ONE OF THE BEST PRECALCULUS TEXTBOOKS EVER WRITTEN!

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  • เผยแพร่เมื่อ 30 ม.ค. 2025

ความคิดเห็น • 97

  • @muchomacho2504
    @muchomacho2504 21 วันที่ผ่านมา +27

    Many years ago on a long plane flight, I was studying a calculus text book when a gentleman told me that it was obsolete because of the advent of personal computers. I smiled and went back to my book.

    • @growthfeeder6041
      @growthfeeder6041 20 วันที่ผ่านมา +4

      Glad you did. Guess what we have similar things is being said nowadays b/c of AI!

    • @David-pq6wt
      @David-pq6wt 20 วันที่ผ่านมา +3

      I love older books. My favorite calculus book is The Calculus by Leithold 3rd edition 1976. It presents material in the theorem proof style. I spent so much time with the book. It was so good. It was a great stepping stone to Spivak.

    • @muchomacho2504
      @muchomacho2504 20 วันที่ผ่านมา

      @ I’m a fan of the late professor Thomas. When you learned from those old books you were left with total confidence. I once went to a class and after the first day there was no doubt I’d ace it because I had already mastered the material that would be covered

    • @michaelnicholson297
      @michaelnicholson297 19 วันที่ผ่านมา +2

      His opinion is about as meaningless as saying that it is no longer required to learn to read, because audio books exist. Or that it is no longer required to learn to write by hand because keyboards are used for tablets and phones (I've seen this actually said). Or that it isn't required to learn to cook because restaurants and grocery takeout exists

    • @lasalleman6792
      @lasalleman6792 17 วันที่ผ่านมา

      Not obsolete, but computers can be helpful.

  • @reginaldwright2608
    @reginaldwright2608 49 นาทีที่ผ่านมา

    I’ve been teaching Mathematics for over 25 years and NOTHING compares to the character of the Modern Introductory Analysis textbook for Precalculus students. The department chair from my high school gave me a copy of the book 40 years ago and I still have it and use it as a resource for my students 👏🏾👏🏾👏🏾👏🏾I’m sooooo thankful for receiving a QUALITY mathematical education from the Atlanta Public school system back in the 70’s and 80’s

  • @KANCHANGANGWAR-u2n
    @KANCHANGANGWAR-u2n 21 วันที่ผ่านมา +13

    "Your enthusiasm for math is contagious, and your kindness makes learning a joy. I'm lucky to find your channel.

    • @citytutoring
      @citytutoring  21 วันที่ผ่านมา +4

      Much appreciated! Thank you!

  • @BreezeTalk
    @BreezeTalk 21 วันที่ผ่านมา +5

    I learn more than only maths from you, sir. An exemplar of the high British beauty my Anglo-Saxon school instilled in me. Different style, sure, similar heart, sure.

  • @BonFlanders
    @BonFlanders 19 วันที่ผ่านมา +4

    Just downloaded a PDF of it, as I couldn't seem to find an original copy! Thank you once again Professor Cromwell!

    • @studiosdetodo8295
      @studiosdetodo8295 19 วันที่ผ่านมา +1

      What are you going to do with the exercises? Like, there are no solutions, i hate this about math books. What if i start doing there exercises and i don't even know if i am doing It well o wrong

    • @BonFlanders
      @BonFlanders 19 วันที่ผ่านมา

      @@studiosdetodo8295 Well, you've got to use AI to your own advantage, so might as well use it as a resource for checking work!

  • @jimbobago
    @jimbobago 20 วันที่ผ่านมา +3

    Another Dolciani book my school district used that I had the blessing of being taught from. I thought it was great when you did the video on the Algebra II book but now I get the bonus of this book being featured. I wouldn't mind seeing a copy of it again some day myself.

    • @KevinKasp-v9u
      @KevinKasp-v9u 20 วันที่ผ่านมา +2

      We used that book in my high school class in Guam in the mid-1970s.

