THE THREE MATH BOOKS THAT CHANGED MY LIFE

[@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?

[@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.

[@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.

[@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.

[@_jampa]

What a delight to find your channel, professor!

[@citytutoring]

Welcome! Thank you!

[@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.

[@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.

[@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

[@GGMike09]

the quality is awesome!!

[@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!

[@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.

[@amirsaeed7759]

Absolutely fantastic content. Happy to have found your channel. I actually have Modern Introductory Analysis by Dolciani. It’s a great math book. I find older math books more rigorous and certainly axiomatic. Precalculus Mathematics by Shanks is great as well.

[@citytutoring]

Thank you! Modern Introductory Analysis is, I dare say, the BEST high school "precalc" text ever written in America. I have not seen any that come close that book! And yes, Precalculus by Shanks...I agree, also an excellent book. I particularly like his chapter on Vectors.

[@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.

[@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!

[@rwharrington87]

10:00 in so far. Your story is funny to me so far, because I had a very similar experience buying Selby’s algebra book in a Barnes and Noble. My gripe with these new style textbooks is how distracting all the images and diagrams are-having to flip pages to find Figure n.m, and by the time you locate it, your train of thought is all but lost.

[@techtodas1169]

Hello, Sir! I'm using a college algebra by Blitzer and Sullivan , and these books are so many unnecessary things and it is too much for me. Do you have any book ecommendations for college algebra?

[@citytutoring]

Sure! But, it will depend on your program of study because some College Algebra textbooks cover different topics, and in different sequences. Are you an undergrad student in the US? I have several different options for College Algebra, but will depend on what topics you need covered.

[@kamimaza]

16:04 yeah, there is an old fashioned algebra, try understanding an algebra book from the 19th century, different notations, symbols, conventions.

[@citytutoring]

True! I have plenty, but the only major difference (Aside from language) is that the 19th century books do not use set notation yet and do not cover some of the later topics. I do quite like the 19th century textbooks and often use them since I also like the exercises in them.

[@cribbsprojects]

Bravo. We do need better math in schools.

[@akshatmishra564]

Hi sir, I am from India I suggest you to try Jee advance Maths paper ( College entry exam in our country for IITs ) You should upload a review video on it because for us Indian students that exam is a Nightmare 💀

[@citytutoring]

I will look into that, thank you!

[@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!

[@kamimaza]

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

[@kamimaza]

18:44 Any Serge Lang book by Springer-Verlag is probably better...

[@citytutoring]

Oh yes, but I would use that textbook for a class of students who want to go on to higher math as a major. Dolciani's books are structured in a way that can bridge gaps in a broader audience and has many more worked examples when compared to Lang's book. I believe both are great, but for different purposes.

[@syahmihakim6041]

25 November 2024, Monday🎉

[@yannisvaroufakis9395]

I had both of the Modern Algebra books in high school. I kept them until about 10 years ago when I decided to clean out the garage and threw them out. I wish I hadn't. I now have an 8-year-old son whom I expect to be helping out with Algebra when he gets to 9th grade. These volumes would have helped me brush up on forgotten skills and would have helped me tutor him properly. My neighbor recently gave me her kid's algebra book that he used in high school about 5 years ago. That thing is a mess. It's practically gibberish. Totally unusable. What has happened? Weren't the people in charge of education today the people who were taught with the same Modern Algebra books?

[@argonwheatbelly637]

Illustrative? Big Ideas?

[@citytutoring]

Oh no! Frustrating, isn't it? I would recommend, if possible, maybe try some used bookstore that might have a Science/Math section in your area. If not, you can get the pdf versions online sometimes. And yes, the books today are a joke and not mathematically rigorous at all (the ones used in the high schools, I mean).

[@ZDTF]

Whats a book

[@agnelomascarenhas8990]

A vector of cellulose pages, with orthogonal bases/pages. User's objective "education" is to extract eigenvalues and eigenvectors.

[@mikecaetano]

Perhaps you should have Kant first instead of Hegel. To claim you know what makes a philosophy good or bad and then to claim that your opinion is a fact. Heh. Yeah, whatever. LOL. And then to prebut somebody who disagrees with your assessment by denigrating their knowledge of history is rather cheap rhetoric. Thank goodness historians refrain from pontificating on mathematics, eh? Beyond that it's great that you found some enlightenment in two of Dolciani's textbooks. I still have mine from 1983 sophomore year in high school. Modern School Mathematics Algebra and Trigonometry 2. I keep it around as a reference.

