Problem in Self-Studying Calculus

[VinciDa]

Hello fellow science enthusiasts! I will start by describing my problem. I am majoring in Computer Science. More importantly, I am taking a course in Single Variable Calculus I. We are using the textbook written by Stewart: Calculus Early Transcendentals. And as I continue read through it, Stewart has absolutely no clue how to convey his ideas lucidly and clearly.

Thus to pass the exams I only memorize the theorems(wait I don't just memorize everything, I do try to understand those that I can) without caring about understanding it. This I fear because I have to understand these concepts in order to apply them and solve problems. For example, I need to understand these mathematical concepts in order to apply them in my future career in Computer Science.

The solution that I thought of was to read a separate textbook called: Elementary Calculus by Frederick S Woods. As I read a free version of it online: I found that it is full of geometrical demonstrations. Another problem was: My geometry is not that good.

I truly wish you guys can help me with this. Anyone have a suggestion on what should I do?

 

[cpsinkule]

https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20
is a very good book for self study. it's also relatively cheap compared to a 200 dollar textbook.

 

[symbolipoint]

Hello fellow science enthusiasts! I will start by describing my problem. I am majoring in Computer Science. More importantly, I am taking a course in Single Variable Calculus I. We are using the textbook written by Stewart: Calculus Early Transcendentals. And as I continue read through it, Stewart has absolutely no clue how to convey his ideas lucidly and clearly.

Thus to pass the exams I only memori...
...
I truly wish you guys can help me with this. Anyone have a suggestion on what should I do?

Learning Calculus is difficult.

Checking an alternative book is a good idea.

I spent a few weeks reviewing some parts of Calc 1 stuff from one of the single-variable Stewart books. The book was good.

Since you are having difficulty currently in Calculus 1, are you willing to keep going through the full semester course, and REPEAT ALL OF THE MATERIAL ON YOUR OWN, as well as repeat the course officially (in case you do not pass)?

 

[MidgetDwarf]

thomas calculus with analytical geometry 3rd ed and simmons calculus. buy both study them and you pass your course.

 

[artfullounger]

https://www.ocf.berkeley.edu/~abhishek/chicmath.htm this may provide some insight for you, it's a generally really great resource for comparing books for a large range of mathematical topics.

More generally everyone seems to love Spivak, although I've never used it. I had the benefit of pretty good mathematical methods teachers so I just used Schaum's Outline of Advanced Mathematics for Engineers and Scientists as a question bank to prep for the finals. It's probably not so useful for learning from, plus this particular outline covers a lot more than single variable calculus (although I would argue pretty much everything in it is useful to know :P )

Also I think you're overstating how much you'll need formal calculus/analysis in comp sci. There's basically 2 routes you can go; full maths/theory style, which I gather is more algebra and number theory oriented anyway, or more general "engineering" style, where just an intuitive idea of what's happening is sufficient, which you can normally get just by solving a few hundred problems in a row (at absolute worst). Plus once you get past the math classes you just end up using wolfram or MATLAB to solve everything anyway (because why waste an hour and a tree in paper solving some horrible integral which just creates numerous opportunities to make algebraic errors when you can just get the answer from wolfram and focus on the physical meaning of it and how it's relevant to whatever you're doing it for).

But yeah, Spivak is supposed to be good. I looked at Apostol way back when but it struck me as very, very dry and I just returned it to the library after a couple weeks of not looking at it.

edit: I'm not suggesting you actually buy any of these books since I know that there are at least 4 different decent quality versions of Spivak floating around the web. Although Schaum's is cheap enough there's not really any reason not to buy it. Make sure you don't get Calculus on Manifolds, this is the more advanced multivariable book.

 

[VinciDa]

Learning Calculus is difficult.

Checking an alternative book is a good idea.

I spent a few weeks reviewing some parts of Calc 1 stuff from one of the single-variable Stewart books. The book was good.

Since you are having difficulty currently in Calculus 1, are you willing to keep going through the full semester course, and REPEAT ALL OF THE MATERIAL ON YOUR OWN, as well as repeat the course officially (in case you do not pass)?

I am willing to do anything to learn calculus. I don't think I would like to relearn calculus from Stewart's book again though. To be fair with the author his exercises are good. But I want the coherent explanations.

