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Thank you very much! Your comment means a lot to me! May you have a prosperous 2025 and yes, all the best wishes for your income growth!

Thank you! Proofs can be very hard, but from my own experience, I can say they are so rewarding once you master the basics! The pleasure one takes in the proof is quite liberating!

@@citytutoring Yeah it does feel nice when you work one out. I'm not a proficient prover. I can do basic ones, and i can spit out the famous ones you learn, if I study them, but i can't say i always gain insight from them. I've been out of math for 16 years and I haven't taken a mathematically demanding stat class in 12. Most of what i do is either direct data analysis, statistical consultation, and some basic computer simulations.

Absolutely agree. So much depends on critical thinking.

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?

@ 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.

So, because the Dolciani textbooks are very hard to find, we have a master copy and work from that. If that fails, we use the copy available on archive.org. Every year, I do get students who are able to find some version of the book online for sale.

Yes, you are correct. Sorry! I did not specify the quadrant, so there are indeed two possibilities. Thank you for bringing up the issue.

Yes, thank you for your suggestion - the data is now linked in the description. I have had similar experiences to what you describe. We’ve reached a point where "I can’t do fractions" seems more like a casual confession than a serious concern. And yes, you’re spot on about future teachers not always having a solid grasp of foundational math. I did not want to say the "quiet part out loud", although I often throw caution to the wind and say it anyway out of my broader concern for the state of Math education. It’s like trying to build a house on a shaky foundation-sure, the house might stand for a while, but it’s only a matter of time before things start to fall apart. I have trained secondary ed teachers who, as you may well have experienced, actually hate math themselves and in many cases they take the Math path because in some districts you get paid more for being a Math teacher due to the teacher shortage. Re: mental health issues. I have not had direct experience with such cases, but have certainly heard of a very troubling increase in the past several decades...mostly from colleagues who tell me similar stories about what they have seen in their experience.

@@citytutoring "I have trained secondary ed teachers who, as you may well have experienced, actually hate math themselves and in many cases they take the Math path because in some districts you get paid more for being a Math teacher due to the teacher shortage." I didn't realise it had gotten that bad. I don't bame people for doing what they needed to do to survive, but that's not great for their students. I wonder if the ciriculum people know this and that's why they give scripted leasons? I would struggle as a high school teacher, it sounds like they place a lot of extra emphasis on lesson plans and things like that. I tried carefully planning my lessons when i startd teaching, but those plans always went out the window after I'm one or two problems in and I see a few confused people, so I do what I can to address that, which means I've deviated from my plan. The US is starting to have generation math truama! It's like each generation gets worse at it, and likes it less.

Yes, so, one of the reasons I have personally been so successful as a Math instructor is because I was, thankfully, liberated from the "lesson planning" bureaucracy and scripts they impose on teachers today. Had I been in a situation like that, I would have resigned. I had always worked within private systems, so that makes life easier in that regard. Yes, it really is that bad. For example, some rural and inner city districts now offer bonuses for Math and Spec. Ed teachers. In fact, we even now have teachers teaching Math who do NOT have a Math degree at all. Now, I'm not one to be obsessed with diplomas and degrees, but when you have instead someone who barely got through Algebra II in high school now TEACHING it (and no evidence that their understanding has changed!), then we have a problem. Personally, I have never followed or written a lesson plan except back in the days of my youth when I was observed by administrators, and even then it was all a show. I would give them a copy of my "lesson plan", go through the motions, and they'd leave after about 20 minutes. As you know, every class will be very different, with different needs, so I always take their temperature first at the beginning of the semester and act accordingly. Some classes, I have started them out with percentages and decimals, other classes, we get right into the Algebraic parts....it really varies. Now that I run an academy though, it is a lot more structured course wise, because students are pre-tested before they can register for a course to adequately see their level.

@@citytutoring Yeah i know some districts are desperate for teachers. I taught at universities in the NYC area, and I know some of the local high schools had difficulty getting math faculty. One of the schools i taught at had programs for taking people with subject matter expertese and giving them teacher training, and did what they could both at the university and out side of it to train teachers in math. It was hard because we didn't always get the best people to work with, but we also got some really good people. We do what we can. I stopped teaching after the first semester of covid. At the time I didn't have a good setup for disance learning, and neither the students or i were enagaged. I'm at the point where i really miss it now, so i'm looking to get back into it.

