THE THREE MATH BOOKS THAT CHANGED MY LIFE

[@emotionalmindedstate]

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

[@emotionalmindedstate]

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.

[@mohdarhamshakir8922]

Thank you, saved my 25 mins

[@wilsonoliveira7447]

Thank you

[@fleurafricaine5740]

information + silence = heaven

[@SargonofQueens]

Thank you for saving my time. I spent five minutes listening to his personal life and decided to quit until I read your comments.

[@BobFrTube]

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!

[@agnelomascarenhas8990]

Mary Dolchiani. There is a beautiful series of books in her name or funded by an organization setup by her, unsure.

[@citytutoring]

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.

[@BobFrTube]

@@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?

[@johnwest7993]

@@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.

[@citytutoring]

@@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.

[@victorortiz1452]

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!

[@getusel]

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?

[@meatsong]

@@getusel The emotional trauma bit was obviously a joke.

[@getusel]

@@meatsong I hope it is.

[@citytutoring]

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...

[@navierstokes2356]

Lo besarías?

[@realtoast7036]

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.

[@Near_edits]

I felt lucky for watching this i am 17 and trying my best to be good at the subject may god bless you!

[@sthetatos]

Do not forget to read a lot of poetry.

[@Revo55]

@@sthetatos can you please explain this

[@dirkghysens7331]

@@Revo55 Doing only left brain stuff is not right.

[@sthetatos]

@@Revo55 The art most familiar with the secret of transmitting abstractions is poetry. If you like math, study geometry. not algebra.

[@Mohamed.GadAllah]

What other stuffs may help for left side of the brain?

[@HaramGuys]

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

[@robfielding8566]

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.

[@citytutoring]

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.

[@Mosrod]

​@@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]

@@Mosrod Thank you!

[@lazry3208]

​@@Mosrodso why wont you recommend the resources here?

[@marchanselthomas]

@@Mosrod Please I'd be forever glad if you could help me too with the resources. Thanks.

[@dhickey5919]

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'.

[@paulgarcia1147]

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.

[@citytutoring]

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.

[@scretching08]

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.

[@ericbwertz]

Same. 8th grade Algebra I !

[@ussdfiant]

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!

[@citytutoring]

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?

[@ussdfiant]

@@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.

[@ussdfiant]

@@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.

[@patrickleung5863]

@@citytutoring Your video came up in my KZbin 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.

[@Optim40]

I love this guy ! We need more people like him.

[@funfactory2012]

This guy is Awesome! We need more Math Heros like him in our public schools.

[@douglasstrother6584]

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!

[@renancambui8719]

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!

[@Lifelong_Learner_USA]

Amen. I have tried unsuccessfully to describe what you describe in this video. Great work.

[@citytutoring]

Thank you!

[@johnwest7993]

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.

[@GeekinInclass10]

These are the type of books I need. I want to be a physicist but I'm also interested in math and CS

[@shahidnasir7851]

Thanks God I read the comments saving my time.

[@CatholicGaming]

10:45 Literally made me cry...I have been at this point in my life before...this just struck a core. Thank you!

[@_jampa]

What a delight to find your channel, professor!

[@citytutoring]

Welcome! Thank you!

[@cypherknot]

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.

[@douglasstrother6584]

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.

[@douglasstrother6584]

Librarians love finding stuff for their Customers.

[@sugatmachale]

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.

[@patrickleung5863]

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.

[@citytutoring]

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.

[@KevinBalch-dt8ot]

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.

[@nelsonbolivar7171]

A. Baldor: Algebra, arithmetic, trigonometry, and geometric. Those books are all we need. Thanks

[@bobdobbs8700]

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.

[@citytutoring]

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!

[@jimbobago]

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.

[@theprofessor5584]

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.

[@citytutoring]

That is very kind of you to say! Thank you! I will always try my best to do what I can.

[@truepenny2514]

What an interesting character you are. I mean that as a compliment. Subscribed.

[@AbdennourSmida-k6q]

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

[@citytutoring]

Greetings, and welcome! I would love to visit Algeria some day! And yes, that is a great Feynman quote!

[@mitchletterman340]

If you being a mathematician creates a negative effect, just be negative as well, to cancel it out.👍🏼

[@josiahgibbs5697]

What is fun about some of her polynomial problems or factoring problems is that when you are all done it equals 1.

[@BreezeTalk]

Please continue making these high quality videos.

[@adamrmoss]

What a nice suit, looks sharp af

[@citytutoring]

Thank you sir!

[@cccbbb-rw5te]

The tie won you a new sub.

[@citytutoring]

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!

[@joegilbody4878]

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]

Are your GED students motivated about Math?

[@joegilbody4878]

@@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

[@citytutoring]

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.

[@joegilbody4878]

@@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.

[@GGMike09]

the quality is awesome!!

[@GungaGaLunga777]

in the 1980s i flunked out of Algebra II. I had no help guidance or mentors. My parents were naive and ignorant. My life would have been completely different had I just gotten the help I was asking for. I'd go to other adults asking for help, and they couldn't help me either. Tragic.

