I was surprised to see Mary Doiciani's name. She taught me to program in 1963 when I was in Junior High and went to a small class for the Hunter College faculty in place of my mother. It was an amazing opportunity that transformed my life!
I am so happy to read this, as you have a first hand account! Could you please tell me how she was as an instructor? I mean, was she a strict teacher with grading, etc? Also, what programing language was used back then? I am also into earlier forms of programming, mainly because I seem to understand those better than today's for some odd reason.
@@citytutoring I, too, want to know why, not just how. I couldn’t learn rote rules - I had to know why, and I didn’t consider myself knowing the subject until I had internalized that understanding. That’s a discussion itself. The class was for faculty rather than part of the curriculum. I was the odd one, being in junior high and was one of the minority who finished the class. That meant it was an informal class among colleagues (plus me). She didn’t just teach us Fortran for the IBM 1620 but also explained how the machine worked at a low level. In light of your video, I realized that deeper understanding played a key role in my career path - and still does. It's interesting to see people outside of their formal roles. At one point, I took a small seminar series co-taught by Arthur Miller. He was known as a fearsome professor (see the movie The Paper Chase), but to us, he was fun to talk to and informal. BTW, you may be interested in Lakoff and Núñez - “Where Mathematics Comes From.” One of my professors (and advisors) was Seymour Paper who taught about cognitive styles. Is our school system capable to taking into account cognitive styles in teaching math?
@@citytutoring, early programming languages were close to pure logic. More modern languages have a pile of 'convenience' features that disguise the fundamental logic of digital computers. Those 'impurities' make programing easier for those who don't grasp the computer logic, and harder for those who do.
@@johnwest7993 That must explain why I have such a hard time with modern programming...I do know a bit of BASIC though, with my Commodore 64...but I had been wanting to be fluent in Python, with mixed success. Granted, honestly I have not put in much of an effort, but it just seems...well, "impure" as you well put it.
1) Peter Selby and Steven L. Slavin's "Practical Algebra: A Self-Teaching Guide" 2) Mary Dolciani: Modern Algebra, Book I, Structure & Method 3) Mary Dolciani: Modern Algebra & Trigonometry, Book II, Structure & Method
Had a look at all of these books. Only peter selby seems reasonable. The rest are somewhat good and not that different from other algebra books out there. Selby is good for connecting different aspects of math together.
Basic Algebra by Jacobson: undergrad/early graduate school "modern algebra" for mathematics majors Modern Algebra by Dolciani: precalculus "basic algebra" for middle/high school students
Professor Cromwell, honestly I struggled in your class but I also appreciated how brutally honest you are and even though in the beginning you kicked me out of class because I was used to getting away with bad manners in my other classes, I'll admit I was pleasantly surprised in your class because you don't put up with nonsense. It's like you're from the 1800s in a younger body but still have that old spirit. All the math I know is thanks to you, and because of you I passed the GMAT! So thank you except for the emotional trauma hehe!
Victor, thank you for your comment. I now remember you...and yes, you started out as someone with bad habits, but I am grateful that we crossed paths because seeing your growth was very rewarding. I'm very much from this present time, but the great classic truths will never change, which is why I have a passion for Mathematics. Why? Because truths will be eternal, and I thoroughly enjoy how the facts are the same now as they were hundreds of years ago. I will certainly keep the classic spirit alive! I hope you are doing well these days...
After I graduated college with a Computer Science degree, I started discovering all kinds of issues with the standard math notation. There are a few changes that can be made so that it is more "algebraic", especially in Calculus. A highly algebraic way of doing things is a bit more verbose, but puts you into a place where you stop memorizing. The other thing that helped was to include bits of Geometric Algebra. Adding directions in space into algebra did WONDERS for my understanding. ie: e_1,e_2,e_3. Learn LaTeX. Do as much math as you can in notepad. Then, learn Lean4. Lean4 could use better tactics, but these tools allow you to really understand what you are doing. It is like getting to know the assembly language of a computer.
Yes sir! Actually, it is one of my next projects: learning LaTeX as I am, unfortunately, woefully behind on the Computer Science aspect of things. When I majored in Math, I wasn't required to take Comp. Sci, but in retrospect, it would have done me a lot of good even if I am personally averse to tech, although slowly accepting its usefulness at least to share math.
@@citytutoring Professor, if you need any help with learning LaTeX, I'd be more than happy to recommend resources, support you with any issues you encounter, or anything you might need. Love the work that you are doing on the channel and best of luck!
@@citytutoring In terms of algebra, I’m currently up to solving quadratic equations. In geometry, I’m studying polygons, specifically parallelograms. I’m also dabbling in proof writing. One book I love is Serge Lang’s Basic Mathematics.
@@citytutoring I’ve been doing this for about 3 years and work through a textbook from beginning to end, doing at least all the odd numbered problems so I can check my work at the end of a section.
@@citytutoring Your video came up in my UA-cam feed because I was searching for tutorials for PCA. And somehow down the line, PCA involves linear algebra- something I came across in college many decades ago.
Exactly the story I experienced. No explanations just memorize a series of rules and take the test. Thank you for explaining the history of the 'Math Wars'.
You're right and spot on. Now 60 years old, I studied from that textbook during the late 1970s and early 1980s during Jr. High school. It is an excellent text. Most of my studies in Algebra I & II, pre-calculus, and Calculus I & II came from independent study.
Olá professor, me chamo Renan e moro aqui no Brasil. Meu inglês não é dos melhores mas a legenda me ajudou. Apenas agora, aos 20 anos fui ver a grandiosidade de saber o porquê das coisas. Questionamentos sempre foram frequentes, mas a depravação mental e a superficiliade das pessoas aqui no país me fizeram por muito tempo sentir angústia e aflição. Tenho sentido uma paixão crescente pela matemática, mas ainda tenho um pouco de medo de enfrentá-la no nivel superior. Tentei uma vez e acabei desistindo, mas videos como o do senhor tem despertado um desejo imenso em contribuir para a ciência e sociedade no geral. Very thanks for the video and than God bless you!
100% agree. An F was an F back then. My love for math started with my 9th grade Algebra teacher, Mr. Likosky. I remember the first day of class he announced that if you were a serious student to please take a seat of front and he would teach you algebra. If you did not care about learning and were a loser to go to back, shut up and he did not care what you did but to not disturb his class, he would gladly fail you. That was 1984. Great teacher.
We need more teachers like that these days! Nowadays, if a teacher said that, there'd probably a be a committee hearing going after him, or it might even hit the front page of the papers, unfortunately.
There was one beautiful book that changed my life: Principles of Mathematical Analysis, by Walter Rubin (generally referred to, even now, as simply "Rudin"). I still have that book, 57 years later, and peruse it from time-to-time. I struggled greatly in my 3rd year real analysis course, until one day, literally, the clouds parted and all became clear, in that course and in subsequent analysis courses I took. The problems in that book forced me to plumb the depth of my little grey cells. Thank you, Walt, and rest in peace.