 

[VinciDa]

https://www.ocf.berkeley.edu/~abhishek/chicmath.htm this may provide some insight for you, it's a generally really great resource for comparing books for a large range of mathematical topics.

More generally everyone seems to love Spivak, although I've never used it. I had the benefit of pretty good mathematical methods teachers so I just used Schaum's Outline of Advanced Mathematics for Engineers and Scientists as a question bank to prep for the finals. It's probably not so useful for learning from, plus this particular outline covers a lot more than single variable calculus (although I would argue pretty much everything in it is useful to know :P )

Also I think you're overstating how much you'll need formal calculus/analysis in comp sci. There's basically 2 routes you can go; full maths/theory style, which I gather is more algebra and number theory oriented anyway, or more general "engineering" style, where just an intuitive idea of what's happening is sufficient, which you can normally get just by solving a few hundred problems in a row (at absolute worst). Plus once you get past the math classes you just end up using wolfram or MATLAB to solve everything anyway (because why waste an hour and a tree in paper solving some horrible integral which just creates numerous opportunities to make algebraic errors when you can just get the answer from wolfram and focus on the physical meaning of it and how it's relevant to whatever you're doing it for).

But yeah, Spivak is supposed to be good. I looked at Apostol way back when but it struck me as very, very dry and I just returned it to the library after a couple weeks of not looking at it.

edit: I'm not suggesting you actually buy any of these books since I know that there are at least 4 different decent quality versions of Spivak floating around the web. Although Schaum's is cheap enough there's not really any reason not to buy it. Make sure you don't get Calculus on Manifolds, this is the more advanced multivariable book.

Dude! Thanks for that link. This is why i love physics forum. I wish I discovered this site when I was a kid. (Although, I hated mathematics back then anyways)

I actually don't know what route I should go to. Whether or not I should delve into analysis on my own or the engineering route of mathematics. The reason why I want to take math seriously is because I saw an mit lecture video on artificial intelligence and they were applying mathematics I have no idea about.

I fear that if I fell short on my mathematics I will be stuck as a programmer for the rest of my life. I don't want that. No one can get wrong on too much mathematics anyways right?

Moreover you mentioned MATLAB and mathematica. We are using mathematica right now. Of course, I have no idea what is the use of it. But right now you gave me a sense of what it is for.

 

[VinciDa]

thomas calculus with analytical geometry 3rd ed and simmons calculus. buy both study them and you pass your course.

I am sorry but can you explain why this books are good?

 

[MidgetDwarf]

A quick search on thes e forums will answer your question.

Simmon's is reader friendly and does not sacrifice rigor. It gives an intuitive understanding. Although, he can be hand wavy with the proofs.

Thomas 3rd ed, is also reader friendly and 98% of theorems are proved in the main text. He explains every line in a example.

 

[VinciDa]

Do you think I need to brush off my geometry with Kiselev first or is it unnecesary for computer science fields in general? I find this problematic since I realyly don't know wht kinds of math my major really need.

 

[MidgetDwarf]

Kiselev would be overkill. However, kiselev is a really well written rigorous book. So it will improve your thinking and math ability anyways. Kiselev has no answers in the back btw. If you are going to use kiselev, use another book with it n post here for help. Not sure for computer science. I am a math major. I know some of my friends took up to calculus 2, linear algebra, discrete math, number theory, and probability classes. Not sure if these are standard classes for a cs major.

 

[VinciDa]

I actually found a copy of Lang and Murrow at my library. Would you recommend it as a supplement for Kiselev. Thanks btw for answering my questions.

 

[VinciDa]

PS. I can't actually read Kiselev right this time perhaps at winter break. Time is not very friendly as always.

 

[MidgetDwarf]

I actually found a copy of Lang and Murrow at my library. Would you recommend it as a supplement for Kiselev. Thanks btw for answering my questions.

Lang is also great. I have it worked 2 chapter. I had to put away because I have to review for fall courses. Lang uses a different axiom "system", then Euclid. Although, they are equivalent. Would be confusing for a person who does not understand the basic of geometry.I believe lang avoids a lot of geometry dealing with circles. I suggest an old edition of Harold Jacobs geometry 1st or 2nd ed. Avoid any edition of above the 2nd.

I really like kiselev and jacobs.

