their lectures) and have them teach globally. It is a whole new world in that respect and it amazes an old guy like me.
I had to chuckle at your unique compliment. I am pleased that you are enjoying my course. It is a wonderful feeling, especially in my old age, to see someone learning from a lecture series I developed over 40 years ago. Thanks for taking the time to write.
This is truly the greatest maths related playlist ever, as someone who only had done maths uptill high school and all of a sudden had to solve problems related to complex numbers later on in life, this playlist was truly a gift to humanity.
Thank you Sir Herbert Gross, you will always be remembered. 🙏
I just saved this to my "EPIC" playlist. This was an EPIC lecture. I'm an MD PhD and practicing academic neurosurgeon that went to Cal and I have seen thousands of lectures in person and online on a multitude of topics and this lecture goes into my Hall of Fame.
Time independent Lectures. Honestly speaking, Professor Herbert belongs to the League of Leibnitz, Euler and Einstein.Geniuses like him with such ability to present such a topic as this in such lucid manner are seldom seen. I am very sure, mit would not have found a replacement. "Men may come, Men may go, but Herbert Gross is a jewel in the Crown"
i never taught someone would be comparable gilbert strang,but he is professor herbert is far superior
Thanks again! The original intent of the complex variable segment of "Calculus Revisited" was to give viewers an overview of the subject and thus (hopefully) to make it easier for them to internalize a more formal, in-deo\pth course. I am very pleased that this seems to have happened in your case. Good luck in your upcoming exam!!!
it saddens my heart when I see people who have chosen profession as teachers and they are so kind and gentle in their words but do not get acknowledgement or are treated badly.
My god. He's so happy. I can't wait to finish all these lectures.
i feel like every math lecture i go to you comment, lol, prof Leonard and like half of Mit's videos
gaming with logan Me? I have commented on a lot of math videoes, lol.
@@loganborghi5727 hello 5 years later : ^)
R.i.p. Professor Gross, you warmed my heart with your passion for teaching and my warmed my brain to math.
I love this guy! What a great lecturer! RIP, Herb. Thanks for this labor of love. It truly is a treasure.
Holy shit! Hebert Gross is the clearest,most articulate, and most eloquent math teacher I've ever heard/had. Absorbing this material was so fast, easy and organic. Thank you for the course!
I love the precision!
Dr. Professor Herbert Gross is easily the best professor of mathematics ever. His videos still remain to this day (2017) the very best of the best. That is not said to diminish in any way whatsoever the other math videos that have been produced by so many other great professors. It would be very wise of any math student to get as much instruction from as many learned math prof's as possible. And with TH-cam, etc., we all have the capability of doing that. But the start and the end of math education in America is and will always be with Prof. Gross. Thank you so much Dr. Gross for your contribution to humanity. It is so crystal clear that you deeply care, and have always cared, and will always care. Dr. Gross is, and has always been. and will always be a true Mensch.
Thank you Major for writing such a tribute to me. I hope that when my time comes to be eulogized, the speaker will be as eloquent as you. Having said that, I want to reinforce what you said about the Internet. More specifically, as well received as my lectures have been, they have still generated “dislikes” from some viewers. It is nice to know that those who don’t like my lectures will be able to find many alternatives to my approach, some of which might resonate with them. It is my opinion that the Internet will eventually revolutionize how we teach. In my own case, I feel blessed that the Internet “cloned” me, at least in the sense that it will enable the 42 year old Herb Gross in the videos to continue teaching even when the present 88 year old Herb Gross.
Thanks for your kind words! My subjective point of view is that for every student, especially the millions who do not intend to pursue a math/science/technology - oriented career, it is far more important for them to learn to understand the logical structure of mathematics and the critical thinking that it involves than to memorize how to ”plug in” numbers to equations.
Hi Everyone. When I was a young man going to university in the 70's there were many of my lecturers that had the same enthusiasm and delivery that Herb did.
They were dedicated professionals who loved what they did and they were good at it.
Just like you see here with Herb, I was lucky enough to have Maths and Physics professors who knew how to teach a subject, because they really understood the material, and knew how to put it across. Thanks Herb.
The first ten minutes of this class is enough for every student to get rid of all the mechanical crap that is teached on high school (and colleges) with respect to complex numbers. We all know that Prof. Gross put a lot of effort to organize these classes and all were worth with.