I love you, my humble mathematician. I have always criticized my teachers, especially in mathematics and physics, for memorizing them without deep understanding. I suffered from that until I saw the scientist Feynman and was inspired by him. Now I use his method of asking questions.Greetings from Algeria Feynman says stay curious
Your video just came up randomly- and I am amazed! I love your presentation. I agree with your ideas. I can feel your enthusiasm for your subject. I will keep watching for more. haha- need to read up on those German philosophies you mentioned.
I caught the tail-end of "New Math". Tom Lehrer's song was the best thing to come out of that. Geometry finally turned-on my Math Lightbulb as a High School Sophomore. That was a rough & rugged road. I encourage everyone who "sucks at Math" to study Geometry and do straight-edge & compass constructions. I re-discovered Physics during my Senior Year and vectored in that direction since. Thanks, Mr. Nicks!
YES! I got this same Selby book in the university book store. It made a huge difference for me, I still have it (it's been a few decades), and my son used it when he was going to college to study engineering.
You just described my story in math. High School teachers never explained the WHY of mathematics. It was so bad that I took 2 math placement tests, one that determined my math competence level. My score placed me among the lower middle tier of student nurses. But the math comprehension test I aced, 100%. The professor who gave the tests told me that the only other person at the small college I went to who had ever aced it was at that moment a physics professor at the University of Chicago. He asked me how I could possibly grasp math concepts so well but have almost zero skill with it. My reply was that no one had ever explained to me the 'why' of math. (BTW, my uncle was a math and physics prof at the college I went to. Ultimately, I taught myself what math I needed during my career as a self-taught electronics technician. BTW, I read 'The Mathematical Experience' and loved it, and I loved it so much that I bought my own copy to read for pleasure simply because it was so interesting. If I'd read it in 7th grade I think I could have broken through the barrier to learning math that had been built up by teachers who refused to explain anything whatsoever about math. In the end I understood that mathematics held fundamental truths and was like an oracle that could predict the future of many, many things, (such as the electronic circuits I was designing,) without ever having to build them and test and rebuild and retest. The math PREDICTED the results! It was magic. It was power. It clarified and simplified so much. I will buy all of the books. Now that I'm retired I finally have time to study and learn. Thank you for this video. I've subscribed.
I found book 1 of Modern Algebra in a thrift store for $4 and after simply browsing through it for a few minutes I knew I had found a treasure! As you said, everything in there is explained axiomatically and with a clear logical progression. I too had trouble with algebra when I was younger, but I don't think I would have if I had learned it from this book. Not only is it clearly written, I find it much more aesthetically pleasing than the glossy math books I had to study from in the 90s with their mostly irrelevant photos of children walking in the park or sorting through candy. Good Lord! I don't even want to imagine what algebra textbooks look like now! The Modern Algebra series books are the McGuffey Readers of math textbooks.
Ah yes, I remember those glossy books of the 1990s! For me, they were absolute rubbish, cluttered, and very strange/unclear explanations. I like how you have mentioned the McGuffey Readers! I think even high schoolers today, unless they had proper training, would be utterly lost as even the current "Ivy League" have difficulty reading even one modern book!
I grew up without any emphasis on the importance of math and the value it gives in life. My story isn't very inspiring but I want to make sure my child has the math education I would have liked. I'll work through these books on my own and use them to train my child. Thank you for posting and thank you for your inspiring story!
Thank you! That is a great idea, and that way you will be grounded in the material to later on have a good foundation with which to help your child. To this day, I still have all my notes from back in those days, and sometimes when I go through them, I am amazed at how nothing has changed (in the good sense, I mean how the mathematical truths and foundations are the same always, even decades later. It gives you a sense of place and security).
Hey, this is excellent. I really enjoy it when people, like this fella, cut through all the cr*p and get to the point. It's so refreshing. And he's full of enthusiasm for his subject. BRILLIANT!!!!!!
A good, mathematician is supposed to seek and not believe. Just listening to him 5 minutes I subscribed as I am now teaching my daughters Mathematics. I always needed an answer to this "WHY" in my life, not just maths.
I think you're the first person who has ever spoken out loud, the words that sum up my own problems with maths. I vividly recall being frustrated with never knowing 'why?' i'm doing something. 'Why?' this works. 'Why?' you use this method and not that. When I asked, i'd always be answered with, 'It just does', 'you don't need to know to be able to use it', 'you'll find out later' etc etc. When you're a kid, eventually you just stop asking. Similar to yourself, I was a top set, Grade 'A' kid...except maths. I was a C/D grade kid in set 3 for maths. (Edit: This is in the UK, btw.)
Thank you for your perspective! Yes, isn't it sad how so many "algorithmic" ways of teaching eventually just stifle curiosity, which also kills creativity? If you ever want to know the "whys", I guarantee you a careful reading of Dolciani from the beginning will get you there. But, if the style is perhaps too old for some, then any textbook really that uses an axiomatic approach. Unfortunately, these days those sort of textbooks are few and far between!
I "shop" for few things, except for books. My local Barnes & Noble used to carry a solid selection of Physics, Math & Engineering books (especially Dover); however, it has been a desert for the past few years. I dusted-off my Library Card and found a ton of good stuff at my Public Library.
Oftentimes I find that the math section of the library is collecting dust because no one uses those books. At my library at least there are some really great books. So, it's a treat to get books from there. Just today I got a two volume book on Number Theory by LeVeque from 1956.
My Algebra II class used Dolciani, Berman, and Wooten in the 1970-71 school year so it's not the revised edition in the amazon link but it had basically the same cover so it still brings back great memories over 50 years later. It was a great book and I had a wonderful teacher. I remember, for example, my teacher showing us that the principle of using two points to determine the equation of a line was how we got the formulas for temperature conversion between Fahrenheit and (as we used to call it) Centigrade (or Celsius). That blew my mind back in the day.
I remember that textbook from my 8th grade algebra class in 1972! I haven't thought of that textbook since I saw this video and it came right back to me.
You earned a follow from me, my friend! I can attest to everything you have said. I'll only add that you have certainly persevered! And are on your way to becoming a great teacher of mathematics! God bless you! I still have my mathematics books from junior high. All by Dolciani! Boy did they save my bacon from junior high to university, and afterwards! Best wishes on your book! I might just have to have a look see! Cheers! 🍻
I am so happy that i find this channel by chance! I graduated with computer science degree and now i decided to study mathematics instead of programming.. just thanks for such serious content
Absolutely! Thank you for watching! You made a good choice! I was offered to study "computer science" under the idea that "Math is useless". Thank God I followed my calling in my life and went ahead with Math. I truly would not be the person I am today without my purely mathematical foundation. Some people will still criticize you for not doing Computer Science, but pay them no mind.
