Self Taught Calc- What to read after Morris Kline?

[Natro]

Hello everyone,

I'm brand new here as a poster. I have been working to teach myself calculus to a solid level before taking classes in calulcus. I want to make sure I have a good foundation before I get "thrown to the wolves" so to speak. I've always been a little scared of math so I want to make sure I'm ready to rock.

Right now I have Calculus Made Easy by Thompson, and Morris Kline's Calculus an Intuitive and Physical Approach. I am just starting on these and am impressed so far!

I know almost nothing about Calculus (never taken any calc classes whatsoever, only College Algebra), particularly how much I need to know to be competitive in a three course Calc sequence.

So I can make sure I have all my ducks in a row, what should I look to read after Morris Kline's book? What would take it to the next level? I am hoping to find something similar to his pedagogy vs an average calc textbook that will probably blow my mind.

However, having not learned the material yet I wanted to ask the opinion of those who have been in my shoes and gone before me. Any suggestions on what comes next after Kline to make sure I have a solid grounding for a 3 course calc sequence?

All I know of is "How To Ace The Rest of Calculus" but it's my understanding this is mainly just a basic overview and not really in depth enough for self-teaching, but I could be wrong.

Thanks a million, and I am more than happy to clarify anything. I just don't know what all I don't know at this point

 

[arildno]

Having seen a bit on Amazon regarding the Kline book, it is fairly short on geometrical interpretation and without much in the sense of rigorous proofs.

1. Be sure to do the exercises!

2. Now that you have gotten a "feeling" about the theme, you really should pick up a more analytical and rigorous textbook, because these so-called "intuitive" books ALWAYS reaches a dead end where you can't proceed any further into the themes.Because progress needs mathematical rigour, not translations into everyday thinking.

 

[Natro]

Having seen a bit on Amazon regarding the Kline book, it is fairly short on geometrical interpretation and without much in the sense of rigorous proofs.

1. Be sure to do the exercises!

2. Now that you have gotten a "feeling" about the theme, you really should pick up a more analytical and rigorous textbook, because these so-called "intuitive" books ALWAYS reaches a dead end where you can't proceed any further into the themes.


Because progress needs mathematical rigour, not translations into everyday thinking.

Thanks for the advice, it is much appreciated. And I can see where you are coming from. I guess I'm just a little intimidated by it all since I don't know much just yet.

Do you have any book suggestions that would provide adequate rigor to be crystallize everything without being too far above my head to grasp? Thanks again!

 

[jk]

You have several good Calculus books to choose from once you've gone through Kline:
A Course of Pure Mathematics by Hardy,
Courant's calculus,
One of several Advanced Calculus books (I like the older ones myself): Edwards, Buck, Woods...
If you are willing to work hard, Creative Mathematics by Wall
..etc
You can also use the text used at your university

 

[arildno]

WEll, I'm Norwegian so I don't know about the precise course structure in the US.
However, I was very fond of Jerrold Marsden's "Real Analysis" (very theoretical treatment, rather than geared towards applications), and from what I know, his Calculus 1,2+3-books for undergraduate study of calculus is well recognized.

Another "classic" is Edwards&Penney's Calculus, but I am not familiar with that one.

Both suggestions are known for ample examples, and with a fairly rigorous treatment, I think.
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Steer clear of names like Michael Spivak and Rudin; they are top-notch mathematicians writing the very best books from the theoretical point of view, but will be very intimidating for self-study.

 

[PAllen]

I am sure there are good modern alternatives, but, if you can find it old and used, I taught myself calculus from:

https://www.amazon.com/dp/B000H5MYSY/?tag=pfamazon01-20

in 10th grade, and highly recommend it (I got 5 on the bc AP exam without ever taking a course, using this book).

 

[micromass]

Steer clear of names like Michael Spivak and Rudin; they are top-notch mathematicians writing the very best books from the theoretical point of view, but will be very intimidating for self-study.

I disagree. Studying Spivak would be ideal. If he studied the easy calculus books, then he will have an intuitive understanding of calculus, so studying a theoretical text should not be impossible right then.
Furthermore, the theory in Spivak is not as difficult as many people think. It are the exercises which tend to be agonizingly hard at times.

Once you studied Morris Kline, I highly recommend taking a look at Spivak. If you find the explanations too difficult, then you can always look at another text. But at least take a look and see what it's about.

 

[arildno]

Furthermore, the theory in Spivak is not as difficult as many people think. It are the exercises which tend to be agonizingly hard at times.

In which case, the self-studying student will despair far more easily than the one having an instructor at his disposal..

Once you studied Morris Kline, I highly recommend taking a look at Spivak. If you find the explanations too difficult, then you can always look at another text. But at least take a look and see what it's about.

I was hoping for an "in-between" text to recommend?

 

[micromass]

In which case, the self-studying student will despair far more easily than the one having an instructor at his disposal..