What I've learned:
1) There are black chalks
2) Things written by white chalks have shadows
3) Some good english
i) About complex numbers
Hes writing with a white marker on a clear plastic board
I like the black chalk
A work of art. Even the toughest portions are executed with clear, concise, grammatically and syntactically correct language.
Hi Alan,
From my subjective point of view your comment is very interesting. More specifically, my complex variable mini-course was meant only to help a student get an idea of what the subject was about before enrolling in a full-fledged course. The same was true about my mini-courses in differential equations and linear algebra. So it is extremely pleasing that someone at your level found it to be valuable. Thank you for taking the time to write.
This is my favorite series of educational mathematics videos. Thank you MIT for making this series available to the general public for free...........
Thanks Gus
One of the great things about the potential of the Internet is that it can make a master teacher available to any student in any location and in any point of time. In essence it may allow us to clone mater teachers. In addition such a delivery system is time-independent, meaning that the viewers are not restricted by the lock-step pace of the traditional school class room.
This is by far the best way that some one can explain complex numbers. Amazing what a good teacher can do...
"When the student is ready the master will appear" ... These lectures, with the amazing responses they are generating, are the perfect example of that! It's amazing how you tie so much together without letting the main points get lost in details ... best introduction I've seen after several undergrad and grad level courses.
+Jon Hofmann Thankyou Jon. My “game plan” in all of my video courses is to use the lectures to emphasize the “great ideas” and the accompanying written material to highlight the “nuts and bolts”. My feeling is that it is my lectures that drive the rest of my wok. I should point out that TH-cam has only the videos but to make use of the course’s written materials one has to go to the
OpenCourseWare website.
+Herb Gross Thank you so much. I'll check that out directly.
Hi Ron,
If color had been an option at the time I would have preferred it. However we went with what we had and I feel very happy that so many viewers were pleased with what the final outcome was. My guess is that people who are visiting the OCW website are looking primarily for good content and it doesn’t matter whether what the delivery system is. I often gave a talk that was entitled “Delivering Stale Donuts in a Rolls Royce Doesn’t Make the Donuts Any Fresher".
A number of viewers have asked me about the square root of a positive number. There are 2 numbers whose square is 4; namerly 2 and -2. Thus one should ask "What is the positive square root of 4?" or "What is the negative square root of 4?" When the sign isn't mentioned it is an agreed-upon convention that
"What is the sqaure root of 4?" means "What is the postive square root of 4?"
These (and his other) lectures are excellent and Herb Gross is a legend for responding to youtube comments and emails until the very end.
A few years before he died I emailed him thanking him for these lectures and mentioned that I live fairly close to him. He responded with something like "perhaps if you're nearby we could meet." I'm sure he was just being polite but I also couldn't pass up an opportunity to meet with a famous youtube celebrity, so I told him sure, I could meet at a park near you. Alas, he was probably busy and didn't respond again.
I don't know if he had children but I can imagine the conversations between them: "Janet, can you call and check on dad? He's talking about going to meet some weirdo from youtube at the playground again!"
So that's my story of how I maybe almost hung out with Herb Gross at the park but didn't.
Professor Gross,
I am on a post-graduate course in complex variables and have previously covered much of the material in your course, Yet I found every one of your lectures full of new facets and insights which have further illuminated and enhanced my understanding of the subject. Like others who have posted comments, I have thoroughly enjoyed viewing your course. Thank you so much for these lectures and the superb clarity of your delivery.
I'm very impressed with not only the clarity of the professor's explanations, but the precision of language employed.
Math is beautiful. Feeling gifted to study math through this course. RIP Sir.
Is this university math?
Mr. Gross, I am in the final year of getting my Math undergraduate degree and I must say you are one of the best teachers I have had to date. You make otherwise difficult concepts easy to understand. Thank you for all your work!
You are by far - one of the most talented teachers I have ever witnessed. We need more teachers like you.
Thank you.
This world needs more professors like you. You make me love math again. Thank you sir!
I never knew math to be so compelling. Professor makes all the difference.
+vysoc
There is an adage that says “The music is not in the guitar”. In that context, a textbook is the guitar and the instructor is the person who is playing the guitar. In that sense it is a truism, in every walk of life, that some guitar players produce better music than others. On a personal note, in producing this calculus series, I did lots of practicing before I “playedany of the piece” in public.
I don't know how i can measure my pleasure to see a senior lecturer as herb Gross.wish you best in your entire life
Thank you for the kind words. I greatly appreciate them. I feel greatly honored by how well my work has been received even though it is almost 50 years since I produced the course.