This was a refreshing video, as I am, just like you, explosively enthusiastic with mathematics. To make a long story short I got into self study and mathematics in 10th grade. From there I took calc i-iii diff eq stat and lin alg before I had left highschool. I am in my first semester of college now but im transferring out to a college that will let me take more mathematics courses.
Thank you for your comment! Taking Calc I-III, Diff Eq, Stats, and Linear Algebra before college is no small feat. Transferring to a college that fuels your mathematical appetite sounds like the perfect next step. Keep us posted on your journey; the math world needs more trailblazers like you!
Wow! What a truly inspiring presentation! At first I thought I would just watch a few minutes. It just got better and better! A really excellent presentation! Thank you 🙏👌❤️
Dolciani also had a Book 2 and a Modern Introductory Analysis book we used in lare 60s and early 70s. There was a Modern Geometry book also. Excellent books!! Also, a Trigonometry book by same authors. I have all 5.
I can’t said that same happened to me but it was kinda similar, when I was at High School in Cuba and I was taking trigonometry’s section on my second year it was a vague teaching in the subject, but fortunately my teacher was aware of my desire to study math at Havana University, and she told me where the proof where and I went right to the page and read both proves, which made me love math more than before, and I also read a book about abstract algebra, which I didn’t finished because it was advanced for me, but the first chapter was readable for a high schooler and It changed my perspective of mathematics.
Hi i am from India same thing happened with me every one pressured me i lost my skills but now I am finally i am recovering well and now iam good at maths . Thanks for sharing your story i am 19 now.
I went to an all boys high school that used the set of Dolciani's texts. I Didn't know how good they were at the time. Started using them in 1963. I remember she highlighted great women mathematicians. I got BS and MS in math. Worked in IT for large banks. Never taught. Now that I'm retired I teach GED math at Library.
@@citytutoring I wish they were. In my case I am definitely teaching to the test. Some are homeless and live in faith based housing. I would say I teach to the test. Would like to have students who had interest in math rather than just passing GED
I definitely understand. A lot of my students have been in similar situations, and they have been the most rewarding to work with (but also the most challenging!). My group of students can be quite confrontational and stubborn, but we are both brutally honest in our own ways and for our own purposes, so we balance each other out in good ways. I can tell you that if they see your passion, many will respond positively. Keep doing what you're doing and you'll see good things happen. However, yes, some are just too far gone and set in horrible habits to turn around positively.
@@citytutoring I had a student who was doing so well. He was staying in a faith based shelter. He had a slip, was urine tested by the shelter. Kicked out and quickly arrested. Never saw him again.
Thank you for sharing your information about mathematics. The rigorous approach is the best, especially when one goes into higher mathematics, like abstract algebra. These books are ones I will look into. I currently read several mathematics books, and I find Dover and Princeton University books to have a rigorous approach. Once again, thank you for sharing.
The book room in our math dept has a bunch of Dochianis I and II (maybe about a class set). The last time I used those books was about 10 years ago. Only had to stop because the books were deteriorating. Wish there was a way turn back time to preserve them.
I'm not really a fan, if I may say so. They are OK for competition type problems, and I won't say they are "bad", but I would be lying if I said that they took a rigorous/set theory approach. They do have very interesting/fun problems, for sure, and they explain things quite well when compared to of course any modern textbook today, but just something about the series rubs me the wrong way.
In the UK, we are lucky to have a ton of excellent maths books published by Oxford University Press and Cambridge University Press as well as numerous other publishers. I prefer the books with lots of exercises and worked examples.
There are many options, but I would have to know more about what specific program of study you are in to give you a good answer. Is this for self-study or for a college?
My high school used the Dolciani Algebra I textbook for freshman algebra in 1978. Calculators were only permitted in science courses. We used the Swokowski textbook for Algebra-Trigonometry.
OMG we used that algebra book for Algebra I in the 70s, and the second book for Algebra II ! By the way, that book you have wasn't "last checked-out" back then -- it was that student's assigned textbook for that year and normally would be the same one given to a student the following year. They tried to get four years out of a textbook back then in my school district, and you had to pay for book repair at the end of the year if you beat the daylights out of it.
Out of curiosity what's your opinion on Gelfand? I read his algebra book and found it to be very enlightening. Taking away the training wheels almost completely and only giving you a brief (but still descriptive and thorough in my opinion) explanation before having you do it was extremely helpful not only in getting better at math but allowing for the creative juices to flow and, though unlikely it may be, I hope that we can adopt that sort of method not only in elite institutions but among public schools because it is frankly embarrassing how poor math is taught in American public schools; not only today but for the past few decades. For example, my Mother, Father, and Grandfather barely understood any math beyond simple geometry and algebra; and if we want to remain competitive not only at the elite level but generally speaking, we need to reintroduce these books in the high school curriculum. Some kids might feel bad occasionally if they do poorly for a brief period sure, but when was the last time someone got seriously bullied in an American high school for being not being nerdy enough?
I very much like Gelfand, and would most definitely recommend his book, but back when I was in school it would have been very difficult to find depending on where you were located. I am familiar with Gelfand's Algebra book and it is delightful. However, my critique of it is that Gelfand does not really go into Axioms or proofs. Like for example, in the chapter on exponents, he does not specify that it is the set of real numbers. The exercises themselves are good, but my style is more "set" oriented...if that makes sense?
I subscribed. That point you made about kids today being coddled is so true. I was told by a tuition centre that I interviewed for that students don't want to be questioned while explaining the material. As it would embarrass them. I was literally gobsmacked. 😂 Eh, the socratic method anyone?
Sounds familiar! It really is sad, isn't it? Especially because as I am sure you have had the experience that students actually love to be questioned if it generates a healthy and funny discussion. I wish we could show those people the dozens of videos of students laughing in Math class, when there is an interesting discussion to be had! Thank you for subscribing, by the way!
I wanted to be a mathematician without any purpose but I am 37 and unfortunately I am an environmental engineer. To be a math person, no goals no purposes no any one only mathematics and you, may be a cup of coffee a little bit rain passion inspiration and joy, passing away years without noticing...
I loved maths because in my class in primary school we had some small text boards framed on the wall which i used to read during break. They contained the properties of addition and multiplication on them and it was almost like a miracle seeing that the simple addition has things which hold true regardless what numbers you try. That was really what got me interested and yes teachers saying there is not enough time to prove X or you won't understand it really made me sad . I remember when studying geometry (not my strong point btw) when we were told that the medians, bisectors and heights of a triangle all intersect eachother in 1 point i was like wow why not 3 points and nobody bothered doing a demonstration for that
Dolciani, the exact same cover was my 8th grade text. I loved the book! That was 1985-86. I guess it will be hard to find these days. Now I need to teach my daughters math and I hope that I can get my hands on the book. I am saddened that there aren’t modern reprints of the book.