And the determined student will get through the text and feel strengthened in his knowledge.

 

[Natro]

I am sure there are good modern alternatives, but, if you can find it old and used, I taught myself calculus from:


in 10th grade, and highly recommend it (I got 5 on the bc AP exam without ever taking a course, using this book).

Thanks for the recommendation, what did you like about it the most? I did some looking but couldn't find much in the way of descriptive material. Thanks again!

 

[Natro]

Thanks for the replies thus far!

To add some amplifying information. I'm 30 years old, I've been working in mortgages and sales most of my adult life after my 4 years in the service. I have never really taken any math classes besides college algebra.

I've had my eyes set on the actuarial field for a while now and have decided that I most likely would like to go back and get a second bachelor's in math (to help with the actuarial pursuit and to also prove to myself I can do it- I'm hard headed that way lol). I really want to be able to hit the ground running on this as I know unless I study on my own for a while beforehand I will be at a theoretical disadvantage since I've been out of the game so long and no longer have fresh math skills.

I want to be ready to rock before I hit the class room. The last thing I want is to be getting my @$$ handed to me by the curriculum as I have no real idea what to expect or how hard it is. I have about six months until I'd be starting class...

Thanks again everyone.


EDIT: In case it helps shed light as to what I may need over the long run, here is the course sequence overall for the B.S. in math I am looking to pursue. Since I already will have a bachelors going into this, I'll pretty much be taking the math classes back to back straight through so it will be intense (for me at least lol).

Calculus I
History and Foundations of Math
Calculus II
Differential Equations
Probability and Statistics
Calculus III
Elementary Linear Algebra
Mathematics Seminar
Intro. to Modern Algebra
Introductory Analysis

 

[jgens]

It are the exercises which tend to be agonizingly hard at times.

From my own experience with Spivak, I think the exercises are actually a lot easier than people make them out to be. When most people start studying from Spivak they have not learned how to read a math book, and as a result, they read through his arguments without really trying to understand the motivation for each proof. This was the problem I had when I first tried to make it through the text. But giving the book a proper read through and giving each theorem the attention it deserves should make most of the exercises easily accessible. Would you agree with this micromass?

 

[micromass]

From my own experience with Spivak, I think the exercises are actually a lot easier than people make them out to be. When most people start studying from Spivak they have not learned how to read a math book, and as a result, they read through his arguments without really trying to understand the motivation for each proof. This was the problem I had when I first tried to make it through the text. But giving the book a proper read through and giving each theorem the attention it deserves should make most of the exercises easily accessible. Would you agree with this micromass?

Yes, I agree. If you already know the math lingo and the way to study a math book, then the exercises are quite all right. But people with not so much experience will find them quite difficult at first.

 

[Locrian]

I've had my eyes set on the actuarial field for a while now and have decided that I most likely would like to go back and get a second bachelor's in math (to help with the actuarial pursuit and to also prove to myself I can do it- I'm hard headed that way lol).

If you're in the US or Canada, be sure to be passing some exams while you study. Outside of the calculus and Probability, most of those classes won't be much benefit on the way to actuarial work.

 

[Dembadon]

Hi, natro. If you are considering a math degree, then I second the recommendation for Spivak's Calculus (make sure it is "Calculus" and NOT "Calculus on Manifolds" ). If you have troubles, you can come to the forums and ask questions. Do not be intimidated; most people run into difficulties at some point, so you will have to push through and be very patient with yourself.

That said, don't try to learn everything before you take the courses. Ambition and curiosity are great, but temper them with realistic goals and expectations for yourself or you'll end up fighting discouragement more than understanding new mathematics.

 

[Natro]

Hi, natro. If you are considering a math degree, then I second the recommendation for Spivak's Calculus (make sure it is "Calculus" and NOT "Calculus on Manifolds" ). If you have troubles, you can come to the forums and ask questions. Do not be intimidated; most people run into difficulties at some point, so you will have to push through and be very patient with yourself.

That said, don't try to learn everything before you take the courses. Ambition and curiosity are great, but temper them with realistic goals and expectations for yourself or you'll end up fighting discouragement more than understanding new mathematics.

Thanks for the advice! I'll try to keep it on an even keel. Haha. Having been so intimidated by math in the past I think I tend towards overkill in preparation. Thanks again for the insight.


Thanks to everyone else as well.

 

[mathwonk]

fischer and zieber was a standard back when there were no fluffy calculus books, in the 1950's. i agree it is a reasonable choice, a notch below spivak. i like courant, having learned from it, but it can be pricey now.

spivak has absolutely no applied topics, while courant links calculus with physics too.

 

[mathwonk]

i think you are getting ahead of yourself. you say you like kline but have just started on it. if i were you i would wait until you have finished it or gotten a good bit further along before exploring harder books. after you have actually learned something from kline you will be better equipped to evaluate the harder books.