This is probably the single greatest introductory lecture to any mathematical subject I have ever encountered. It's conceptually clear, mathematically precise and beautifully explained by someone who clearly both knows exactly what he's talking about and who he's speaking to. And I absolute love how carefully Prof. Herbert words his statements. If every mathematics teacher in the world taught like Prof. Herbert Gross, we'd all be mathematicians right now.
Thanks for that very complimentary comment. Although I appreciate the gift I have for teaching I believe that much of the credit for this course belongs to my “boss” Harold Mickley, who allowed me to take as much time as I needed to produce a script with which I was satisfied (in this case the script was the prewritten “green boards”). In addition to that, whenever a video was completed, he and I would go over it line by line to ensure that there were no major glitches in it (we let minor verbal and written typos go because correcting them meant redoing the entire lecture). In short, I think I would have done a decent job regardless but with Harold’s expertise to help guide me, the series has become sort of a cult classic. My only regret is that Harold passed away before he had a chance to read the kind comments that viewers such as you have written!
I belong to PhD in chemistry, but always more interested in mathematics and physics...complex analysis has great importance in quantum mechanics (or chemistry). I loved the way of your teaching and the flow in which you poured the concepts in my mind. Kudos sir...thankew
RIP Professor Gross. Your lectures would always inspire people!!
Absolutely incredible. I just finished the series on Complex Variables and thoroughly loved every single one. Thank you so very much.
My friends always say that complex number is difficult to visualize, and I thought so as well, but this video clears it up so well with those examples. Thank you.
I literally love you, Mr. Herbert Gross! Very clear and simple explanation. Jumping now to part two of the complex analysis.
I was in need of a refresher on complex numbers for a project at work, as it's been some years since I've last had to work with them, and I have to say I'm quite pleased I stumbled upon this splendid lecture series. Wow. If only my original complex analysis professor had been as succinct as yourself, Herb Gross, perhaps I might have retained it far better. Thank you so very much.
I was searching for resources to understand more of complex variables and I happened to stumble upon this. Herbert Gross, you are truly a great teacher, I ended up enjoying this video. I felt like I was learning for the fun of it when I was watching this, rather than studying for the sake of understanding the confusion I have in class. This video is truly "old but gold".
Thank you for these amazing lectures.
Thanks for your kind words. In my opinion the difference between work and play is the degree of enjoyment rather than the degree of difficulty. In that sense it is not contradictory for students to learn and have fun simultaneously! I am pleased that you seem to have done both.
I was genuinely shocked to see the actual professor from these lectures, Professor Herbert Gross, taking the time to reply to individual comments on this video. I just wanted to say thanks for taking the time to interact, continue to teach and spread mathematics to the public even after all of this time. I'm working on my first assignment for a Math 300 level course in Analysis of Complex Variables and am finding this helpful. It's very nice to know MIT and yourself have made these resources available for students. It's much appreciated. Thank you Professor Gross!
Thank you for the very kind words. I continue to be amazed by well-received these videos are even from students who are taking calculus for the first time. When the videos were made over 40 years ago, they were meant to be a review for practicing engineers and scientists who wanted to refresh their calculus backgrounds. Out of respect and appreciation for the viewers who have taken the time to comment I feel it is appropriate for me to acknowledge them while I still can
As I approach the age of 85, I realize that I might not be able to do acknowledge these comments much longer but I feel very good knowing that these videos will go on helping others even when I am no longer here.
Herb Gross thank you for contributions. We are learning much from great people like you.
@@hgross3comcast Rest In Peace, Sir!!! Your works speak for you when even you are not around here among us. My sincere respect for everything you have done for us!!!
You are the best mathematics professor I have ever seen. Your explanations are very clear and easy to follow. I could have gone much farther if you had been my teacher. I have always loved math from a distance and watching your lectures has brought it into a much sharper focus for me. Thank You!
Prof. Gross, Thank you for producing these videos. I am a chemical engineer and theorist, I watch your video series at least once a year as a refresher in the "game" of mathematics. Whenever I meet a person, whom is interested in improving their understanding of mathematics, I recommend your videos. You do a wonderful job of presenting the true beauty of mathematics.
Dear Raul,
Thank you for the very kind words (as well as for your endorsement of my work). It is greatly appreciated. I am particularly pleased that you refer others to my work, especially since I worry that people who might benefit the most from my work might not even know that it exists!