Yes, I absolutely do because those were the books that I self-studied from since my school back then did not, unfortunately, have the rigor I wanted. There are exercises A for more basic ones, exercises B for more intermediate, and then you get exercises C for more challenging ones, so I very much like that too, and you can check for answers in the back of the book.
Dolciani did my high school math book in the late 80s. It was entitled “Algebra: Structure and Method Book 1.” It is much cheaper. I wonder if there is much difference. I’m trying to help my daughter.
Any book by Dolciani will still be better than any book available today. However, the one from the late 80s is slightly less "axiomatic" than the earlier versions, but still thoroughly solid. If you can get a copy of the 1970s or even early 1980s versions, that would be great, but if not, then definitely go for the cheaper late 80s version. Or, alternatively, the book is available online as a pdf...if that works. Personally, I'm not a "pdf man", so I prefer a physical book when I can get one.
Allyn Washington's Basic Technical Math With Calculus, a College staple would be the first book I'd take into the cave or bunker, if I thought the world was coming to an end. It starts with the number line and ends with Advanced Calculus. Along the way it presents a splendid and masive collection from all the sciences and technology fields, so you'd never have to add extra texts from Archetecture or electronics or hydraulics etc. It trully is a summary of science and technology since the beginning of time.
It's strange how memories work. I'm going to be 57 Nov 30th and once I saw that book cover, I immediately remembered it when I was young. Just blew my mind how something so long ago and so meaningless just happened to come back from my memories. Not sure why UA-cam just happened to show your channel also. Pretty wierd. Oh! And it's the red Algebra book at 14:18 is what I'm talking about.
I’m 52 and exactly the same. The cover rang a bell in my head. I have aphantasia but somehow I can recall the classroom and my teacher’s face albeit vaguely. That book and that class must have been a real impact in my life..
@@stevesskychannel3099 I always wondered if all the memories we had throughout our lives are laying dormant in our minds but no one has figured out how to retrieve them all. It's funny on an electronic device we have storage we can modify but we can't do that with our own memories. Also! I think it would be helpful to at least figure out how to "delete" traumatic memories. Hopefully there are people working in this field if it exists. It could really impact humanity.
I haven’t watch all the video time but in during the first 10 minutes you mention many times the feeling of not knowing or the desire to know why something has to be done. I am so annoyed myself at the fact that the axiom of choice has not been proven. When I ask a professor they always say “in here we have to believe is true”, why? I hate believing in not proven things in mathematics. Like, what if one day I decide not to “believe” in the axiom of choice, does that mean I can’t go to math class in university? Like I have to forget about the Hahn-Banach theorem in some sense? It’s uncomfortable.
Hello sir I love mathmatics,I believe only mathmatics is the only language that can define universe..but never got good books nor great teachers..now I am 32 subscribing your channel to explore my love for math...
Absolutely fantastic content. Happy to have found your channel. I actually have Modern Introductory Analysis by Dolciani. It’s a great math book. I find older math books more rigorous and certainly axiomatic. Precalculus Mathematics by Shanks is great as well.
Thank you! Modern Introductory Analysis is, I dare say, the BEST high school "precalc" text ever written in America. I have not seen any that come close that book! And yes, Precalculus by Shanks...I agree, also an excellent book. I particularly like his chapter on Vectors.
Just after coming across this video. I am a policeman in my forties who gave up acdemia because my maths was not up to scratch. Love maths now as a pastime. I am a fan of yours now 😊
I was surprised to see Mary Doiciani's name. She taught me to program in 1963 when I was in Junior High and went to a small class for the Hunter College faculty in place of my mother. It was an amazing opportunity that transformed my life!
Mary Dolchiani. There is a beautiful series of books in her name or funded by an organization setup by her, unsure.
I am so happy to read this, as you have a first hand account! Could you please tell me how she was as an instructor? I mean, was she a strict teacher with grading, etc? Also, what programing language was used back then? I am also into earlier forms of programming, mainly because I seem to understand those better than today's for some odd reason.
@@citytutoring I, too, want to know why, not just how. I couldn’t learn rote rules - I had to know why, and I didn’t consider myself knowing the subject until I had internalized that understanding. That’s a discussion itself.
The class was for faculty rather than part of the curriculum. I was the odd one, being in junior high and was one of the minority who finished the class. That meant it was an informal class among colleagues (plus me). She didn’t just teach us Fortran for the IBM 1620 but also explained how the machine worked at a low level. In light of your video, I realized that deeper understanding played a key role in my career path - and still does.
It's interesting to see people outside of their formal roles. At one point, I took a small seminar series co-taught by Arthur Miller. He was known as a fearsome professor (see the movie The Paper Chase), but to us, he was fun to talk to and informal.
BTW, you may be interested in Lakoff and Núñez - “Where Mathematics Comes From.” One of my professors (and advisors) was Seymour Paper who taught about cognitive styles. Is our school system capable to taking into account cognitive styles in teaching math?
@@citytutoring, early programming languages were close to pure logic. More modern languages have a pile of 'convenience' features that disguise the fundamental logic of digital computers. Those 'impurities' make programing easier for those who don't grasp the computer logic, and harder for those who do.
@@johnwest7993 That must explain why I have such a hard time with modern programming...I do know a bit of BASIC though, with my Commodore 64...but I had been wanting to be fluent in Python, with mixed success. Granted, honestly I have not put in much of an effort, but it just seems...well, "impure" as you well put it.
1) Peter Selby and Steven L. Slavin's "Practical Algebra: A Self-Teaching Guide"
2) Mary Dolciani: Modern Algebra, Book I, Structure & Method
3) Mary Dolciani: Modern Algebra & Trigonometry, Book II, Structure & Method
Had a look at all of these books. Only peter selby seems reasonable. The rest are somewhat good and not that different from other algebra books out there. Selby is good for connecting different aspects of math together.
Thank you, saved my 25 mins
Thank you
information + silence = heaven
Thank you for saving my time. I spent five minutes listening to his personal life and decided to quit until I read your comments.
Basic Algebra by Jacobson: undergrad/early graduate school "modern algebra" for mathematics majors
Modern Algebra by Dolciani: precalculus "basic algebra" for middle/high school students
Professor Cromwell, honestly I struggled in your class but I also appreciated how brutally honest you are and even though in the beginning you kicked me out of class because I was used to getting away with bad manners in my other classes, I'll admit I was pleasantly surprised in your class because you don't put up with nonsense. It's like you're from the 1800s in a younger body but still have that old spirit.
All the math I know is thanks to you, and because of you I passed the GMAT! So thank you except for the emotional trauma hehe!
If you get into trauma for every little thing you encounter, you are not ready for life. How would you get into trauma in mathematics class?