  • @quando2302
    @quando2302 20 วันที่ผ่านมา +3

    I'm from the UK and studying a Bachelor of Science in Economics. I've a new found interest in rigorous mathematics and I'd begun to study mathematics myself. Going from Pre Calc all the way up to Vector Calculus at this point in time which I'm studying in college now.
    Your channel is so helpful in helping me identify weak points in my previous study and I definitely have high interest in studying analysis as a topic in itself.

  • @mpmcd81
    @mpmcd81 20 วันที่ผ่านมา +2

    Let me also say that you are spot on right about the use of tables in a math class. It is the best- the very best- way to understand inverse functions. I bring them out with my students. The biggest problem that I have with the books is the ability to provide immediate feedback to a caseload of 120 students.

    • @getshorty7549
      @getshorty7549 20 วันที่ผ่านมา

      What are your thoughts on graphing calculators? Do you expect your students to know how to properly plot and construct graphs by hand rather than (or in addition to) using a graphing device?

    • @mpmcd81
      @mpmcd81 20 วันที่ผ่านมา

      They are just another tool. There are a lot of things that, for better and for worse, students must be comfortable doing with them on AP exams or they will be in a world of hurt. And once students get the multiple representations, they are helpful. But they are not a substitute for doing things by hand and understanding the impacts of multilicative and additive transformations. Sometimes they are necessary for efficiently finding polynomial zeros.

  • @ricardoy1413
    @ricardoy1413 20 วันที่ผ่านมา

    Beautiful content, I really appreciate your passionate presentations. I acquired some Mary Dolciani's books last year and have been astonished by its contents. One of the books I purchased was the one you presented, and like you, I was amazed.
    Long love to the channel

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +1

      Thank you! Dolciani's books are truly eye-opening aren't they? May you enjoy them!

    • @ricardoy1413
      @ricardoy1413 20 วันที่ผ่านมา

      True masterpiece, rigorous but not obnoxious, clear but not dry.

  • @Nidhsa
    @Nidhsa 3 วันที่ผ่านมา

    We never learned that functions were subsets of cartesian products in high school, but I still knew that :)

  • @writerightmathnation9481
    @writerightmathnation9481 18 วันที่ผ่านมา

    I missed the New Math education craze by about 5 to ten years; one of my research collaborators and coauthors who’s a decade older than me was educated in the New Math system, and swears by it. I’ve known for some time that it included a set theoretical foundation in the pedagogical aspects, so I’ve wanted to inculcate such rigor into lower level courses, but I wasn’t previously familiar with specific textbooks in New Math. I appreciate your discussion here for several reasons, and specifically because it introduces me to Professor Dolciani’s books.

  • @LogarithmicSpiral6823
    @LogarithmicSpiral6823 20 วันที่ผ่านมา +2

    Absolutely thrilling. And to think: textbooks aren't even used in high schools anymore, or at least in my area. If our country is no longer focused on cultivating STEM alumni like it used to be around the time this book was published, then what exactly does our country even focus on? I couldn't tell. Excellent video, as always. Thanks for recommending these timeless textbooks.
    Also, what are your thoughts on math competitions, such as IMO or even smaller contests? On the one hand, I think they somewhat contradict the essence of mathematics in the first place, as math is not about being better than other people; it's about revealing the truths of the universe. On the other hand, being able to participate in these competitions forces you to advance much farther in mathematics than a lot of people (for lack of better word), and I know participation in these competitions also looks great on college/university applications. Would love to know your thoughts.

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +5

      Yes, you are absolutely correct about textbooks. The general trend across the country is "no more textbooks". On the other hand, such a trend is not surprising to me because in many cases, students are not even trained up in the practice of reading even a single novel in a reasonable amount of time.
      We have, collectively, lost our focus as a country. If we have no guiding plan, no guiding ideology of purpose, we are just drifters.
      Re: Math competitions. I have trained students who find it a joy to participate in IMO, and in my opinion, that can be a lot of fun, and beneficial as an extracurricular activity, but I do not like to turn a Math class into a competition of that nature. As you well state, Math is about the revelation of truths. I want all my students, even those who say they "don't care" to know the Math axioms as a logical foundation of truths. So, for some students the IMO is a lot of fun, and a really good thing to mention on applications, of course, but I would not make it my focus, personally. Also, some of those students get into the bad habit of just being around other IMO participants, which stunts their overall social capabilities as they become too insular within that group, and from my point of view, Math is a highly social activity. To sum up, yes, IMO is great and should be offered as an extracurricular when possible, but a Math class is not IMO, and most IMO problems do not really test logical foundations, although a knowledge of them is assumed.

