Read Online Precalculus: a Prelude to Calculus, 3rd Edition, Sheldon Axler, 2017, Wiley

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Sheldon Axler's "Algebra & Trigonometry" vs. "Precalculus: A Prelude."

• Thread starter ghostwind
• Offset date Jun 2, 2014

Hi all,

I've been looking and searching effectually for a good book for some pre-calculus review, and decided on one of Sheldon Axler's books. Looking at his site and the contents of both books (links beneath), I'1000 not sure what the departure is betwixt them, other than some re-ordering of things in the newer "Precaculus.." volume. In fact, the "Algebra & Trigonometry" book seems if anything to have a bit more than, which is a tad confusing. Maybe the newer "Precalculus.." books has corrections, better layout, etc.? Anyone use whatsoever or have any opinion on which to get? Check them out below. Besides the marketing reasons, why would anyone go the "Precalculus.." over "Algebra & Trigonometry"?

http://algebratrig.axler.net

vs.

http://precalculus.axler.cyberspace

Thank you!

Answers and Replies

I expect they volition both be proof-based merely the algebra/trig i will be at a lower level, for young people.

If this is for some kind of habitation schooling situation, definitely don't use one of these. Youngsters shouldn't be learning from proof books, flow.

PS. I've looked at the precalculus ane before but not the alg/trig, it may exist dissimilar in style.

I have the A & T book now and used to have the 1st ed of the Pre C book (the grey one). The A and T book has 125 more pages-a lot of the departure is from Ch. seven Systems of Equations, esp. department 7.4 Matrix Algebra, which was not in the Pre C book. To me, the books are about the same: they're both a scrap likewise tough for me. I'm using Blitzer's 3rd ed. of Pre C, it'southward a lot easier for me. I might try Axler's book when I'm finished with Blitzer's. Hope this helps.

I wait they will both be proof-based but the algebra/trig i will be at a lower level, for young people.

If this is for some kind of domicile schooling state of affairs, definitely don't use one of these. Youngsters shouldn't exist learning from proof books, flow.

PS. I've looked at the precalculus one earlier just not the alg/trig, it may be different in fashion.

What practice you mean by proof-based? Why is information technology bad? What practice you mean past youngsters? Do you mean all youngsters? Some? Many? Most?

People of all ages do good from understanding what they are doing and why.
Rote learning is not the best way.

What do you hateful past proof-based? Why is it bad? What do you mean by youngsters? Practise you mean all youngsters? Some? Many? Most?

People of all ages benefit from understanding what they are doing and why.
Rote learning is not the best way.

I mean, preteens and young teenagers have short attention spans, they need short lessons with some kind of "cash value", something to hold the interest. They want to run into a number line, not a successor axiom.

And if you read the introduction to his Precalculus book, it reads very similar to the linear algebra one, that this is existent math, if you're not spending an hr per page, y'all're going to fast, question and probe everything told to y'all, yadda yadda. I mean it'due south just not suitable for young first-fourth dimension learners in full general.

I approximate I should accept posted a bit about myself. I am an adult pupil going back to finish my undergraduate degree that I put off as I worked in the IT field for many years (about 20 years). I took calculus ane-three before, and did very well, establish it intuitive and not that hard to be honest, just I forgot virtually of it, and not only that, simply the algebra and trig that are so of import to understadning it. And so this summer my program is to review all the "pre" calculus mathematics on my own before I showtime schoolhouse in the autumn and accept calculus 20+ years later. Things volition come dorsum, merely I've got to piece of work at information technology too. So I've been looking for a good, succinct, book that I can use to go and review all the things I've forgotten. And the Axler books I mentioned seem right on the coin for me. I don't desire a 1000+ folio volume with pretty pictures, 100 exercises, etc. I'm fine reading text like Axler's - in fact I prefer it. The math books I used 20+ years ago were less heavy and (I experience) ameliorate written, though I could accept gotten lucky at the university I went to. Needless to say I didn't continue any! :(

Anyway, I've looked again the the "Table of Contents" for both books I linked, and they seem to actually exist exactly the same. The order of topics is a bit dissimilar, as I was maxim, and really small-scale stuff is shuffled around, but either will attain the same thing I experience. I'm probably just nitpicking. If you go to the links and look at the table of contents for both you'll see they are indeed the aforementioned. Same rigor, etc. I'one thousand not sure why a "Precalculus" book is even needed when yous have an "Algebra & Trigonometry", equally that IS precalculus...I think "precalculus" is somewhat a confusing subject, and possibly because high schools in the US break down algebra I 2, geometry, and trig too much. Anyway I digress...