@@getusel The emotional trauma bit was obviously a joke.
@@meatsong I hope it is.
Victor, thank you for your comment. I now remember you...and yes, you started out as someone with bad habits, but I am grateful that we crossed paths because seeing your growth was very rewarding. I'm very much from this present time, but the great classic truths will never change, which is why I have a passion for Mathematics. Why? Because truths will be eternal, and I thoroughly enjoy how the facts are the same now as they were hundreds of years ago. I will certainly keep the classic spirit alive! I hope you are doing well these days...
Lo besarías?
I felt lucky for watching this i am 17 and trying my best to be good at the subject may god bless you!
Do not forget to read a lot of poetry.
@@sthetatos can you please explain this
@@Revo55 Doing only left brain stuff is not right.
@@Revo55 The art most familiar with the secret of transmitting abstractions is poetry. If you like math, study geometry. not algebra.
After I graduated college with a Computer Science degree, I started discovering all kinds of issues with the standard math notation. There are a few changes that can be made so that it is more "algebraic", especially in Calculus. A highly algebraic way of doing things is a bit more verbose, but puts you into a place where you stop memorizing. The other thing that helped was to include bits of Geometric Algebra. Adding directions in space into algebra did WONDERS for my understanding. ie: e_1,e_2,e_3.
Learn LaTeX. Do as much math as you can in notepad. Then, learn Lean4. Lean4 could use better tactics, but these tools allow you to really understand what you are doing. It is like getting to know the assembly language of a computer.
Yes sir! Actually, it is one of my next projects: learning LaTeX as I am, unfortunately, woefully behind on the Computer Science aspect of things. When I majored in Math, I wasn't required to take Comp. Sci, but in retrospect, it would have done me a lot of good even if I am personally averse to tech, although slowly accepting its usefulness at least to share math.
@@citytutoring Professor, if you need any help with learning LaTeX, I'd be more than happy to recommend resources, support you with any issues you encounter, or anything you might need. Love the work that you are doing on the channel and best of luck!
@@Mosrod Thank you!
@@Mosrodso why wont you recommend the resources here?
@@Mosrod Please I'd be forever glad if you could help me too with the resources. Thanks.
Hello friend, I’m a physician in my 50s studying mathematics as a hobby. I just stumbled across your channel and look forward to exploring!
Welcome! Thank you. I hope that the content can be of use to you. At what level of Mathematics are you starting out with for study?
@@citytutoring In terms of algebra, I’m currently up to solving quadratic equations. In geometry, I’m studying polygons, specifically parallelograms. I’m also dabbling in proof writing. One book I love is Serge Lang’s Basic Mathematics.
@@citytutoring I’ve been doing this for about 3 years and work through a textbook from beginning to end, doing at least all the odd numbered problems so I can check my work at the end of a section.
@@citytutoring Your video came up in my UA-cam feed because I was searching for tutorials for PCA. And somehow down the line, PCA involves linear algebra- something I came across in college many decades ago.
Exactly the story I experienced. No explanations just memorize a series of rules and take the test. Thank you for explaining the history of the 'Math Wars'.
Amen. I have tried unsuccessfully to describe what you describe in this video. Great work.
Thank you!
You're right and spot on. Now 60 years old, I studied from that textbook during the late 1970s and early 1980s during Jr. High school. It is an excellent text. Most of my studies in Algebra I & II, pre-calculus, and Calculus I & II came from independent study.
Same. 8th grade Algebra I !
You look like a really elegant likeable person. I like the way you speak. I hope you do good things in the world and help people.
That is very kind of you to say! Thank you! I will always try my best to do what I can.
Olá professor, me chamo Renan e moro aqui no Brasil. Meu inglês não é dos melhores mas a legenda me ajudou.
Apenas agora, aos 20 anos fui ver a grandiosidade de saber o porquê das coisas.
Questionamentos sempre foram frequentes, mas a depravação mental e a superficiliade das pessoas aqui no país me fizeram por muito tempo sentir angústia e aflição.
Tenho sentido uma paixão crescente pela matemática, mas ainda tenho um pouco de medo de enfrentá-la no nivel superior. Tentei uma vez e acabei desistindo, mas videos como o do senhor tem despertado um desejo imenso em contribuir para a ciência e sociedade no geral.
Very thanks for the video and than God bless you!
100% agree. An F was an F back then. My love for math started with my 9th grade Algebra teacher, Mr. Likosky. I remember the first day of class he announced that if you were a serious student to please take a seat of front and he would teach you algebra. If you did not care about learning and were a loser to go to back, shut up and he did not care what you did but to not disturb his class, he would gladly fail you. That was 1984. Great teacher.
We need more teachers like that these days! Nowadays, if a teacher said that, there'd probably a be a committee hearing going after him, or it might even hit the front page of the papers, unfortunately.
There was one beautiful book that changed my life: Principles of Mathematical Analysis, by Walter Rubin (generally referred to, even now, as simply "Rudin"). I still have that book, 57 years later, and peruse it from time-to-time. I struggled greatly in my 3rd year real analysis course, until one day, literally, the clouds parted and all became clear, in that course and in subsequent analysis courses I took. The problems in that book forced me to plumb the depth of my little grey cells. Thank you, Walt, and rest in peace.
Why is Rubin referred to as Rudin?
Oh, THAT book. Great book, but not very beginner friendly!!
Yes my analysis book was Rubin. Compact. Did not enjoy it that much but I want to get my hands on it again.
I love this guy ! We need more people like him.
This guy is Awesome! We need more Math Heros like him in our public schools.
I love you, my humble mathematician. I have always criticized my teachers, especially in mathematics and physics, for memorizing them without deep understanding. I suffered from that until I saw the scientist Feynman and was inspired by him. Now I use his method of asking questions.Greetings from Algeria Feynman says stay curious
Greetings, and welcome! I would love to visit Algeria some day! And yes, that is a great Feynman quote!
Your video just came up randomly- and I am amazed! I love your presentation. I agree with your ideas. I can feel your enthusiasm for your subject. I will keep watching for more.
haha- need to read up on those German philosophies you mentioned.
Thank you very much! Your comment means a lot to me! I promise to do my best each time I make a video for Math.
These are the type of books I need. I want to be a physicist but I'm also interested in math and CS
I caught the tail-end of "New Math". Tom Lehrer's song was the best thing to come out of that.
Geometry finally turned-on my Math Lightbulb as a High School Sophomore. That was a rough & rugged road. I encourage everyone who "sucks at Math" to study Geometry and do straight-edge & compass constructions.
I re-discovered Physics during my Senior Year and vectored in that direction since. Thanks, Mr. Nicks!
YES! I got this same Selby book in the university book store. It made a huge difference for me, I still have it (it's been a few decades), and my son used it when he was going to college to study engineering.