    • @upendrachaitnya2970
      @upendrachaitnya2970 18 วันที่ผ่านมา +1

      Greatful for the question and Sincere Gratitude to Sir. I got insights for me and my young learners.

  • @vanessaford8630
    @vanessaford8630 6 ชั่วโมงที่ผ่านมา

    I think its best learning and doing Math without a calculator and/or computers for everything. Mental arithmetic is greater

  • @Bobbyd23
    @Bobbyd23 3 วันที่ผ่านมา

    Appreciate your passion. Baby Rudin would be my equivalent

  • @mpmcd81
    @mpmcd81 20 วันที่ผ่านมา

    I found this one on Open Library, and this is an outstanding read.

  • @krish-ut9de
    @krish-ut9de 13 วันที่ผ่านมา

    now we need "THE BEST CALCULUS BOOK EVER WRITTEN!!" hahaha, great video

  • @orsonyancey4131
    @orsonyancey4131 21 วันที่ผ่านมา +3

    I used the Dolciani Book1 and Book 2 copyright 1962 when I was in high school, but I did not
    appreciate mathematics as much as I do today, after having a career in engineering. Mary Dolciani
    is one of the greatest.

    • @kevinmadden1645
      @kevinmadden1645 20 วันที่ผ่านมา +1

      Her textbooks are geared for honors math students but not the average math student.

    • @udaymahajani1990
      @udaymahajani1990 20 วันที่ผ่านมา

      What are book 1 and book 2?

    • @kevinmadden1645
      @kevinmadden1645 20 วันที่ผ่านมา

      @@udaymahajani1990 I believe they refer to Algebra 1 and Algebra 2.

    • @orsonyancey4131
      @orsonyancey4131 20 วันที่ผ่านมา

      @@udaymahajani1990 Starting in the early 1960's after Sputnik, Dr. Mary Dolciani lead the School Mathematics Study Group (SMSG) with the task of improving mathematics education in the US. Her most famous math. books are Modern Algebra Structure and Method Book 1 (red cover) for 9th graders and Modern Algebra and Trigonometry Structure and Method Book 2 (green book) for 11th graders. Most US public schools used these books during the 1960's and the 1970's. Today, the Dolciani books are the first choice for home schooling.

    • @orsonyancey4131
      @orsonyancey4131 20 วันที่ผ่านมา

      @@kevinmadden1645 I have seen today that the Dolciani math books are still used in schools for courses for honors students. But believe it or not, the Dolciani books were used in the 1960's, and 1970's for many of the high school math courses, including the courses taught to collage prep students, i.e. the high school students who were being prepared to attend college.

  • @bterry101
    @bterry101 21 วันที่ผ่านมา

    I used both Dolciani books in HS in the 70's - tough. I hope and assume you will prepare your upcoming book with similar structure and completeness. Looking forward to your release !!

  • @orsonyancey4131
    @orsonyancey4131 21 วันที่ผ่านมา +1

    I too am a fan of the Dolciani books. I have this book, also.

  • @Lokie-cd2hw
    @Lokie-cd2hw 20 วันที่ผ่านมา +3

    I have the teacher's edition with fantastic notes throughout the text. I also have the solutions manual. This book gives a very heavy treatment of vectors that no other precalculus comes close to. Dolciani made millions on the sale of her books much like Stewart did. Her millions support a foundation that supports mathematics education. She died in 1985 at the age of 62.

    • @kevinmadden1645
      @kevinmadden1645 20 วันที่ผ่านมา

      She skimped on logarithms and that is a drawback .

