THE THREE MATH BOOKS THAT CHANGED MY LIFE
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- Опубліковано 5 лют 2025
- As I mentioned in the video, here are the links to the three math books that changed my life for the better:
1) Peter Selby and Steven L. Slavin's "Practical Algebra: A Self-Teaching Guide". www.amazon.com...
2) Mary Dolciani: Modern Algebra, Book I, Structure & Method: www.amazon.com...
3) Mary Dolciani: Modern Algebra & Trigonometry, Book II, Structure & Method: www.amazon.com...
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.
Man, does this resonate with me! I'm now 61 and have decided to finally really learn this as a hobby. As a kid, I had resigned myself to being ignorant of math. I was always curious and amazed by friends who seemed to "get it", when in reality, they were simply naturally talented at memorizing tasks and steps. They had no need or curiosity to understand the process or "why". They simply memorized steps and moved on. Yet, I was unable to get beyond my need to fully understand the 3D nature of algebra, and the why, and the relationships between the various steps and purposes.
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?
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.
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.
What other stuffs may help for left side of the brain?
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.
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 !
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
Your story is precisely my own and I cannot tell you much of a relief that is. It's time to relearn correctly. The start of a new personal era
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'.
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!
I love this guy ! We need more people like him.
You have the voice and thoughts of a motivational speaker. I stumbled upon your videos last night and have liked what I watched. I am computer science BS and applied mathematics BS student at a state university. Good day to you sir!
@indefinite115: I very much appreciate your kind comment! I wish you all the best in your studies and beyond!
@@citytutoring Thank you for the well wishes.
This guy is Awesome! We need more Math Heros like him in our public schools.
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.
Amen. I have tried unsuccessfully to describe what you describe in this video. Great work.
Thank you!
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.
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!
Professor Cromwell, as a mathematician myself who struggled at math while in high school, I appreciate and thank you for your dedication to helping those in "mathematical need." Your way of explaining things is very engaging, by which I believe yourself to be an excellent math teacher.
Subscribed!
Thank you for your support! I always appreciate kind comments, and the fact that you have a similar background of struggling in mathematics is all the better!
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.
Great video! Thank you! I appreciate your presentation and information!
I remember that Dolciani Modern Algebra from my 1972 Algebra class!
These are the type of books I need. I want to be a physicist but I'm also interested in math and CS
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.
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.
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.
What a delight to find your channel, professor!
Welcome! Thank you!
A. Baldor: Algebra, arithmetic, trigonometry, and geometric. Those books are all we need. Thanks
I used her books in middle school many years ago. I bought used copies of them recently to teach youngsters Introductory Analysis, Algebra, and Trigonometry.
thank you for this! love your passion!
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.
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.
Professor Cromwell, you are so passionate and charismatic about math. i wish i was in your math classes. you are cool af. i am subbed.
Thank you very much for your compliment! I try to do my best, and yes, I really enjoy math!
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.
@ 3:43 : I love this perspective , I think new generation can't understand it well , these days you hear everywhere ,you are wonderful !!
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!
Here is two book I would suggest to build up an intuition and love for maths:
1) Alex Adventure in Numberland
2) Measurements - By Lockheart.
THANK YOU SO MUCH FOR MAKING THIS VIDEO AND SHARING YOUR EXPERIENCE WITH US.
My pleasure! Thank you for stopping by!
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!
Thanks God I read the comments saving my time.
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!
@@citytutoring I revisited this video and saw this comment for the first time. It was actually a very complicated and long story, where the mathematics department at my school placed itself in opposition to my interests. Which I found to be startling, and I was left speechless when they were uninterested in my enthusiasm, and did everything in their power to keep me from accelerating my journey... But finding your videos makes me so inspired and hopeful that there are people who truly care not just about mathematics, but also about helping others!
Please continue making these high quality videos.
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.
What an interesting character you are. I mean that as a compliment. 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!
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.
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 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.
I could swear that I had that book in high school. The front cover looks very familiar but I graduated in 1975 so if that book you are holding up is the first edition, I guess it was published after I graduated. I remember in ninth grade having a book like that. I bombed that year and was really depressed. I took the class again in summer school prior to eleventh grade. Then I took a geometry class in eleventh grade that used a textbook with a different publisher. By twelfth grade I was obsessed with math and took a course in intermediate algebra and trigonometry by the same publisher as the first edition. I loved those old textbooks especially the first and the third ones I mentioned with their shiny covers.
