Books on Combinatorics, Permutations and Probability

[chiraganand]

Hello!

I am looking for textbooks to relearn Combinatorics, Permutations Combinations and Probability and also Matrix algebra( decomposition, etc). I had done these many years ago and the course/books provided to me at that time weren't that great. So I want to relearn this with a more intiutive explanation. I am an engineer and not a mathematician. Any pointers on courses or books on these topics?

Thanks and Regards!

 

[jasonRF]

I think Strang has a couple of textbooks that do a good job at presenting matrix algebra with intuitive explanations. Used copies of old editions can often be found quite cheap, but if you have access to a library it is always best to browse and find what works for you. The text I'm most familiar with is
https://www.amazon.com/dp/0155510053/?tag=pfamazon01-20
When I was in graduate school studying electrical engineering I needed a linear algebra reference (the undergrad course I took used no textbook); I picked up a copy since it was commonly used by other students as well as faculty. If you have already seen basic matrix algebra before then it is not a difficult read. It does cover LU, QR and singular value decompositions, if those are what you are looking for.

EDIT: if you don't have a reasonable understanding of basic matrix algebra then this book may not be the most suitable for you. When it is used as a class text, it is often for a second course in linear algebra that focusses on applications, although it is sometimes used for a first course.

He also has a text "Introduction to Linear Algebra" that is used more often for truly introductory classes for folks that haven't necessarily seen any matrix algebra before, but I'm not very familiar with it.

Note that Strang is only good for the matrix algebra part. His coverage of the underlying theory of abstract vector spaces and linear transformations is somewhat shallow, although it is sufficiently deep to support the matrix algebra he covers.

jason

 

[paralleltransport]

Linear algebra by gilbert strang is a great book. Very appropriate for engineers too (has lots of applications). There are online lectures on MIT ocw (18.06).

For probability/combinatorics I really liked Sheldon Ross's book. Doesn't have any measure theory but has a lot of solved problems (some highly nontrivial!)

 

[chiraganand]

I think Strang has a couple of textbooks that do a good job at presenting matrix algebra with intuitive explanations. Used copies of old editions can often be found quite cheap, but if you have access to a library it is always best to browse and find what works for you. The text I'm most familiar with is
https://www.amazon.com/dp/0155510053/?tag=pfamazon01-20
When I was in graduate school studying electrical engineering I needed a linear algebra reference (the undergrad course I took used no textbook); I picked up a copy since it was commonly used by other students as well as faculty. If you have already seen basic matrix algebra before then it is not a difficult read. It does cover LU, QR and singular value decompositions, if those are what you are looking for.

EDIT: if you don't have a reasonable understanding of basic matrix algebra then this book may not be the most suitable for you. When it is used as a class text, it is often for a second course in linear algebra that focusses on applications, although it is sometimes used for a first course.

He also has a text "Introduction to Linear Algebra" that is used more often for truly introductory classes for folks that haven't necessarily seen any matrix algebra before, but I'm not very familiar with it.

Note that Strang is only good for the matrix algebra part. His coverage of the underlying theory of abstract vector spaces and linear transformations is somewhat shallow, although it is sufficiently deep to support the matrix algebra he covers.

jason

Thank you I am reading strang now. It covers loads of the basics and is good

 

[chiraganand]

Linear algebra by gilbert strang is a great book. Very appropriate for engineers too (has lots of applications). There are online lectures on MIT ocw (18.06).

For probability/combinatorics I really liked Sheldon Ross's book. Doesn't have any measure theory but has a lot of solved problems (some highly nontrivial!)

Thank you. i started Ross.. the first chapter is fine, it gives a lot of explanation.. but when you dive into probabibility theory and axioms, i think its getting a bit confusing for me.. I am reading the first course on probability

 

[Frimus]

'Probability: For the Enthusiastic Beginner' by David Morin with a lot of interesting examples and exercises. Author's name is a guarantee of quality.

 

[MidgetDwarf]

I like https://www.amazon.com/dp/1138369918/?tag=pfamazon01-20 .

Blitzstein offers intuitive explanations, and some interesting problems. Gets you thinking in terms of probability. I own the first edition, and it was great. Never looked at the second edition.

I thought Morin's book was too chatty. Not a bad book, but the explanations can go on forever.

 

[chiraganand]

I think Strang has a couple of textbooks that do a good job at presenting matrix algebra with intuitive explanations. Used copies of old editions can often be found quite cheap, but if you have access to a library it is always best to browse and find what works for you. The text I'm most familiar with is
https://www.amazon.com/dp/0155510053/?tag=pfamazon01-20
When I was in graduate school studying electrical engineering I needed a linear algebra reference (the undergrad course I took used no textbook); I picked up a copy since it was commonly used by other students as well as faculty. If you have already seen basic matrix algebra before then it is not a difficult read. It does cover LU, QR and singular value decompositions, if those are what you are looking for.

EDIT: if you don't have a reasonable understanding of basic matrix algebra then this book may not be the most suitable for you. When it is used as a class text, it is often for a second course in linear algebra that focusses on applications, although it is sometimes used for a first course.

He also has a text "Introduction to Linear Algebra" that is used more often for truly introductory classes for folks that haven't necessarily seen any matrix algebra before, but I'm not very familiar with it.

Note that Strang is only good for the matrix algebra part. His coverage of the underlying theory of abstract vector spaces and linear transformations is somewhat shallow, although it is sufficiently deep to support the matrix algebra he covers.

jason

So is there any book other than Strang? I tried going through it but get lost pretty quickly

 

[paralleltransport]

You may want to follow the online lectures here: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/. If it's still too hard, you may need to review high school algebra.

Lecture 1 of this covers probability and axioms: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/

It should be straightforward. Although I liked ross better, the problems are more fun. I learned probability by solving problems tbh, no having some deep understanding of axioms.