Another book I looked at is this:

https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

Lang's book linked to a higher place seems to be a good little gem, just not certain if it'due south enough on its own. Ideally I would but use one book. Axler or Lang. Any opinions?

Last edited by a moderator: May 6, 2017

Lang covers everything you demand in order to succesfully study calculus and college math. It doesn't cover more or less. So it most definitely is plenty on its own.

Lang covers everything you lot need in order to succesfully study calculus and higher math. It doesn't cover more or less. And so it most definitely is plenty on its own.

I looked and the merely thing I saw maybe lacking a tad was the trig section, but I could exist wrong simply going on the table of contents from Amazon's "Look Inside".

I forgot to mention that some other precious stone seems to be this:

https://www.amazon.com/dp/1592441300/?tag=pfamazon01-20

Final edited by a moderator: May 6, 2017

I judge I should have posted a bit about myself. I am an adult student going dorsum to finish my undergraduate degree that I put off equally I worked in the IT field for many years (almost twenty years). I took calculus 1-3 before, and did very well, found it intuitive and not that difficult to be honest, merely I forgot well-nigh of it, and not merely that, only the algebra and trig that are so of import to understadning it. Then this summertime my programme is to review all the "pre" calculus mathematics on my own earlier I start school in the fall and have calculus xx+ years later on. Things will come back, but I've got to work at it as well. So I've been looking for a adept, succinct, book that I can utilise to go and review all the things I've forgotten. And the Axler books I mentioned seem correct on the money for me. I don't desire a g+ folio volume with pretty pictures, 100 exercises, etc. I'1000 fine reading text like Axler'southward - in fact I adopt it. The math books I used 20+ years ago were less heavy and (I feel) ameliorate written, though I could accept gotten lucky at the university I went to. Needless to say I didn't go on whatsoever! :(

It sounds like yous know what y'all desire. Of the Axler books you mentioned, I'd choose the precalculus one; it's probably the one he wrote first and will accept a nicely abstract approach.

While it may be true that I may know what I want, that doesn't make information technology easier to navigate dozens of books to observe a proficient one. This has proven to exist more than taxing than I expected. I'm really surprised at how bad most books have become, content watered down, 1000 examples, etc. Axler'due south books seem refreshing, only perhaps there are even better ones. Similar Lang's "Bones Mathematics". Then I'm curious and looking for opinions. While 1-2 books are skilful, also many (for me at least) leads to confusion, strange overlap, etc.

In the process I'm as well looking for a decent Calculus book to review from. At that place again seem to be the g+ page ones with dozens of examples, not enough theory, etc. Then there are ones that are on the other end - theory and non meant for review. The best I've seen so far, and please chime in, in terms of striking a good rest in terms of theory and application is George Simmons' "Calculus with Analytic Geometry" second ed.

https://www.amazon.com/dp/0070576424/?tag=pfamazon01-20

MIT uses it, merely I haven't seen much talk about it. A lot of talk about Apostol (Caltech uses information technology) and Spivak on this forum, merely they seem a bit on the theory end for review. Thoughts?

Concluding edited by a moderator: May 6, 2017

Simmons is an excellent writer. I similar all his books. Unfortunately, I take never had the chance of reading his calculus volume. Just I have no doubt it's very good.

If you're not much into theory, then Spivak and Apostol are not good choice. I recall Simmons will exist all-time for you.

I very much like theory, but wonder if Apostol or Spivak are the all-time choices when going back to review Calculus. When I took it, I found it easy and got top grades, only that was a while ago. I need something to kick me back into things. One affair I practise know from experience, is that starting with the incorrect book can be OK for a little while. You lot may practise well and go superlative grades in Calc I-III, Linear Algebra, Diff Eq, etc. But if you are coming from a more "computational approach - i.e. applied science math courses", yous will have trouble when afterwards taking more advanced math courses which are more theoretical in nature. So for me, fifty-fifty now, the best way to start is with more words, less pictures, more imagination, more than proof-based, etc. But in that location has to be a balance, and I'thou not sure how counterbalanced Apotol or Spivak are.