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.
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.
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.
My suggested videos bring me over here and thank you GOD!
I pretty much: LIKED you Sir!
I have a copy of Spiegel's Differential Equations which is quite good
Richard Hammack Book of Proof is my favorite!
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!
What is fun about some of her polynomial problems or factoring problems is that when you are all done it equals 1.
I was fortunate to have been taught from Modern Algebra during my junior high years.
For me Hillier & Lieberman's Operations Research - and the answer book - was the best Math text I ever read. I only worked through the first eight chapters though. It covered a lot of subjects.
10:45 Literally made me cry...I have been at this point in my life before...this just struck a core. Thank you!
I wonder if there is such useful books for college level intro to discrete math (combinatorics and counting).
Ty for this. Inspirational.
Leibniz, The Last Man Who Knew Everything
Mike Hockney, visionary.
"Math is the realest thing of all. Existence is mathematical, energy is mathematical, and you yourself are 100% mathematical. You will never know who you are - you will never arrive at the answer to your existence and the meaning of your life - until you understand what you are. You are pure math - whether you like it or not! You are an individual, autonomous, self-solving, self-optimising node in an unimaginably vast, collective, cosmic, self-solving, self-optimising mathematical equation ... the equation of existence. The answer to existence is inside you right now. Only math can extract it. Isn’t it time you learned what math actually is?”
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.
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!
I love listening to a mathematician , please make an Abstract Algebra course and share your view point about the subject. I personally love Hangerford's book
Cool! I had the Dolciani Book 1 in Junior High.
I would love it a company printed an English version of the Spanish Language Baldor math books. They are old school in content and the perfect carry/study size.
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.
Incredible, I purchased your recommended first book, Practical Algebra 6 months ago to help me with algebra on khanacademy! I'll be sure to look up the other 2. Thank you.
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!
Dolciani was what I learned from in H.S. in the 80's. You're right. The older books were better b/c the professors still used legacy techniques of instruction handed down through the mathematical lineage.
German here, sir. I speak french quite good. What do you think about the Bourbaki books? I guess that these are also very rigorous and based on axioms, theorems, explanation of vocabulary etc. Can you say anything about whether or not they might be worth it?
have a nice day
Thank you for your question. Bourbaki books are excellent, but it depends on what your goals are, and what your mathematical background is. I believe they would be challenging for high school students to tap into initially.
When I was in high school we used the Dolciani: Modern Algebra & Trigonometry, Book 2 Structure and Method, just like the one in your video.. I don't know if it was my teacher or me but I failed, and had to take the course again in summer school. I passed. I went to community college and took algebra and failed. I changed community colleges, different instructor and a different book and did well. I still find it difficult to relate to doing math with letters not numbers. I did not relate to the Dociani book. Later I found a high school algebra book with a 1947 copyright, by Walter W. Hart titled A First Course in Algebra. I am assuming this is not the Modern Algebra you are speaking of, however I did find this book very easy for me to relate to, as it had problems and examples I understood. When my instructor started of with a+b+c=d, I was instantly lost, and didn't understand why anyone would add letters. Also I was never told how algebra would help me solve real world problems. I was told "you will need this later" but was never told why I would need algebra later. Later in college, I took statistics and was scared to death. The professor looked past retirement, with only a band of white hair left around his other wise bald head. I told this professor at the beginning of the class I was terrible at math. He asked me "who told you that?" I told him my story. He asked where I went to high school, and I told him. He said that's your problem. He said if I would listen to him and do the homework I would be fine, and he would explain everything. I made a B. I also landed a job as a Quality Engineer, which is all statistics. I worked as a Quality Engineer for thirty three years. The teacher can make all the difference. I later found out that the other section of Algebra in my hight school, did well with the same teacher. The difference was there was a female student whose mom had taught math, in the other section. She would tutor her daughter at night, and the daughter would tutor the other section of students in study hall. Sometimes a good teacher can make a difference. I am seventy years old and not giving up my math journey. I am retired, and want to master math as much as I can. I don't want to feel defeated and beaten, as I did in high school and college. I really appreciate you sharing your story, and I plan to look for Selby's book. Thank you.