With that in mind, there is a favor that I would like to ask of you. More specifically, except for the 5 years that I spent developing and producing the MIT “Calculus Revisited” video series, the rest of my teaching career was devoted to helping math-phobic adults overcome their fear of basic mathematics. Upon my retirement in 2003, I began developing my own website (www.mathasasecondlanguage.org) where all my work in arithmetic and algebra is available for anyone to use free of charge. I am hoping that you will let others know about the website because, as I mentioned above, I worry that people will not know that the website exists (especially since I don’t have the same name recognition as MIT!!)
In any event, thanks again for your comment and I send you my best wishes and warmest regards!!
i'm a chinese students ~I was thrilled after i sew through your video courses ~the concept is so clear, the idea is so inspiring ~ i respect you~
This is one of the best lectures I've ever heard. Never before have I felt such a concrete grasp on the concept of complex numbers.
What an astoundingly brilliant teacher Herbert Gross is. Thank you sir. Wonderful!
The best lecture ever.Some people are just born to know how to transfer great knowledge in a simple way.Thank you. :)
Only someone that truly understands the subject can give such clear insight on the mysterious world of complex analysis. Thank you!
This is 2019 and I cant even express how awesome of a lecture this is! Till today I had never seen such good description and explanation. THANK YOUUU!
This video was so amazing. The energy of the delivery and the content itself was amazing. As a mechanical engineering student I tend to learn things in a very intuitive and visual manner, which is why complex numbers always scared me. But the way the real implications of the imaginary numbers were discussed, made me understand it in a heart beat. Can't wait to finish rest of the Lectures, and thank you so much for going through the trouble of recording them!
Thank you so much for posting these videos!! I love how you teach math! Your passion really shows and you make it very easy to understand. I'm a new undergraduate, very passionate about math, and these are the types of lectures I've been looking for for months! I think your integration of teaching the beautiful big concepts of mathematics along with the precise/practical problems is just the right balance and I wish the education system in America would do it this way. Thanks again so much!
Thanks Ashwith. It's an example that illustrates that there is nothing imaginary about "imaginary" numbers. In my mind it is results such as this that make mathematics a true liberal arts course that transcends its value to only math/science majors.
Prof. Gross, your classes are a great success among students and instructors in Joinville, SC, Brazil. Yes, we must be carefull as you are, to explain students that there is a difference between Euler´s formula e^(iθ):=cosθ+isinθ , and (e)^(iθ), understood as the irrational number e raised to a complex power, which can have infinite different values. Many, many thanks.
Mr Herb you are a real hero! I am an applied math graduate student (close to graduation) and I find your videos very clear, enjoyable, and humorous! I am taking 8xxx complex analysis course this semester sucking the life out of me, but I love math because it will help me solve real world problems!
As always, Herb, your brilliance, clarity, and joy shines through. Thank you for sharing it with us all.
Thanks, Michael. Making these videos was a labor of love then; and now it is pure love that I feel when read all the nice messages the videos have elicited. I have been amply rewarded by the show of support I have received from viewers like you.
Herb, i want to say THANK YOU very much for this amazing lecture. i finished my engineering without really understanding why do we need complex numbers and i always felt overwhelmed with it. but not after this video
+Doaa Al-Otoom You're very welcome. Making the videos was a labor of love for me and I am delighted that the course is helping you and, hopefully, many others.
Mr. Gross, I want to thank you whole heartedly for your presentation on these videos. You make the topics easier for me to swallow and at the same time being amazed by the content itself I have the feeling that of course I can concquer this. Although the course is from some years in the past, the topic is still very much the same I suppose. What more mathematical marvels await me?! I can only study this as a hobby for my age has reached a point that pursuing a job or even a carreer would make me my own laughingstock. This be as it may, often wishing I found this interest earlier in life, I can't help but being amazed at every new topic I am learning and ultimatily understanding. Once again, thank you! Sincerely yours, Jurgen Koopman - Holland, Vianen
THE STUDENTS ARE IN A GREAT NEED FOR ONLINE LECTURES FOR COMPLEX ANALYSIS (with theorem-proof kind), i beg you MIT put something like that online,there is so much calculus in R courses and so little in C
on the other side this is a great insight into subject and a lecturer does an amazing job,thank you for sharing this :)
Such an amazing teacher! You're helping out big time in ORLANDO, FL! I recommend your videos to all my classmates. Thank you!