I very much similar theory, but wonder if Apostol or Spivak are the all-time choices when going dorsum to review Calculus. When I took it, I institute it easy and got height grades, but that was a while ago. I need something to kicking me back into things. 1 affair I do know from feel, is that starting with the incorrect book can be OK for a niggling while. You may do well and become pinnacle grades in Calc I-III, Linear Algebra, Diff Eq, etc. But if y'all are coming from a more "computational approach - i.e. engineering math courses", you will have trouble when after taking more advanced math courses which are more theoretical in nature. So for me, even now, the best way to start is with more words, less pictures, more imagination, more proof-based, etc. Simply there has to be a residuum, and I'grand not sure how balanced Apotol or Spivak are.

Apostol really has a expert remainder. It's more theoretical than other books, but information technology's also practical. If you're already familiar with some calculus (peradventure long long ago), and if you lot're non agin to theory, so attempt Apostol.

Spivak would probably have too much theory for now.

OK, maybe I should outset a new thread every bit this is diverging into Calculus books, every bit I got the original topic out of the way. But I'll try it here first and promise people chime in :)

I've looked at the 2 schools I need to choose betwixt for attending starting this autumn, and what books they use for their calculus curriculum.

Schoolhouse 1 uses Thomas' "Calculus Early Transcendentals (twelfth Edition)":

https://world wide web.amazon.com/dp/0321588762/?tag=pfamazon01-20

School 2 uses "Stewart's Calculus: Concepts and Contexts (4th Edition)":

https://www.amazon.com/dp/0495557420/?tag=pfamazon01-20

These seem similar to me from browsing them on Amazon's site, only don't know enough details about either.

Then the question is, which additional calculus volume would best supplement either the Thomas or Stewart books? I'd like to supplement to better exist prepared for the subsequently courses, which will be more theoretical and harder. I'thousand not sure a polish transition from either the Thomas or Stewart volume will exist easy without some other volume to supplement.

So given all this, mayhap it'southward easier at present to recommend either the Apostol, Simmons, or Spivak books? Which combo would piece of work best?

Thomas/Stewart + Apostol
Thomas/Stewart + Simmons
Thomas/Stewart + Spivak

Last edited by a moderator: May 6, 2017

And so what book did y'all cull for algebra/precalculus? And how long practice yous think it'll take to work through information technology? Because I presume y'all desire to become through that before starting calculus. Also that could influence your decision on which calculus book to purchase.

I chose Axler'due south "Precalculus 2d Edition". It will have me 2 months at about to get through it at present that I have information technology and have looked through it.

Thomas/Stewart + Apostol and Thomas/Stewart + Simmons would exist overkill, I'd go with Thomas/Stewart + Spivak

By the mode, I beloved these beautiful books, you should check it out :

Analysis by Its History by Ernst Hairer and Gerhard Wanner
Geometry past Its History by Alexander Ostermann and Gerhard Wanner

I chose Axler's "Precalculus 2nd Edition". It volition accept me two months at most to get through it now that I accept it and have looked through it.

Ok, that is what I was waiting to see. [strike]This should set yous in good stead for Apostol. If you like Axler, that is my recommendation. Otherwise, come back wiser later and yous'll be better equipped to cull a book to follow information technology with.[/strike]

Wow, $ninety for Apostol book 1, $240 new, who are they trying to kid? I'll follow this with a new post with some recommendations.

Final edited past a moderator: May 6, 2017

Cheers.

I oasis't looked at Lang's Calc stuff still, but information technology seems the recommendation was considering Apostol'south price was too high? How do you think they compare in content and presentation, price aside. Information technology seems Apostol was your beginning choice, but curious about more than of an insight in improver to the recommendation.

To your previous postal service, yes I practice similar the Axler book, and find it easy to work with, and things coming dorsum rapidly. It might have been twenty years agone I took these things, merely I gauge my encephalon cells are still there for the most part :) So I think calculus will come up back quickly besides.

