Strategies for Tackling Proofs in Spivak Calculus

[mendem03]

I am having a really difficult time doing these proofs and want to know how i need to confront them and if there is a good strategy to solving these.
I am in first year university. I understood the problem the prof went over but when i try to do on my own, I am just not able to prove them. I don't know how to even start with some of them

 

[Studiot]

Difficult to know what to suggest without quite a bit more background information.

What are you studying for instance?

What part of Spivak is causing difficulty?

What is your maths background - have you ever seen anything like this before, perhaps high school calculus?

 

[mendem03]

We are studying chapter one and I have never done this kind of math before

 

[Studiot]

You don't go long on replies do you?

So why are you studying Spivak? What is your course now?

Spivak is one of the most thorough books of its kind but it is intended for those starting a serious pure maths course. It contains much unecessary detail for those who only need to use maths (eg engineers).

Are you aware of the second book which goes with it?

Supplement to the Calculus

(also by Spivak)

 

[mendem03]

I am in the computer science program and this is a recommended course.
I don't know about the second book but I'm going to guess we will be using that one for calculus 2 in 2nd semester

 

[Studiot]

I can't imagine why a computer scientist (engineer?) would use Spivak to study calculus.
I suggest you get hold of a second year and ask for pointers as to the relevance.

The second book (Supplement to the Calculus) is not part2 it is just what is says on the tin. Further explanation including solutions to all the problems not explicitly solved in the main book.

Since I still don't have any idea if this is your first exposure to any form of calculus it is hard to make further recommendations.

Concrete Mathematics by Graham, Knuth and Patashink
(A foundation for computer science)
Probably contains your needs and would be a valuable reference in times to come.

Discrete Mathematics by Biggs

Covers similar ground but is more formal.

There are many good calculus books out there, designed for all sorts of purposes.

Stewart's various books are very popular at the moment

An Introduction to Infinitesimal Calculus by Gaunt
is old but also good.

go well

 

[Robert1986]

Hmm, CS, that explains the brevity of responses, then, doesn't it? You make it sort of tough to help you. Which problems, specifically, are giving you trouble?

There is a Spivak Online Study Group around here, somewhere.

 

[raymo39]

Ive also spent some time with spivak, but having studied mathematical physics, i honestly cannot imagine why you would be using it. Most CS math courses tend to deal with discrete mathematics, and mandatory undergraduate math courses usually begin with building into multivariable calculus and linear algebra. Spivak is very good at what it does, which is give a solid groundwork into real analysis.

May i also suggest stewart (the body of material covered by this text is very broad, and also surprisingly well explained), alternatively there is Kreyzsig (Advanced Engineering Mathematics) might be better for later understanding.
Also check out Discrete Mathematics with Applications Susanna Epp, very good first year text for introductions to logic and understanding how to construct a proof

 

[lavinia]

I am having a really difficult time doing these proofs and want to know how i need to confront them and if there is a good strategy to solving these.
I am in first year university. I understood the problem the prof went over but when i try to do on my own, I am just not able to prove them. I don't know how to even start with some of them

If you just don't give up and try to figure out what you don't understand and what information you are missing in order to solve the problem, it will suddenly come to you. The more you do this the better you will get.

 

[mendem03]

Ok let me explain everything
I am currently going to University of Toronto in first year
I am in the computer science program and the courses we are recommended to take are:
mata31h3 calculus 1, mata37h3 calculus 2, mata27h3 linear algebra 1, csca08h3, csca65h3 and another computer science course.
And I am having trouble approaching this questions.

here is one proof i tried can someone tell me if I am no the right track

Question
if a < b, then -b < -a

proof
if a < b then a-b<0 and b-a>0
so a-b<0<b-a
so -b<-a