 

[micromass]

Lang uses a different axiom "system", then Euclid. Although, they are equivalent.

Lang doesn't specify an axiom system if I remember well. But if he did, it would not be equivalent to Euclid. Lang does analytic geometry which is a very strong system, much stronger than what Euclid uses.

 

[DeldotB]

I've worked through all of Stewart's early transcendentals and I agree with you for the most part. I also worked through most Thomas analytical geometry and I would suggest that! Although I've head a lot about how good Lang is, I haven't found the time to actually sit down and work through it.

 

[Jaeusm]

For example, I need to understand these mathematical concepts in order to apply them in my future career in Computer Science.

As mentioned previously, calculus doesn't play a big role in computer science. Linear algebra and everything that falls under discrete math are far more applicable.

I fear that if I fell short on my mathematics I will be stuck as a programmer for the rest of my life.

What exactly do you want to do in computer science?

 

[VinciDa]

That is very good question. A question that I myself don't know a specific answer. However, I am considering to get my masters in Computer Science specializing in Artificial Intelligence. Its more of an inclination rather than the idea that I am absolutely sure that that is what I will do.

The problem with that question is my only exposure at this moment with CS is programming. I never really had an idea what really is CS. And I am certain at least with my limited knowledge right now that CS is more than that. I hope my descriptions make sense.

 

[VinciDa]

Lang doesn't specify an axiom system if I remember well. But if he did, it would not be equivalent to Euclid. Lang does analytic geometry which is a very strong system, much stronger than what Euclid uses.

So do you recommend Lang first before Jacobs or the other way around? I just want to be sure because I have only the winter break to actually learn Geometry.
Also to help, I actually read and nearly completed the Book 1 of Euclid's Elements. So its not that I have absolutely no clue what Geometry is. But my knowledge of it is incomplete and fragile. I just don't want it to get in my way of learning the mathematics necessary with my chosen major.

 

[VinciDa]

I've worked through all of Stewart's early transcendentals and I agree with you for the most part. I also worked through most Thomas analytical geometry and I would suggest that! Although I've head a lot about how good Lang is, I haven't found the time to actually sit down and work through it.

I am actually working through Thomas right now. Merely using Stewart as a book that I need for Homework. I really don't know why Stewart's Book became popular. It is so clear to me that his prose is incoherent.

 

[VinciDa]

By the way, since it was pointed above, I want to ask why is that Calculus and the continuous form of Mathematics not applicable to Computer Science. I never really understood that.

 

[russ_watters]

By the way, since it was pointed above, I want to ask why is that Calculus and the continuous form of Mathematics not applicable to Computer Science.

Could you reword that please, it doesn't make sense. I can't tell if you are asking why calculus is or isn't applicable. It is applicable -- and even if it wasn't, school isn't just for learning things in your particular discipline.

 

[symbolipoint]

Calculus not being important in Computer Science is nonsense. If one must include computer programming as part of Computer Science, then some programmers create programs (software) which include instructions or code for computing derivatives (rates of change) for data, REAL-WORLD data, as in an industrial or business activity. May someone tell us that this is not Calculus!

 

[VinciDa]

As mentioned previously, calculus doesn't play a big role in computer science. Linear algebra and everything that falls under discrete math are far more applicable.

I mean to say that this man says that Calculus doesn't play a big role in CS.



Moreover the professor in this video says that "Mathematics in its continuous form" doesn't have a big role in CS too. That discrete mathematics and similar form of mathematics are much more useful. And that high school math and calculus has nothing to do with CS. My question is why is that so? I never understood why.

 

[symbolipoint]

VinciDa,
Helpful video. The general point makes more sense now. Yes, as he said, computer science and programming "infiltrate" every other science.

 

[IGU]

And that high school math and calculus has nothing to do with CS. My question is why is that so? I never understood why.

I think this is just an indication that you have no idea what CS is. That's okay, but if you think it's what you want to do you ought to have some notion of what it means. Why don't you try to describe what it actually is that you want to do without using the shortcut of saying CS? Then maybe you can describe what subfields of mathematics might play a role.

At this point your definitions are very fuzzy so you aren't able to reason about the subject properly. You aren't even able to formulate very meaningful questions. What you are doing right now is studying calculus from a really bad book, and following a course of study that somebody else told you to follow. It's no wonder you are not happy with it.