[@citytutoring]

I had to read Kant in college, and unfortunately I have to say was one of the worst experiences (mostly because my epistemological framework was very different). I did not denigrate their "knowledge of history". But, if someone is going to criticize someone else precisely for that reason, they should at least show evidence that they know what they are talking about. When I read Hegel by the way, I did not have any standard (for obvious reasons, as I was 16 years old) as to what makes a philosophy "good" or "bad. I do now have a standard, however. As for my opinion being a fact, I think and can say confidently that if we look at two of the most terrible ideologies that developed in the 19th and 20th centuries, they undeniably came from Germany. Of course, you have to accept that fascism, Nazism, and communism are terrible things...so if you don't then I will concede that someone could not accept my affirmation.

[@John-pp2jr]

1:17 taught not teached.

[@citytutoring]

Sorry? I said "The instructors teach them different things"...."Teached" doesn't exist in the English language.

[@B-Mike]

Total crap. Continuously “I I I” “me me me” “smart smart smart”. Master of “word salad”.

[@citytutoring]

Thank you for your in-depth critique! I'll take a word salad over intellectual starvation any day!

[@citytutoring]

@@nkanyezitshabalala5256 I don't recall saying I was fully able to understand what Hegel was saying, but I did read his book...specifically, The Science of Logic. For me, reading was not something unusual as I had started reading at a very early age. As for the German comment, I think most people can safely agree that Nazism and Communism are terrible ideas...you may be the solitary exception. I am not here to argue with you, however, as I am interested in Math primarily, so I will address your statement about the book in a subsequent comment.

[@citytutoring]

@@nkanyezitshabalala5256 As for your comment about Dolciani's book: You just dismissed a great book with the grace of someone who’s skimmed the Cliff Notes and expects to be taken seriously. Allow me to inject a little clarity into this hazy critique of Dolciani's Algebra texts. First, the accusation that these books “aren’t all that more ‘rigorous’ or even more difficult than the average algebra textbook” is like saying a symphony isn’t all that different from elevator music because both involve instruments. Dolciani’s works define rigor in high school mathematics-they systematically build concepts with a precision that elevates the student’s understanding beyond rote memorization into structured logical thinking. If that’s not rigor, then perhaps you confuse “rigor” with “making students cry” and assumes they’re synonymous. Also, your claim that the books “refer to various axioms but don’t present the contents axiomatically” is an odd mix of misunderstanding and hypocrisy. The goal of these books isn’t to rebrand Euclid’s Elements for teens-it’s to introduce students to foundational principles while keeping the material digestible and engaging. If an axiom-based approach for high schoolers is too “bogging down” , why even critique Dolciani for striking the perfect balance? Finally, the claim that “most of your claims aren’t substantive” is an ironic accusation from someone making vague, unsubstantiated generalizations themselves. Dolciani’s books, with their structured explanations and diverse problem sets, have withstood the test of time precisely because they equip students with problem-solving tools that transcend rote high school math. Criticizing them for not conforming to a hyper-deductive structure is like berating a Lamborghini for not having cupholders-missing the point entirely.

[@citytutoring]

@nkanyezitshabalala5256: I don't need to do anything except share Mathematical truths. Yes, The Science of Logic was a hard read indeed, so? Are you saying there is no possibility that a high school student could have attempted to read the book? Surely you are not saying that, right? Even my librarian, back then, warned me about it, so I was very aware of what I was getting into, and again, to be clear, I never claimed to have understood the book on a first read. However, it did help me very much later on in college when I had to take philosophy courses whether I wanted to or not, so having that background in at least being FAMILIAR with the text greatly helped. I had chosen Hegel because already back in high school I was interested in political philosophy as well, so Hegel was recommended to me by a teacher. I will repeat what I said about German philosophy: all of the most horrific isms of the 19th and 20th century come from Germany. Maybe you're OK with fascism and communism; I certainly am not. Perhaps practice what you preach? Maybe learn some philosophy before you comment on it, or at least admit you are OK with German fascism and communism, which is clearly what I was referring to. It doesn't take much work to figure it out. Thank you again for bringing traffic to my channel, and if you feel you can do better, start your own channel and let's see how you do.

[@citytutoring]

@@nkanyezitshabalala5256 this last comment told me all I needed to know about you. You are a troll. If you seriously believe I have not seen college algebra before, when I actually teach college courses, then you must be some kind of joker or, worst case scenario, disgruntled individual. Take your trolling elsewhere.

[@knowledgeckr786]

Sorry Sir you didn't leave a good impression on me for being a true thinker in any field of knowledge. Reason your style of argument is like proud politician and not a researcher of books. Your statements about different non mathematics topics are questionable. Sorry.

[@citytutoring]

I am sorry but I wasn't aware that I was involved in an audition to impress you. Sorry to be more interested in mathematics and success than in the opinion of some random armchair critic, especially given that you have provided no reason for your empty "critique". What "statements" are you referring to?

[@victorortiz1452]

Lol you didn't know?? This guy is totally about politics!

[@lucasbomfim00]

@@citytutoring He's talking about germany being the source of all bad philosophy and politics.