I don't intend to utilize Apostol, Lang, Simmons, or Spivak for review over the summertime (I may if I accept time), but to simply complement the Stewart or Thompson texts, as I feel they are too computational and will non ready me best for later courses as I was saying. I take a personal instance of this if I may deviate for a minute here. When I was a physics pupil back in the day (at Cornell), I took mostly the math department variants of Calc I-Iii, Linear Algebra, etc. Just one semester I needed to double upward and had to take two of the math courses in the engineering department. Similar things, but more applied instead of theoretical. I did very well, As, etc. Merely the post-obit semester, when taking a Mathematical Physics course which used 2 texts and special notes (ane text was this one - https://world wide web.amazon.com/dp/0201007274/?tag=pfamazon01-20), for the first time in my life with math, I had a bit of a struggle at first. It wasn't that the fabric was harder, but that I wasn't able to merely read the books anymore. And I call back some of that had to practise with having taken the engineering maths courses instead of the pure math courses the semester prior. I felt I came in inadequately prepared, had to work more at it, and it was very challenging. I ended upwards doing well, just yeah, I nonetheless think (and this is why I'chiliad asking here) that a more theoretical approach initially, even in beginner courses, volition prepare one better for later on, more than advanced texts. Thoughts?

I'yard also curious, how DO people here experience about Stewart/Thompson? Same every bit me? I wanted to become some discussion going more in depth, besides the welcome recommendations also.

Terminal edited by a moderator: May 6, 2017

I haven't looked at Lang'south Calc stuff however, but it seems the recommendation was because Apostol's price was too high? How exercise you think they compare in content and presentation, price aside. It seems Apostol was your first choice, merely curious about more of an insight in improver to the recommendation.

This type of word doesn't involvement me, the question you should be request is not, how practise they compare, you should be asking, this is what I desire, which one is closer to what I want? Or better however, are these books sufficient for my needs?

Also realise that whatever we say well-nigh books here, someone will come up along later and answer and say, "In my opinion, the new edition of book X is really great, they've totally improved it!". Then I don't even want to get there.

What does i say when ane recommends a book? Is it, this is a volume I would use, or, this is a volume I think you would apply?

If I always say, this is the book I would cull, this would be unfair. There are many expert books out there and many people out in that location. One can't always say, this is the volume I would use. It has to be, this is a book that could piece of work for you lot.

And how does one guess that? It'south a combination of reputation and perception. You perceive what type of book the person wants and choose a book based on reputation. For example, Apostol and Lang have reputations, are both rigorous books, and seeing that the author wants a rigorous volume, that is the direction that the recommendations go.

I accept used Spivak and Axler books before and seen Apostol. I have to make a decision, a book in the style of Axler. Having seen Apostol, that is in the style of Axler. But the toll is insane. Lang is cheaper and recommended many times on this forum. And both volumes can exist had for less than one book of the old book. Both are rigorous calculus books.

This should be a slam dunk. Buy information technology or don't, that is all.

What does i say when one recommends a volume? Is it, this is a book I would use, or, this is a volume I think y'all would utilize?

If I ever say, this is the book I would choose, this would exist unfair. At that place are many proficient books out there and many people out at that place. One can't e'er say, this is the book I would use. Information technology has to exist, this is a book that could work for you.

And how does 1 judge that? Information technology's a combination of reputation and perception. Y'all perceive what blazon of book the person wants and choose a book based on reputation. For example, Apostol and Lang accept reputations, are both rigorous books, and seeing that the author wants a rigorous volume, that is the direction that the recommendations get.

I have used Spivak and Axler books before and seen Apostol. I have to brand a decision, a book in the mode of Axler. Having seen Apostol, that is in the style of Axler. Merely the price is insane. Lang is cheaper and recommended many times on this forum. And both volumes can be had for less than one book of the quondam volume. Both are rigorous calculus books.

This should be a slam douse. Buy it or don't, that is all.

I hold with this very much. Great postal service!

But I want to brand articulate that Lang and Apostol are ii very different books and are meant for different audiences. Both are on the rigorous side of calculus books. But Lang is clearly intended for a kickoff course in the subject, allow'due south say at a HS level. Apostol is more rigorous than Lang (Lang leaves out epsilon-delta arguments which I agree practise non reall belong in a kickoff course). I would use Lang for a (honors) course in a university. Withal, Apostol focuses in the exercises a lot on computations (which tend to be quite catchy in comparison with other calc books). Spivak is even more theoretical than Apostol since its exercise tend to exist almost all theoretical. Spivak is more than of an analysis book in my opinion.