I was starting to fall asleep when I answered this, so I’m editing and clarifying. Obviously, I'm not Alfred, but I know a bit about this. In my opinion, you can never know too much linear algebra. Stephen Boyd, Lieven Vandenberghe - Introduction to Applied Linear Algebra, is a great place to start, especially if your math background is modest or if you’re rusty. Even if you are doing great mathematically he presents some material in here that you might not have seen or may present material in a contest that is more relevant to you. It doesn’t cover some of the material in a traditional linear algebra book, because of this you’ll also want a traditional linear algebra book. Gilbert Strang - Introduction to Linear Algebra. I own the 3rd edition, I’ve looked at the 5th and 6th, they aren’t interchangeable, but they’ll all get the job done. Strang has a unique way of doing linear algebra, if it works for you, you’ll really get something from the book. David Poole - Linear Algebra A Modern Introduction. I don’t have tremendous experience with this book, but it has the right content. Howard Anton, Chris Rorres - Elementary Linear Algebra Applications. I don’t have tremendous experience with this book, but it has the right content. By right content I mean the traditional linear algebra stuff plus the SVD Sheldon Axler - Linear Algebra Done Right is very well regarded, and the author gives away the newest edition (4th) of the book for free on his webpage. I own the second edition of the book, It's harder than the above linear algebra books, and requires some facility with proof writing. While a cool book, that will certainly give you insight into linear algebra, it won't be as directly applicable to data science You should also get a book or two on linear models. They are work horse tools in statistics, and are a great place reinforce linear algebra concepts. John Fox - Applied Regression Analysis and Generalized Linear Models 2nd or 3rd edition as well as the resources on Fox’s webpage. It’s comprehensive and talks about the geometry and theory behind the linear models. For probability and math stat, I would recommend Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton - Modern Mathematical Statistics With Applications 3rd edition. I own the first edition. This a very accessible probability and mathematical statistics book that has modern topics like logistic regression and Bayesian statistics, but the coverage of Bayesian statistics is not included in the first edition and is not well developed in the second. John Rice - Mathematical Statistics and Data Analysis. I used the 3rd edition for a math stat class in grad school. I looked at the second edition and it’s pretty similar. It has a great balance between probability and statistics. It includes coverage of sampling theory, and non-parametric stat. It’s more in depth than Devore and Birk, but less in depth than the next book… George Casella, Roger L. Berger - Statistical Inference 2nd edition. This was a supplemental book for the class that I used Rice in. It’s been the mainstay book for PhD level math stat courses for over 20 years. It has all of the standard topics, but in more depth. I would hold off on this one. You may not need this level of detail. If you need a basic book Allan Bluman - Elementary Statistics: A Step By Step Approach This is a giant Rabbit hole that you can go down. I own at least 5 linear algebra books, and atleast 5 mathstat books, with a few additional books on probability and on math stat seperately. I also own 5 linear model books.

@ Thanks a lot.

@@pratikmaitra4190 You're welcome. I'm good with the math and stat part of data science, but I am weak at the comp sci stuff. If there is anything else you're looking for feel free to ask.

Thank you for your question, and thank you Walter274 for such a detailed response and your assistance with the matter. I will defer to Walter's answer, because I would have made similar recommendations since I am familiar with those titles and they are the closest you will get, as far as I know, to your objective with data science.

@@citytutoring You're welcome. I'm happy to help people when i can.

Yes, that is indeed a major problem in this country. There is an alarming number of people who truly believe a President is responsible for setting prices, and worse yet, they believe a new president has the power to unilaterally "lower" inflation. I sometimes wonder if they believe there is some hidden magic wand that creates or destroys inflation on a whim. We have a country where logic is not taught in any meaningful way, hence why you also get people who say, for example, they are "against" Obamacare, but they also tell you they believe in more affordable/accessible healthcare. You can't have it both ways, but here we are.

Your experience relates academic natural selection-only the mathematically fittest survive! The lack of alarm at the attrition rate is almost poetic, like everyone just accepts that higher math is a trial by fire. The '1% Club' does feel apt! I often begin a semester with about 45 - 50 enrolled students. By the end of the term, there's about 9/10 left depending on the course. Unfortunately, there are now some colleges that make you pass students, regardless of any evidence of academic ability.