HG You are a great professor. So humble personality and clarity of presentation!! And sense of humor. It's a privilege to watch this video on complex numbers which half of people don't even understand, but mechanically do it.
I have had many great instructors in my many, many years as a student and take great pride in my in my day-in and night-out work as a university mathematics professor. In fact sometimes I even find myself believing that I'm really good at what I do, due primarily in part that I love doing it! I have always appreciated the balance of craftsmanship and creativity which must be sought in order to improve as an educator, and it wasn't until a few hours ago when I for the first time followed one of the links to one of professor Gross' lectures on complex line integration that it became clear to me that not only do I have A LOT of room for improvement, but also that perfection IS possible!!Your instruction is almost as humbling as it is inspirational. It has given me chills (not kidding) to consider how much your 34 minute lecture enhanced my understanding, and helped bridge connections among so many areas of complex analysis, calculus and beyond. You are without exaggeration THE BEST TEACHER I'VE EVER SEEN IN MY ENTIRE LIFE! :-D Thank you Professor Herbert Gross! BRAVO!
+Christopher Berghout
Your glowing tribute makes me feel quite humble. To this day I recall the angst I experienced when Harold Mickley, the founding director of MIT’s Center for Advanced Engineering Study (CAES) told me that he wanted me to make a video version of my “Calculus Revisited” course. At the time, my only previous experience was teaching at a small community college and I worried about how my course would be perceived by those who were bona fide university professors. It was a huge leap forward from teaching Fellows in the privacy of a small classroom.
Comments such as yours validate the time I spent, together with Harold, meticulously planning each lecture and reviewing the prewritten black boards (actually they were green) prior to my presenting each lecture. So thank you for the very kind words. Should you care to communicate with me further, please feel free to write to me at hgross3@comcast.net.
Professor Gross, you are brilliant, thank you for being such an inspirational person.
Oh,my god great professor,I am extremely lucky that I can hear professor's lecture,in the time of releasing from MIT,every sentence of the lecture is extremely inspiring,the treasure of professor's lecture will be internal,thanks again,it is great honor to watch lectures and comment on this.
You are just a killer sir!!.. First time in my life you have led to this depth of mathematics... YOU ARE GREAT!!! NO WORDS
This is really tremendous teaching ! The analogy presented at the beginning showing expansion of the integer number set to include fractions .... in order to find solutions for certain kinds of problems where it actually makes sense to have a solution.... is really brilliant and beautiful. Thanks so much! Many years have passed since this teaching took place but I've never seen it done better.
Thanks James.
You’ve hit upon the “slippery slope” I was on in developing this course. On the one hand my presentations had to be relatively rigorous (at least rigorous enough so as to not make mathematicians weep); while at the same time it had to be sufficiently transparent to my target audience (namely, engineers and scientists who were coming to MIT for post graduate study) to hold their interest. And based upon the many comments I have seen, it seems that my approach helped a lot of viewers.
At age 88 I am developing my own website (www.mathasasecondlanguage.org) where I am trying to bring this same approach to arithmetic and algebra. All of my work in those is being made available on the website for anyone to use free of charge.
Thanks again for your kind words and I send you my best wishes and warmest regards.
Many thanks to this great lecturer, for the simplest and best introduction to complex numbers and analysis!
This got to be the best lecture ever on introduction to complex numbers. Thank you.
Oh man. Are you the real Herbert Gross? I never thought I would get a real reply back! That's crazy! I have watched close to every lecture of yours that MIT has uploaded! You are an amazing lecturer. I've never seen an explanation as clear as yours anywhere else. This series on complex numbers and the "calculus revisted" in particular are fantastic. Thanks for making them!
I noticed Dr. Gross was in the comments, so I needed to thank you for all your fantastic lectures. You are a brilliant teacher with a natural ability to relate higher level math in clear and engaging ways.
I can't be more grateful for such a gifted professor. He has made me love mathematics even more. We need more professors like him!
Nielzen E
Dear Nielzen,
Thank you for the very kind words. While it might not address your comment directly, I am very pleased that OCW has effectively cloned me. More specifically, the fact that this video, at the time I am writing this, has had almost 126,000 views from viewers from around the world and since so many comments indicate that my videos have had aprofound positive impact on many students indicates that I have been a “virtual instructor” for many students. The reason I mention this is that my course is not alone not alone, While there is a lot of clutter on the internet
there are many courses that have had the same effect as my course has had. So my thought is that the courses that are available on the internet are a game changer to how courses are currently taught. For better or for worse, the fact exists with respect to any video is that every viewer, in every location and at every point of time sees exactly the same thing! What could possibly be more systemic than this???