I empathize all that is beingness said, but I have already said, "While information technology may be truthful that I may know what I want, that doesn't arrive easier to navigate dozens of books to find a good one. " So I don't see how asking for more insight and personal opinions is a bad thing. Yeah I like Axler, and information technology's fine. If I got Lang'due south "Basic Mathematics" instead, it might as well be fine and l would like it just as much. And I would have no problem describing the differences between them if someone asked. That's all actually. And so when I saw Apostol then Lang, I was just curious for more insight, as price volition not play a role for me.

So for me, aye, I like to see how they compare. Because as y'all say, these are some of the ones with smashing reputations, but distinct differences in writing way, etc. So it goes without maxim they are all good - Spivak, Apostol, Simmons, Lang, etc. A comparison for me would assist. A descriptive one. Yep, I tin buy them all on Amazon, play the read and return game, simply why not enquire others that might have used them? I don't see the impairment.

Plainly I make up my own mind in the finish, but I don't heed people chiming in with different views and opinions. Again, I don't see the damage. There could nonetheless be more harm in making a recommendation based on an intuition. And if someone knew what they really wanted, then there would exist no question to begin with.

I suppose information technology's gotten off topic, which is why I said perhaps I should start a new thread, simply information technology'southward all fine with me. I gave a personal case of why I thought the manner I did, and was hoping to hear from others also.

To get back to the topic, really information technology comes downwards to what works best with Thomas/Stewart equally a *supplement*. If one has feel with either Thomas, Stewart, and the others mentioned as possible supplements, then that'south what I wanted to hear. To brand a recommendation without knowing Thomas or Stewart would exist unfair. Otherwise information technology'due south all fine with me.

I concord with this very much. Great mail service!

Simply I want to make clear that Lang and Apostol are two very dissimilar books and are meant for dissimilar audiences. Both are on the rigorous side of calculus books. But Lang is clearly intended for a first course in the field of study, let's say at a HS level. Apostol is more rigorous than Lang (Lang leaves out epsilon-delta arguments which I agree exercise not reall belong in a outset course). I would use Lang for a (honors) course in a academy. Notwithstanding, Apostol focuses in the exercises a lot on computations (which tend to be quite catchy in comparison with other calc books). Spivak is even more theoretical than Apostol since its practice tend to be almost all theoretical. Spivak is more than of an analysis volume in my opinion.

Thanks. Yes, this is more like what I'one thousand looking for. So Lang then doesn't brand sense to supplement either Thomas or Stewart, based on what yous say. For me, a supplement to a Thomas or a Stewart would be the book that is different than the computational style I see in those. So back to Apostol, Simmons, and Spivak :)

One thing though is you lot said you similar Lang. And I'm curious why. I'm curious why people like they books they do and how they learn. And discussion about that is but positive in my opinion. Similar I said to a higher place, possibly I'd like Lang's "Bones Mathematics" just as much (or more fifty-fifty) than Axler's "Precalculus". I had to make a decision, and went with Axler. I could accept gotten both, returned, one, etc. And again, I can do that with all of these. But am curious about why people similar certain books, backgrounds, etc. Once again, all replies are helpful.

Obviously I make up my own mind in the end, just I don't listen people chiming in with different views and opinions. Again, I don't see the harm. In that location could nevertheless be more damage in making a recommendation based on an intuition.

Would you lot rather have had no recommendation? I recommended and establish you cheap books that many people, people nosotros tin surely trust, like and capeesh. That's as much as I could do.

Would you rather have had no recommendation? I recommended and found you cheap books that many people, people we can surely trust, like and appreciate. That'due south every bit much as I could do.

"Seriously upset"?? No, not at all. Non sure where that came from. Considering I asked for details on Apostol vs. Lang when I said cost should not factor in? Descriptive recommendations are always skillful. Otherwise I take to gauge.