Yeah I would often have semesters where only 1/4 to 1/3 or so of my students would get a C- or above. I'm no that hard of a teacher. If you pay attention when i teach you'll know what many of the test questions will be, because i say things like this would be a good exam question, and when i'm done, i'll ask are there questions. I tell them i will do this on the first day of class.

@@walter274 As a nation or even as a society, my wish would be to advance the average student to understanding several topics of calculus. They may not grasp the finest points but should at least see an equation and know what they're looking at.

@@dhickey5919 I would be happy if high schools made students take 4 years of math instead of 3. If coleges and universities had to do less remediation because the students were better prepared, those remediatial class could become a semester of calculus. That will never happen, because peopple are too greedy. That would require more spending for the school district, which people don't want to pay for. A lot of people just want low taxes.

I was very blessed to have had "remedial" options in my high school. Yes, as far back as the late 20th century, where I went to high school you HAD to have 4 years of Math, and English to even be considered for graduation, and we also had a course that was mandatory called "Strategies" if you were honors or college prep. "Strategies" was a Math course designed to specifically prepare you to take the SAT. It was taught by one of our toughest and "meanest" (I say this in a good way) Math teachers. Of course, discipline problems were also swiftly dealt with. If any student even dared to disrupt a class, they'd first get a verbal warning. If they kept up the nonsense, kicked out of class. Today? Too many of our schools are circuses.

Yeah, I distinctly recall as an elementary school kid, when I was home sick from school, my mom would bring me cheap paperbacks by George Gamow and Isaac Asimov on math and physics. And I retained more from reading these popular books than all of my university & grad school education. 😂

@CondorAHLS Obviously a very fine and truly loving mother. Best wishes to you and mothers and fathers who truly love their children.

Oh, I am very much an admirer of Chrystal's Algebra and have solved problems in the book. As for Euler's Algebra, that is another excellent source, although I would recommend it as a supplement given that the way the topics are presented would be quite confusing/challenging to a beginning student today if they are in the United States. Of course, I am passionate about structured logical thinking, but I'm afraid even many teachers would have trouble teaching right out of that book. So, that is why I use it as supplementary material.

So I can put them in the category of dolciani's algebra I mean, Are they rigours?

@mohamedwalid-g2u Absolutely! However, for example in Chrystal, the language might be dated if you are using it to teach students, and some of the notation is very old-fashioned, so if you are using it be sure to adapt it with the modern notation that everyone can understand.

Actually I am student trying to re-learn the subject

I would say to any high school student who needs inspiration that the key to success in their personal future is to know that they can only truly be free and successful if they are educated and take in every day as if it was their last race to win! If I, who started out as a failure in math made it to being a mathematician, they can achieve their goals in whatever subject as long as one thing never dies: their passionate curiosity and desire to succeed in all they do, and not accepting "no" as the only definitive answer to their plans.

From Lord Beaverbrook’s book “Success” (London: Stanley Paul & Co., 1921), Chapter VI: Education, pp. 61-62: “Read anything and read everything… There are, of course, in addition, certain special branches of education needing teaching which are of particular value to the business life. Foremost among these are mathematics and foreign languages. It is not suggested that a knowledge of the higher mathematics is essential to a successful career; none the less it is true that the type of mind which takes readily to mathematics is the kind which succeeds in the realm of industry and finance.”

Thank you for letting me know about that! How very sad for our students...

@ I don’t want to blame anyone but I think that It is because most of the parents, teachers and government staff don’t take an active role in the education of the new generation, and unfortunately they don’t care or they reject the value of education compared with other social or personal responsibility.

The United States launched humans to the moon from Florida. How we don't have the best math and physics in this state is beyond me.

@@Mambialasombra Yes, unfortunately this has been my experience. Personally, I have been blessed to deal with very serious parents, but I do work with a lot of colleagues who have shown me literal horror stories about what they experience. Also, at the risk of sounding irresponsible in my assessments, I also do think that many teachers leave a lot to be desired with some of their behaviors. I do not say this in a judgmental way, because I know we all have our struggles, but more of a constructive observation because I am a firm believer that no matter how utterly disrespectful a student can be, and many times they are, they still respond based on the standards you project.

@@dhickey5919 I bet it is because teachers are not being incentivized enough, and some times schools put to much responsibilities over some professors (I’ve been witness of that) and they just give the classes but don’t really teach, reasons are more than obvious. But I’m not justifying anyone, just stating it and hoping that we all could do something about it.