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา

      Ah yes! The teacher's edition is truly fantastic! I wish I were able to get a copy since the notes are excellent!

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา

      @@kevinmadden1645 I do agree with that as well! That is one drawback, especially because logarithms have so many properties that students should know by the time they get to Calculus.

    • @upendrachaitnya2970
      @upendrachaitnya2970 18 วันที่ผ่านมา

      Greatful Ever Sir.

  • @DO-nz8dv
    @DO-nz8dv 19 วันที่ผ่านมา

    When I studied College Algebra, The Principle of Mathematical Induction was a quick 20 minute lesson with some examples before we moved on to The Binomial Theorem. Such injustice to such a beautiful and powerful method of proof.

  • @charlesu.farleigh3596
    @charlesu.farleigh3596 19 วันที่ผ่านมา +1

    I have this exact book. My 11th grade math book that I forgot to turn in.

  • @XXavierSin-XXs
    @XXavierSin-XXs 9 วันที่ผ่านมา

    Wait, you live in Virginia?? Sir, we are in the same state, and I had no idea. I stumbled across your channel because I am trying to learn how to learn. I know that might sound silly. I did not do well in high school 8 years ago, and I am now trying to improve my ability in any and all fields. I have 2 daughters and want them to have a good role model and to have seen me build a career in the medicine. Cheers, friend! You're barely 2 and a half hours away! Wow!

    • @citytutoring
      @citytutoring  9 วันที่ผ่านมา

      Thank you! I hope my channel helps! And that's OK...it is never too late to reform yourself. What truly matters is having the right mindset, which you seem to have.

  • @chrisd561
    @chrisd561 21 วันที่ผ่านมา

    Good day to you in the Old Dominion!

  • @EvanRajala
    @EvanRajala 8 วันที่ผ่านมา +1

    12:48
    would you wager the ABSOLUTELY oldest would ALWAYS be best, or like a specific time range (example: "modern math" era 50's - 60's --- when would you say the "modern math" era would be? ) ?

  • @PaladinLeeroy42069
    @PaladinLeeroy42069 21 วันที่ผ่านมา +3

    This issue is why so many scientists and engineers in undergrad think Linear Algebra is just a bunch of matrix operations. That’s because that’s all they have to do in that course now, and try convincing them to read a rigorous abstract textbook on the subject in their freetime among all their other tough classes they have to juggle

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +4

      Yes! The 'matrix operations' version of Linear Algebra-the fast-food equivalent of a gourmet meal. Convincing engineers to read an abstract Linear Algebra textbook in their free time? Ha! What a howl!

    • @douglasstrother6584
      @douglasstrother6584 20 วันที่ผ่านมา +1

      One of my Physics/Math Lightbulb Moments was in my Quantum Mechanics course (Prof. George Gaspari, UC Santa Cruz); during one of our discussions, he showed me the connection between the Schrödinger Equation, as an example of a Sturm-Liouville Equation, and Linear Algebra. The computations were still difficult, but the mathematical structure became straight-forward. After that, figuring out the physics of selection rules became the challenging part of the course.

  • @andrewgrzadzielewski2906
    @andrewgrzadzielewski2906 13 วันที่ผ่านมา

    That was my high school math book, and I still use it in my high school math classes. My principal thinks I should be using a newer book. I will switch when I find a better book. Been looking for 40 years.

    • @citytutoring
      @citytutoring  13 วันที่ผ่านมา

      The fact that you are even allowed to use it means, to me, that at least you teach at a decent high school. Thank you for your work with students and if you are using this book, I have no doubt you truly love Math! How are your students doing with the book? Do you notice any progress in their understanding?

    • @andrewgrzadzielewski2906
      @andrewgrzadzielewski2906 11 วันที่ผ่านมา

      @@citytutoring My students love the book, and I love using it. I think their long-term understanding of the material benefits from the use of this book.