Thomas/Stewart + Apostol and Thomas/Stewart + Simmons would be overkill, I'd go with Thomas/Stewart + Spivak

Past the fashion, I beloved these beautiful books, yous should check it out :

Analysis past Its History by Ernst Hairer and Gerhard Wanner
Geometry by Its History by Alexander Ostermann and Gerhard Wanner

I'one thousand starting to call back (for me) this is the best option (Thomas or Stewart + Spivak). Mulling over things over the last few days or so, things are coming dorsum to me quicker than I thought, and in the process of looking at these suggested and discussed books, a few things are becoming more apparent, or rather more clear to me. I volition interruption things down a bit, as the thread did go off topic and diverge, merely that's how my mind went as well :) Simply in the end, every bit I said, with all the input, things are more than clear to me now.

1. Initially, per the title of the original post, I was but curious about Axler's two books which I've found are really almost identical since. I'm using his "Precalculus" one as it's newer, and going through it pretty fast and prissy. All good there. I could accept gone with Lang's "Bones Mathematics", but had to decide, and just went with Axler. So that'southward that :)

2. The thread diverged off of Axler and precalculs textbooks (i.e. Lang'due south "Basic Mathematics", Simmons "Precalculus in a Nutshell", etc.), as math was coming back to me, and as I also knew I'd have to look at a calculus book to complement the ones used in the places I've applied to stop my degree (Thomas & Stewart). Once I looked the the syllabi and saw the schools used Thomas and/or Stewart, I looked them up on Amazon and other places, and as I said before, they seemed too computational and weak on theory. Too practical and simplistic for what I desire. Not saying they are bad, just non for me. The trend towards those types of books is bad IMO, more on that afterwards though. I gave an example of when I took a course that used a like text at Cornell in the technology department, and how using a text similar that was not the best foundation for later more theory-based math courses. So I wanted to make certain I wouldn't be in the same gunkhole.

iii. After some more than looking into the books, reading the replies here, in other threads, etc. I came to a few observations. In that location seem to be 3 master types/styles of calculus textbooks (in the United states at least): The more than "applied", applied, and computational books that seem to be revised every other yr or so (Thomas, Stewart, etc.), the intermediate books that aim to strike a residual between computation/application and theory (Lang, Simmons, etc.), and the ones that lean more than towards theory (Apostol, Spivak, etc.). I'm sure each has an audience, but for me, I detect information technology a scrap concerning that the offset group is so dominant in colleges and universities in the Usa. Why? Because I see it as the simplification of content and a drive towards calculating instead of imagining. I believe that that start group should be eliminated, just it won't, and in fact the contrary - everything seems to exist going in that management. I think a book like Simmons' Calculus or Lang'south Calculus (I've looked at them both) are perfectly fine for students to learn from, and strike that ideal balance betwixt theory and applicability. Are they more challenging? Maybe, just so what? Isn't challenge part of it? I'grand not saying calculus should be merely for a select few, or made to be overly complicated, but to water it down is a pitiful state of affairs. But that'south society today, especially in the United states. I suppose it comes down to many things, but a lack of a good high school curriculum across the state is hurting. My parents are from Eastern Europe. My male parent is a civil engineer. I have many friends from there that are non math majors, merely similar my father, took a ton of theoretical math courses that even math undergrads don't take in the US as part of their curriculum. They would accept no issue with Spivak as a first form. But they are improve prepared out of loftier school. They are used to theory and rigor. They are not put off past it, and IMO, they are better for it. They too had no choice in the affair, just equally I don't. Which brings me to my final point and conclusion. I (like others) have no choice in what textbooks the college I'k attending will use for its math courses. For good or bad, I volition have to employ Thomas or Stewart. Now I KNOW that is not enough from prior experience. It only isn't. So I want to supplement that. I can't replace it, I can only supplement. And in the finish, Spivak seems to be the best, as it's on the opposite end, and together a residuum will exist reached.

Anyway, this thread (and forum) have been helpful. I will try to contribute as I can in return. Although off topic, I hope it has been informative.

Last edited: Jun 10, 2014

Thomas calculus with anylitical geometry 2nd or 3ed. Maybe (4th not sure how much information technology changed from 3). Is really a well written book. Information technology is definitely different from the modern thomas cal books.

Spivak would exist overkill. To sympathise spivak u must first consummate the book,"How to Solve it".

There are also cheap versions of apostol on abebooks. The books are international editions from the Indian market. I got myne for 10 bucks because I did not want to ruin my hardcover 1st ed.

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