Teachers can make all the difference in the world. By developing a positive learning environment and encouraging a mindset in their students in which they feel good about their progress. Thus creating the belief in their ability to succeed. Why? Because a teacher explained a subject in a way and at a pace that a student can keep up and have their questions answered in a nonjudgemental way allowing the student to have a positive self worth.
I had to watch this video just from the display of my Algebra textbook. That was a great book.
Mine were more big picture or biographical, all of which finally got it through to me that if I wanted to be a scientist, I needed to be able to do math. Because as a kid I couldn't see much use in anything past arithmetic.
These date me pretty badly, but Men of Mathematics, by ET Bell, Cosmos, by Carl Sagan, and Chaos, by James Gleick. The discussion of how most things in nature are nonlinear, but can follow predictable patterns was the biggest eye-opener to me since I first understood the utility of y = mx + b.
You remind me of the young Al Pacino in the Godfather movie series😀😀😀By the way I own one copy of this book, we used to call the red book!
Thank you for sharing this information. As a student who is struggling with math, this video eases me. Beautiful neck tie though 😊
Wow! You are intense! But that’s your point. No touchy-feely. “You learn math or I’ll bust your f’in cajones!” How nice.
I love your passion about Math
21:11 It may be hard to believe, but Omar Khayyam was born in Iran at 1048, born in Neyshabur in Iran, so first of all he was not an Arab, secondly, he was not a Muslim he was an atheist . By the way i love your classic style, im a physicist from iran
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 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).
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've managed to buy the book, just waiting now for delivery
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.
the quality is awesome!!
Thank you, for being straight forward, with your students and audiences.
Yes, I remember those Junior High School days, too!
And, yes, I think kids NEED to be told: difficult subjects ARE DIFFICULT for a reason.
There is no "fun way" to make difficult subjects fun or easy, like all these crazy people (teaches and non-teachers alike) keep saying (to make us feel better, for FAILING to discipline ourselves, to invest the necessary time and effort, to learning DIFFICULT matters)...
Or, to paraphrase Euclid, there is NO SHORT CUT to any thing.
Even kings and powerful people still need to work hard and work long and work diligently, if they want to learn mathematics or any difficult subject matter...
The BS that I hear all the time --- Oh, it's just my teacher... he/she's just terrible --- is just not being honest, with ourselves, with others, and with society. Math, physics, biology, chemistry, trigonometry, calculus, algebra, topology, cosmology, genetics, virology.... they ARE HARD subjects.
It is NOT the teachers fault --- from elementary, to Junior High/Middle School, to High School, to College --- that we can't learn or don't learn complex subject matters; it is OUR fault, if we don't understand things.... And that's largely --- assuming we have average, workable neuron connections (without too many disability issues) --- because, for whatever reason, we're not able or willing to sit down, for HOURS AND HOURS AND HOURS... to study subject matters that we don't immediately understand, in our first & haphazard encounter with them.
Thank you so much 👍
Great video! I too am very disappointed with math instruction for high school students. My sixteen year old daughter is doing fairly well in her math classes, but the curriculum leaves out subjects that I believe are essential, such as plane geometry proofs. I have tried to help her to understand mathematics from a rigorous point of view. I hope in planting the seeds of clear and rigorous thinking that she will benefit later on; not only in mathematics but generally in life.
The Dolciani books were used in my High School
Something to add. I feel that students who struggle feel more success when they search for their understanding because most of the time, they didn't get it the first time because they were distracted in class. So when a student takes the time out of his/her life to learn, they are more likely to make sense of it.
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.
If you being a mathematician creates a negative effect, just be negative as well, to cancel it out.👍🏼
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
I consider myself quite lucky because although I live in an era of the U.S were math(and many other subjects) are taught horribly. My parents sent me to a small charter school that properly took its time to tell you the why in math. In my freshman year we took Euclidean geometry and it was entirely axiomaticslly based with us as a class presenting and developing different proofs as we go on. It was all wonderful, but due to some problems I had with the school I left and am currently in a public school as a senior. Once you live your life having seen true education and then come to public school it's utterly shocking. I to am a little obsessed with math. In my previous it was not all that strange, but now it feels like some wall separating me from everyone else as if the fundamental way I think of things(not just math) is different. Luckily though I applied to a university that seems to uphold similar values as my previous school and I am currently taking a proof class in the school. All this to say is that I really like your story and I really wish there are more people who can understand what it means to teach math.
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!
Awesome! All the way from Nepal here,sir.