  • @amirsaeed7759
    @amirsaeed7759 18 วันที่ผ่านมา

    I’m fortunate to own a copy of Modern Introductory Analysis and Modern Trigonometry by Dolciani. Modern Algebra and Trigonometry by J.Vincent Robinson. Pre-Calculus Mathematics by Shanks. All fantastic math books compared to today’s commercialized math textbooks books a la Cengage.

  • @2ndavenuesw481
    @2ndavenuesw481 20 วันที่ผ่านมา +1

    I have that one somewhere.

  • @orsonyancey4131
    @orsonyancey4131 20 วันที่ผ่านมา

    If it is O.K. with you Prof. Cromwell, I would like to post a request out to all of the readers of this channel to please post in what schools and at what dates did you use any of the Dolciani mathematics books as course textbooks. It is interesting to see what schools used the Dolciani math. books, how long ago or how recent. Today, the home schoolers are big fans of the Dolciani books. I can only wish that Houghton-Mifflin aka McDougal-Littell would re-publish some of these gems. The solution manuals are rare.

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +1

      Absolutely! No problem at all!

    • @orsonyancey4131
      @orsonyancey4131 20 วันที่ผ่านมา

      @@citytutoring Thank you, Sir.

  • @theslashbro4474
    @theslashbro4474 16 วันที่ผ่านมา

    What do you think of how the British teach mathematics? A-Levels, and GCSEs, and the sort.

    • @citytutoring
      @citytutoring  15 วันที่ผ่านมา +3

      Not a perfect system, but much better than anything you get in America, test wise.

  • @lasalleman6792
    @lasalleman6792 17 วันที่ผ่านมา

    Expensive.

  • @cmdstraker
    @cmdstraker 20 วันที่ผ่านมา

    Going back to the test we went over last time, would you let a student assume the ring structure of polynomials as a given?

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +1

      Yes, of course (At least, if they are my students), but unfortunately, the term "ring structure" is highly unusual in most public schools these days, which is of course a shame.

    • @cmdstraker
      @cmdstraker 20 วันที่ผ่านมา

      @@citytutoring While it's not really an issue when dealing with quadratics, being able to divide polynomials is useful once the degree goes higher.

  • @mpmcd81
    @mpmcd81 20 วันที่ผ่านมา +2

    It’s not the teachers. It’s the standards. Everything is about getting to calculus. As important as this is, the standards are not rigorous. And the standards are what teachers are legally required to teach.

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +1

      Yes, indeed! The vast majority of problems in schools I see come from admins and politicians. The teachers are, usually, stuck in the middle and placed on the front lines of combat with no support at all from either admins, politicians, or parents (in many cases). I personally have been blessed to deal with great parents, but mostly because in my case they decide to pay to come to me, so usually know exactly what they want, and how they want it. However, at the public school level, it must be quite a horror show!
      I really do believe that if there was a massive teacher walkout/outrage, nationwide, things would change. I just don't see the unity at this point, and that is why things will remain the same for the time being...unfortunately.

  • @orsonyancey4131
    @orsonyancey4131 21 วันที่ผ่านมา +1

    In my opinion, the Dolciani Book 1 and Book 2 copyright 1990 to 2000 in which the lead author is
    Richard Brown are also good books. Moreover, the Solution Manuals are readily available. I agree that the math books written after about year 2000 are not as good.

    • @Lokie-cd2hw
      @Lokie-cd2hw 20 วันที่ผ่านมา +1

      Brown was the lead author in the Structure and Method series of Dolciani's books. The writing is more friendly and less formal than in the previous Modern School Mathematics series where Wooton was a lead author.

  • @brunnocarvalho1941
    @brunnocarvalho1941 21 วันที่ผ่านมา

    🌻🌻

  • @cmdstraker
    @cmdstraker 20 วันที่ผ่านมา

    The idea that somebody from New York would stand for higher standards in education seems extraordinary.

    • @kevinmadden1645
      @kevinmadden1645 20 วันที่ผ่านมา

      @@cmdstraker Good Comment !

  • @CondorAHLS
    @CondorAHLS 20 วันที่ผ่านมา

    Such a shame the original Dolciani books haven’t been reprinted and used copies can’t be found or if found cost an arm and a leg.

