Books on Combinatorics, Permutations and Probability

In summary: Overall, it is a good reference for those looking to relearn matrix algebra with intuitive explanations. Additionally, for probability and combinatorics, books by Gilbert Strang and Sheldon Ross are recommended. While Strang's book may not be suitable for beginners, Ross's book provides a lot of explanations and solved problems for those interested in the subject. There are also other books such as "Probability: For the Enthusiastic Beginner" by David Morin and "Introduction to Probability" by Joseph K. Blitzstein that may be worth considering. Ultimately, it is important to browse and find what works best for you, whether it be through online lectures, used books, or access to a library.
  • #1
chiraganand
113
1
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!
 
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  • #2
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
 
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  • #3
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!)
 
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  • #4
jasonRF said:
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
 
  • #5
paralleltransport said:
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
 
  • #6
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  • #7
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.
 
  • #8
jasonRF said:
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
 
  • #9
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.
 

Related to Books on Combinatorics, Permutations and Probability

1. What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects and sets in a systematic way.

2. What are permutations?

Permutations are arrangements of objects or symbols in a specific order. The number of permutations for a set of objects is calculated using factorials.

3. How is probability related to combinatorics and permutations?

Probability is the likelihood of an event occurring. Combinatorics and permutations are used to calculate the number of possible outcomes in a given situation, which is then used to determine the probability of a specific event happening.

4. What are some real-world applications of combinatorics, permutations, and probability?

Combinatorics, permutations, and probability are used in a variety of fields, such as computer science, genetics, finance, and statistics. Some examples include analyzing DNA sequences, predicting stock market trends, and designing efficient computer algorithms.

5. Are there any recommended books on combinatorics, permutations, and probability?

Yes, there are many excellent books on these topics, including "Concrete Mathematics" by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, "Introduction to Combinatorics" by Martin J. Erickson, and "Introduction to Probability" by Dimitri P. Bertsekas and John N. Tsitsiklis.

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