THANK YOU SO MUCH FOR MAKING THIS VIDEO AND SHARING YOUR EXPERIENCE WITH US.
My pleasure! Thank you for stopping by!
Can anyone list the books?
You just described my story in math. High School teachers never explained the WHY of mathematics. It was so bad that I took 2 math placement tests, one that determined my math competence level. My score placed me among the lower middle tier of student nurses. But the math comprehension test I aced, 100%. The professor who gave the tests told me that the only other person at the small college I went to who had ever aced it was at that moment a physics professor at the University of Chicago. He asked me how I could possibly grasp math concepts so well but have almost zero skill with it. My reply was that no one had ever explained to me the 'why' of math. (BTW, my uncle was a math and physics prof at the college I went to.
Ultimately, I taught myself what math I needed during my career as a self-taught electronics technician. BTW, I read 'The Mathematical Experience' and loved it, and I loved it so much that I bought my own copy to read for pleasure simply because it was so interesting. If I'd read it in 7th grade I think I could have broken through the barrier to learning math that had been built up by teachers who refused to explain anything whatsoever about math. In the end I understood that mathematics held fundamental truths and was like an oracle that could predict the future of many, many things, (such as the electronic circuits I was designing,) without ever having to build them and test and rebuild and retest. The math PREDICTED the results! It was magic. It was power. It clarified and simplified so much.
I will buy all of the books. Now that I'm retired I finally have time to study and learn. Thank you for this video. I've subscribed.
What a nice suit, looks sharp af
Thank you sir!
Thanks God I read the comments saving my time.
What a delight to find your channel, professor!
Welcome! Thank you!
What an interesting character you are. I mean that as a compliment. Subscribed.
A. Baldor: Algebra, arithmetic, trigonometry, and geometric. Those books are all we need. Thanks
I found book 1 of Modern Algebra in a thrift store for $4 and after simply browsing through it for a few minutes I knew I had found a treasure! As you said, everything in there is explained axiomatically and with a clear logical progression. I too had trouble with algebra when I was younger, but I don't think I would have if I had learned it from this book. Not only is it clearly written, I find it much more aesthetically pleasing than the glossy math books I had to study from in the 90s with their mostly irrelevant photos of children walking in the park or sorting through candy. Good Lord! I don't even want to imagine what algebra textbooks look like now! The Modern Algebra series books are the McGuffey Readers of math textbooks.
Ah yes, I remember those glossy books of the 1990s! For me, they were absolute rubbish, cluttered, and very strange/unclear explanations. I like how you have mentioned the McGuffey Readers! I think even high schoolers today, unless they had proper training, would be utterly lost as even the current "Ivy League" have difficulty reading even one modern book!
I grew up without any emphasis on the importance of math and the value it gives in life. My story isn't very inspiring but I want to make sure my child has the math education I would have liked.
I'll work through these books on my own and use them to train my child. Thank you for posting and thank you for your inspiring story!
Thank you! That is a great idea, and that way you will be grounded in the material to later on have a good foundation with which to help your child. To this day, I still have all my notes from back in those days, and sometimes when I go through them, I am amazed at how nothing has changed (in the good sense, I mean how the mathematical truths and foundations are the same always, even decades later. It gives you a sense of place and security).
Hey, this is excellent.
I really enjoy it when people, like this fella, cut through all the cr*p and get to the point.
It's so refreshing. And he's full of enthusiasm for his subject.
BRILLIANT!!!!!!
Thank you for your support! I do like to cut out the clutter and nonsense as much as I can, and get straight to work!
A good, mathematician is supposed to seek and not believe. Just listening to him 5 minutes I subscribed as I am now teaching my daughters Mathematics. I always needed an answer to this "WHY" in my life, not just maths.
I love your passion about Math
the quality is awesome!!
I think you're the first person who has ever spoken out loud, the words that sum up my own problems with maths. I vividly recall being frustrated with never knowing 'why?' i'm doing something. 'Why?' this works. 'Why?' you use this method and not that. When I asked, i'd always be answered with, 'It just does', 'you don't need to know to be able to use it', 'you'll find out later' etc etc. When you're a kid, eventually you just stop asking. Similar to yourself, I was a top set, Grade 'A' kid...except maths. I was a C/D grade kid in set 3 for maths.
(Edit: This is in the UK, btw.)
Thank you for your perspective! Yes, isn't it sad how so many "algorithmic" ways of teaching eventually just stifle curiosity, which also kills creativity? If you ever want to know the "whys", I guarantee you a careful reading of Dolciani from the beginning will get you there. But, if the style is perhaps too old for some, then any textbook really that uses an axiomatic approach. Unfortunately, these days those sort of textbooks are few and far between!
@@citytutoring Thank you. The Dolciani books are proving difficult to source at a reasonable price, unsurprisingly. The hunt goes on!
I "shop" for few things, except for books. My local Barnes & Noble used to carry a solid selection of Physics, Math & Engineering books (especially Dover); however, it has been a desert for the past few years. I dusted-off my Library Card and found a ton of good stuff at my Public Library.
Librarians love finding stuff for their Customers.
Oftentimes I find that the math section of the library is collecting dust because no one uses those books. At my library at least there are some really great books. So, it's a treat to get books from there. Just today I got a two volume book on Number Theory by LeVeque from 1956.
My Algebra II class used Dolciani, Berman, and Wooten in the 1970-71 school year so it's not the revised edition in the amazon link but it had basically the same cover so it still brings back great memories over 50 years later. It was a great book and I had a wonderful teacher. I remember, for example, my teacher showing us that the principle of using two points to determine the equation of a line was how we got the formulas for temperature conversion between Fahrenheit and (as we used to call it) Centigrade (or Celsius). That blew my mind back in the day.
I remember that textbook from my 8th grade algebra class in 1972! I haven't thought of that textbook since I saw this video and it came right back to me.
You earned a follow from me, my friend! I can attest to everything you have said. I'll only add that you have certainly persevered! And are on your way to becoming a great teacher of mathematics! God bless you! I still have my mathematics books from junior high. All by Dolciani! Boy did they save my bacon from junior high to university, and afterwards! Best wishes on your book! I might just have to have a look see! Cheers! 🍻
Thank you very much! I really appreciate you, and your kind words of encouragement.
I am so happy that i find this channel by chance! I graduated with computer science degree and now i decided to study mathematics instead of programming.. just thanks for such serious content
Absolutely! Thank you for watching! You made a good choice! I was offered to study "computer science" under the idea that "Math is useless". Thank God I followed my calling in my life and went ahead with Math. I truly would not be the person I am today without my purely mathematical foundation. Some people will still criticize you for not doing Computer Science, but pay them no mind.