[@pollensalta]

THANK YOU SO MUCH FOR MAKING THIS VIDEO AND SHARING YOUR EXPERIENCE WITH US.

[@citytutoring]

My pleasure! Thank you for stopping by!

[@ericbwertz]

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.

[@citytutoring]

Ahh that makes sense! Thank you!

[@johnfox9169]

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.

[@dan-florinchereches4892]

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

[@SirNose687]

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.

[@alirezaansari1164]

I love your passion about Math

[@eavalos3]

I am 53 years old and I was never good at math. Today, at 53, I set myself the personal challenge of learning math. Now that I reflect on my poor performance in math classes, I realize that it wasn't because I was a fool. I simply had no interest in learning. My goal: To get to a level where I can understand Spivak's Calculus book (and all of this just by self-study). I have already started my studies and I am currently in Arithmetic, but unlike when I was a uninterested young student, I am now interested in understanding the whys of things. Please wish me luck. Greetings from México.

[@citytutoring]

Thank you for your comment and for your perspective! You will be challenged in the beginning, but it will all be for the better! I wish you all the best in this journey, and you will see how liberating it truly is because it changes the mindset and makes you sharper.

[@Mambialasombra]

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.

[@vimalneha]

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.

[@PsychologyNutshelled]

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.

[@jorgemonasterio8361]

Ty for this. Inspirational.

[@orsonyancey4131]

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.

[@citytutoring]

You can't go wrong with that!

[@NyteRazor]

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 KZbin 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.

[@stevesskychannel3099]

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..

[@NyteRazor]

@@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.

[@stevesskychannel3099]

@@NyteRazor My mind has autodelete of traumatic memories. Having aphantasia helps I believe because I can’t have flashbacks.

[@nigellbutlerrr2638]

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.

[@citytutoring]

Indeed! I do like the UK materials as well!

[@tonywims8848]

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!

[@citytutoring]

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).

[@billofrights5064]

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.

[@Zane_Zaminsky]

Hey, champ. Click on the description and you’ll get the IMMEDIATE answer.

[@jonw4308]

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.

[@SmeeUncleJoe]

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.

[@nine-l3y]

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.

[@kdog3908]

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.)

[@citytutoring]

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!

[@kdog3908]

@@citytutoring Thank you. The Dolciani books are proving difficult to source at a reasonable price, unsurprisingly. The hunt goes on!

[@mcleanblades9234]

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.

[@ackamack101]

That first book by Dolciani and Wooton really brings back memories for me as it was the book I used in 10th grade for the second part of Algebra I in 1986-87. I always struggled with Algebra and Geometry, and they aren’t the best of memories for me. Something about the process always eluded me. I would think I would have something right, only to find I had made errors in my equations. The funny thing is that I am a musician and have played the piano for most of my life, and one of the comments I always get is “Oh, you’re a musician. You must be great at math!” To which I tell them Not really. I see the math connection in aspects of music but I always struggled with the maths outside of arithmetic. 🙁 Maybe I should pick up a copy of that book and try dipping my toe back into the world of Algebra again after almost 4 decades of being away from it.

[@citytutoring]

I definitely recommend the books to you, and that you try out the problems! There's no drawback to stimulating the mind! At City Tutoring, my academy, we are very old school and nothing has changed precisely because we use the same books and maintain the same standards that were not unusual in the 20th century. May I ask what sort of music are you composing?

[@ackamack101]

@ That’s wonderful that you do that. I should revisit soma Algebra for sure. As for piano, I just play, I don’t really compose. Adolescent piano lessons that turned into classical pieces (Bach, Mozart, Beethoven etc as well as some modern composers). I had a late start at the piano (right before 8th grade, but wanted to start around 4th grade but didn’t have a piano) and I went away from it for a period in my early 20s, but have been making up for lost time ever since. It’s once of my favorite things, really. And it stimulates the mind for sure. Thanks again for the great video.

[@integralsun]

His opinion on German philosophers cracked me up. It’s good he went with math.

[@mullerss1]

My suggested videos bring me over here and thank you GOD! I pretty much: LIKED you Sir!

[@kevinfinke6927]

Cool! I had the Dolciani Book 1 in Junior High.

[@markkennedy9767]

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?

[@citytutoring]

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!

[@TheLycheegreentea]

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.

[@jeebusthegreat8819]

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?

[@citytutoring]

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?

[@jeebusthegreat8819]

@@citytutoring I understand that and I'll certainly be checking out Dolciani's book thank you for the recommendation.

[@mohammaddaudibrahim3501]

No pictures, no fluff - everything is explained by axioms, proofs; excellent book recommendation. 17:30

[@borisdelaine9797]

I had to watch this video just from the display of my Algebra textbook. That was a great book.

[@Focalope]

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.

[@nihilisticnirvana]

What a distinguished gentleman

[@samthom7873]

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!!!!!!

[@citytutoring]

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!

[@SSi-nq3rt]

you don’t become, you just are 😊

[@albirtarsha5370]

Thank God I went to high school in the 70s.

