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.

Thank you and welcome! Are you a Math student?

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.

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

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.

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

Welcome! Thank you!

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?

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.

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?

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

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

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

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.

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.

Illustrative? Big Ideas?

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).

I will look into that, thank you!

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!

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

@@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.

@@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.

@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.

@@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.

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

Librarians love finding stuff for their Customers.

Oftentimes I find that the math section of the library is collecting dust because no one uses those books. At my library at least there are some really great books. So, it's a treat to get books from there. Just today I got a two volume book on Number Theory by LeVeque from 1956.

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?

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

I plan to discuss the complex numbers and their exponents in another video series.

Wonderful! There's another video on Vectors coming up too, as there is a lot more to say! Definitely balance everything out with rest!

Exactly!

The real question is: would x even show up for the therapy sessions?

Ah yes, thank you for bringing this to my attention, I realized I put in the other index. I will put a clarification in the description!

For the last one?

@@citytutoring Should be 2^3 = 8. Personally, I like writing the radicals as exponential fractions right away to save time.

Thank you!