@citytutoring All the best Prof. You really deserve all kinds of support 🙏
This was a refreshing video, as I am, just like you, explosively enthusiastic with mathematics. To make a long story short I got into self study and mathematics in 10th grade. From there I took calc i-iii diff eq stat and lin alg before I had left highschool. I am in my first semester of college now but im transferring out to a college that will let me take more mathematics courses.
Thank you for your comment! Taking Calc I-III, Diff Eq, Stats, and Linear Algebra before college is no small feat. Transferring to a college that fuels your mathematical appetite sounds like the perfect next step. Keep us posted on your journey; the math world needs more trailblazers like you!
Wow! What a truly inspiring presentation! At first I thought I would just watch a few minutes. It just got better and better! A really excellent presentation! Thank you 🙏👌❤️
Thank you for your kind comment!
Dolciani also had a Book 2 and a Modern Introductory Analysis book we used in lare 60s and early 70s. There was a Modern Geometry book also. Excellent books!! Also, a Trigonometry book by same authors. I have all 5.
The tie won you a new sub.
Ha! Thank you! It's rare these days that I get a positive comment about my appearance, so I very much appreciate any praise in these times!
I can’t said that same happened to me but it was kinda similar, when I was at High School in Cuba and I was taking trigonometry’s section on my second year it was a vague teaching in the subject, but fortunately my teacher was aware of my desire to study math at Havana University, and she told me where the proof where and I went right to the page and read both proves, which made me love math more than before, and I also read a book about abstract algebra, which I didn’t finished because it was advanced for me, but the first chapter was readable for a high schooler and It changed my perspective of mathematics.
Do you have takes on calculus books?
I do, and plan to discuss that soon at some point. Are you a Calculus student?
Hi i am from India same thing happened with me every one pressured me i lost my skills but now I am finally i am recovering well and now iam good at maths . Thanks for sharing your story i am 19 now.
Please continue making these high quality videos.
Mathematics and Holy Spirit-- that's what I'M talkin'bout! Understanding math happens better with the power of prayer!
We need more Math people in this country. What is great about math is that you can prove it. You can't prove subjects such as religion.
You should be a motivational speaker too. Your delivery is both unique and humorous.
Thank you! In a sense, I think I already am since I constantly have to motivate my students who are terrified of Math!
Thank you. I will search online and order.
Great video, very helpful. Modern Algebra was the *Freshman* text at Whitefish Bay HS in WFB, WI. Brilliant text, fantastic school.
I went to an all boys high school that used the set of Dolciani's texts. I Didn't know how good they were at the time. Started using them in 1963. I remember she highlighted great women mathematicians. I got BS and MS in math. Worked in IT for large banks. Never taught. Now that I'm retired I teach GED math at Library.
Are your GED students motivated about Math?
@@citytutoring I wish they were. In my case I am definitely teaching to the test. Some are homeless and live in faith based housing. I would say I teach to the test. Would like to have students who had interest in math rather than just passing GED
I definitely understand. A lot of my students have been in similar situations, and they have been the most rewarding to work with (but also the most challenging!). My group of students can be quite confrontational and stubborn, but we are both brutally honest in our own ways and for our own purposes, so we balance each other out in good ways. I can tell you that if they see your passion, many will respond positively. Keep doing what you're doing and you'll see good things happen. However, yes, some are just too far gone and set in horrible habits to turn around positively.
@@citytutoring I had a student who was doing so well. He was staying in a faith based shelter. He had a slip, was urine tested by the shelter. Kicked out and quickly arrested. Never saw him again.
Thank you for sharing this information. As a student who is struggling with math, this video eases me. Beautiful neck tie though 😊
Thank you for sharing your information about mathematics. The rigorous approach is the best, especially when one goes into higher mathematics, like abstract algebra. These books are ones I will look into. I currently read several mathematics books, and I find Dover and Princeton University books to have a rigorous approach. Once again, thank you for sharing.
Thank you so much 👍
Awesome! All the way from Nepal here,sir.
Books are not available on Amazon india
The book room in our math dept has a bunch of Dochianis I and II (maybe about a class set). The last time I used those books was about 10 years ago. Only had to stop because the books were deteriorating. Wish there was a way turn back time to preserve them.
What's your opinion on AOPS books?
I'm not really a fan, if I may say so. They are OK for competition type problems, and I won't say they are "bad", but I would be lying if I said that they took a rigorous/set theory approach. They do have very interesting/fun problems, for sure, and they explain things quite well when compared to of course any modern textbook today, but just something about the series rubs me the wrong way.
In the UK, we are lucky to have a ton of excellent maths books published by Oxford University Press and Cambridge University Press as well as numerous other publishers.
I prefer the books with lots of exercises and worked examples.
Indeed! I do like the UK materials as well!
Thank you for the useful knowledge sir. I am sure this video will help guide me to great things in the future. Also subscribed!
Thank you! I can tell you that I would not be the successful man I am today without these great mathematical foundations.
@ Yes sir indeed. Thank you again for all you do!
please give me advice on discrete math books which on is the best .
What's the easiest book to lean Econometrics? Thanks 🙂
There are many options, but I would have to know more about what specific program of study you are in to give you a good answer. Is this for self-study or for a college?
@@citytutoring Self study - thank you for your help!
My high school used the Dolciani Algebra I textbook for freshman algebra in 1978. Calculators were only permitted in science courses. We used the Swokowski textbook for Algebra-Trigonometry.
I had to watch this video just from the display of my Algebra textbook. That was a great book.
No pictures, no fluff - everything is explained by axioms, proofs; excellent book recommendation. 17:30
OMG we used that algebra book for Algebra I in the 70s, and the second book for Algebra II !
By the way, that book you have wasn't "last checked-out" back then -- it was that student's assigned textbook for that year and normally would be the same one given to a student the following year. They tried to get four years out of a textbook back then in my school district, and you had to pay for book repair at the end of the year if you beat the daylights out of it.
Ahh that makes sense! Thank you!
Out of curiosity what's your opinion on Gelfand? I read his algebra book and found it to be very enlightening. Taking away the training wheels almost completely and only giving you a brief (but still descriptive and thorough in my opinion) explanation before having you do it was extremely helpful not only in getting better at math but allowing for the creative juices to flow and, though unlikely it may be, I hope that we can adopt that sort of method not only in elite institutions but among public schools because it is frankly embarrassing how poor math is taught in American public schools; not only today but for the past few decades. For example, my Mother, Father, and Grandfather barely understood any math beyond simple geometry and algebra; and if we want to remain competitive not only at the elite level but generally speaking, we need to reintroduce these books in the high school curriculum. Some kids might feel bad occasionally if they do poorly for a brief period sure, but when was the last time someone got seriously bullied in an American high school for being not being nerdy enough?
I very much like Gelfand, and would most definitely recommend his book, but back when I was in school it would have been very difficult to find depending on where you were located. I am familiar with Gelfand's Algebra book and it is delightful. However, my critique of it is that Gelfand does not really go into Axioms or proofs. Like for example, in the chapter on exponents, he does not specify that it is the set of real numbers. The exercises themselves are good, but my style is more "set" oriented...if that makes sense?
