Finite Math worth self learning or will I see the topics in future math courses?

[MidgetDwarf]

I google searched finite math after reading the course description in my community college course catalog.
I am a math major and is fine math work learning or should I use my time wisely and learn other branches of math. Ie ode, pde, proof writing etc.

Will my future classes cover some of the topics in finite math? What is a good introduction book to finite math?

My background consist of:cal 1 and 2, linear algebra, and statistics.

 

[lurflurf]

Finite math is a very broad subject. You would for sure like to know something about it. It is likely that the community college course is not primarily for math majors. As such you may or may not find it worth taking.

A book I like is Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik.

 

[verty]

An amazingly complete looking book, but one that seems to be impossible to find, is one by Karoly Jordan: Calculus of Finite Differences. One can find a preview on books.google.com, look for the 1965 edition, one of them has a preview. Here is a link to it that may stop working.

It seems to be an amazing book and contains more than Concrete Mathematics does. I don't know where to find such content.

 

[certainly]

An amazingly complete looking book, but one that seems to be impossible to find, is one by Karoly Jordan: Calculus of Finite Differences. One can find a preview on books.google.com, look for the 1965 edition, one of them has a preview. Here is a link to it that may stop working.

It seems to be an amazing book and contains more than Concrete Mathematics does. I don't know where to find such content.

I believe that person is also known as Charles Jordan. Here is a book by Charles Jordan having the same title and number of pages as the one you mentioned, also the list of brief contents corresponds with the link you provided. This book is available on amazon, see https://www.amazon.com/s/ref=nb_sb_... differences charles jordan&tag=pfamazon01-20. I even found it for free online, the quality is bad, but it's still readable :-)

 

[verty]

I believe that person is also known as Charles Jordan. Here is a book by Charles Jordan having the same title and number of pages as the one you mentioned, also the list of brief contents corresponds with the link you provided. This book is available on amazon, see https://www.amazon.com/s/ref=nb_sb_... differences charles jordan&tag=pfamazon01-20. I even found it for free online, the quality is bad, but it's still readable :-)

Thank you so much, I saw this a few years ago and was certainly interested in it but couldn't find anything more about it. I like how it has partial difference equations, it obvious parallels calculus quite closely which surely must be a good organizing theme.

Ok, so I'm going to enjoy reading this book and am very grateful to you, Mr Certainly.

I should now give an answer to MidgetDwarf about his questions, what topics will be useful and what is a good introductory book.

Something to realize, MidgetDwarf, is that there are many topics in finite math and some of them are quite deep. It's unlikely that any survey book will go deeply into any particular thing. As Lurflurf says, you may find that course to be quite elementary. I personally would choose those other courses you mentioned for that reason, or substitute it with for example a more advanced probability class or a mathematical logic class.

An example survey book is Bona - A Walk Through Combinatorics, but as I say any survey book is going to be quite shallow.

Concrete Mathematics is focused on math that Knuth found to be relevant to computer algorithms. It doesn't go that deep but what it covers is covered well and a lot of it you will struggle to find elsewhere. My one complaint is that it is quite difficult, more difficult than is typical for undergrad books.

Probability is often included under the umbrella of finite math. Have you done the probability distributions, I mean Poisson random variables, stuff like that? If not, a good book is Ross - An Introduction to Probability. The earlier editions are quite affordable.

Mathematical Logic, the one by Hodel looks very good.

Number Theory, Apostol's Introduction to Analytic Number Theory looks good.

There is also graph theory although I wouldn't bother. There is also game theory.

So there are deep topics and deep books. Your best bet is to pick which topics you want to learn about and get more focused books on those topics.

This one above by Jordan for example goes further in the direction of Knuth's book, which is something I was looking for and I'm glad Certainly has helped me out.

PS. You can probably tell I don't particularly like the survey books, hence why I chose books that are more likely to suit a math major. And I apologize for editing this post multiple times but I want it to reflect a complete version of what I was trying to say. Thank you.

 

[micromass]

It seems to be an amazing book and contains more than Concrete Mathematics does. I don't know where to find such content.

I just want to say that both Jordan's book and Knuth's book contain quite different contents. Both are very well-written though.
The calculus of finite differences can also be found in many numerical analysis books. And then there's of course the umbral calculus.

 

[certainly]

Thank you so much, I saw this a few years ago and was certainly interested in it but couldn't find anything more about it. I like how it has partial difference equations, it obvious parallels calculus quite closely which surely must be a good organizing theme.

Ok, so I'm going to enjoy reading this book and am very grateful to you, Mr Certainly.

And thank you for bringing a wonderful book to my attention :-)

And then there's of course the umbral calculus.

From wikipedia:-

An example involves the Bernoulli polynomials. Consider, for example, the ordinary binomial expansion (which contains a binomial coefficient):

and the remarkably similar-looking relation on the Bernoulli polynomials:

Compare also the ordinary derivative

to a very similar-looking relation on the Bernoulli polynomials:

These similarities allow one to construct umbral proofs, which, on the surface, cannot be correct, but seem to work anyway. Thus, for example, by pretending that the subscript n − k is an exponent:

and then differentiating, one gets the desired result:

Now you got me hooked!