[@Silvermist78]

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 🙏👌❤️

[@citytutoring]

Thank you for your kind comment!

[@Caribbeanmon]

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.

[@energyexecs]

Thank you. I will search online and order.

[@Muna_Safrar]

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

[@citytutoring]

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.

[@Muna_Safrar]

@citytutoring All the best Prof. You really deserve all kinds of support 🙏

[@Te-bj1yk]

I remember having both red and green books.

[@stevesskychannel3099]

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.

[@TheGrmany69]

You got the grothendieck's experience growing up: it's not the subject you struggle with but the crowd around that is spitting nonsense, and receiving accreditations!

[@batmob8437]

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! 🍻

[@citytutoring]

Thank you very much! I really appreciate you, and your kind words of encouragement.

[@romanisayev4826]

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...

[@bobross7005]

You should be a motivational speaker too. Your delivery is both unique and humorous.

[@citytutoring]

Thank you! In a sense, I think I already am since I constantly have to motivate my students who are terrified of Math!

[@dandanver7359]

Great video, very helpful. Modern Algebra was the *Freshman* text at Whitefish Bay HS in WFB, WI. Brilliant text, fantastic school.

[@pilotpawanc]

Can anyone list the books?

[@liamow3298]

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 😊

[@JR-uc3nk]

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.

[@citytutoring]

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!

[@Mozartedrick]

Thank you for sharing this information. As a student who is struggling with math, this video eases me. Beautiful neck tie though 😊

[@peterpanino2436]

Thinking, Feeling, Talking: What is most important to you?

[@citytutoring]

You have asked a very broad question. But, if you are referring to my approach to math, then thinking, of course-it's the foundation of logic. Feeling is useful as a check, but only if it's rational. Talking? Only after thinking, and preferably not about feelings. Nowadays, one tends to hear much more the phrase "I feel" rather than "I think", unfortunately.

[@peterpanino2436]

@@citytutoring Thank you for your wise answer!

[@eyesyc]

Fyi ( and it seems like you are aware) older texts of the same version line are filled with more information. In older versions very important things are omitted. I bought a first edition linear algebra from Otto breschter and the class was on version 6. They left out so many things I remember to this day. I can tell you ten ways if A is invertible or not.

[@citytutoring]

Yes, that is correct. Indeed many of the new texts go, as we say, a mile wide, but an inch deep.

[@goodfractalspoker7179]

Thank you for the useful knowledge sir. I am sure this video will help guide me to great things in the future. Also subscribed!

[@citytutoring]

Thank you! I can tell you that I would not be the successful man I am today without these great mathematical foundations.

[@goodfractalspoker7179]

@ Yes sir indeed. Thank you again for all you do!

[@Lokie-cd2hw]

Dolciani's third algebra book in the series was Modern Introductory Analysis. She did not title it as Precalculus as books are today. I remember it as being rigorous and it had lots of proofs to be done in section C of the problem sets. If you have the teachers's edition you have a really good book to learn from. If you find this edition it is very expensive. The solutions book is great too to check your work and method of solving. I like being able to check if I'm right or wrong, or just get stuck.

[@Chihab-z8o]

Thank you so much 👍

[@michaelpapa1148]

Video quality has improved! Love to see it. Content as good as always. Thank you for making these videos.

[@citytutoring]

Thank you! And even better improvements are coming soon! I appreciate you!

[@michaelpapa1148]

@

[@doobu691]

좋은 말씀이네요

[@Wutizgo]

This is an amazing video

[@jondaly4501]

I recognize Modern Algebra I; probably from freshman math in 1982-83. In an earlier video you mentioned that probability and statistics aren't mathematics. I've heard that before but never heard anything explanation why.

[@citytutoring]

Statistics? That’s just math’s awkward cousin-useful at parties, perhaps, but utterly lacking in sophistication. Now in all seriousness, Stats are little more than a patchwork of approximations, a craft of guesswork masquerading as science. While pure mathematicians construct timeless truths from axioms, statisticians busy themselves tweaking models to fit data that could change with tomorrow's whim. Someone can call it practical, and it may well be, but practicality is not depth -after all, even carpentry is practical, but no one mistakes it for architecture. Bertrand Russell put it best: "Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means."

[@kamimaza]

16:25 The only math war is Bourbaki vs everyone else.

[@MarkKoerner-c8c]

I can't say that any math book changed my life. Like most people, I don't recall math book authors or publishers terribly well. I do know that we had math books from the same publisher from 1st- through 5th- or 6th grade and that we annoyed our teachers by calling the supposed bundles of sticks (as in "this picture shows that if you have 4 groups of 5 sticks, you have 20 sticks") "sticks of dynamite." E.g., "This picture shows that if you have 22 sticks of dynamite and you take away 4 sticks of dynamite, then you have only 18 sticks of dynamite!" It was all great fun until our 5th grade teacher opened the book for the first time and said, "I guess these pictures are supposed to show bundles of sticks, but to me, they've always looked like sticks of dynamite, so if that's what you want to call them, go right ahead." We didn't know whether to be elated that we'd found a kindred soul or devastated because our little game was over.