@@citytutoring I understand that and I'll certainly be checking out Dolciani's book thank you for the recommendation.
What is fun about some of her polynomial problems or factoring problems is that when you are all done it equals 1.
How about your grade 1 math book? Didn't have an effect on you?
I subscribed. That point you made about kids today being coddled is so true. I was told by a tuition centre that I interviewed for that students don't want to be questioned while explaining the material. As it would embarrass them. I was literally gobsmacked. 😂 Eh, the socratic method anyone?
Sounds familiar! It really is sad, isn't it? Especially because as I am sure you have had the experience that students actually love to be questioned if it generates a healthy and funny discussion. I wish we could show those people the dozens of videos of students laughing in Math class, when there is an interesting discussion to be had! Thank you for subscribing, by the way!
What a distinguished gentleman
Love this guy! … Engaging discussion of a potentially dry, uninteresting subject matter 😊
@pelephant94: I appreciate that...it means a lot to me when someone finds this material useful!
I wanted to be a mathematician without any purpose but I am 37 and unfortunately I am an environmental engineer. To be a math person, no goals no purposes no any one only mathematics and you, may be a cup of coffee a little bit rain passion inspiration and joy, passing away years without noticing...
you don’t become, you just are 😊
Where can I, as someone from Europe, obtain the book by Dolciani without paying $1,300 for it?
You can get it for free on archive.org.
Cool! I had the Dolciani Book 1 in Junior High.
What's a good discrete mathematics book?
Knuth Concrete Mathematics
I loved maths because in my class in primary school we had some small text boards framed on the wall which i used to read during break.
They contained the properties of addition and multiplication on them and it was almost like a miracle seeing that the simple addition has things which hold true regardless what numbers you try. That was really what got me interested and yes teachers saying there is not enough time to prove X or you won't understand it really made me sad .
I remember when studying geometry (not my strong point btw) when we were told that the medians, bisectors and heights of a triangle all intersect eachother in 1 point i was like wow why not 3 points and nobody bothered doing a demonstration for that
Dolciani, the exact same cover was my 8th grade text. I loved the book! That was 1985-86. I guess it will be hard to find these days. Now I need to teach my daughters math and I hope that I can get my hands on the book. I am saddened that there aren’t modern reprints of the book.
If you being a mathematician creates a negative effect, just be negative as well, to cancel it out.👍🏼
Im an engineering major with a passion for mathematics, do you feel that the Dolciani books would be also great for self study?
Yes, I absolutely do because those were the books that I self-studied from since my school back then did not, unfortunately, have the rigor I wanted. There are exercises A for more basic ones, exercises B for more intermediate, and then you get exercises C for more challenging ones, so I very much like that too, and you can check for answers in the back of the book.
Dolciani did my high school math book in the late 80s. It was entitled “Algebra: Structure and Method Book 1.” It is much cheaper. I wonder if there is much difference. I’m trying to help my daughter.
Any book by Dolciani will still be better than any book available today. However, the one from the late 80s is slightly less "axiomatic" than the earlier versions, but still thoroughly solid. If you can get a copy of the 1970s or even early 1980s versions, that would be great, but if not, then definitely go for the cheaper late 80s version. Or, alternatively, the book is available online as a pdf...if that works. Personally, I'm not a "pdf man", so I prefer a physical book when I can get one.
I am in my 60's. After a career in engineering, I have rediscovered the Dolciani math books. I am having fun studying the
Dolciani Book 1 and Book 2.
You can't go wrong with that!
Allyn Washington's Basic Technical Math With Calculus, a College staple would be the first book I'd take into the cave or bunker, if I thought the world was coming to an end. It starts with the number line and ends with Advanced Calculus. Along the way it presents a splendid and masive collection from all the sciences and technology fields, so you'd never have to add extra texts from Archetecture or electronics or hydraulics etc. It trully is a summary of science and technology since the beginning of time.
It's strange how memories work. I'm going to be 57 Nov 30th and once I saw that book cover, I immediately remembered it when I was young. Just blew my mind how something so long ago and so meaningless just happened to come back from my memories. Not sure why UA-cam just happened to show your channel also. Pretty wierd. Oh! And it's the red Algebra book at 14:18 is what I'm talking about.
I’m 52 and exactly the same. The cover rang a bell in my head. I have aphantasia but somehow I can recall the classroom and my teacher’s face albeit vaguely. That book and that class must have been a real impact in my life..
@@stevesskychannel3099 I always wondered if all the memories we had throughout our lives are laying dormant in our minds but no one has figured out how to retrieve them all. It's funny on an electronic device we have storage we can modify but we can't do that with our own memories. Also! I think it would be helpful to at least figure out how to "delete" traumatic memories. Hopefully there are people working in this field if it exists. It could really impact humanity.
@@NyteRazor My mind has autodelete of traumatic memories. Having aphantasia helps I believe because I can’t have flashbacks.
I haven’t watch all the video time but in during the first 10 minutes you mention many times the feeling of not knowing or the desire to know why something has to be done. I am so annoyed myself at the fact that the axiom of choice has not been proven. When I ask a professor they always say “in here we have to believe is true”, why? I hate believing in not proven things in mathematics. Like, what if one day I decide not to “believe” in the axiom of choice, does that mean I can’t go to math class in university? Like I have to forget about the Hahn-Banach theorem in some sense? It’s uncomfortable.
I have Dolciani's Algebra, Trigonometry and Introductory Analysis on ebook.
Hello sir I love mathmatics,I believe only mathmatics is the only language that can define universe..but never got good books nor great teachers..now I am 32 subscribing your channel to explore my love for math...
Thank you for your kind comment and for subscribing! Welcome.
좋은 말씀이네요
Absolutely fantastic content. Happy to have found your channel. I actually have Modern Introductory Analysis by Dolciani. It’s a great math book. I find older math books more rigorous and certainly axiomatic. Precalculus Mathematics by Shanks is great as well.
Thank you! Modern Introductory Analysis is, I dare say, the BEST high school "precalc" text ever written in America. I have not seen any that come close that book! And yes, Precalculus by Shanks...I agree, also an excellent book. I particularly like his chapter on Vectors.
His opinion on German philosophers cracked me up. It’s good he went with math.
Thank You 🙏
Informative
This is an amazing video
good to know, thanks.
Just after coming across this video. I am a policeman in my forties who gave up acdemia because my maths was not up to scratch.
Love maths now as a pastime.
I am a fan of yours now 😊
So many videos refuse to cut to the chase. When this happens, I cut my losses and move on. I didn’t anticipate this from a math instructor.
Hey, champ. Click on the description and you’ll get the IMMEDIATE answer.