  • @davidbennett8126
    @davidbennett8126 21 วันที่ผ่านมา

    What do you think of these books? Advanced Mathematics by Richard G. Brown and Mathematics Higher Level (Core) by Fabio Cirrito, Nigel Buckle, and Ian Dunbar?

    • @citytutoring
      @citytutoring  21 วันที่ผ่านมา +3

      Re: Advanced Mathematics by Richard G. Brown -- I do like the 1980s versions of the book, and I actually have a copy. Normally, I will include some problems on my tests as "extras" from his textbook. My only critique of the book is that (at least in the version I am familiar with, which is from 1987), he does not include set theory or set notation. The problems themselves are good, however, and the explanations are spot on!
      Re: Mathematics Higher Level (Core), that is a solid option, and I would gladly recommend it if you have a copy of it for your students. I very much like that they begin with set builder notation, and discuss intervals, etc right from the beginning, as well as LITERAL linear equations, which have been neglected in schools for far too long in this country.

    • @bryanbain3509
      @bryanbain3509 21 วันที่ผ่านมา

      Fun fact: Richard Brown's son is DaVinci Code author Dan Brown

    • @citytutoring
      @citytutoring  21 วันที่ผ่านมา

      Interesting!

    • @mpmcd81
      @mpmcd81 20 วันที่ผ่านมา

      The 1980’s book by Brown and Robbins is a tremendous text. I read the entire book cover to cover in high school over the summer.

  • @writerightmathnation9481
    @writerightmathnation9481 18 วันที่ผ่านมา

    I really appreciated coming across this video, so I’ll write to you sometime soon. You may appreciate some of my comments on videos. My videography on TH-cam isn’t really up to snuff yet, as I just barely started thinking so far about how I would build a channel myself. I created it only to make some basic videos available to my students when I was teaching university mathematics. I recently retired, so I plan to turn a lot of my lecture notes into textbooks and I’m involved in such projects now. Perhaps you’d be willing to collaborate on a project of that sort sometime?
    More to come in a letter.
    Have a great day!

    • @citytutoring
      @citytutoring  18 วันที่ผ่านมา

      Yes, that would indeed be interesting. Thank you! I look forward to your letter.

  • @earltaylor6071
    @earltaylor6071 19 วันที่ผ่านมา +2

    Great lecture professor! Thank you! From a 54 year old who continues to an affinity for math and abstract thinking.👍🏿🇮🇱👍🏻

  • @growthfeeder6041
    @growthfeeder6041 20 วันที่ผ่านมา +2

    I love the rigor with which you deal with Mathematics. It is especially nice that you do b/c this drive towards everything should be easy, no effort should be expended towards mastery just turns me off.

    • @citytutoring
      @citytutoring  20 วันที่ผ่านมา +2

      Thank you! After witnessing the disastrous results even decades ago, I made it one of my missions in life to never tolerate mediocrity from either instructors or, of course, students. They might find it painful now, but there's nothing like having a purpose and sense of accomplishment.

  • @walter274
    @walter274 19 วันที่ผ่านมา

    Can't you just skip the tables, and simply use all of the good explanations in it. The tables are just a tool to ease computation.

  • @getshorty7549
    @getshorty7549 20 วันที่ผ่านมา

    I have the 1990s updated edition with the color explosion and the solutions manual to that edition. I’ve been working through “How to Prove it” and Chartrand’s “Mathematical Proofs” simultaneously.

  • @writerightmathnation9481
    @writerightmathnation9481 18 วันที่ผ่านมา

    I missed the New Math education craze by about 5 to ten years; one of my research collaborators and coauthors who’s a decade older than me was educated in the New Math system, and swears by it. I’ve known for some time that it included a set theoretical foundation in the pedagogical aspects, so I’ve wanted to inculcate such rigor into lower level courses, but I wasn’t previously familiar with specific textbooks in New Math. I appreciate your discussion here for several reasons, and specifically because it introduces me to Professor Dolciani’s books.