Professor Herbert Gross, you're lectures are amazing! I wish I discovered them before. I never realized I could get the expressions for cos(nA) and sin(nA) using complex numbers. That's brilliant (I do, however, feel a bit stupid now for not noticing this before :-( ). I would always do it the "hard" way using trigonometry. Thank you for these videos!
thank you Herb Gross for your RARE Talent of Lecturing in a most straight forward manner. You deserve all the credit . thank you.
Thank you for the very kind words, Phillip. I would say that the late Harold Mickley, the founding Director of MIT’s Center for Advanced Engineering Study (CAES), deserves the credit as well. I was 38 years old at the time, teaching at a community college and had only a B. A. degree when Harold recruited me to develop the “Calculus Revisited” program for CAES. I was overwhelmed by the faith he had in my ability. Had it not been for Harold, I would have been like the tree in the forest that fell with no one there to hear it. 45 years have passed since I completed that project and I am still in awe by how well the course has been received. Being able to work with Harold remains a major highlight of my professional career.
thank you Herb for your reply. I feel that it is your ability to leave NOTHING to the imagination that makes your Lectures so CLEAR and Concise. Toss in your moments of HUMOR and you have a HIT on your hands.. For example when you talked about the guy that had his feet in the oven and an Ice Pack on his head and HE claimed that on AVERAGE he was just fine.. LOL.. or how about when you mentioned the Guy that fell off the Empire State bldg and someone asked how he was doing and he responded with, SO FAR, SO GOOD.... lol... but it was your TIMING of those Humorous comment that were, well, TIMELY.. so THANK YOU... I'm still going through your videos.. I have to admit.. It is hard to believe that you only had a BA degree at the time you taped those lectures... Your grasp of the PURITY of Math and your way of Conveying it reflect the Magic and Talent in your Presentation.... By the way, I"m 63 years old and I'm FINALLY enjoying the chance to reLEARN Calculus and Physics without the pressure of getting Good Grades.. THANKS HERB..
Thank you for your in-depth response to my comment, The truth is that it was never my intention to become a mathematician. In fact my aspiration was to become a high school math teacher. In terms of a sports analogy, I preferred to become a coach than to become a player. However to become a good coach you have to understand the sport even better than most players do; and it was for that reason that I decided to enroll in a math Ph.D. program at MIT.
In my 5th year at MIT, I was given the opportunity to become the founding math department chairperson at Corning (NY) Community College. The word “community” resonated with me and so began my full time 50 year teaching career. I never did complete my doctoral studies and I was able to get by with only my B.A. from Brandeis University. Through MIT‘s name recognition, I became known internationally by how well I taught calculus; but my “pride and joy” was teaching basic math to math-challenged adults with the hope of having them get over their fear of mathematics. In fact since my retirement in 2003 I have been busy developing my own website (www.mathasasecondlanguage.org) where all of my work in arithmetic and algebra is available for anyone to use free of charge.
As an anecdotal aside, Harold Mickley really enjoyed my sense of humor but asked me to try to avoid telling jokes in the lectures because he anticipated that the average viewer would view a given video more than once and he was afraid they might become annoyed having to hear the same joke over and over. So what you are seeing with respect to my sense of humor is a very subdued Herb Gross.
And now you know the rest of the story!!!
+Herb Gross
Being a Physics graduate of some vintage, with real-life experience and occupation veering far from that discipline, it was sheer serendipity to have discovered these wonderful lectures on the 'Going Back to School' route. Thank you, Mr. Herbert Gross. I was also curious to know when these lectures were actually recorded - the black and white presentation gives these lectures a reverential polish. Bless you, Sir.
+Sumit Dutta Gupta From another comment down below Herb Gross mentions that it was around 1972 when these where recorded.
Thank you for the information.
Don, of course there is. This particular course is useful for physicists, and I am learning it right now for electrical engineering.
Awesome course! As a college student in China, I'm impressed by your systematic teaching ways!
Dr. Herbert Gross, thank you for this teaching. You are a great teacher with a kind smile on your face. This lecture removed most of my confusions regarding complex variables. ☺
Rest In Peace,Sir!!!! You truely lived a life.My sincere respect for everything you have done for us!!!
This has really got me energised to study complex numbers more! Thanks Professor Gross.
Thank you for the very kind words. I truly appreciate what you have said and I wish you much success and fulfillment.
Your courses are helping me understand calculus and complex variables I'm almost through with my 1st year of Electronics and the math classes were challenging last semester so this semester i'm studying a lot more.. thanks Mr. Gross..
This is the most clear explanation possible for a very complex theme.
These lectures are just amazing!
It has been over 40 years since I developed the course and I don't have total recall of what was included and what was omitted. My guerss is that if it isn't in the lecture on integrating complex valued functions it wasn't included in my work. My complex variable videos were meant to be an introduction to the subject rather than a complete course. It was intended as a "heads up" as to what the topic entailed.
I love that the lecturer taught at both MIT and a community college: good teachers are needed everywhere!
Thank you, Gonzalo. It was like two different careers. In terms of a sports analogy, I played math at MIT but I coached math at the community college. I loved both jobs. And in that spirit I am as proud of the basic math material that I have made available on my own website (www.mathasasecondlanguage.org) as I am of the video courses I made for MIT.
An absolute joy to watch and learn from. Thank you so much for providing these lectures.
Thanks R T
What amazes me the most is that my video lectures are receiving the type of response that one would hopefully expect to receive for a good live lecture. It gives me hope that I will be able to teach others effectively even when I am no longer here. And now that I am in my 90th year, I find this thought to be particularly appealing!
Sir you are amazing in your way of teaching!! Never had teachers like you in my life!!!
Thanks Ogechi. It has been over 40 years since I have even looked at complex variables so I must leave it to others to advise you about textbooks. However if you go to wwwocwmitedu and look under “supplementary resources” you will find “Calculus Revisited” listed under “mathematics”. My study guide, supplementary notes and lectures for my segment on complex variables are all available there. And if you Google “herb gross math” you will find other references to work that I’ve done.
MIT, I love you too! Very nice what you are doing. I am donating to the opencourse and I will ask my friends on facebook to donate too. This service is VERY great to humanity.
I just clicked at a random video. That man got my attention so much, that i now want to study calculus and i will watch the rest of the videos.
I never memorized a proof. Rather I would read the proof and make sure I understood it (even though I might not know how the author discovered it). I would then try to see why it was important and how it was to be used in what followed. I found that once I became comfortable with the theorem and its applications, the proof became easier for me to internalize.
I hope this helps even a little!!
I don't think I am brilliant. However I do know that for over 50 years teaching has always been a labor of love for me;and messages such as yours give me much satisfaction. Thanks for taking the time to comment.
Thank you very much for explaining this so clearly. I'm learning this on my own because I'm switching careers (I'm an accountant). I've also noticed you're commenting on these lectures. You are an amazing human being! Thank you for helping us all in our quest to understand mathematics.
Thanks Scott.
I guess I’m programmed to acknowledge anyone who takes the time to comment about my work and the influence it might have had on them. Comments such as yours serve to validate to me that it was well worth the time and effort it took for me to produce the calculus series. My current goal is to complete my own website (www.mathasasecondlanguage.com) where I am uploading all of my work in arithmetic and algebra for anyone to use free of charge.
Once again, thanks for writing and I extend to you my very best wishes for success in all of your endeavors, especially in your change of careers.
That man in video must be few decades dead. Bless him.
Awesome lecture, absolutely awesome. If you read this Mr. Herb Gross, I want to thank you. You have succinctly and brilliantly 'uncovered' in 40 minutes what would otherwise have taken many long classes.
Thank you for the very kind words. I think they are words that would please every teacher; and I appreciate your having taken the time to comment. As a matter of common decency I try to respond to every message, except for those that in my mind don’t seem to require a response. I invite viewers to write to me directly at hgross3@comcast.net so that I don’t clutter this website with lengthy messages.
Your comment reminded me of one of my favorite sayings, namely, “The job of a good teacher is not to cover ground but rather to uncover it”. And I am pleased that this happened when you watched my presentation. I hope this continues to happen as you continue to watch more of the presentations.
Feel free to keep me informed of your progress. In the meantime I send you my best wishes
This guy is one of the best mathematicians i've ever listened! Maybe the best!
@Herb Gross: Your lections are top - I am very attired in them and I learned many new things. Greetings from Germany.
You were a great professor. I learn so much from you lecture. You were clear.